research article radiation and heat transfer in the...

Hindawi Publishing CorporationInternational Journal of Atmospheric SciencesVolume 2013 Article ID 503727 26 pageshttpdxdoiorg1011552013503727

Research ArticleRadiation and Heat Transfer in the AtmosphereA Comprehensive Approach on a Molecular Basis

Hermann Harde

Laser Engineering and Materials Science Helmut-Schmidt-University Hamburg Holstenhofweg 85 22043 Hamburg Germany

Correspondence should be addressed to Hermann Harde hardehsu-hhde

Received 29 April 2013 Accepted 12 July 2013

Academic Editor Shaocai Yu

Copyright copy 2013 Hermann Harde This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We investigate the interaction of infrared active molecules in the atmosphere with their own thermal background radiation as wellas with radiation from an external blackbody radiator We show that the background radiation can be well understood only interms of the spontaneous emission of the molecules The radiation and heat transfer processes in the atmosphere are describedby rate equations which are solved numerically for typical conditions as found in the troposphere and stratosphere showing theconversion of heat to radiation and vice versa Consideration of the interaction processes on a molecular scale allows to developa comprehensive theoretical concept for the description of the radiation transfer in the atmosphere A generalized form of theradiation transfer equation is presented which covers both limiting cases of thin and dense atmospheres and allows a continuoustransition from low to high densities controlled by a density dependent parameter Simulations of the up- and down-wellingradiation and its interaction with the most prominent greenhouse gases water vapour carbon dioxide methane and ozone inthe atmosphere are presentedThe radiative forcing at doubled CO

2concentration is found to be 30 smaller than the IPCC-value

1 Introduction

Radiation processes in the atmosphere play a major role inthe energy and radiation balance of the earth-atmospheresystem Downwelling radiation causes heating of the earthrsquossurface due to direct sunlight absorption and also due tothe back radiation from the atmosphere which is the sourceterm of the so heavily discussed atmospheric greenhouse oratmospheric heating effect Upward radiation contributes tocooling and ensures that the absorbed energy from the sunand the terrestrial radiation can be rendered back to spaceand the earthrsquos temperature can be stabilized

For all these processes particularly the interaction ofradiation with infrared active molecules is of importanceThesemolecules strongly absorb terrestrial radiation emittedfrom the earthrsquos surface and they can also be excited by someheat transfer in the atmosphere The absorbed energy is rera-diated uniformly into the full solid angle but to some degreealso re-absorbed in the atmosphere so that the radiationunderlies a continuous interaction and modification processover the propagation distance

Although the basic relations for this interaction ofradiation with molecules are already well known since thebeginning of the previous century up to now the correctapplication of these relations their importance and theirconsequences for the atmospheric system are discussed quitecontradictorily in the community of climate sciences

Therefore it seems necessary and worthwhile to give abrief review of the main physical relations and to present onthis basis a new approach for the description of the radiationtransfer in the atmosphere

In Section 2 we start from Einsteinrsquos basic quantum-theoretical considerations of radiation [1] and Planckrsquos radi-ation law [2] to investigate the interaction of molecules withtheir own thermal background radiation under the influenceof molecular collisions and at thermodynamic equilibrium[3 4] We show that the thermal radiation of a gas can bewell understood only in terms of the spontaneous emissionof the molecules This is valid at low pressures with only fewmolecular collisions as well as at higher pressures and highcollision rates

2 International Journal of Atmospheric Sciences

In Section 3 also the influence of radiation from anexternal blackbody radiator and an additional excitation bya heat source is studied The radiation and heat transferprocesses originating from the sun andor the earthrsquos surfaceare described by rate equations which are solved numericallyfor typical conditions as they exist in the troposphere andstratosphereThese examples right away illustrate the conver-sion of heat to radiation and vice versa

In Section 4 we derive the Schwarzschild equation [5ndash11] as the fundamental relation for the radiation transferin the atmosphere This equation is deduced from pureconsiderations on a molecular basis describing the thermalradiation of a gas as spontaneous emission of the moleculesThis equation is investigated under conditions of only fewintermolecular collisions as found in the upper mesosphereor mesopause as well as at high collision rates as observed inthe troposphere Following some modified considerations ofMilne [12] a generalized form of the radiation transfer equa-tion is presented which covers both limiting cases of thinand dense atmospheres and allows a continuous transitionfrom low to high densities controlled by a density dependentparameter This equation is derived for the spectral radianceas well as for the spectral flux density (spectral intensity) asthe solid angular integral of the radiance

In Section 5 the generalized radiation transfer equationis applied to simulate the up- and downwelling radiationand its interaction with the most prominent greenhousegases water vapour carbon dioxide methane and ozone inthe atmosphere From these calculations a detailed energyand radiation balance can be derived reflecting the differentcontributions of these gases under quite realistic conditionsin the atmosphere In particular they show the dominantinfluence of water vapour over the full infrared spectrum andthey explain why a further increase in the CO

2concentration

only gives marginal corrections in the radiation budgetIt is not the objective of this paper to explain the

fundamentals of the atmospheric greenhouse effect or toprove its existence within this framework Nevertheless thebasic considerations and derived relations for the molecularinteraction with radiation have some direct significance forthe understanding and interpretation of this effect and theygive the theoretical background for its general calculation

2 Interaction of Molecules with Thermal Bath

When a gas is in thermodynamic equilibrium with itsenvironment it can be described by an average temperature119879119866 Like anymatter at a given temperature which is in unison

with its surrounding it is also a source of gray or blackbodyradiation as part of the environmental thermal bath At thesame time this gas is interacting with its own radiationcausing some kind of self-excitation of the molecules whichfinally results in a population of themolecular states given byBoltzmannrsquos distribution

Such interaction first considered by Einstein [1] is repli-cated in the first part of this section with some smallermodifications but following themain thoughts In the secondpart of this section also collisions between the molecules are

Em

En

ΔE = hmn = hc120582mn

Figure 1 Two-level system with transition between states119898 and 119899

included and some basic consequences for the description ofthe thermal bath are derived

21 Einsteinrsquos Derivation ofThermal Radiation Themoleculesare characterized by a transition between the energy states119864

119898

and 119864119899with the transition energy

Δ119864 = 119864119898minus 119864

119899= ℎ]

119898119899=

ℎ119888

120582119898119899

(1)

where ℎ is Planckrsquos constant 119888 the vacuum speed of light ]119898119899

the transition frequency and 120582119898119899

is the transitionwavelength(see Figure 1)

Planckian Radiation The cavity radiation of a black bodyat temperature 119879

119866can be represented by its spectral energy

density 119906120582(units Jm3120583m) which obeys Planckrsquos radiation

law [2] with

119906120582=8120587119899

4ℎ119888

1205825

1

119890ℎ119888119896119879119866120582 minus 1 (2)

or as a function of frequency assumes the form

119906] = 1199061205821205822

119888119899=8120587119899

3ℎ]3

1198883

1

119890ℎ]119896119879119866 minus 1 (3)

This distribution is shown in Figure 2 for three differenttemperatures as a function of wavelength 119899 is the refractiveindex of the gas

Boltzmannrsquos Relation Due to Boltzmannrsquos principle the rela-tive population of the states 119898 and 119899 in thermal equilibriumis [3 4]

119873119898

119873119899

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866 (4)

with119873119898and119873

119899as the population densities of the upper and

lower state 119892119898and 119892

119899the statistical weights representing the

degeneracy of these states 119896 as the Boltzmann constant and119879119866as the temperature of the gasFor the moment neglecting any collisions of the

molecules between these states three different transitions cantake place

Spontaneous Emission The spontaneous emission occursindependent of any external field from 119898 rarr 119899 and ischaracterized by emitting statistically a photon of energyℎ]

119898119899into the solid angle 4120587with the probability 119889119882119904

119898119899within

the time interval 119889119905

119889119882119904

119898119899= 119860

119898119899119889119905 (5)

International Journal of Atmospheric Sciences 3

0 2 4 6 8 10Wavelength 120582 (120583m)

6

5

4

3

2

1

0

times10minus3

Spec

tral

ener

gy d

ensit

yu120582

(Jm

3120583

m)

T = 2000K T = 1500K T = 1000K

Figure 2 Spectral energy density of blackbody radiation at differenttemperatures

119860119898119899

is the Einstein coefficient of spontaneous emissionsometimes also called the spontaneous emission probability(units sminus1)

Induced Absorption With the molecules subjected to anelectromagnetic field the energy of themolecules can changein that way that due to a resonant interaction with theradiation the molecules can be excited or de-excited When amolecule changes from 119899 rarr 119898 it absorbs a photon of energyℎ]

119898119899and increases its internal energy by this amount while

the radiation energy is decreasing by the same amountThe probability for this process is found by integrating

over all frequency components within the interval Δ] con-tributing to an interaction with the molecules

119889119882119894

119899119898= 119861

119899119898intΔ]119906]119892 (]) 119889] sdot 119889119905 (6)

This process is known as induced absorptionwith119861119899119898

as Ein-steinrsquos coefficient of induced absorption (units m3

sdotHzJs)119906] as the spectral energy density of the radiation (unitsJm3Hz) and 119892(]) as a normalized lineshape function whichdescribes the frequency dependent interaction of the radia-tion with the molecules and generally satisfies the relation

int

infin

0

119892 (]) 119889] = 1 (7)

Since 119906] is much broader than 119892(]) it can be assumed tobe constant over the linewidth and with (7) the integral in(6) can be replaced by the spectral energy density on thetransition frequency

intΔ]119906]119892 (]) 119889] = 119906]119898119899 (8)

Then the probability for induced absorption processes simplybecomes

119889119882119894

119899119898= 119861

119899119898119906]119898119899

119889119905 (9)

Induced Emission A transition from 119898 rarr 119899 caused by theradiation is called the induced or stimulated emission Theprobability for this transition is

119889119882119894

119898119899= 119861

119898119899intΔ]119906]119892 (]) 119889] sdot 119889119905 = 119861119898119899119906]119898119899119889119905 (10)

with 119861119898119899

as the Einstein coefficient of induced emission

Total Transition Rates Under thermodynamic equilibriumthe total number of absorbing transitions must be the sameas the number of emissions These numbers depend on thepopulation of a state and the probabilities for a transition tothe other state According to (5)ndash(10) this can be expressedby

119861119899119898119906]119898119899

119873119899= (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898 (11)

or more universally described by rate equations

119889119873119898

119889119905= +119861

119899119898119906]119898119899

119873119899minus (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

119889119873119899

119889119905= minus119861

119899119898119906]119898119899

119873119899+ (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

(12)

For 119889119873119898119889119905 = 119889119873

119899119889119905 = 0 (12) gets identical to (11) Using

(4) in (11) gives

119892119899119861119899119898119906]119898119899

= 119892119898(119861

119898119899119906]119898119899

+ 119860119898119899) 119890

minusℎ]119898119899119896119879119866 (13)

Assuming that with 119879119866also 119906]119898119899 gets infinite 119861119898119899 and 119861119899119898

must satisfy the relation

119892119899119861119899119898

= 119892119898119861119898119899 (14)

Then (13) becomes

119861119898119899119906]119898119899

119890ℎ]119898119899119896119879119866 = 119861

119898119899119906]119898119899

+ 119860119898119899 (15)

or resolving to 119906]119898119899 gives

119906]119898119899=119860119898119899

119861119898119899

1

119890ℎ]119898119899119896119879119866 minus 1 (16)

This expression in Einsteinrsquos consideration is of the same typeas the Planck distribution for the spectral energy densityTherefore comparison of (3) and (16) at ]

119898119899gives for 119861

119898119899

119861119898119899

=119892119899

119892119898

119861119899119898

=1198601198981198991198883

81205871198993ℎ]3119898119899

=119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992 (17)

showing that the induced transition probabilities are alsoproportional to the spontaneous emission rate 119860

119898119899 and in

units of the photon energy ℎ]119898119899 are scaling with 1205822

22 Relationship to Other Spectroscopic Quantities The Ein-stein coefficients for induced absorption and emission aredirectly related to some other well-established quantities inspectroscopy the cross sections for induced transitions andthe absorption and gain coefficient of a sample


221 Cross Section and Absorption Coefficient Radiationpropagating in 119903-direction through an absorbing sample isattenuated due to the interaction with the molecules Thedecay of the spectral energy obeys Lambert-Beerrsquos law heregiven in its differential form

119889119906]

119889119903= minus120572

119899119898(]) 119906] = minus120590119899119898 (])119873119899

119906] (18)

where 120572119899119898(]) is the absorption coefficient (units cmminus1)

and 120590119899119898(]) is the cross section (units cm2) for induced

absorptionFor a more general analysis however also emission

processes have to be considered which partly or completelycompensate for the absorption losses Then two cases haveto be distinguished the situation we discuss in this sectionwhere the molecules are part of an environmental thermalbath and on the other hand the case where a directedexternal radiation prevails upon a gas cloud which will beconsidered in the next section

In the actual case (18) has to be expanded by two termsrepresenting the induced and also the spontaneous emissionQuite similar to the absorption the induced emission isgiven by the cross section of induced emission 120590

119898119899(]) the

population of the upper state 119873119898 and the spectral radiation

density 119906] The product 120590119898119899(]) sdot 119873

119898now describes an

amplification of 119906] and is known as gain coefficientAdditionally spontaneously emitted photons within a

considered volume element and time interval 119889119905 = 119889119903 sdot

119899119888 contribute to the spectral energy density of the thermalbackground radiation with

119889119906] = ℎ]119898119899119860119898119899119889119905119873

119898119892 (]) =

ℎ]119898119899

119888119899119860119898119899119889119903119873

119898119892 (]) (19)

Then altogether this gives

119889119906]

119889119903= minus120590

119899119898(])119873

119899119906] + 120590119898119899 (])119873119898

119906] +ℎ]

119898119899

119888119899119860119898119899119873119898119892 (])

(20)

As we will see in Section 25 and later in Section 33 orSection 4 (19) is the source term of the thermal backgroundradiation in a gas and (20) already represents the theoreticalbasis for calculating the radiation transfer of thermal radia-tion in the atmosphere

The frequency dependence of 120590119899119898(]) and 120590

119898119899(]) and

thus the resonant interaction of radiation with a moleculartransition can explicitly be expressed by the normalizedlineshape function 119892(]) as

120590119898119899(]) = 1205900

119898119899119892 (]) 120590

119899119898(]) = 1205900

119899119898119892 (]) (21)

Equation (20) may be transformed into the time domain by119889119903 = 119888119899 sdot 119889119905 and additionally integrated over the lineshape119892(]) When 119906] can be assumed to be broad compared to 119892(])

the energy density119906 as the integral over the lineshape ofwidthΔ] becomes

intΔ]

119889119906]

119889119905119889] =

119889119906]119898119899

119889119905Δ] =

119889119906

119889119905

= minus119888

119899(120590

0

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ ℎ]119898119899119860119898119899119873119898

(22)

This energy density of the thermal radiation 119906 (units Jm3)can also be expressed in terms of a photon density 120588

119866[mminus3

]

in the gas multiplied with the photon energy ℎ sdot ]119898119899

with

119906 = 119906]119898119899Δ] = 120588

119866sdot ℎ]

119898119899 (23)

Since each absorption of a photon reduces the population ofstate 119899 and increases119898 by the same amountmdashfor an emissionit is just oppositemdashthis yields

119889120588119866

119889119905=119889119873

119899

119889119905= minus

119889119873119898

119889119905

= minus119888119899

ℎ]119898119899

(1205900

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ 119860119898119899119873119898

(24)

which is identical with the balance in (12) Comparison ofthe first terms on the right side and applying (17) gives theidentity

119861119899119898119906]119898119899

119873119899=119892119898

119892119899

119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992119906]119898119899

119873119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119873119899119906]119898119899

(25)

and therefore

1205900

119899119898=119892119898

119892119899

1198601198981198991205822

119898119899

81205871198992 (26)

Comparing the second terms in (12) and (24) results in

1205900

119898119899=1198601198981198991205822

119898119899

81205871198992=119892119899

119892119898

1205900

119899119898 (27)

So together with (21) and (27) we derive as the finalexpressions for 120590

119899119898(]) and 120590

119898119899(])

120590119898119899(]) =

119892119899

119892119898

120590119899119898(]) =

1198601198981198991205822

119898119899

81205871198992119892 (])

120590119898119899(]) =

ℎ]119898119899

119888119899119861119898119899119892 (]) 120590

119899119898(]) =

ℎ]119898119899

119888119899119861119899119898119892 (])

(28)

222 Effective Cross Section and Spectral Line IntensityOften the first two terms on the right side of (20) are unifiedand represented by an effective cross section 120590

119899119898(]) Further


Cros

s sec

tion

(cm

2)

Snm

Frequency

Δmn

mn

Figure 3 For explanation of the spectral line intensity

relating the interaction to the total number density 119873 of themolecules it applies

120590119899119898(])119873 = 120590

119899119898(])119873

119899minus 120590

119898119899(])119873

119898

= 120590119899119898(])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

=ℎ]

119898119899

119888119899119861119899119898119892 (])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

(29)

and 120590119899119898(]) becomes

120590119899119898(]) =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (]) (30)

Integration of (30) over the linewidth gives the spectral lineintensity 119878

119899119898of a transition (Figure 3)

