modeling atmospheric aerosol backscatter at co_2 laser wavelengths 3: effects of changes in...

Modeling atmospheric aerosol backscatter at CO2 laserwavelengths. 3: Effects of changes in wavelengthand ambient conditions

Glenn K. Yue, G. S. Kent, U. 0. Farrukh, and Adarsh Deepak

The effects of changes in wavelength and ambient conditions on the atmospheric backscatter at CO2 wave-

lengths have been examined. It has been found that, with the exception of (NH4 )2 SO4-containing aerosols,

whose size distributions have relatively large numbers of small particles, the variation of backscatter with

CO2 wavelength is less than a factor of -3. However, for such (NH4 )2 SO4 aerosol distributions, the variation

of backscatter function with CO2 wavelengths between 9.1 and 11.1 Atm may reach 1 order of magnitude.

The effects of ambient humidity and temperature changes are negligibly small when the relative humidity

is low (<75%). However, for a humid environment (>90%), a few percent change in humidity or a few de-

grees change in temperature may cause noticeable change in backscatter from aerosol particles of small

sizes.

1. Introduction

The factors governing 3co, the aerosol backscatter-ing function at CO2 laser wavelengths, estimated fromthe reported measurements of aerosol properties, canbe divided into three general categories. The firstcategory contains those factors related to the aerosolparticle characteristics such as the aerosol shape, con-centration, size distribution, composition, and errorsin these quantities associated with the measurementtechnique. The second contains factors related to thoseambient conditions which have a direct influence on theproperties of aerosol, such as relative humidity andtemperature. The third contains factors related to theradiation source, such as the wavelength of the laser. Intwo companion papers, 1 2 we have discussed some im-portant factors that may affect the estimated Sco2values and the modeling techniques used to obtain co2-This paper reports the results of a study made of theeffect of changes in radiation wavelength on /co 2 . Thewavelengths used in this parametric study are CO2 laserwavelengths ranging from 9.1 to 11.1 um. In addition,the changes of ico2 due to the growth and evaporationof aerosols are being presented here. These changes ofthe optical properties of aerosol particles may result

The authors are with Institute for Atmospheric Optics & RemoteSensing, P.O. Box P, Hampton, Virginia 23666.

Received 27 December 1982.0003-6935/83/111671-08$01.00/0.(© 1983 Optical Society of America.

from local fluctuations in temperature and water vaporconcentration or may occur when aerosol particles aretransported to a new region of the atmosphere whereambient parameters are different.

Since large variations occur in aerosol size distribu-tions, we have used two approaches in this study. Thefirst approach is to calculate oC02 for aerosols with alognormal size distribution and different mode radii.The aerosol size dependence of the effect of wavelengthor changing ambient conditions on /Co can be semi-quantitatively determined by this approach. Thesecond approach has been to calculate the fco 2 valuesfor some typical aerosol size distributions measured indifferent regions of the atmosphere for differentwavelengths and under a variety of ambient conditions.The calculated changes in fco 2 are the expected changesthat may be observed from field measurements.

II. Effects of Wavelength Change on'1co2

An important input parameter in' calculating Sco2

from' the Mie code is the complex refractive index of theaerosol at the wavelength under consideration. Thecomposition or type of aerosol particle can usually beidentified by in situ measurements: Common aerosolmaterials found in the lowest 20 km of the atmosphereare 75% H2SO4 solution, water soluble (consisting ofammonium and calcium sulfate and organic material),dust, soot, clay, and (NH4)2SO4. The wavelength de-pendence of the complex refractive indices of thesecommon aerosol materials are usually available inpublished papers or reports.,'- 7 The refractive indicesof these substances at CO2 laser wavelengths ranging

1 June 1983 / Vol. 22, No. 1 1 / APPLIED OPTICS 1671

0

-4 - oa 6666066,I i I Iii' i

co - C 0 00 -' 4 / C') ,t: _; -I- tv Nq , -

I _,Icc00010 '18 Cl CID

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I a- cc o o

- C-D C!I IIC11 o o o

_I t- cc Co

-4 >N CD

CM O CD O

I- tD " N

0 Icc1

* t O~ a

I I Icc0 maIZ- 0~ -':

I

Cl 0-Cc N' CO C ,M O,.

I0o .z. .coCD O C

| C'D _ XI I I C I N Cccoo 1001

I .Cl 10 ._ - ,-4 "4C'! Cc ta'-! ci~I4 - '-4 NC .

I N - 8 O 0

V- N Cq r- N 0Cf0

I ) ( O N

0 5 6 CO C) iX

I o I r s CD I X

CI t-cc d.) - aC

I-N O t-. c <) Ni "| ( -N 0Clt 0 a- -4LoMCI

-444C5 CD -4

C> C) ,~C> 8 O -4C 100 tO o I . -

0cs''4 " cc 0 co,, X

C,! Cl _ I -4 "I

O a' -CD 146666061 cc-4 10a C C ccCn 00 -4E_ I

'i Ci cs _! I

0

-4 -4Is x, 1

1.0 0,I- CD

I CI Z ) O. t

10-5

10-6

In10-7

E -

E~I03=

CC1 -

r 10-10

10-11

10-12

10

I05

10-s

10-7

,'1 0-8

Th l0'8E

cc 10-9

Ca 10-10

10 11

10-12 C

-2

1-2

0-5

10-6

10-7

I

IE

LUJ

10-8

1 0-9

10-10

10-11

1o-121010-1 100 101

MODE RRDIUS, m

(a)

10-5

10-6

10-7

I1;,

E

LLtn

10-8

1 0-3

10-10

1010-1 100 101

MODE RDIUS, pm

(C)

-2

-2

10-1 100

MODE RRDIUS, pm

(b)