119878119899119898

= intΔ]120590119899119898(]) 119889] =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

) (31)

as it is used and tabulated in data bases [13 14] to characterizethe absorption strength on a transition

223 Effective Absorption Coefficient Similar to 120590119899119898(]) with

(30) and (31) an effective absorption coefficient on a transi-tion can be defined as

120572119899119898(]) = 120590

119899119898(])119873

=ℎ]

119898119899

119888119899119861119899119898119873119899(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (])

= 119878119899119898119873119892 (]) = 1205720

119899119898119892 (])

(32)

which after replacing 119861119899119898

from (17) assumes the morecommon form

120572119899119898(]) =

1198601198981198991198882

81205871198992]2119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

=1198601198981198991205822

81205871198992119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

(33)

Nm

Nn

WGmn Amn

Cmn

WGnm Cnm

Figure 4 Two-level system with transition rates due to stimulatedspontaneous and collisional processes

23 Collisions Generally the molecules of a gas underliecollisions which may perturb the phase of a radiatingmolecule and additionally cause transitions between themolecular states The transition rate from 119898 rarr 119899 due tode-exciting nonradiating collisions (superelastic collisionsof 2nd type) may be called 119862

119898119899and that for transitions from

119899 rarr 119898 (inelastic collisions of 1st type) as exciting collisions119862119899119898 respectively (see Figure 4)

231 Rate Equations Then with (25) and the abbreviations119882

119866

119898119899and119882119866

119899119898as radiation induced transition rates or transi-

tion probabilities (units sminus1)

119882119866

119898119899= 119861

119898119899119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119898119899119906]119898119899

119882119866

119899119898= 119861

119899119898119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119906]119898119899

=119892119898

119892119899

119882119866

119898119899

(34)

the rate equations as generalization of (12) or (24) and addi-tionally supplemented by the balance of the electromagneticenergy density or photon density (see (22)ndash(24)) assume theform

119889119873119898

119889119905= + (119882

119866

119899119898+ 119862

119899119898)119873

119899minus (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889119873119899

119889119905= minus (119882

119866

119899119898+ 119862

119899119898)119873

119899+ (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889120588119866

119889119905= minus119882

119866

119899119898119873119899+119882

119866

119898119899119873119898+ 119860

119898119899119873119898

(35)

At thermodynamic equilibrium the left sides of (35) aregetting zero Then also and even particularly in the presenceof collisions the populations of states 119898 and 119899 will bedetermined by statistical thermodynamics So adding thefirst and third equation of (35) together with (4) it is foundsome quite universal relationship for the collision rates

119862119899119898

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866119862

119898119899 (36)

showing that transitions due to inelastic collisions are directlyproportional to those of superelastic collisions with a pro-portionality factor given by Boltzmannrsquos distribution From(35) it also results that states which are not connected by anallowed optical transition nevertheless will assume the samepopulations as those states with an allowed transition


232 Radiation Induced Transition Rates When replacing119906]119898119899

in (34) by (3) the radiation induced transition rates canbe expressed as

119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)

Inserting some typical numbers into (37) for example atransition wavelength of 15120583m for the prominent CO

2-

absorption band and a temperature of 119879119866

= 288K wecalculate a ratio119882119866

119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899

almost the same is found for the population ratio (see (4))with 119873

119898119873

119899= 0036 At spontaneous transition rates of the

order of 119860119898119899

= 1 sminus1 for the stronger lines in this CO2-

band then we get a radiation induced transition rate of only119882

119866

119898119899= 119882

119866

119899119898= 003-004 sminus1

Under conditions as found in the troposphere with colli-sion rates between molecules of several 109 sminus1 any inducedtransition rate due to the thermal background radiation isorders of magnitude smaller and even up to the stratosphereand mesosphere most of the transitions are caused bycollisions so that above all they determine the population ofthe states and in any case ensure a fast adjustment of a localthermodynamic equilibrium in the gas

Nevertheless the absolute numbers of induced absorp-tion and emission processes per volume scaling with thepopulation density of the involved states (see (35)) can bequite significant So at a CO

2concentration of 400 ppm

the population in the lower state 119899 is estimated to be about119873119899sim 7 times 10

20mminus3 (dependent on its energy above theground level) Then more than 1019 absorption processes perm3 are expected and since such excitations can take placesimultaneously on many independent transitions this resultsin a strong overall interaction of the molecules with thethermal bath which according to Einsteinrsquos considerationseven in the absence of collisions leads to the thermodynamicequilibrium

24 Linewidth and Lineshape of a Transition The linewidthof an optical or infrared transition is determined by differenteffects

241 Natural Linewidth and Lorentzian Lineshape Formolecules in rest and without any collisions and also neglect-ing power broadening due to induced transitions the spectralwidth of a line only depends on the natural linewidth

Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)

which for a two-level system and 120591119899≫ 120591

119898is essentially

determined by the spontaneous transition rate 119860119898119899

asymp 1120591119898

120591119899and 120591

119898are the lifetimes of the lower and upper state

The lineshape is given by a Lorentzian 119892119871(]) which in the

normalized form can be written as

119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)

242 Collision Broadening With collisions in a gas thelinewidth will considerably be broadened due to state andphase changing collisions Then the width can be approxi-mated by

Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)

where 119862phase is an additional rate for phase changing colli-sions The lineshape is further represented by a Lorentzianonly with the new homogenous width Δ]

119898119899(FWHM)

according to (40)

243 Doppler Broadening Since the molecules are at anaverage temperature 119879

119866 they also possess an average kinetic

energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)

with 119898119866as the mass and V2 as the velocity of the molecules

squared and averaged Due to a Doppler shift of the movingparticles the molecular transition frequency is additionallybroadened and the number of molecules interacting withintheir homogeneous linewidth with the radiation at frequency] is limited This inhomogeneous broadening is determinedby Maxwellrsquos velocity distribution and known as Dopplerbroadening The normalized Doppler lineshape is given by aGaussian function of the form

119892119863(]) =

2radicln 2radic120587Δ]

119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)

with the Doppler linewidth

Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12

= 716 sdot 10minus7]

119898119899radic119879119866

119872 (43)

where 119872 is the molecular weight in atomic units and 119879119866

specified in K

244 Voigt Profile For the general case of collision andDoppler broadening a convolution of 119892

119863(]1015840) and 119892

119871(] minus

]1015840) gives the universal lineshape 119892119881(]) representing a Voigt

profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840

=radicln 2120587radic120587

Δ]119898119899

Δ]119863

times int

infin

0

exp(minus(]1015840 minus ]

119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)


25 Spontaneous Emission as Thermal Background RadiationFrom the rate equations (35) it is clear that also in thepresence of collisions the absolute number of spontaneouslyemitted photons per time should be the same as that withoutcollisions This is also a consequence of (36) indicatingthat with an increasing rate 119862

119898119899for de-exciting transitions

(without radiation) also the rate 119862119899119898

of exiting collisions isgrowing and just compensating for any losses even when thebranching ratio 119877 = 119860

119898119899119862

119898119899of radiating to nonradiating

transitions decreases In other words when the moleculeis in state 119898 the probability for an individual spontaneousemission act is reduced by the ratio 119877 but at the same timethe number of occurring decays per time increases with 119862

119898119899

Then the spectral power density in the gas due tospontaneous emissions is (see (19))

119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)

representing a spectral generation rate of photons of energyℎ]

119898119899per volume Photons emerging from a volume element

generally spread out into neighbouring areas but in the sameway there is a backflow from the neighbourhood whichin a homogeneous medium just compensates these lossesNevertheless photons have an average lifetime before theyare annihilated due to an absorption in the gas With anaverage photon lifetime

120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898

is the mean free path of a photon in thegas before it is absorbed we can write for the spectral energydensity

119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)

The same result is derived when transforming (20) intothe time domain and assuming a local thermodynamicequilibrium with 119889119906]119889119905 = 0

(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)

With 120572119899119898(]) from (33) and Boltzmannrsquos relation (4) then the

spectral energy density at ]119898119899

is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)

This is the well-known Planck formula (3) and shows thatwithout an additional external excitation at thermodynamicequilibrium the spontaneous emission of molecules can beunderstood as nothing else as the thermal radiation of a gason the transition frequency

This derivation differs insofar from Einsteinrsquos consid-eration leading to (16) as he concluded that a radiationfield interacting with the molecules at thermal and radiationequilibrium just had to be of the type of a Planckianradiator while here we consider the origin of the thermalradiation in a gas sample which exclusively is determinedand rightfully defined by the spontaneous emission of themolecules themselves This is also valid in the presence ofmolecular collisions Because of this origin the thermalbackground radiation only exists on discrete frequenciesdetermined by the transition frequencies and the linewidthsof the molecules as long as no external radiation is presentBut on these frequencies the radiation strength is the sameas that of a blackbody radiator

Since this spontaneous radiation is isotropically emittingphotons into the full solid angle 4120587 in average half of theradiation is directed upward and half downward

3 Interaction of Molecules with ThermalRadiation from an External Source

In this section we consider the interaction of molecules withan additional blackbody radiation emitted by an externalsource like the earthrsquos surface or adjacent atmospheric layersWe also investigate the transfer of absorbed radiation to heatin the presence of molecular collisions causing a rise ofthe atmospheric temperature And vice versa we study thetransfer of a heat flux to radiation resulting in a cooling of thegas An appropriate means to describe the mutual interactionof these processes is to express this by coupled rate equationswhich are solved numerically

31 Basic Quantities

311 Spectral Radiance The power radiated by a surfaceelement 119889119860 on the frequency ] in the frequency interval 119889]and into the solid angle element 119889Ω is also determined byPlanckrsquos radiation law

119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)

with 119868]Ω(119879119864) as the spectral radiance (units Wm2Hzsterad) and 119879

119864as the temperature of the emitting surface

of the source (eg earthrsquos surface) The cosine term accountsfor the fact that for an emission in a direction given by theazimuthal angle 120593 and the polar angle 120573 only the projectionof 119889119860 perpendicular to this direction is efficient as radiatingsurface (Lambertian radiator)

312 Spectral Flux DensitymdashSpectral Intensity Integrationover the solid angle Ω gives the spectral flux density Thenrepresenting 119889Ω in spherical coordinates as 119889Ω = sin120573119889120573119889120593


120593

120573

dA

d120593

d120573

Figure 5 Radiation from a surface element 119889119860 into the solid angle119889Ω = sin120573119889120573119889120593

with 119889120593 as the azimuthal angle interval and 119889120573 as the polarinterval (see Figure 5) this results in

119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)

or in wavelengths units

119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)

119868120582and 119868] also known as spectral intensities are specified

in units of Wm2120583m and Wm2Hz respectively Theyrepresent the power flux per frequency or wavelength and persurface area into that hemisphere which can be seen fromthe radiating surface element The spectral distribution of aPlanck radiator of 119879 = 299K as a function of wavelength isshown in Figure 6

32 Ray Propagation in a Lossy Medium

321 Spectral Radiance Radiation passing an absorbingsample generally obeys Lambert-Beerrsquos law as already appliedin (18) for the spectral energy density 119906] The same holds forthe spectral radiance with

119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)

where 119889119903 is the propagation distance of 119868]Ω in the sampleThis is valid independent of the chosen coordinate systemThe letter 119903 is used when not explicitly a propagation

35

30

25

20

15

10

5

00 10 20 30 40 50 60

Wavelength (120583m)

Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K

Figure 6 Spectrum of a Planck radiator at 299K temperature

z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573

Figure 7 Radiation passing a gas layer

perpendicular to the earthrsquos surface or a layer (119911-direction)is meant

322 Spectral Intensity For the spectral intensity which dueto the properties of a Lambertian radiator consists of a bunchof rays with different propagation directions and brightnesssome basic deviations have to be recognized So because ofthe individual propagation directions spreading over a solidangle of 2120587 only for a homogeneously absorbing sphere andin a spherical coordinate system with the radiation source inthe center of this sphere the distances to pass the sample andthus the individual contributions to the overall absorptionwould be the same

But radiation emerging from a plane parallel surfaceand passing an absorbing layer of thickness Δ119911 is bettercharacterized by its average expansion perpendicular to thelayer surface in 119911-direction This means that with respect tothis direction an individual ray propagating under an angle 120573to the surface normal covers a distance Δ119897 = Δ119911cos120573 beforeleaving the layer (see Figure 7) Therefore such a ray on oneside contributes to a larger relative absorption and on theother side it donates this to the spectral intensity only withweight 119868]Ωcos120573119889Ω due to Lambertrsquos law

This means that to first order each individual beamdirection suffers from the same absolute attenuation andparticularly the weaker rays under larger propagation angles120573 waste relatively more of their previous spectral radianceThus especially at higher absorption strengths and longerpropagation lengths the initial Lambertian distribution willbe more and more modified A criterion for an almostunaltered distribution may be that for angles 120573 le 120573max theinequality 120572

119899119898sdot Δ119911cos120573 ≪ 1 is satisfied The absorption


loss for the spectral intensity as the integral of the spectralradiance 119868]Ω (see (51)) then is given by

int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)

The cosine terms under the integral sign just compensate and(54) can be written as

119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)

This differential equation for the spectral intensity shows thatthe effective absorption coefficient is twice that of the spectralradiance or in other words the average propagation length ofthe radiation to pass the layer is twice the layer thicknessThislast statementmeans thatwe also can assume radiationwhichis absorbed at the regular absorption coefficient 120572

119899119898 but is

propagating as a beam under an angle of 60∘ to the surfacenormal (1cos 60∘ = 2) In practice it even might give senseto deviate from an angle of 60∘ to compensate for deviationsof the earthrsquos or oceanic surface from a Lambertian radiatorand to account for contributions due to Mie and Rayleighscattering

The absorbed spectral power density 119871] (power pervolume and per frequency) with respect to the 119911-directionthen is found to be

119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)

with 119868](0) as the initial spectral intensity at 119911 = 0 as given by(51)

An additional decrease of 119871] with 119911 due to a lateralexpansion of the radiation over the hemisphere can beneglected since any propagation of the radiation is assumedto be small compared to the earthrsquos radius (consideration ofan extended radiating parallel plane)

Integration of (56) over the lineshape 119892(]) within thespectral intervalΔ] gives the absorbed power density119871 (unitsWm3) which similar to (23) may also be expressed as lossor annihilation of photons per volume (120588

119864in mminus3) and per

time Since the average propagation speed of 119868] in 119911-directionis 1198882119899 also the differentials transform as 119889119911 = 1198882119899sdot119889119905 With119868] from (51) this results in

119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)

or for the photon density 120588119864in terms of the induced transi-

tion rates119882119864

119899119898and119882119864

119898119899caused by the external field

119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878

119899119898119873Δ] as an averaged absorption

coefficient over the linewidth (see also (32)) and with

119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)

Similar to (37) these rates are again proportional to thespontaneous transition probability (rate) 119860

119898119899 but now they

depend on the temperature 119879119864of the external source and the

propagation depth 119911Due to the fact that radiation from a surface with a

Lambertian distribution and only from one hemisphere isacting on the molecules different to (37) a factor of 14appears in this equation

At a temperature 119879119864= 288K and wavelength 120582 = 15 120583m

for example the ratio of induced to spontaneous transitionsdue to the external field at 119911 = 0 is

119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)

For the case of a two-level system 119860119898119899

can also be expressedby the natural linewidth of the transition with (see (38))

Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)

With a typical natural width of the order of only 01 Hz in the15 120583m band of CO

2 then the induced transition rate will be

less than 001 sminus1 Even on the strongest transitions around42 120583m the natural linewidths are onlysim100Hz and thereforethe induced transition rates are about 10 sminus1

Despite of these small rates the overall absorption of anincident beam can be quite significant In the atmospherethe greenhouse gases are absorbing on hundred thousands oftransitions over long propagation lengths and at molecularnumber densities of 1019ndash1023 per m3 On the strongest linesin the 15120583m band of CO

2 the absorption coefficient at the

center of a line even goes up to 1mminus1 Then already within adistance of a fewm the total power will be absorbed on thesefrequencies So altogether about 85 of the total IR radiationemerging from the earthrsquos surface will be absorbed by thesegases

323 Alternative Calculation for the Spectral Intensity Forsome applications it might be more advantageous first tosolve the differential equation (53) for the spectral radianceas a function of 119911 and also 120573 before integrating overΩ


Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm

Figure 8 Two-level system with transition rates including anexternal excitation

Then an integration in 119911-direction over the length 119911cos120573with a 119911-dependent absorption coefficient gives

119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)

and a further integration overΩ results in

119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)

First integrating over 120593 and introducing the optical depthint119911

0120572119899119898(1199111015840)119889119911

1015840= 120591 as well as the substitution 119906 = 120591cos120573

we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)

with 119868](0) = 120587119868]Ω(0) (see (51)) and the exponential integral

1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)

Since the further considerations in this paper are concen-trating on the radiation transfer in the atmosphere underthe influence of thermal background radiation it is moreappropriate to describe the interaction of radiation with themolecules by a stepwise propagation through thin layers ofdepth Δ119911 as given by (55)

33 Rate Equations under Atmospheric Conditions As afurther generalization of the rate equations (35) in thissubsection we additionally consider the influence of theexternal radiation which together with the thermal back-ground radiation is acting on the molecules in the presenceof collisions (see Figure 8)

And different to Section 2 the infrared active moleculesare considered as a trace gas in an open system the

atmosphere which has to come into balance with its environ-mentThenmolecules radiating due to their temperature andthus loosing part of their energy have to get this energy backfrom the surrounding by IR radiation by sensitive or latentheat or also by absorption of sunlight This is a consequenceof energy conservation

The radiation loss is assumed to be proportional to theactual photon density 120588

119866and scaling with a flux rate 120601

This loss can be compensated by the absorbed power ofthe incident radiation for example the terrestrial radiationwhich is further expressed in terms of the photon density120588119864(see (57)) and it can also be replaced by thermal energy

Therefore the initial rate equations have to be supplementedby additional relations for these two processes

It is evident that both the incident radiation and theheat flux will be limited by some genuine interactions Sothe radiation can only contribute to a further excitation aslong as it is not completely absorbed At higher moleculardensities however the penetration depth of the radiationin the gas is decreasing and therewith also the effectiveexcitation over some longer volume element Integrating (55)over the linewidth while using the definitions of (31) and (32)and then integrating over 119911 results in

119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)

which due to Lambert-Beerrsquos law describes the averagedspectral intensity over the linewidth as a function of thepropagation in 119911-direction From this it is quite obvious todefine the penetration depth as the length 119871

119875 over which the

initial intensity reduces to 1119890 and thus the exponent in (67)gets unity with

119871119875=

Δ]

2119878119899119898119873119878

(68)

From (68) also the molecular number density119873119878is found at

which the initial intensity just drops to 1119890 after an interactionlength 119871

119875 Since 119873

119878characterizes the density at which an

excitation of the gas gradually comes to an end and in thissense saturation takes place it is known as the saturationdensity where 119873

119878and also 119878

119899119898refer to the total number

density119873 of the gasSince at constant pressure the number density in the

gas is changing with the actual temperature due to Gay-Lussacrsquos law and the molecules are distributed over hundredsof states and substates the molecular density contributing toan interaction with the radiation on the transition 119899 rarr 119898 isgiven by [15]

119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)

where 1198730is the molecular number density at an initial

temperature 1198790 119864

119899is the energy of the lower level 119899 above


the ground state and119875(119879119866) is the total internal partition sum

defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)

In the atmosphere typical propagation lengths are of theorder of several km So for a stronger CO

2transition in the

15 120583m band with a spontaneous rate 119860 = 1 sminus1 119873119899119873 =

119873119899119873

0= 007 a spectral line intensity 119878

119899119898or integrated cross

section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)

= 6 times 10minus13m2Hz = 2 times 10minus19 cmminus1

(moleculessdotcmminus2)

(71)

and a spectral width at ground pressure of Δ] = 5GHzthe saturation density over a typical length of 119871

119875= 1 km

assumes a value of 119873119878asymp 4 times 10

18moleculesm3 Since thenumber density of the air at 1013 hPa and 288K is 119873air =

255 times 1025mminus3 saturation on the considered transition

already occurs at a concentration of less than one ppm Itshould also be noticed that at higher altitudes and thus lowerdensities also the linewidth Δ] due to pressure broadeningreduces This means that to first order also the saturationdensity decreases with Δ] while the gas concentration inthe atmosphere at which saturation appears almost remainsconstant The same applies for the penetration depth

For the further considerations it is adequate to introducean average spectral intensity 119868]119898119899 as

119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)

or equivalently an average photon density

120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)

which characterizes the incident radiation with respect to itsaverage excitation over 119871

119875in the rate equations In general

the incident flux 120588119864(0) onto an atmospheric layer consists of

two terms the up- and the downwelling radiationAny heat flux supplied to the gas volume contributes

to a volume expansion and via collisions and excitation ofmolecules this can also be transferred to radiation energySimultaneously absorbed radiation can be released as heat

in the gas Therefore the rate equations are additionallysupplemented by a balance for the heat energy density of theair119876 [Jm3] which under isobaric conditions andmaking useof the ideal gas equation in the form 119901air = 119873air sdot 119896 sdot 119879119866 can bewritten as

Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)

or after integration

119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)

Here 119888119901represents the specific heat capacity of the air at

constant pressure with 119888119901= (1198912 + 1) sdot 119877

119866119872air where 119891 are

the degrees of freedom of a molecule (for N2and O

2 119891 = 5)

and 119877119866= 119896 sdot 119873

119860is the universal gas constant (at room

temperature 119888119901= 101 kJkgK) 120588air is the specific weight

of the air (at room temperature and ground pressure 120588air =129 kgm3) which can be expressed as 120588air = 119898air sdot 119873air =119872air119873119860

sdot119873air = 119872air119873119860sdot 119901air(119896119879119866)with119898air as the mass of

an air molecule119872air the mol weight119873119860Avogadrorsquos number

119873air the number density and 119901air the pressure of the airThe thermal energy can be supplied to a volume element

by different means So thermal convection and conductivityin the gas contribute to a heat flux j

119867[J(ssdotm2)] causing

a temporal change of 119876 proportional to div j119867 or for one

direction proportional to 120597119895119867119911120597119911 j

119867is a vector and points

from hot to cold Since this flux is strongly dominated byconvection it can be well approximated by 119895

119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ

119862as the heat transfer coefficient typically of the

order of ℎ119862asymp 10ndash15Wm2K At some more or less uniform

distribution of the incident heat flux over the troposphere(altitude 119867

119879asymp 12 km) the temporal change of 119876 due to

convection may be expressed as 120597119895119867119911120597119911 = ℎ

119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K

Another contribution to the thermal energy originatesfrom the absorbed sunlight which in the presence of col-lisions is released as kinetic or rotational energy of themolecules Similarly latent heat can be set free in the air Inthe rate equations both contributions are represented by asource term 119902SL [J(ssdotm

3)]Finally the heat balance is determined by exciting and de-

exciting collisions changing the population of the states 119899 and119898 and reducing or increasing the energy by ℎ sdot ]

119898119899

Altogether this results in a set of coupled differentialequations which describe the simultaneous interaction ofmolecules with their self-generated thermal backgroundradiation as well as with radiation from the earthrsquos surface


andor a neighbouring layer this all in the presence ofcollisions and under the influence of heat transfer processes

119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875

(1 minus 119890minus(2ℎ]119898119899(Δ]119888119899))(119861119899119898119873119899minus119861119898119899119873119898)119871119875) 120588

119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)

To symbolize themutual coupling of these equations here weuse a notation where the radiation induced transition ratesare represented by the Einstein coefficients and the respectivephoton densities A change to the other representation iseasily performed applying the identities

119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)

It should be noticed that the rate equation for 120588119864could

also be replaced by the incident radiation as given by (73)However since 120588

119864approaches its equilibrium value within

a time constant 120591 = Δ](ℎ]119898119899(119861

119899119898119873119899minus 119861

119898119899119873119898)) short

compared with other processes for a uniform representationthe differential form was preferred

For the special case of stationary equilibrium with119889119873

119899119889119905 = 119889119873

119898119889119905 = 0 from the first rate equation we get

for the population ratio

119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860

119898119899(see (37) and (60)) in the limit of pure

spontaneous decay processes reaches its maximum value of44 while in the presence of collisions with collision ratesin the troposphere of several 109 sminus1 it rapidly converges to35 given by the Boltzmann relation at temperature 119879

119866and

corresponding to a local thermodynamic equilibriumFor the general case the rate equations have to be

solved numerically for example by applying the finite ele-ment method While (76) in the presented form is onlyvalid for a two-level system a simulation under realisticconditions comparable to the atmosphere requires someextension particularly concerning the energy transfer fromthe earthrsquos surface to the atmosphere Since the main tracegases CO

2 water vapour methane and ozone are absorbing

the incident infrared radiation simultaneously on thousandsof transitions as an acceptable approximation for this kindof calculation we consider these transitions to be similar andindependent from each other each of them contributing tothe same amount to the energy balance In the rate equationsthis can easily be included by multiplying the last term in theequation for the energy density 119876 with an effective number119872tr of transitions

In this approximation the molecules of an infrared activegas and even amixture of gases are represented by a ldquostandardtransitionrdquo which reflects the dynamics and time evolution ofthemolecular populations under the influence of the incidentradiation the background radiation and the thermal heattransfer 119872tr is derived as the ratio of the total absorbedinfrared intensity over the considered propagation length tothe contribution of a single standard transition

An example for a numerical simulation in the tropo-sphere more precisely for a layer from ground level upto 100m is represented in Figure 9 The graphs show theevolution of the photon densities 120588

119866and 120588

119864 the population

densities 119873119899and 119873

119898of the states 119899 and 119898 the accumulated

heat density 119876 in the air and the temperature 119879119866of the gas

(identical with the atmospheric temperature) as a function oftime and as an average over an altitude of 100m

As initial conditions we assumed a gas and air temper-ature of 119879

119866= 40K a temperature of the earthrsquos surface

of 119879119864= 288K an initial heat flux due to convection of

119895119867119911

= 3 kWm2 a latent heat source of 119902SL = 3mWm3and an air pressure of 119901air = 1013 hPa The interactionof the terrestrial radiation with the infrared active gases isdemonstrated for CO

2with a concentration in air of 380 ppm

corresponding to a molecular number density of 1198730

=

97 times 1021mminus3 at 288K The simulation was performed for

a ldquostandard transitionrdquo as discussed before with a transitionwavelength 120582 = 15 120583m a spontaneous transition rate 119860

119898119899=

1 sminus1 statistical weights of 119892119898

= 35 and 119892119899

= 33 aspectral width of Δ] = 5GHz a collisional transition rate119862119898119899

= 108 sminus1 (we do not distinguish between rotational

and vibrational rates [10]) a penetration depth 119871119875= 100m

and assuming a photon loss rate of 120601 = 75 times 105 sminus1 For

this calculation a density and temperature dependence of Δ]and 119862

119898119899was neglected Since under these conditions a single

transition contributes 0069Wm2 to the total IR-absorptionof 212Wm2 over 100m119872tr = 3095 transitions represent theradiative interaction with all active gases in the atmosphere


605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)

Figure 9 Solution of the rate equations for the troposphere (close to the earthrsquos surface) representing the evolution of (a) the photon density120588119866

(b) the photon density 120588119864(c) the lower and (d) the upper population density (e) the thermal energy density and (f) the gas- (air)-temperature

as a function of time

The evolution for another gas and transition can easilydisplayed by replacing the respective parameters for the othertransition and recalibrating the effective transition number

To ensure reproducible results and to avoid any insta-bilities the time interval for the stepwise integration ofthe coupled differential equation system has to be chosensmall enough to avoid changes comparable to the size of acomputed quantity itself or the calculated changes have to berestrict by some upper boundaries taking into account somesmaller repercussions on the absolute time scale The latterprocedure was applied which accelerates the calculations byseveral orders of magnitude

A simulation is done in such a way that starting from theinitial conditions for the populations the photon densitiesand the temperature in a first step modified populationand photon densities as well as a change of the heat densityover the time interval Δ119905 are determined The heat changecauses a temperature change Δ119879

119866(see (74)) and gives a

new temperature which is used to calculate a new collisiontransfer rate 119862

119899119898by (36) a corrected population 119873

119899by (69)

and a new population119873119898for the upper state by (4)The total

internal partition sum for CO2is deduced from data of the

HITRAN-database [13] and approximated by a polynomial ofthe form

119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)

The new populations are used as new initial conditionsfor the next time step over which again the interaction ofthe molecules with the radiation and any heat transfer iscomputed In this way the time evolution of all coupledquantities shown in Figure 9 is derived For this simulationit was assumed that all atmospheric components still exist ingas form down to 40K

The relatively slow evolution of the curves is due to thefact that the absorbed IR radiation as well as the thermal fluxis mostly used to heat up the air volume which at constant airpressure is further expanding and the density decreasing

Population changes of the CO2states induced by the

external or the thermal background radiation are coupledto the heat reservoir via the collisional transition rates 119862

119898119899

and 119862119899119898

(see last rate equation) which are linked to eachother by (36) As long as the calculated populations differfrom a Boltzmann distribution at the gas-temperature 119879

119866


the two terms in the parenthesis of this rate equation do notcompensate and their difference contributes to an additionalheating amplified by the effective number of transitions Rea-sons for smaller deviations from a local thermal equilibriumcan be the induced population changes due to the externalradiation as well as temperature and density variations withaltitude and daytime or some local effects in the atmosphereAlso vice versa when the gas is supplied with thermal energythe heat can be transferred to electromagnetic energy andreradiated by the molecules (radiative cooling)

The photon density 120588119866(Figure 9(a)) shows the sponta-

neous emission of the molecules and determines the thermalbackground radiation of the gas It is mostly governed bythe population of the upper state and in equilibrium is self-adjusting on a level where the spontaneous generation rate119860119898119899

sdot 119873119898is just balanced by the induced transition rates

(optical and collision induced) and the loss rate120601120588119866 the latter

dependent on the density and temperature variations in theatmosphere

Figure 9(b) represents the effective photon density 120588119864

available to excite the gas over the layer depth119871119875by terrestrial

radiation and back radiation from the overlaying atmosphereThe downwelling part was assumed to originate from a layerof slightly lower temperature than the actual gas temperature119879119866with a lapse rate also varying with 119879

119866 The curve first

declines since with slightly increasing temperature the lowerstate which is not the ground state of CO

2 is stronger

populated (see also Figure 9(c)) and therefore the absorptionon this transition increases while according to saturationeffects the effective excitation over 119871

119875decreases With

further growing temperature 120588119864again increases caused by

the decreasing gas density and also reduced lower populationaccompanied by a smaller absorption

Figures 9(c) and 9(d) show the partial increase as wellas the depletion of the lower state and the simultaneousrefilling of the upper state due to the radiation interactionand thermal heatingThe populations are displayed in relativeunits normalized to the CO

2number density119873

0at 288K

The heat density of the air and the gas (air) temperatureare plotted in Figures 9(e) and 9(f) Up to about 80K (first70 h) heating is determined by convection while at highertemperatures radiative heatingmore andmore dominates Aninitial heat flux of 3 kWm2 seems relatively large but quicklyreduces with increasing temperature and at a difference of 3 Kbetween the surface and lower atmosphere similar to latentheat does not contribute tomore than 40Wm2 representingonly 10 of the terrestrial radiation

In principle it is expected that a gas heated by an externalsource cannot get warmer than the source itself This isvalid for a heat flux caused by convection or conduction inagreement with the second law of thermodynamics but itleads to some contradictionwith respect to a radiation source

In a closed system as discussed in Section 2 thermalradiation interacting with the molecules is in unison withthe population of the molecules and both the radiationand the gas can be characterized by a unique temperature119879119866 In an open system with additional radiation from an

external source of temperature 119879119864 the prevailing radiation

interacting with the molecules consists of two contributionswhich in general are characterized by different temperaturesand different loss processes So 119879

119864determines the spectral

intensity and distribution of the incident radiation and inthis sense defines the power flux which can be transferredto the molecules when this radiation is absorbed But itdoes not describe any direct heat transfer which alwaysrequires a medium for the transport and by nomeans definesthe temperature of the absorbing molecules At thermalequilibrium and in the presence of collisions the moleculesare better described by a temperature deduced from thepopulation ratio119873

119898119873

119899given by the Boltzmann relation (4)

This temperature also determines the spontaneous emissionand together with the losses defines the thermal backgroundradiation

Since an absorption on a transition takes place as longas the population difference 119873

119899minus 119873

119898is positive (equal

populations signify infinite temperature) molecules can bewell excited by a thermal radiation source which has a tem-perature lower than that of the absorbing gas Independent ofthis statement it is clear that at equilibrium the gas can onlyreradiate that amount of energy that was previously absorbedfrom the incident radiation andor sucked up as thermalenergy

In any way for the atmospheric calculations it seemsreasonable to restrict the maximum gas temperature tovalues comparable to the earthrsquos surface temperature Anadequate condition for this is a radiation loss rate

120601 ge119888119899

4119871119875

(1 minus 119890minus(2ℎ]119898119899(Δ]119888119899))(119861119899119898119873119899minus119861119898119899119873119898)119871119875) (80)

as derived from the rate equations at stationary equilibriumand with up- and downwelling radiation of the same magni-tude

A calculation for conditions as found in the upper strato-sphere at about 60 km altitude is shown in Figure 10 The airpressure is 073 hPa the regular temperature at this altitude is2427 K and the number density of air is119873air = 22times10

22mminus3The density of CO

2reduces to 119873 = 83 times 10

18mminus3 at aconcentration of 380 ppmAt this lower pressure the collisioninduced linewidth is three orders of magnitude smaller anddeclines to about Δ] = 5MHz Under these conditionsthe remaining width is governed by Doppler broadeningwith 34MHz At this altitude any terrestrial radiation foran excitation on the transition is no longer available Theonly radiation interacting with the molecules originates fromneighbouring molecules and the own background radiation

As initial conditions we used a local gas and air temper-ature 119879

119866= 250K slightly higher than the environment with

119879119864= 2427K the latter defining the radiation (up and down)

from neighbouring molecules The heat flux 119895119867119911

from or toadjacent layers was assumed to be negligible while a heatwell due to sun light absorption by ozone with sim15Wm2

over sim50 km in this case is the only heat source with 119902SL =

03mWm3 The calculation was performed for a collisionaltransition rate 119862

119898119899= 10

5 sminus1 a photon loss rate of 120601 =

75 times 104 sminus1 a layer depth of 119871

119875= 1 km and an effective

number of transitions 119872tr = 1430 (absorption on standard


31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)

Figure 10 Solution of the rate equations for the stratosphere (60 km altitude) representing the evolution of (a) the photon density 120588119866 (b)

the photon density 120588119864 (c) the lower and (d) the upper population density (e) the thermal energy density and (f) the gas (atmospheric)

temperature as a function of time

transition 28 times 10minus4Wm2 total IR-absorption over 1 km04Wm2)

Similar to Figure 9 the graphs show the evolution ofthe photon densities 120588

119866and 120588

119864 the population densities

119873119899and 119873

119898of the states 119899 and 119898 the heat density 119876 in

air and the temperature 119879119866

of the gas as a function oftime But different to the conditions in the tropospherewhere heating of the atmosphere due to terrestrial heat andradiation transfer was the dominating effect the simulationsin Figure 10 demonstrate the effect of radiative cooling in thestratosphere where incident radiation from adjacent layersand locally released heat is transferred to radiation andradiated to space An increased reradiation will be observedas represented by the upper graph till the higher temperaturediminishes and the radiated energy is in equilibriumwith thesupplied energy flux

Due to the lower density and heat capacity of the air atthis reduced pressure the system comes much faster to astationary equilibrium

34 Thermodynamic and Radiation Equilibrium Thermody-namic equilibrium in a gas sample means that the population

of themolecular states is given by the Boltzmann distribution(4) and the gas is characterized by an average temperature119879

119866

On the other hand spectral radiation equilibrium requiresthat the number of absorptions in a considered spectralinterval is equal to the number of emissions While withoutan external radiation generally any thermodynamic equilib-rium in a sample will be identical with the spectral radiationequilibrium in the presence of an additional field thesecases have to be distinguished since the incident radiationalso induces transitions and modifies the populations of themolecular states deviating from the Boltzmann distribution

Therefore it is appropriate to investigate the populationratio more closely and to discover how it looks like undersome special conditions This is an adequate means todetermine what kind of equilibrium is found in the gassample

For this we consider the total balance of absorption andemission processes as given by the rate equations (76) Understationary equilibrium conditions (see (78)) it is

(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)


With (17) (34) and (59) we can write

(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)

At local thermodynamic equilibrium119862119898119899

and119862119899119898

are linkedto each other by (36) But even more generally we canconclude that (36) is valid as long as the molecules can bedescribed by a Maxwellian velocity distribution and can becharacterized by an average temperature (see also [12])

Thus applying (36) and introducing some abbreviations

119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)

after elementary rearrangement (82) becomes

119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)

It is easy to be seen that for large 120576 and thus high collisionrates (84) approaches to a Boltzmann distribution Also for120576 = 0 (no collisions) and 119868] = 0 (no external radiation) thisgives the Boltzmann relation while for 120576 = 0 and 119868] ≫ (119888119899) sdot

119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)

This equation shows that under conditions as found in theupper atmosphere (small collision rates) the populations areapproximated by a modified Boltzmann distribution (righthand side for ℎ]

119898119899gt 119896119879

119864) which with increasing spectral

intensity is more and more determined by the temperature119879119864of the external radiation source Under such conditions

the normal thermodynamic equilibrium according to (4) isviolated and has to be replaced by the spectral radiationequilibrium

4 Radiation Balance and Radiation Transferin the Atmosphere

Amore extensive analysis of the energy and radiation balanceof an absorbing sample not only accounts for the net absorbedpower from the incident radiation as considered in (53)ndash(66) but it also includes any radiation originating from thesample itself as well as any re-radiation due to the externalexcitation This was already investigated in some detail inSection 33 however with the view to a local balance andits evolution over time In this section we are particularlyconcentrating on the propagation of thermal radiation in an

infrared active gas and how this radiation is modified due tothe absorption and re-emission of the gas

Two perspectives are possible an energy balance forthe sample or a radiation balance for the in- and outgoingradiationHerewe discuss the latter case Scattering processesare not included

We consider the incident radiation from an externalsource with the spectral radiance 119868]Ω(119879119864) as defined in (50)Propagation losses in a thin gas layer obey Lambert-Beerrsquoslaw Simultaneously this radiation is superimposed by thethermal radiation emitted by the gas sample itself and asalready discussed in Section 25 this thermal contributionhas its origin in the spontaneous emission of the moleculesFor small propagation distances 119889119903 in the gas both contribu-tions can be summed up yielding

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)

The last term is a consequence of (19) or (45) when trans-forming the spectral energy density 119906] of the gas to a spectralintensity (119888119899) sdot119906] and considering only that portion (1198884120587119899) sdot119906] emitted into the solid angle interval 119889Ω Equation (86)represents a quite general form of the radiation balance in athin layer and it is appropriate to derive the basic relationsfor the radiation transfer in the atmosphere under differentconditions The differential 119889119903 indicates that the absolutepropagation length in the gas is meant

41 Schwarzschild Equation in Dense Gases In the tropo-sphere the population of molecular states is almost exclu-sively determined by collisions between the molecules evenin the presence of stronger radiation Then due to theprevious discussion a well-established local thermodynamicequilibrium can be expected and from (47) or (48) we find

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)

with 119861]Ω(119879119866) = (1198884120587119899) sdot 119906] as the spectral radiance of thegas also known as Kirchhoff-Planck-function and given by(50) but here at temperature 119879

119866 To distinguish between the

external radiation and the radiating gas we use the letter 119861(from background radiation) which may not be mixed withthe Einstein coefficients 119861

119899119898or 119861

119898119899 Then we get as the final

result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)

This equation is known as the Schwarzschild equation [5ndash7] which describes the propagation of radiation in anabsorbing gas and which additionally takes into account thethermal background radiation of the gas While deriving thisequation no special restrictions or conditions concerning thedensity of the gas or collisions between the molecules haveto be made only that (36) is valid and the thermodynamic


z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573


equilibrium is given In general this is the case in thetroposphere up to the stratosphere

Another Derivation Generally the Schwarzschild equation isderived from pure thermodynamic considerations The gasin a small volume is called to be in local thermodynamicequilibrium at temperature 119879

119866 when the emitted radiation

from this volume is the same as that of a blackbody radiator atthis temperatureThen Kirchhoff rsquos law is strictly valid whichmeans that the emission is identical to the absorption of asample

The total emission in the frequency interval (] ] + 119889])during the time 119889119905may be 4120587120576(])The emissivity 120576(])may notbe mixed with 120576 = 119862

119899119898119861

119899119898in (83) Then with the spectral

radiance 119861]Ω(119879119866) as given by (50) and with the absorptioncoefficient 120572

119899119898(]) it follows from Kirchhoff rsquos law (see eg

[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)

For an incident beam with the spectral radiance 119868]Ω andpropagating in 119903-direction we then get

119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)

which is identical with (88)

42 Radiation Transfer Equation for the Spectral IntensityNormally the radiation and by this the energy emitted intothe full hemisphere is of interest so that (88) has to beintegrated over the solid angle Ω = 2120587 As already discussedin Section 32 for this integration we have to have in mindthat a beam propagating under an angle120573 to the layer normal(see Figure 11) only contributes an amount 119868]Ω cos120573119889Ω tothe spectral intensity (spectral flux density) due to LambertrsquoslawThe same is assumed to be true for the thermal radiationemitted by a gas layer under this angle

On the other hand the propagation length through a thinlayer of depth 119889119911 is increasing with 119889119897 = 119889119911cos120573 so that the120573-dependence for both terms 119868]Ω and 119861]Ω disappears

Therefore analogous to (54) and (55) integration of(88) over Ω gives for the spectral intensity propagating in119911-direction

int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)

or with the definition for 119868] = 120587 sdot 119868]Ω and analogous 119861] =

120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)

Equation (92) is a 1st-order differential equation with thegeneral solution

119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)

or after some transformation

119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)

Usually the density of the gas the total pressure and thetemperature are changing over the propagation path of theradiation Therefore (94) has to be solved stepwise for thinlayers of thicknessΔ119911 overwhich120572

119899119898and119861] can be assumed

to be constant (see Figure 12) With the running index 119894 fordifferent layers then (94) can be simplified as follows

119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)

The intensity in the 119894th layer is calculated from the previousintensity 119868119894minus1] of the (119894 minus 1)th layer with the values 120572119894

119899119898(])

and 119861119894](119879119894) of the ith layer In this way the propagation over

the full atmosphere is stepwise calculated The first termin (95) describes the transmission of the incident spectralintensity over the layer thickness while the second termrepresents the self-absorption of the thermal backgroundradiation into forward direction and is identical with thespontaneous emission of the layer into one hemisphere

43 Schwarzschild Equation in a Thin Gas Equation (88)was derived under the assumption of a local thermodynamicequilibrium in the gas which is generally the case at highergas pressures and therefore higher collision rates of the


Δz

Ii TiG 120572inm() Bi

(TiG)

Iiminus1 Timinus1G 120572iminus1nm () Biminus1

(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )

Figure 12 Stepwise calculation of the spectral intensity by theradiation transfer equation

molecules At low pressures however the population of themolecular states can also significantly be determined byinduced transitions caused by the incident radiation (seeSection 34) and then it gives more sense to consider themonochromatic or spectral radiation equilibrium whichmeans that the gas re-emits all monochromatic radiation ithas absorbed

Since this absorption is caused by the total spectralradiation incident within the solid angle Ω = 2120587 119868]Ω hasto be integrated overΩ Then the absorbed spectral intensityover the interval 119889119903 is found from (51) together with (53)Thismust be equal to the spectral power density emitted by the gasas spontaneous emission into the full solid angle 4120587Thus weobtain

120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)

Only 14120587 of (96) contributes to the spectral radiance and(86) changes to

119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)

This differential equation for the spectral radiance in thingases was derived only assuming the absorption and sub-sequent emission due to the external radiation and in thisrespect orientated at the standard considerations as foundin the literature (see eg [12]) A more rigorous derivationof this equation however also has to take into account theemission originating from the thermal background radiationof the molecules as long as their temperature and thus theirkinetic energy are not zero This is considered in the nextsubsection

Extended Schwarzschild Equation in aThinGasWe start from(86) which already describes quite generally the propagationof radiation under conditionswhen a sample not only absorbsbut also emits on the same frequencies as the incidentradiation Again requesting radiation equilibrium the totalbalance of absorption and emission processes is given by the

rate equations (76) which under stationary conditions resultsin (see (81))

(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)

With (34) and (59) we find

(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)

Some rearrangement of (100) and multiplication with ℎ]119898119899

gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)

At local thermodynamic equilibrium we know that due to(36) the term 119862

119899119898119873119899minus119862

119898119899119873119898will be zero and trivially it is

also zero in the absence of any collisions (119862119898119899

= 119862119899119898

= 0)Thus we can expect that in a thin gas with only few collisionseven under radiation equilibrium this term is quite small andtherefore can be neglected The general case including thisterm will be discussed in the next paragraph So with (33)and dividing (101) by 4120587 as well as using the relations (1198884120587119899)sdot119906] = 119861]Ω and 119868] = 120587119868]Ω we get

1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)

Inserting (102) in (86) then gives the extended Schwarzschildequation in thin gases

119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)

44 Generalized Schwarzschild Equation The objective is tofind an expression which describes the radiation transfer forboth limiting cases at high collision rates in a dense gas asgiven by (88) as well as at negligible collisions in a thin gasrepresented by (103) For similar considerations howeverdifferent results see for example [12]

We start from (81) or with the abbreviations of (83) from(84) These equations again contain the balance of all up anddown transitions Elementary transformation yields

(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)


and some further rearrangements give (see on the left side theexpansion by +1 minus 1)

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)

With the identity (see (33) and (83))

120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)

and multiplying (105) with (ℎ]1198981198994120587) sdot 119860

119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)

Defining a relative material parameter

120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)

and inserting (107) and (108) into (86) we get

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)

With the abbreviation

120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)

where 120594 assumes values from 34 le 120594 le 1 for 0 le 120578 le infin(109) can be represented in the more compact form

119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)

This is the generalized Schwarzschild equation which is validat low as well as at high gas densities and where the transitionfromone to the other limiting case is controlled by the densitydependent parameter 120578 According to (108) and (83) togetherwith (36) 120578may be expressed as

120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)

Therefore any variations of 120578 and thereby also of 120594 originatefrom the pressure dependent collision transfer rate 119862

119898119899

which is changing with the altitude above the earthrsquos surfaceso that all these parameters become a function of 119911 Withoutany collisions 120578 gets zero and thus 120594 = 34 Then (111) isidentical with (103) On the other hand at high gas densitiesand high collision rates with 120578 ≫ 1 and 120594 rarr 1 (111)converges towards (88)

45 Generalized Radiation Transfer Equation for the SpectralIntensity In order to derive the basic radiation transferequation (RTE) for the spectral intensity expanding in 119911-direction analogous to (91) we have to integrate (111) overthe solid angle Ω = 2120587

int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)

or with the definitions of 119868] and 119861]

119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)

This is the generalized RTE for the spectral intensity orig-inating from a Planckian radiator of temperature 119879

119864and

propagating through an absorbing gas layer of temperature119879119866Similar to (92)ndash(94) the solution of (114) is found to be

119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)

and a stepwise numerical integration can be obtained by

119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)


It should be recalled that under conditions of strongerabsorption and longer path lengths radiation emerging fromthe individual layers may deviate from the assumed Lamber-tian radiation law (see Section 32)This can result in a slightlytoo strong absorption caused by those rays propagatingunder larger angles to the layer normal However since theserays only provide relatively small contributions to the totalabsorption this only causes relatively small deviations

Another effectmay result fromdeviations of the rays fromgeometric optics caused by inhomogeneities and scatteringprocesses in the atmosphere Therefore altogether it seemsreasonable to apply a slightly smaller effective absorptioncoefficient 2120594119894120572119894

119899119898in (116) The factor of two had its origin

in an effective average path length through a layer of 2Δ119911corresponding to an average propagation direction 120573 = 60

∘Therefore assuming a slightly smaller average angle of 120573 asymp

50∘might approximatemore realistically the conditions in the

atmosphere

5 Simulation of Radiation Transfer inthe Atmosphere

Infrared active gases in the atmosphere have a significantinfluence on the energy and radiation balance of the earth-atmosphere system as this was already discussed in somedetail in Section 33 They absorb short wavelength radia-tion from the sun and long wavelength radiation from theearth This absorbed energy as well as thermal energy (afterconversion to internal energy) is again reradiated uniformlyinto all directions This emission is the origin of the up-and downwelling radiation of the atmosphere itself whichtogether with any terrestrial or cloud radiation determinesthe total radiation observed in up- or downward direction

The most important infrared active gases are watervapour CO

2 CH

4 and O

3 which have stronger absorption

bands in the infrared distributed over a wide spectral rangefrom about 3 to 200120583m or 50 to 3330 cmminus1

Particularly CO2is believed to be the main culprit of

anthropogenic global warming and is made responsible forthe increasing temperature over the last 150 years Thereforeit is worthwhile to lookmore carefully how this gas influencesthe absorption and radiation balance in the atmosphere Atthe same time this is an instructive example for the usefulapplicability of the theoretical background presented in thispaper

51 Absorption and Emission Spectrum of CO2 The strongest

absorption band of this molecule is located around 42 120583mor 2350 cmminus1 But for the absorption-emission balance in theatmosphere even more important is the ten times weakerabsorption band at 15 120583m (670 cmminus1) which almost coincideswith the spectral maximum of the terrestrial radiation (seeFigure 6) and therefore primarily determines the interactionof CO

2molecules with the radiation

Figure 13 shows the respective absorption spectrum for380 ppm of CO

2in dry air for different propagation lengths

at a pressure of 1013 hPa and a temperature of 288K Thered lines are markers indicating the center and strength

00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion

Wavenumber (cmminus1)

00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


Figure 13 Absorption spectra for 380 ppm of CO2in dry air at

different propagation lengths (air pressure 1013 hPa temperature288K)

of an individual transition while the blue curve is thesuperposition of all line profiles and represents the degreeof transmissionmdashor inversely the degree of absorptionmdashofincident radiation at these wavenumbers On the 119876-branch(band center) radiation is almost completely absorbed after alength of only 1m and with increasing propagation distanceeven the weaker lines of the 119875- and 119877-branches reflect totallysaturated absorption At 1 km or more only the far wings ofthe band structure still show some rest transmission

On the other hand from Sections 3 and 4 we know thatan absorbing gas with a temperature comparable to that of anexternal radiation sourcemdashhere the earthrsquos surfacemdashwill actas own radiator andmodify the incident radiation noticeablyFigure 14 displays a simulation for the upwelling radiation


500600

70080002 08 14 20

000102030405

Altitude above ground (km) Wavenumber (cmminus1 )

Spec

tral

inte

nsity

(Wm

2c

mminus1)

Figure 14 Spectral intensity radiated by 380 ppm of CO2in dry air

at different altitudes (groundpressure 1013 hPa ground temperatureof the gas 288K)

00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K

Figure 15 Spectral intensity emitted by 380 ppm of CO2in dry air


emitted by only 38 ppmCO2in dry air (1100th of the regular

concentration) at different altitudes above groundThis calculation is based on (116) and uses for the vertical

air pressure and temperature profile the US Standard Atmo-sphere [17] On the band center the radiation already rapidlyattains a maximum spectral intensity of 047W(m2

sdotcmminus1)and with increasing altitude a broader plateau is graduallydeveloping which at higher altitudes again slightly decreases

This can be observed more pronounced in Figure 15for a series of calculations up to 10 km altitude with aconcentration of 380 ppm of CO

2in dry air

The broad plateaus essentially reflect the actual tempera-ture of the gas at the specific altitudes The higher shouldersof the curves from 4ndash10 km are an indication that withreducing pressure and thus decreasing linewidths the wingsof the absorption band become more transparent and alsoradiation from lower therefore warmer andmore intensivelyradiating layers can contribute to the observed spectra

All radiative transfer calculations were performed onthe program-platform MolExplorer [18] as line-by-line cal-culations and rely on the actual HITRAN08-database [13]For the numerical integration of (116) a layer thicknessof 100m was used over which the pressure density and

10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500


Figure 16 Transmission through wet air over 10 km altitude Watervapour concentration at ground is 146 at 288K

temperature were considered to be constant According to(112) 120578 is determined by the ratio 119862

119898119899119860

119898119899 Since up to

the mesopause the collision rate 119862119898119899

is still larger than 1 sminus1and the spontaneous emission rate on the CO

2transitions

119860119898119899

le 1 sminus1 120578 is larger 1 and thus 120594 asymp 1 Therefore for thisabsorption band the original Schwarzschild equation (88) isstill a good approximation up to an altitude of about 90 km

52 Influence of Water Vapour The strongest impact on theradiation in the atmosphere originates from water in itsdifferent aggregate states So thicker cumulus or altostratuscloud layers can totally absorb and reradiate infrared radia-tion or ice crystals in the tropopause may cause scatteringof the radiation But also atmospheric water vapour has asignificant influence which with respect to the scope ofthis paper will be considered in more detail This strongimpact results from the fact that H

2O molecules possess

strong absorption bands and single absorption lines whichare almost continuously spread over broader regions of theinfrared spectrum

Figure 16 shows the spectral transmission throughwet airon a logarithmic scale over an altitude of 10 km The watervapour concentration at the ground at 288K is assumed tobe 146 as an average over the three climate zones tropicsmid-latitudes and the polar regions It is deduced fromGPS measurements [19] and decreases exponentially withaltitude because of the temperature dependence of the vapourpressure (for details see [20])

From 10ndash360 cmminus1 and 1400ndash1800 cmminus1 the atmosphereis completely opaque Only between 800 and 1100 cmminus1

and above 2200 cmminus1 the so-called atmospheric windowsit becomes quite transparent for radiation from the earthrsquossurface

But at the same time the water molecules are strongemitters radiating at their respective temperature as this isrepresented in Figure 17 As direct comparison are also shownPlanck distributions of different temperatures Althoughwater molecules are ideal blackbody radiators on theirstronger transitions their spectral intensity is significantlylower than the surface emission of the earth Again this resultsfrom the fact that the spectral components observed at thetropopause in 125 kmheight originate from layers of different


00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)

Water vapour emissionPlanck 288K surface

Planck 270K 28 kmPlanck 245K 66 km

Figure 17Water vapour emission at 125 kmaltitude Concentrationat ground is 14615 ppm As comparison are shown Planck curves at288K 270K and 245K

altitude and therefore different temperatureThese layersmaybe characterized by an optical depth 120591

119899119898(]) = 120572

119899119898(])Δ119911 asymp 1

at frequency ] Otherwise a new absorption-emission cyclewould occur within the layer thickness or over the furtherpath up to the observation altitude

So within spectral regions of medium or lower absorp-tion the envelope of the emission curve can be representedquite well by a Planck distribution of 270K correspondingto an altitude of 28 km while in the spectral intervalsof very high opacity (10ndash400 cmminus1 and 1350ndash1800 cmminus1) adistribution with 245K and an altitude of 66 km fits muchbetter

53 Radiation Transfer under Atmospheric Conditions Whileit was the objective of the previous two subsections topresent the individual spectral properties of the two mostimportant infrared active gases in the atmosphere and toidentify their interaction with the atmospheric radiation inthis paragraph we investigate their common influence on theup- and downwelling radiation Figure 18 shows the impactof both gases on the emitted radiation at 125 km altitude

The blue curve represents the total radiation emittedfrom the earthrsquos surface and the atmosphere while thecontribution only from the atmosphere is depicted as greengraph Below 750 cmminus1 and above 1300 cmminus1 both curvesare completely identical and appear as a unique line Onlyover the central atmospheric window the influence of theunderlying terrestrial radiation shown as pink graph can beidentified as increased intensity while in the outer regionsthis radiation is completely absorbed by water vapour andCO

2 Similar to Figure 17 the dominant influence of thewater

lines over the whole spectral range can be seen but nowsuperimposed by the strong absorption band of CO

2around

670 cmminus1 The water vapour concentration at ground againwas assumed to be 14615 ppm

To assess the more or less strong influence of increasingCO

2concentrations in the atmosphere as heavily discussed

with respect to anthropogenic global warming Figure 19compares two simulations which were performed with

00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)

Only atmosphereEarth and atmospherePlanck 288K surface

Figure 18 Total upwelling radiation in 125 km altitude (blue) andemission of only the atmosphere by water vapour and CO

2(green)

Surface radiation is shown as pink line


Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K

Figure 19 Upwelling radiation at 125 km altitude with 380 ppm(blue line) and 760 ppmCO

2(red line)Water vapour concentration

is 14615 ppm and temperature at ground 288K

380 ppm (blue line) and 760 ppm (red curve) of CO2at

average global conditions Due to the strongly saturatedabsorption and emission on the CO

2band around 670 cmminus1

the broad funnel changes neither its depth nor its widthOnly the wings and the weak absorption bands at 970 and1070 cmminus1 which are all strongly superimposed by intensewater lines contribute to a slightly higher absorption

Subtraction of the integrated spectra yields an intensitydifference of 58Wm2 so this amount is less reradiatedby the troposphere at doubled CO

2concentration While

these calculations were done under clear sky conditions atan average cloudiness of 50 and a cloud altitude of 5 kmthis reduces to about 43Wm2 Under new quasiequilibriumconditions it is found that 61 of this amount amplifies theback radiation the other 39 go to space (see also [20])An enhanced downward emission from the stratosphere athigher CO

2concentration [21 22] is partly shielded by the

cloudiness and in the radiation balance further compensated



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K

Figure 20 Downwelling radiation from TOA to ground with380 ppm (blue line) and 760 ppm CO

2(red line) Water vapour

concentration is 14615 ppm and temperature at ground 288K

by increased losses of the sun flux which is absorbed by theearthrsquos surface (shortwave radiative forcing) So altogetherabout 26Wm2 would contribute to the radiative forcing andthus to global heating at doubled CO

2concentration

An example for the downwelling radiation is shown inFigure 20 The calculations start at the intersection of themesosphere to the mesopause in 86 km altitude (TOA) andtrack the emission as well as the absorption down to theearthrsquos surfaceThe simulations again include water vapour inthe tropospherewith the ground concentration of 14615 ppmCO

2 and CH

4as well mixed gases over the whole altitude

with concentrations for CO2of 380 ppm (blue line) and

760 ppm (red line) for CH4with 18 ppm and O

3spread

over the stratosphere and tropopause with a maximum of7 ppmaround 38 kmaltitude Except the smaller contributionfrom O

3around 1020 cmminus1 all the radiation originates from

the lower troposphere and is over wide regions identicalwith a blackbody source of 288K The integral radiationin downward direction is 312Wm2 representing 80 of ablackbody source at that temperature and corresponding to61 of the total intensity radiated only by the atmosphereThe difference between ordinary and doubled CO

2concen-

trations at clear sky is 44Wm2 while at average cloudinessthat amount which contributes to an additional heating ofthe earth is the same as discussed above

The calculated radiative forcing of 26Wm2 at doubledCO

2concentration is 11Wm2 smaller than that of Myhre

et al [22] Up to some degree this discrepancy is expectedto result from different atmospheres used for the calcula-tions So most of the spectroscopic computations in theliterature are based on the US Standard 1976 AtmosphereHowever the corresponding water vapour concentration ofthis data basis is only half of that found in the average globalatmosphere (AGA) and also only half of that derived fromactual GPS measurements [19] as used in our calculationsFurther deviations might result from different concepts forexample not assuming thermal equilibrium or calculating

with different effective path lengths of the radiation throughthe atmosphere

To demonstrate the reliability and validity of the pre-sented simulations we compare our calculations with twomeasurements which were recorded under quite differentconditions Figure 21(a) shows a measurement of the outgo-ing infrared emission spectrum of the cloud-free atmosphereas detected by a satellite in 20 km altitude looking downwardover the polar ice sheet [23]

The simulation shown in Figure 21(b) was performed fora ground temperature of 266K a water vapour content atthe surface of 2100 ppm a CO


(blue graph) and 760 ppm (red line) a CH4concentration of

18 ppm and a slightly varying O3concentration of 1ndash3 ppm

over the tropopauseOn the other hand Figure 22(a) gives an example for

the downwelling radiance recorded by a ground station inReno over one day with strongly varying cloud coverage[24] Figure 22(b) shows the simulations based on (111) butsuperimposed by a Planckian distribution which accountsfor the emitted radiation of the clouds This Planck radiationis defined by the cloud temperature and thus the cloudaltitude and it contributes to the spectrum with a weightingfactor given by the cloud coverage

The ground temperatures varied from 282 to 288K overthe day and the water vapour concentration was assumedto be 3000 ppm while for the other gases the standardconditions were applied

All characteristic features of the measured spectra arewell reproduced The smaller deviations in the shape ofthe CO

2funnel as well as in the form of the downward

radiation at 670 cmminus1 and also discrepancies in the O3band

structure around 1050 cmminus1 mainly originate from a lackof knowledge of some experimental parameters So theresolution of the spectrometers and also the acceptance angleof the detection optics have significant influence on theshape widths and intensity of the measured spectra Butalso inaccurate or missing atmospheric parameters like thepressure and temperature profile over the path length duringthemeasurements or the vapour and gas concentrations willlimit the exact reproducibility of the measured spectra

It should be emphasized that themeasurements in Figures21 and 22 show the up- and downwelling spectral radiancethat is radiation which is collected within a restricted solidangle This angle is normally determined by the receiveroptic which causes a spatial filtering and essentially detectsrays transmitting the atmosphere on a shorter way (mostlyperpendicular to the earthrsquos surface) In contrast to thisFigures 19 and 20 were calculated for the spectral intensitywhich spreads out over the whole hemisphere in upwardor downward direction and corresponds to an average pathlength about twice that of the radiance Therefore due tothe shorter effective interaction length particularly the wingsof the spectral bands and lines in Figures 21 and 22 appearless broadened and saturated Additionally at the lowertemperatures and dryer air the water lines are less dominantso that under clear sky conditions the atmosphere gets muchmore transparent particularly within the spectral windowfrom 800 to 1200 cmminus1


120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)

Figure 21 Upwelling radiance (a) measured from a satellite over the polar ice sheet [23] (b) calculated with 380 ppm (blue line) and 760 ppmCO

2(red line) Water vapour concentration is 2100 ppm and ground temperature 268K

140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900


0713R clear temperature inversion1025T clear sky no inversion1321T cirrus cloud overhead1530T cirrus and altocumulus overheadBlackbody 2755KBlackbody 2883K

March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K

Cirrus ch = 15km co = 06 TE = 285KAltocumulus ch = 3km co = 08 TE = 288K

140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)

Figure 22 Downwelling radiance (a) measured at ground with varying cloud coverage [24] (b) calculated with water vapour concentrationof 3000 ppm and different temperatures

These examples clearly demonstrate that the basic inter-action processes of infraredmolecules with thermal radiationare well understood and that the presented radiation transfercalculations are in excellent agreement with the observationseven under the quite complex conditions in the atmosphereFrom this we can also conclude that simulations of the type asshown in Figures 19ndash21 with different concentrations of CO

2

in the atmosphere are quite reliable and give an importantassessment for the impact of greenhouse gases on our climate

54 Absorption of Terrestrial Radiation The dominant influ-ence of water vapour on the radiation and energy budget inthe atmosphere can also be deduced from an analysis of pureabsorption spectra So under conditions as discussed beforewith an average global water vapour content of 146 at thesurface and a temperature of 288K the overall absorptionof the terrestrial radiation only caused by water vapour isalready 777Together withmethane and ozone in the atmo-sphere the absorption increases to 807 On the other hand


80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption

CO2 concentration (ppm)

2 absorption12 CO

Figure 23 Absorption of terrestrial radiation as a function of theCO

2concentration

CO2alone at a concentration of 380 ppm would contribute

to 241 but in the presence of other gases its influence isrepelled to 46 which is due to the strong spectral overlapwith the other components particularly with water vapourand the total absorption only climbs up to 853

As already outlined in Sections 33 and 51 the centreof the CO

2absorption band around 670 cmminus1 rapidly goes

into saturation with increasing propagation length and alsowith increasing concentrationOnly thewings and theweakerabsorption bands at 970 and 1070 cmminus1 still contribute to aslightly rising absorption with increasing CO

2concentration

This is shown in Figure 23 demonstrating that due to thespectral overlap and the strong saturation behaviour adoubling of CO

2under clear sky conditions only donates

additional 12 to the total absorptionWith cloudiness this contribution is even further pushed

down to less than 1 and from this 39 will be reradiatedto space So altogether only about 06 correspondingto 24Wm2 of the total terrestrial radiation (391Wm2 at28815 K) or 08 with respect to the total back radiation of312Wm2 (see Section 53) can contribute to an additionalglobal heating at doubled CO

2concentration This result is

in quite good agreement with the previous calculation of theradiative forcing and demonstrates why a further increase inthe CO

2concentration only gives marginal corrections in the

radiation budgetBased on the simple assumption that due to the back

radiation the natural greenhouse effect causes a globaltemperature increase of approximately 33 K and that thesurface temperature linearly responds to any changes in theenergy or radiation budget an increase in this budget of lessthan 1 should only contribute to a temperature increase ofabout 03 KThis is in clear contradiction to the IPCC whichissues an official climate sensitivity (temperature increase atdoubled CO

2) of 119862

119878= 32K [25] But even a more sophis-

ticated consideration based on an energy balance model forthe surface-atmosphere system and distinguishing betweenthree climate zones including the shortwave radiation budgetas well as water vapour and lapse rate feedback only gives aclimate sensitivity of 06 K [20] which is still 5x smaller thanthe IPCC value

6 Conclusion

The paper reviews the basic relations for the interactionof radiation with infrared active molecules and presents anew theoretical concept for the description of the radiationtransfer in the atmosphere Starting from Einsteinrsquos funda-mental considerations on the quantum nature of radiationit is shown that the thermal radiation of a gas can be wellunderstood only in terms of the spontaneous emission of themolecules The interaction with radiation from an externalblackbody source in the presence of the background radiationand under the influence of molecular collisions is elabo-rately investigated The energy and radiation balance in theatmosphere including heat transfer processes are describedby rate equations which are solved numerically for typicalconditions as found in the troposphere and stratosphereThese simulations demonstrate the continuous and dominantconversion process of heat to radiation and vice versa

Consideration of the radiation interaction on amolecularbasis allows to derive the Schwarzschild equation describingthe radiation transfer in the atmosphere This equation isinvestigated under conditions of only few intermolecularcollisions as found in the upper mesosphere as well as at highcollision rates as observed in the troposphere A generalizedform of the radiation transfer equation is presented whichcovers both limiting cases of thin and dense atmospheres andallows a continuous transition from low to high densitiescontrolled by a density dependent parameter This equationis derived for the spectral radiance as well as for the spectralflux density (spectral intensity)

The radiation transfer equation is applied to simulatethe up- and downwelling radiation and its interaction withthe most prominent greenhouse gases water vapour carbondioxide methane and ozone in the atmosphere The radi-ation in upward direction is the only possibility to renderany absorbed energy to space and by this to keep theatmospheric temperature in balance with all the supplieddirect and indirect energy from the sun On the other handthe downwelling part determines the back radiation fromthe atmosphere to the earthrsquos surface which is the sourceterm of the so heavily discussed atmospheric greenhouse oratmospheric heating effect While the upwelling radiationonly contributes to cooling as long as the radiation canescape to space the downwelling part only causes heatingwhen it reaches the surface

Propagation of radiation in the atmosphere is not theresult of a single event It underlies continuous absorptionand reemission processes in the gas which are determinedby the mean free absorption length and strongly depend onthe frequency of the radiation as well as on the gas densityRadiation also converts into molecular kinetic energy andvia exciting collisions changes back to radiation This kineticenergy of the molecules results from absorbed long- andshortwave radiation as well as from sensible and latent heatdue to convection and evapotranspiration from the surfaceto the atmosphere

So any propagation of the radiation in the atmospherecan be described similar to a diffusion process of particles(photons) which are partly annihilated and again created


while propagating through the atmosphereThis propagationin a gas is just described by the radiation transfer equation(111) for the spectral radiance and by (116) for the spectralintensity (spectral flux density) and these equations are validindependent if an external radiation or the eigen radiation ofthe atmosphere in up or down direction is calculated

An asymmetry in the up- and downwelling eigen radia-tion (only from atmosphere) will be found with a strongercontribution in downward direction which is caused by thelapse rate as well as the density profile over the atmospherewith higher temperature and pressure at lower atmosphericlayers and therefore a higher net downward radiation Calcu-lations for the radiative forcing at doubledCO

2concentration

and at an average cloudiness give a 30 smaller forcing thanapplied by the IPCC

Thermal radiation is electromagnetic radiation and noheatTherefore in the sameway as radiowaves can propagatefrom a colder antenna to a warmer receiver microwavescan be absorbed by a hot chicken or CO

2-laser radiation

(106 120583m) can be used for welding and melting of metals upto several thousand ∘C so any back radiation from colder andhigher atmospheric layers can be absorbed by the lower andwarmer layers and this back radiation can also be absorbedby awarmer surface of the earthwithout violating the 2nd lawof thermodynamics As long as the surface is assumed to bea black or gray absorber it does not filter any frequencies ofthe incoming radiation in the same way as it does not rejectany frequencies of the broad Planck spectrum of a thermalradiator independent if it has a higher or lower temperaturethan the earth Radiation converts to heat after an absorptionfollowed by an emission in accordance with a newly adjustingthermodynamic equilibriumwhich only requires that the netenergy transfer is in balance

References

[1] A Einstein ldquoQuantentheorie der Strahlungrdquo Zeitschrift furPhysik vol 18 p 121 1917

[2] M Planck ldquoUber eine Verbesserung der Wienschen Spek-tralgleichungrdquo Verhandlungen der Deutschen PhysikalischenGesellschaft vol 2 no 56 pp 519ndash525 1900

[3] L Boltzmann ldquoallgemeine Satze uber WarmegleichgewichtrdquoWiener Berichte vol 63 pp 679ndash711 1871

[4] L Boltzmann ldquoWeitere Studien uber das Warmegleichgewichtunter Gasmolekulenrdquo Wiener Berichte vol 66 pp 275ndash3701872

[5] A Schuster ldquoRadiation through a Foggy Atmosphererdquo TheAstrophysical Journal vol 21 pp 1ndash22 1905

[6] K Schwarzschild ldquoUber das Gleichgewicht in der solarenAtmospharemdashon the equilibrium of the sunrsquos atmosphererdquoNachrichten der Koniglichen Gesellschaft der Wissenschaften zuGottingen vol 195 p 41 1906

[7] K Schwarzschild ldquoDiffusion and absorption in the sunrsquos atmo-sphererdquo Sitz K Preuss Akad Wiss p 1183 1914

[8] G C Wick ldquouber ebene Diffusionsproblemerdquo Zeitschrift furPhysik vol 121 no 11-12 pp 702ndash718 1943

[9] S Chandrasekhar ldquoOn the radiative equilibrium of a stellaratmosphere IIrdquo Astrophysical Journal vol 100 article 76 1944

[10] R M Goody and Y L Yung Radiation Theoretical BasisOxford University Press Oxford UK 1989

[11] M L Salby Physics of the Atmosphere and Climate CambridgeUniversity Press Cambridge UK 2012

[12] E A Milne ldquoEffect of collisions on monochromatic radiativeequilibriumrdquoTheRoyalAstronomical Society vol 88 article 4931928

[13] L S Rothman I E Gordon A Barbe et al ldquoThe HITRAN2008molecular spectroscopic databaserdquo Journal of QuantitativeSpectroscopy and Radiative Transfer vol 110 no 9-10 pp 533ndash572 2009

[14] N Jacquinet-Husson N A Scott A Chedin et al ldquoThe 2003edition of the GEISAIASI spectroscopic databaserdquo Journal ofQuantitative Spectroscopy and Radiative Transfer vol 95 no 4pp 429ndash467 2005

[15] S S Penner Molecular Spectroscopy and Gas EmissivitiesAddison-Wesley Reading Mass USA 1959

[16] C H Townes and A L Schawlow Spectroscopy Dover NewYork NY USA 1975

[17] US Standard Atmosphere 1976[18] H Harde and J Pfuhl MolExplorermdashA Program-Platform for

the Calculation of Molecular Spectra and Radiation Transfer inthe Atmosphere Helmut-Schmidt-University Hamburg Ham-burg Germany 2013

[19] S Vey Bestimmung und Analyse des atmospharischen Wasser-dampfgehaltes aus globalen GPS-Beobachtungen einer Dekademit besonderem Blick auf die Antarktis [Doctoral theses] Tech-nische Universitat Dresden Dresden Germany 2007

[20] H HardeWas tragt CO2wirklich zur globalen Erwarmung bei

Spektroskopische Untersuchungen und Modellrechnungen zumEinfluss von H

2O CO

2 CH

4und O

3auf unser Klima Books on

Demand Norderstedt Germany 2011[21] V Ramanathan L Callis R Cess et al ldquoChemical interactions

and effects of changing atmospheric trace gasesrdquo Reviews ofGeophysics vol 25 pp 1441ndash1482 1987

[22] G Myhre E J Highwood K P Shine and F Stordal ldquoNewestimates of radiative forcing due to well mixed greenhousegasesrdquo Geophysical Research Letters vol 25 no 14 pp 2715ndash2718 1998

[23] Data Courtesy of D Tobin Space Science and EngineeringCenter University ofWisconsin-Madison MadisonWis USA1986

[24] Graphic fromPat Arnott University ofNevada RenoNev USA2008 ATMS 749

[25] D A Randall R A Wood S Bony et al ldquoClimate modelsand their evaluation in Climate Change 2007 The PhysicalScience Basisrdquo in Contribution of Working Group I to the FourthAssessment Report of the Intergovernmental Panel on ClimateChange S SolomonDQinMManning et al Eds CambridgeUniversity Press Cambridge UK 2007

Submit your manuscripts athttpwwwhindawicom

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Geological ResearchJournal of


Geology Advances in


In Section 3 also the influence of radiation from anexternal blackbody radiator and an additional excitation bya heat source is studied The radiation and heat transferprocesses originating from the sun andor the earthrsquos surfaceare described by rate equations which are solved numericallyfor typical conditions as they exist in the troposphere andstratosphereThese examples right away illustrate the conver-sion of heat to radiation and vice versa

In Section 4 we derive the Schwarzschild equation [5ndash11] as the fundamental relation for the radiation transferin the atmosphere This equation is deduced from pureconsiderations on a molecular basis describing the thermalradiation of a gas as spontaneous emission of the moleculesThis equation is investigated under conditions of only fewintermolecular collisions as found in the upper mesosphereor mesopause as well as at high collision rates as observed inthe troposphere Following some modified considerations ofMilne [12] a generalized form of the radiation transfer equa-tion is presented which covers both limiting cases of thinand dense atmospheres and allows a continuous transitionfrom low to high densities controlled by a density dependentparameter This equation is derived for the spectral radianceas well as for the spectral flux density (spectral intensity) asthe solid angular integral of the radiance

In Section 5 the generalized radiation transfer equationis applied to simulate the up- and downwelling radiationand its interaction with the most prominent greenhousegases water vapour carbon dioxide methane and ozone inthe atmosphere From these calculations a detailed energyand radiation balance can be derived reflecting the differentcontributions of these gases under quite realistic conditionsin the atmosphere In particular they show the dominantinfluence of water vapour over the full infrared spectrum andthey explain why a further increase in the CO

2concentration

only gives marginal corrections in the radiation budgetIt is not the objective of this paper to explain the

fundamentals of the atmospheric greenhouse effect or toprove its existence within this framework Nevertheless thebasic considerations and derived relations for the molecularinteraction with radiation have some direct significance forthe understanding and interpretation of this effect and theygive the theoretical background for its general calculation

2 Interaction of Molecules with Thermal Bath

When a gas is in thermodynamic equilibrium with itsenvironment it can be described by an average temperature119879119866 Like anymatter at a given temperature which is in unison

with its surrounding it is also a source of gray or blackbodyradiation as part of the environmental thermal bath At thesame time this gas is interacting with its own radiationcausing some kind of self-excitation of the molecules whichfinally results in a population of themolecular states given byBoltzmannrsquos distribution

Such interaction first considered by Einstein [1] is repli-cated in the first part of this section with some smallermodifications but following themain thoughts In the secondpart of this section also collisions between the molecules are

Em

En

ΔE = hmn = hc120582mn

Figure 1 Two-level system with transition between states119898 and 119899

included and some basic consequences for the description ofthe thermal bath are derived

21 Einsteinrsquos Derivation ofThermal Radiation Themoleculesare characterized by a transition between the energy states119864

119898

and 119864119899with the transition energy

Δ119864 = 119864119898minus 119864

119899= ℎ]

119898119899=

ℎ119888

120582119898119899

(1)

where ℎ is Planckrsquos constant 119888 the vacuum speed of light ]119898119899

the transition frequency and 120582119898119899

is the transitionwavelength(see Figure 1)

Planckian Radiation The cavity radiation of a black bodyat temperature 119879

119866can be represented by its spectral energy

density 119906120582(units Jm3120583m) which obeys Planckrsquos radiation

law [2] with

119906120582=8120587119899

4ℎ119888

1205825

1

119890ℎ119888119896119879119866120582 minus 1 (2)

or as a function of frequency assumes the form

119906] = 1199061205821205822

119888119899=8120587119899

3ℎ]3

1198883

1

119890ℎ]119896119879119866 minus 1 (3)

This distribution is shown in Figure 2 for three differenttemperatures as a function of wavelength 119899 is the refractiveindex of the gas

Boltzmannrsquos Relation Due to Boltzmannrsquos principle the rela-tive population of the states 119898 and 119899 in thermal equilibriumis [3 4]

119873119898

119873119899

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866 (4)

with119873119898and119873

119899as the population densities of the upper and

lower state 119892119898and 119892

119899the statistical weights representing the

degeneracy of these states 119896 as the Boltzmann constant and119879119866as the temperature of the gasFor the moment neglecting any collisions of the

molecules between these states three different transitions cantake place

Spontaneous Emission The spontaneous emission occursindependent of any external field from 119898 rarr 119899 and ischaracterized by emitting statistically a photon of energyℎ]

119898119899into the solid angle 4120587with the probability 119889119882119904

119898119899within

the time interval 119889119905

119889119882119904

119898119899= 119860

119898119899119889119905 (5)


0 2 4 6 8 10Wavelength 120582 (120583m)

6

5

4

3

2

1

0

times10minus3

Spec

tral

ener

gy d

ensit

yu120582

(Jm

3120583

m)

T = 2000K T = 1500K T = 1000K


119860119898119899






119889119882119894

119899119898= 119861

119899119898intΔ]119906]119892 (]) 119889] sdot 119889119905 (6)




int

infin

0

119892 (]) 119889] = 1 (7)


intΔ]119906]119892 (]) 119889] = 119906]119898119899 (8)


119889119882119894

119899119898= 119861

119899119898119906]119898119899

119889119905 (9)


119889119882119894

119898119899= 119861

119898119899intΔ]119906]119892 (]) 119889] sdot 119889119905 = 119861119898119899119906]119898119899119889119905 (10)

with 119861119898119899



119861119899119898119906]119898119899

119873119899= (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898 (11)


119889119873119898

119889119905= +119861

119899119898119906]119898119899

119873119899minus (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

119889119873119899

119889119905= minus119861

119899119898119906]119898119899

119873119899+ (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

(12)

For 119889119873119898119889119905 = 119889119873


(4) in (11) gives

119892119899119861119899119898119906]119898119899

= 119892119898(119861

119898119899119906]119898119899

+ 119860119898119899) 119890

minusℎ]119898119899119896119879119866 (13)



119892119899119861119899119898

= 119892119898119861119898119899 (14)

Then (13) becomes

119861119898119899119906]119898119899

119890ℎ]119898119899119896119879119866 = 119861

119898119899119906]119898119899

+ 119860119898119899 (15)


119906]119898119899=119860119898119899

119861119898119899

1

119890ℎ]119898119899119896119879119866 minus 1 (16)


119898119899gives for 119861

119898119899

119861119898119899

=119892119899

119892119898

119861119899119898

=1198601198981198991198883

81205871198993ℎ]3119898119899

=119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992 (17)


119898119899 and in





119889119906]

119889119903= minus120572

119899119898(]) 119906] = minus120590119899119898 (])119873119899

119906] (18)






119898119899(]) the







119889119906] = ℎ]119898119899119860119898119899119889119905119873

119898119892 (]) =

ℎ]119898119899

119888119899119860119898119899119889119903119873

119898119892 (]) (19)


119889119906]

119889119903= minus120590

119899119898(])119873

119899119906] + 120590119898119899 (])119873119898

119906] +ℎ]

119898119899

119888119899119860119898119899119873119898119892 (])

(20)



119898119899(]) and


120590119898119899(]) = 1205900

119898119899119892 (]) 120590

119899119898(]) = 1205900

119899119898119892 (]) (21)



intΔ]

119889119906]

119889119905119889] =

119889119906]119898119899

119889119905Δ] =

119889119906

119889119905

= minus119888

119899(120590

0

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ ℎ]119898119899119860119898119899119873119898

(22)


119866[mminus3

]


with

119906 = 119906]119898119899Δ] = 120588

119866sdot ℎ]

119898119899 (23)


119889120588119866

119889119905=119889119873

119899

119889119905= minus

119889119873119898

119889119905

= minus119888119899

ℎ]119898119899

(1205900

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ 119860119898119899119873119898

(24)


119861119899119898119906]119898119899

119873119899=119892119898

119892119899

119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992119906]119898119899

119873119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119873119899119906]119898119899

(25)

and therefore

1205900

119899119898=119892119898

119892119899

1198601198981198991205822

119898119899

81205871198992 (26)


1205900

119898119899=1198601198981198991205822

119898119899

81205871198992=119892119899

119892119898

1205900

119899119898 (27)


119899119898(]) and 120590

119898119899(])

120590119898119899(]) =

119892119899

119892119898

120590119899119898(]) =

1198601198981198991205822

119898119899

81205871198992119892 (])

120590119898119899(]) =

ℎ]119898119899

119888119899119861119898119899119892 (]) 120590

119899119898(]) =

ℎ]119898119899

119888119899119861119899119898119892 (])

(28)


119899119898(]) Further


Cros

s sec

tion

(cm

2)

Snm

Frequency

Δmn

mn



120590119899119898(])119873 = 120590

119899119898(])119873

119899minus 120590

119898119899(])119873

119898

= 120590119899119898(])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

=ℎ]

119898119899

119888119899119861119899119898119892 (])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

(29)

and 120590119899119898(]) becomes

120590119899119898(]) =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (]) (30)



119878119899119898

= intΔ]120590119899119898(]) 119889] =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

) (31)




120572119899119898(]) = 120590

119899119898(])119873

=ℎ]

119898119899

119888119899119861119899119898119873119899(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (])

= 119878119899119898119873119892 (]) = 1205720

119899119898119892 (])

(32)



120572119899119898(]) =

1198601198981198991198882

81205871198992]2119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

=1198601198981198991205822

81205871198992119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

(33)

Nm

Nn

WGmn Amn

Cmn

WGnm Cnm






119866

119898119899and119882119866



119882119866

119898119899= 119861

119898119899119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119898119899119906]119898119899

119882119866

119899119898= 119861

119899119898119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119906]119898119899

=119892119898

119892119899

119882119866

119898119899

(34)


119889119873119898

119889119905= + (119882

119866

119899119898+ 119862

119899119898)119873

119899minus (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889119873119899

119889119905= minus (119882

119866

119899119898+ 119862

119899119898)119873

119899+ (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889120588119866

119889119905= minus119882

119866

119899119898119873119899+119882

119866

119898119899119873119898+ 119860

119898119899119873119898

(35)


119862119899119898

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866119862

119898119899 (36)





119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)


2-



119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899


119898119873


order of 119860119898119899



119866

119898119899= 119882

119866

119899119898= 003-004 sminus1








Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)




asymp 1120591119898

120591119899and 120591




119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)


Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)


119898119899(FWHM)

according to (40)



energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)



119892119863(]) =


119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)


Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12


119898119899radic119879119866

119872 (43)


specified in K


119863(]1015840) and 119892

119871(] minus


profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840


Δ]119898119899

Δ]119863

times int

infin

0


119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 2 4 6 8 10Wavelength 120582 (120583m)

6

5

4

3

2

1

0

times10minus3

Spec

tral

ener

gy d

ensit

yu120582

(Jm

3120583

m)

T = 2000K T = 1500K T = 1000K


119860119898119899






119889119882119894

119899119898= 119861

119899119898intΔ]119906]119892 (]) 119889] sdot 119889119905 (6)




int

infin

0

119892 (]) 119889] = 1 (7)


intΔ]119906]119892 (]) 119889] = 119906]119898119899 (8)


119889119882119894

119899119898= 119861

119899119898119906]119898119899

119889119905 (9)


119889119882119894

119898119899= 119861

119898119899intΔ]119906]119892 (]) 119889] sdot 119889119905 = 119861119898119899119906]119898119899119889119905 (10)

with 119861119898119899



119861119899119898119906]119898119899

119873119899= (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898 (11)


119889119873119898

119889119905= +119861

119899119898119906]119898119899

119873119899minus (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

119889119873119899

119889119905= minus119861

119899119898119906]119898119899

119873119899+ (119861

119898119899119906]119898119899

+ 119860119898119899)119873

119898

(12)

For 119889119873119898119889119905 = 119889119873


(4) in (11) gives

119892119899119861119899119898119906]119898119899

= 119892119898(119861

119898119899119906]119898119899

+ 119860119898119899) 119890

minusℎ]119898119899119896119879119866 (13)



119892119899119861119899119898

= 119892119898119861119898119899 (14)

Then (13) becomes

119861119898119899119906]119898119899

119890ℎ]119898119899119896119879119866 = 119861

119898119899119906]119898119899

+ 119860119898119899 (15)


119906]119898119899=119860119898119899

119861119898119899

1

119890ℎ]119898119899119896119879119866 minus 1 (16)


119898119899gives for 119861

119898119899

119861119898119899

=119892119899

119892119898

119861119899119898

=1198601198981198991198883

81205871198993ℎ]3119898119899

=119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992 (17)


119898119899 and in





119889119906]

119889119903= minus120572

119899119898(]) 119906] = minus120590119899119898 (])119873119899

119906] (18)






119898119899(]) the







119889119906] = ℎ]119898119899119860119898119899119889119905119873

119898119892 (]) =

ℎ]119898119899

119888119899119860119898119899119889119903119873

119898119892 (]) (19)


119889119906]

119889119903= minus120590

119899119898(])119873

119899119906] + 120590119898119899 (])119873119898

119906] +ℎ]

119898119899

119888119899119860119898119899119873119898119892 (])

(20)



119898119899(]) and


120590119898119899(]) = 1205900

119898119899119892 (]) 120590

119899119898(]) = 1205900

119899119898119892 (]) (21)



intΔ]

119889119906]

119889119905119889] =

119889119906]119898119899

119889119905Δ] =

119889119906

119889119905

= minus119888

119899(120590

0

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ ℎ]119898119899119860119898119899119873119898

(22)


119866[mminus3

]


with

119906 = 119906]119898119899Δ] = 120588

119866sdot ℎ]

119898119899 (23)


119889120588119866

119889119905=119889119873

119899

119889119905= minus

119889119873119898

119889119905

= minus119888119899

ℎ]119898119899

(1205900

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ 119860119898119899119873119898

(24)


119861119899119898119906]119898119899

119873119899=119892119898

119892119899

119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992119906]119898119899

119873119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119873119899119906]119898119899

(25)

and therefore

1205900

119899119898=119892119898

119892119899

1198601198981198991205822

119898119899

81205871198992 (26)


1205900

119898119899=1198601198981198991205822

119898119899

81205871198992=119892119899

119892119898

1205900

119899119898 (27)


119899119898(]) and 120590

119898119899(])

120590119898119899(]) =

119892119899

119892119898

120590119899119898(]) =

1198601198981198991205822

119898119899

81205871198992119892 (])

120590119898119899(]) =

ℎ]119898119899

119888119899119861119898119899119892 (]) 120590

119899119898(]) =

ℎ]119898119899

119888119899119861119899119898119892 (])

(28)


119899119898(]) Further


Cros

s sec

tion

(cm

2)

Snm

Frequency

Δmn

mn



120590119899119898(])119873 = 120590

119899119898(])119873

119899minus 120590

119898119899(])119873

119898

= 120590119899119898(])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

=ℎ]

119898119899

119888119899119861119899119898119892 (])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

(29)

and 120590119899119898(]) becomes

120590119899119898(]) =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (]) (30)



119878119899119898

= intΔ]120590119899119898(]) 119889] =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

) (31)




120572119899119898(]) = 120590

119899119898(])119873

=ℎ]

119898119899

119888119899119861119899119898119873119899(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (])

= 119878119899119898119873119892 (]) = 1205720

119899119898119892 (])

(32)



120572119899119898(]) =

1198601198981198991198882

81205871198992]2119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

=1198601198981198991205822

81205871198992119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

(33)

Nm

Nn

WGmn Amn

Cmn

WGnm Cnm






119866

119898119899and119882119866



119882119866

119898119899= 119861

119898119899119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119898119899119906]119898119899

119882119866

119899119898= 119861

119899119898119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119906]119898119899

=119892119898

119892119899

119882119866

119898119899

(34)


119889119873119898

119889119905= + (119882

119866

119899119898+ 119862

119899119898)119873

119899minus (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889119873119899

119889119905= minus (119882

119866

119899119898+ 119862

119899119898)119873

119899+ (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889120588119866

119889119905= minus119882

119866

119899119898119873119899+119882

119866

119898119899119873119898+ 119860

119898119899119873119898

(35)


119862119899119898

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866119862

119898119899 (36)





119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)


2-



119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899


119898119873


order of 119860119898119899



119866

119898119899= 119882

119866

119899119898= 003-004 sminus1








Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)




asymp 1120591119898

120591119899and 120591




119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)


Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)


119898119899(FWHM)

according to (40)



energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)



119892119863(]) =


119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)


Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12


119898119899radic119879119866

119872 (43)


specified in K


119863(]1015840) and 119892

119871(] minus


profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840


Δ]119898119899

Δ]119863

times int

infin

0


119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



119889119906]

119889119903= minus120572

119899119898(]) 119906] = minus120590119899119898 (])119873119899

119906] (18)






119898119899(]) the







119889119906] = ℎ]119898119899119860119898119899119889119905119873

119898119892 (]) =

ℎ]119898119899

119888119899119860119898119899119889119903119873

119898119892 (]) (19)


119889119906]

119889119903= minus120590

119899119898(])119873

119899119906] + 120590119898119899 (])119873119898

119906] +ℎ]

119898119899

119888119899119860119898119899119873119898119892 (])

(20)



119898119899(]) and


120590119898119899(]) = 1205900

119898119899119892 (]) 120590

119899119898(]) = 1205900

119899119898119892 (]) (21)



intΔ]

119889119906]

119889119905119889] =

119889119906]119898119899

119889119905Δ] =

119889119906

119889119905

= minus119888

119899(120590

0

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ ℎ]119898119899119860119898119899119873119898

(22)


119866[mminus3

]


with

119906 = 119906]119898119899Δ] = 120588

119866sdot ℎ]

119898119899 (23)


119889120588119866

119889119905=119889119873

119899

119889119905= minus

119889119873119898

119889119905

= minus119888119899

ℎ]119898119899

(1205900

119899119898119873119899minus 120590

0

119898119899119873119898) 119906]119898119899

+ 119860119898119899119873119898

(24)


119861119899119898119906]119898119899

119873119899=119892119898

119892119899

119888

119899

1

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992119906]119898119899

119873119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119873119899119906]119898119899

(25)

and therefore

1205900

119899119898=119892119898

119892119899

1198601198981198991205822

119898119899

81205871198992 (26)


1205900

119898119899=1198601198981198991205822

119898119899

81205871198992=119892119899

119892119898

1205900

119899119898 (27)


119899119898(]) and 120590

119898119899(])

120590119898119899(]) =

119892119899

119892119898

120590119899119898(]) =

1198601198981198991205822

119898119899

81205871198992119892 (])

120590119898119899(]) =

ℎ]119898119899

119888119899119861119898119899119892 (]) 120590

119899119898(]) =

ℎ]119898119899

119888119899119861119899119898119892 (])

(28)


119899119898(]) Further


Cros

s sec

tion

(cm

2)

Snm

Frequency

Δmn

mn



120590119899119898(])119873 = 120590

119899119898(])119873

119899minus 120590

119898119899(])119873

119898

= 120590119899119898(])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

=ℎ]

119898119899

119888119899119861119899119898119892 (])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

(29)

and 120590119899119898(]) becomes

120590119899119898(]) =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (]) (30)



119878119899119898

= intΔ]120590119899119898(]) 119889] =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

) (31)




120572119899119898(]) = 120590

119899119898(])119873

=ℎ]

119898119899

119888119899119861119899119898119873119899(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (])

= 119878119899119898119873119892 (]) = 1205720

119899119898119892 (])

(32)



120572119899119898(]) =

1198601198981198991198882

81205871198992]2119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

=1198601198981198991205822

81205871198992119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

(33)

Nm

Nn

WGmn Amn

Cmn

WGnm Cnm






119866

119898119899and119882119866



119882119866

119898119899= 119861

119898119899119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119898119899119906]119898119899

119882119866

119899119898= 119861

119899119898119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119906]119898119899

=119892119898

119892119899

119882119866

119898119899

(34)


119889119873119898

119889119905= + (119882

119866

119899119898+ 119862

119899119898)119873

119899minus (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889119873119899

119889119905= minus (119882

119866

119899119898+ 119862

119899119898)119873

119899+ (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889120588119866

119889119905= minus119882

119866

119899119898119873119899+119882

119866

119898119899119873119898+ 119860

119898119899119873119898

(35)


119862119899119898

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866119862

119898119899 (36)





119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)


2-



119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899


119898119873


order of 119860119898119899



119866

119898119899= 119882

119866

119899119898= 003-004 sminus1








Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)




asymp 1120591119898

120591119899and 120591




119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)


Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)


119898119899(FWHM)

according to (40)



energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)



119892119863(]) =


119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)


Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12


119898119899radic119879119866

119872 (43)


specified in K


119863(]1015840) and 119892

119871(] minus


profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840


Δ]119898119899

Δ]119863

times int

infin

0


119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Cros

s sec

tion

(cm

2)

Snm

Frequency

Δmn

mn



120590119899119898(])119873 = 120590

119899119898(])119873

119899minus 120590

119898119899(])119873

119898

= 120590119899119898(])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

=ℎ]

119898119899

119888119899119861119899119898119892 (])119873

119899(1 minus

119892119899

119892119898

119873119898

119873119899

)

(29)

and 120590119899119898(]) becomes

120590119899119898(]) =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (]) (30)



119878119899119898

= intΔ]120590119899119898(]) 119889] =

ℎ]119898119899

119888119899119861119899119898

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

) (31)




120572119899119898(]) = 120590

119899119898(])119873

=ℎ]

119898119899

119888119899119861119899119898119873119899(1 minus

119892119899

119892119898

119873119898

119873119899

)119892 (])

= 119878119899119898119873119892 (]) = 1205720

119899119898119892 (])

(32)



120572119899119898(]) =

1198601198981198991198882

81205871198992]2119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

=1198601198981198991205822

81205871198992119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (])

(33)

Nm

Nn

WGmn Amn

Cmn

WGnm Cnm






119866

119898119899and119882119866



119882119866

119898119899= 119861

119898119899119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119898119899119906]119898119899

119882119866

119899119898= 119861

119899119898119906]119898119899

=119888

119899

1

ℎ]119898119899

1205900

119899119898119906]119898119899

=119892119898

119892119899

119882119866

119898119899

(34)


119889119873119898

119889119905= + (119882

119866

119899119898+ 119862

119899119898)119873

119899minus (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889119873119899

119889119905= minus (119882

119866

119899119898+ 119862

119899119898)119873

119899+ (119882

119866

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

119889120588119866

119889119905= minus119882

119866

119899119898119873119899+119882

119866

119898119899119873119898+ 119860

119898119899119873119898

(35)


119862119899119898

=119892119898

119892119899

119890minusℎ]119898119899119896119879119866119862

119898119899 (36)





119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)


2-



119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899


119898119873


order of 119860119898119899



119866

119898119899= 119882

119866

119899119898= 003-004 sminus1








Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)




asymp 1120591119898

120591119899and 120591




119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)


Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)


119898119899(FWHM)

according to (40)



energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)



119892119863(]) =


119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)


Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12


119898119899radic119879119866

119872 (43)


specified in K


119863(]1015840) and 119892

119871(] minus


profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840


Δ]119898119899

Δ]119863

times int

infin

0


119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




119882119866

119898119899=

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 119882

119866

119899119898=119892119898

119892119899

119860119898119899

119890ℎ]119898119899119896119879119866 minus 1 (37)


2-



119898119899119860

119898119899= 0037 Assuming that 119892

119898= 119892

119899


119898119873


order of 119860119898119899



119866

119898119899= 119882

119866

119899119898= 003-004 sminus1








Δ]119898119899

=1

2120587120591119898

+1

2120587120591119899

asymp119860119898119899

2120587(38)




asymp 1120591119898

120591119899and 120591




119892119871(]) =

Δ]1198981198992120587

(] minus ]119898119899)2

+ (Δ]1198981198992)

2 int

infin

0

119892119871(]) 119889] = 1

(39)


Δ]119898119899

asymp1

2120587(119860

119898119899+ 119862

119898119899+ 119862

119899119898+ 119862phase) (40)


119898119899(FWHM)

according to (40)



energy

119864kin =3

2119896119879

119866=119898119866

2V2 (41)



119892119863(]) =


119863

exp(minus(] minus ]

119898119899)2

(Δ]1198632)

2ln 2) (42)


Δ]119863= 2]

119898119899(2119896119879

119866

1198981198661198882

ln 2)12


119898119899radic119879119866

119872 (43)


specified in K


119863(]1015840) and 119892

119871(] minus


profile of the form

119892119881(]) = int

infin

0

119892119863(]1015840) 119892

119871(] minus ]1015840) 119889]1015840


Δ]119898119899

Δ]119863

times int

infin

0


119898119899)2

(Δ]1198632)

2ln 2)

sdot119889]1015840

(] minus ]1015840)2

+ (Δ]1198981198992)

2

(44)






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






119898119899119862



119898119899


119889119906]

119889119905= ℎ]

119898119899119860119898119899119873119898119892 (]) (45)




120591ph = 119897ph119899

119888=

119899

120572119899119898119888 (46)

where 119897ph = 1120572119899119898


119906] = ℎ]119898119899119860119898119899120591ph119873119898

119892 (]) =119899

119888ℎ]

119898119899

119860119898119899

120572119899119898

119873119898119892 (]) (47)


(120590119899119898(])119873

119899minus 120590

119898119899(])119873

119898) 119906]= 120572119899119898119906]

=119899

119888ℎ]

119898119899119860119898119899119873119898119892 (])

(48)



is found to be

119906]119898119899=8120587119899

3ℎ]3

119898119899

1198883

1

(119892119898119873119899119892

119899119873119898minus 1)

=8120587119899

3ℎ]3

119898119899

1198883

1

119890ℎ]119898119899119896119879119866 minus 1

(49)






31 Basic Quantities


119868]Ω (119879119864) 119889119860 cos120573119889]119889Ω

=2ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1119889119860 cos120573119889]119889Ω

(50)






120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


120593

120573

dA

d120593

d120573



119868] = int

2120587

Ω

119868]Ω (119879119864) cos120573119889Ω

= int

2120587

120593=0

int

1205872

120573=0

119868]Ω (119879119864) cos120573 sin120573119889120573119889120593

=2120587ℎ]31198992

1198882

1

119890ℎ]119896119879119864 minus 1

(51)


119868120582=119888119899

1205822119868] =

2120587ℎ11988821198993

1205825

1

119890ℎ119888119896119879119864120582 minus 1 (52)





119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (53)


35

30

25

20

15

10

5

00 10 20 30 40 50 60


Spec

tral

inte

nsity

(Wm

minus2120583

mminus1)

Earth299K


z

120573

Δz

IΩ cos 120573dΩ

Δzcos 120573









int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



int119889119868]Ω (119911) cos120573119889Ω119889119911

= minus120572119899119898(]) int

2120587

0

int

1205872

0

119868]Ω

cos120573cos120573

sin120573119889120573119889120593

(54)


119889119868] (119911 119879119864)

119889119911= minus2120572

119899119898(]) 119868] (119911 119879119864) (55)


119899119898 but is



119871] (119911) =119889119868] (119911)

119889119911= minus2120572

119899119898(]) 119868] (0) 119890

minus2120572119899119898(])119911 (56)






119871 (119911) =2119899

119888intΔ]

119889119868]

119889119905119889] =

2119899

119888

119889119868]119898119899

119889119905Δ] = 2

119889120588119864

119889119905ℎ]

119898119899

= minus119860119898119899

2119873119899(119892119898

119892119899

minus119873119898

119873119899

)ℎ]

119898119899

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(57)



119899119898and119882119864


119889120588119864

119889119905= minus119882

119864

119899119898119873119899+119882

119864

119898119899119873119898

= minus119860119898119899

4(119892119898

119892119899

119873119899minus 119873

119898)

1

119890ℎ]119898119899119896119879119864 minus 1119890minus2120572119899119898119911

(58)

with 120572119899119898

= 1205720

119899119898Δ] = 119878



119882119864

119898119899(119911) =

1198601198981198991205822

119898119899

81205871198992ℎ]119898119899

119868]119898119899(119911) =

1205900

119898119899

ℎ]119898119899

119868]119898119899(119911)

=119860119898119899

4

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1

119882119864

119899119898=119892119898

119892119899

119882119864

119898119899

(59)








119882119864

119898119899

119860119898119899

= 00093 asymp 1 (60)



Δ]119873119898119899

=119860119898119899

2120587 (61)

Then (59) becomes

119882119864

119898119899(119911) =

120587

2Δ]119873

119898119899

119890minus2119878119899119898119873119911Δ]

119890ℎ]119898119899119896119879119864 minus 1 (62)









Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Nm

Nn

WGmn

AmnCmn

WGnm

WEmn

WEnmCnm



119868]Ω (119911) = 119868]Ω (0) 119890minus(1 cos120573) int119911

0120572119899119898(119911

1015840)1198891199111015840

(63)


119868] (119911) = int

2120587

0

int

1205872

0

119868]Ω (119911) cos120573 sin120573119889120573119889120593

= 119868]Ω (0) int

2120587

0

int

1205872

0

119890minus(1cos120573)int119911

0120572119899119898(119911

1015840)1198891199111015840

times cos120573 sin120573119889120573119889120593

(64)


0120572119899119898(1199111015840)119889119911


we can write

119868] (120591) = 2120587119868]Ω (0) 1205912int

infin

120591

119890minus119906

1199063119889119906

= 119868] (0) 1205912(119864

1(120591) + 119890

minus120591(1

1205912minus1

120591))

(65)


1198641(120591) = int

infin

120591

119890minus119906

119906119889119906 = minus05772 minus ln 120591 +

infin

sum

119896=1

(minus1)119896+1120591119896

119896 sdot 119896 (66)










119868]119898119899(119911) = 119868]119898119899

(0) 119890minus2119878119899119898119873119911Δ] (67)




119871119875=

Δ]

2119878119899119898119873119878

(68)



119875 Since 119873



119878and also 119878




119873119899= 119873

0

1198790

119879119866

119892119899119890minus119864119899119896119879119866

119875 (119879119866) (69)






defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



defined as [15 16]

119875 (119879119866) = sum

119894

119892119894119890minus119864119894119896119879119866

(70)


2transition in the


119873119899119873



section of

119878119899119898

= 1205900

119899119898=1198601198981198991205822

81205871198992

119873119899

119873(1 minus

119892119899

119892119898

119873119898

119873119899

)



(71)


119875= 1 km






119868]119898119899=

1

119871119875

int

119871119875

0

119868]119898119899(119911) 119889119911

=Δ]

2119878119899119898119873119871

119875

119868]119898119899(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(72)


120588119864=119899

119888

Δ]

ℎ]119898119899

119868]119898119899=

Δ]

2119878119899119898119873119871

119875

120588119864(0) sdot (1 minus 119890

minus2119878119899119898119873119871119875Δ])

(73)







Δ119876 = 119888119901120588airΔ119879119866 = (

119891

2+ 1)

119877119866

119872air

119872air119873119860

119901air119896119879

119866

Δ119879119866

=7

2

119901air119879119866

Δ119879119866

(74)


119876 (119879119866) =

7

2119901air int

119879119866

1198790

1

1198791015840

119866

1198891198791015840

119866=7

2119901air ln(

119879119866

1198790

) (75)



119866119872air where 119891 are


2 119891 = 5)

and 119877119866= 119896 sdot 119873













119867119911= ℎ

119862sdot (119879

119864minus

119879119866) with ℎ






119862119867

119879sdot (119879

119864minus119879

119866)

with ℎ119862119867

119879asymp 1mWm3K




119898119899




119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



119889119873119898

119889119905= +(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

minus (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889119873119899

119889119905= minus(

ℎ]119898119899

Δ]119861119899119898(120588119866+ 120588

119864) + 119862

119899119898)119873

119899

+ (ℎ]

119898119899

Δ]119861119898119899(120588119866+ 120588

119864) + 119862

119898119899+ 119860

119898119899)119873

119898

119889120588119866

119889119905= minus

ℎ]119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119866+ 119860

119898119899119873119898minus 120601120588

119866

119889120588119864

119889119905= +

119888119899

2119871119875


119864(0)

minusℎ]

119898119899

Δ](119861

119899119898119873119899minus 119861

119898119899119873119898) 120588

119864

119889119876

119889119905= +

ℎ119862

119867119879

(119879119864minus 119879

119866) + 119902SL minus ℎ]119898119899 (119862119899119898119873119899

minus 119862119898119899119873119898)

(76)


119882119866

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119866= 119861

119898119899119906]119898119899

119882119864

119898119899=ℎ]

119898119899

Δ]119861119898119899120588119864= 119861

119898119899

119899

119888119868]119898119899

119882119866119864

119899119898=119892119898

119892119899

119882119866119864

119898119899

(77)





119899119898119873119899minus 119861

119898119899119873119898)) short



119899119889119905 = 119889119873



119873119898

119873119899

=ℎ]

119898119899119861119899119898(120588119866+ 120588

119864) Δ] + 119862

119899119898

ℎ]119898119899119861119898119899(120588119866+ 120588

119864) Δ] + 119862

119898119899+ 119860

119898119899

=119882

119866

119899119898+119882

119864

119899119898+ 119862

119899119898

119882119866

119898119899+119882119864

119898119899+ 119860

119898119899+ 119862

119898119899

(78)

which at 119879119866sim 119879

119864= 288K and 120582 = 15 120583m due to 119882119866

119898119899=

4119882119864

119898119899= 0037119860



119866and







119866and 120588


densities 119873119899and 119873







119895119867119911




=



119898119899=


= 35 and 119892119899









605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


605040

20

0010

70

30

300270210600 30Time (h)

15090 120 180 240

Phot

on d

ensit

y120588 G

times10

10(m

minus3)

(a)

120100

80

40

0020

140

60

Time (h)

Phot

on d

ensit

y120588Etimes10

7(m

minus3)

300270210600 30 15090 120 180 240

(b)

1005000

150200250

Time (h)

Rela

tive p

opul

atio

nN

nN

0(

)

300270210600 30 15090 120 180 240

(c)

005000

010015020025

Time (h)

Rela

tive p

opul

atio

nN

mN

0(

)

300270210600 30 15090 120 180 240

(d)

2000

1600

1400

1200

1800

Time (h)

Ther

mal

ener

gyQ

(kJ m

minus3)

300270210600 30 15090 120 180 240

(e)

300250200150

0

10050

Time (h)

Gas

tem

pera

ture

TG

(K)

300270210600 30 15090 120 180 240

(f)










119899by (69)




119875 (119879119866) = 0894 sdot 119879

119866+ 3 times 10

minus91198794

119866 (79)





119898119899

and 119862119899119898


119866













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in













2 is stronger







0at 288K








119898119873




119899minus 119873




120601 ge119888119899

4119871119875














119898119899= 10






31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


31

30

29

32

282550

Time (min)10 15 20

Phot

on d

ensit

y120588 G

times10

8(m

minus3)

(a)

400

410

395

405

390

Phot

on d

ensit

y120588Etimes10

5(m

minus3)

2550Time (min)

10 15 20

(b)

890880

900910920

Rela

tive p

opul

atio

nN

nN

0(

)

2550Time (min)

10 15 20

(c)

0190

0186

0194

0198

0202

Rela

tive p

opul

atio

nN

mN

0(

)

2550Time (s)

10 15 20

(d)

1420

141414121410

14161418

Ther

mal

ener

gyQ

(kJ m

minus3)

2550Time (min)

10 15 20

(e)

250

248

246

242

244

Gas

tem

pera

ture

TG

(K)

2550Time (min)

10 15 20

(f)






119866and 120588


119873119899and 119873







119866




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(81)



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



(119861119899119898(119906] +

119899

119888sdot 119868]) + 119862119899119898)119873119899

= (119861119898119899(119906] +

119899

119888sdot 119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(82)


and119862119899119898



119906] +119899

119888sdot 119868] = 119880]

119862119899119898

119861119899119898

= 120576

119860119898119899

119861119899119898

=119892119899

119892119898

81205871198992

1205822119898119899

ℎ]119898119899

119888119899=119892119899

119892119898

120581

(83)


119873119898

119873119899

=119892119898

119892119899

119880] + 120576

119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866)

(84)


119906] (84) changes to

119873119898

119873119899

asymp119892119898

119892119899

119868]

119868] + (119888119899) 120581=119892119898

119892119899

1

1 + 4 (119890ℎ]119898119899(119896119879119864) minus 1) 1198902119878119899119898119873119911Δ]

asymp1

4

119892119898

119892119899

119890minusℎ]119898119899119896119879119864119890

minus2119878119899119898119873119911Δ]

(85)


119898119899gt 119896119879









119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) (86)



ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888

4120587119899120572119899119898119906] = 120572119899119898119861]Ω (119879119866) (87)




119899119898or 119861


result

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(88)



z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


z

120573

dz

IΩ cos 120573dΩ

BΩ cos 120573dΩ

dzcos 120573







119899119898119861




[8ndash11])

120576 (]) = 120572119899119898(]) sdot 119861]Ω (119879119866) (89)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) + 120576 (])

= minus120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866)

(90)





int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(]) int

2120587

0

int

1205872

0

(minus119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593

(91)


120587 sdot 119861]Ω

119889119868] (119911)

119889119911= 2120572

119899119898(]) (minus119868] (119911 119879119864) + 119861] (119879119866 (119911))) (92)


119868] (119911) = 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

times [2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840))

times1198902 int1199111015840

0120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840+ 119868] (0) ]

(93)


119868] (119911) = 119868] (0) 119890minus2int119911

0120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(94)




119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120572119894

119899119898(])Δ119911

+ 119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120572119894

119899119898(])Δ119911

) (95)


119899119898(])





Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Δz


(TiG)


(Timinus1G )

Ii+1 Ti+1G 120572i+1nm () Bi+1

(Ti+1G )




120572119899119898(]) int

Ω

119868]Ω (119903 119879119864) cos120573119889Ω

= 120572119899119898(]) 119868] (119903 119879119864) equiv ℎ]119898119899119860119898119899

119873119898119892 (])

(96)


119889119868]Ω

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864) +

1

4120587120572119899119898(]) 119868] (119903 119879119864) (97)

With 119868] = 120587119868]Ω (97) becomes

119889119868]Ω

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) (98)




(119882119866

119899119898+119882

119864

119899119898+ 119862

119899119898)119873

119899= (119882

119866

119898119899+119882

119864

119898119899+ 119860

119898119899+ 119862

119898119899)119873

119898

(99)


(119892119898

119892119899

119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119862119899119898)119873119899

= (119888119899

ℎ]119898119899

1198601198981198991205822

119898119899

81205871198992(119906] +

119899

119888119868]) + 119860119898119899

+ 119862119898119899)119873

119898

(100)


gives

1198601198981198991205822

119898119899

81205871198992(119892119898

119892119899

119873119899minus 119873

119898)(

119888

119899119906] + 119868])

+ ℎ]119898119899(119862

119899119898119873119899minus 119862

119898119899119873119898)

= ℎ]119898119899119860119898119899119873119898

(101)


119899119898119873119899minus119862



= 119862119899119898


1

4120587120572119899119898(119888

119899119906] + 119868]) = 120572119899119898 (119861]Ω +

1

4119868]Ω)

=ℎ]

119898119899

4120587119860119898119899119873119898119892 (])

(102)


119889119868]Ω (119903)

119889119903= minus

3

4120572119899119898(]) 119868]Ω (119903 119879119864) + 120572119899119898 (]) 119861]Ω (119879119866 (119903))

(103)



(119880] + 120581 + 120576 sdot 119890ℎ]119898119899(119896119879119866))119873

119898=119892119898

119892119899

(119880] + 120576)119873119899 (104)



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



(120581 + 120576 (119890ℎ]119898119899(119896119879119866) + 1 minus 1))119873

119898

= (119892119898

119892119899

119873119899minus 119873

119898)119880] +

119892119898

119892119899

120576119873119899

(120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1))119873

119898= (

119892119898

119892119899

119873119899minus 119873

119898) (119880] + 120576)

119873119898=119873119899(119892

119898119892

119899minus 119873

119898119873

119899) (119880] + 120576)

120581 + 120576 (119890ℎ]119898119899(119896119879119866) minus 1)

(105)


120572119899119898

=ℎ]

119898119899

119888119899

119860119898119899

120581119873119899(119892119898

119892119899

minus119873119898

119873119899

)119892 (]) (106)


119898119899119892(]) we obtain

ℎ]119898119899

4120587119860119898119899119873119898119892 (]) =

119888119899

4120587

120572119899119898(119880] + 120576)

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

= 120572119899119898

119861]Ω + (14) 119868]Ω + ((119888119899)4120587) 120576

1 + (120576120581) (119890ℎ]119898119899(119896119879119866) minus 1)

(107)


120578 =119888119899

4120587

120576

119861]Ω

=119888119899

4120587

119862119899119898

119861119899119898

1198882

2ℎ]31198981198991198992(119890ℎ]119898119899(119896119879119866) minus 1)

=120576

120581(119890ℎ]119898119899(119896119879119866) minus 1)

(108)


119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) 119868]Ω (119903 119879119864)

+ 120572119899119898

119861]Ω + (14) 119868]Ω + 120578119861]Ω

1 + 120578

119889119868]Ω (119903)

119889119903= minus120572

119899119898(]) (1 minus

14

1 + 120578) 119868]Ω (119903 119879119864)

+ 120572119899119898(]) 119861]Ω (119879119866 (119903))

(109)


120594 = 1 minus14

1 + 120578=3 + 4120578

4 + 4120578 (110)


119889119868]Ω (119903)

119889119903= 120572

119899119898(] 119903) (minus120594 sdot 119868]Ω (119903 119879119864) + 119861]Ω (119879119866 (119903)))

(111)


120578 =120576

120581(119890ℎ]119898119899(119896119879119866) minus 1) =

119892119899

119892119898

119862119899119898

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

=119862119898119899

119860119898119899

(119890ℎ]119898119899(119896119879119866) minus 1)

119890ℎ]119898119899(119896119879119866)asymp119862119898119899

119860119898119899

(112)


119898119899



int119889119868]Ω (119911) cos120573119889Ω119889119911

= 120572119899119898(] 119911) int

2120587

0

int

1205872

0

(minus120594 (119911) 119868]Ω (119911 119879119864) + 119861]Ω (119879119866 (119911)))

times sin120573119889120573119889120593(113)


119889119868] (119911)

119889119911= 2120572

119899119898(] 119911) (minus120594 (119911) 119868] (119911 119879119864) + 119861] (119879119866 (119911)))

(114)


119864and


119868] (119911)

= 119868] (0) 119890minus2int119911

0120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

+ 2int

119911

0

120572119899119898(] 1199111015840) 119861] (119879119866 (119911

1015840)) 119890

minus2int119911

1199111015840 120594(11991110158401015840)120572119899119898(]119911

10158401015840)11988911991110158401015840

1198891199111015840

(115)


119868119894

] (Δ119911) = 119868119894minus1

] 119890minus2120594119894120572119894

119899119898(])Δ119911

+1

120594119894119861119894

] (119879119894

119866) sdot (1 minus 119890

minus2120594119894120572119894

119899119898(])Δ119911

)

(116)








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in








atmosphere




2 CH

4 and O











00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion


1m

10m

100

m1

km

P-branch R-branch

Q-branch00

02

04

06

08

10

610 625 640 655 670 685 700 715 730

Tran

smiss

ion







500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


500600

70080002 08 14 20

000102030405


Spec

tral

inte

nsity

(Wm

2c

mminus1)



00

01

02

03

04

05

500 587 675 762 850


01 km2km

4km6km

8km10km

Spec

tral

inte

nsity

(Wm

2c

mminus1)

287K

275K

262K

249K236K223K








2in dry air



10E + 00

10E minus 01

10E minus 02

10E minus 03

10E minus 04

10E minus 05

Log

tran

smiss

ion

10 632 1255 1877 2500




119898119899119860

119898119899 Since up to



2transitions

119860119898119899










00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)





119899119898(]) = 120572

119899119898(])Δ119911 asymp 1







2around





00

01

02

03

04

10 632 1255 1877 2500


Spec

tral

inte

nsity

(Wm

2c

mminus1)



2(green)



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K















Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



Spec

tral

inte

nsity

(Wm

2c

mminus1)

00

01

02

03

04

10 632 1255 1877 2500

760ppm CO2

380ppm CO2

Planck 288K





2concentration


2 and CH




3spread




2concen-




















120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


120

100

80

60

40

20

0

Wavelength (120583m)25 20 18 15 14 13 12 11 10 9 8 7 6

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700


Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

400 725 1050 1375 1700

760ppm CO2

380ppm CO2

CO2CO2

O3

H2O

H2O


Planck T = 268K

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



140

120

100

80

60

40

20

0500 700 900 1100 1300 1500 1700 1900



March 18 2008

Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(a)

500 750 1000 1250 1500 1750 2001


Clear sky TE = 282K

Planck T = 288K


140

120

100

80

60

40

20

0Spec

tral

radi

ance

(mW

m2s

rcm

minus1)

(b)



2




80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


80

82

84

86

88

0 200 400 600 800

Abso

rptio

n (

)

46 CO2 absorption


2 absorption12 CO


2concentration






2concentration










2) of 119862



6 Conclusion









2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




2concentration



2-laser radiation


References






















2O CO

2 CH

4und O

















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

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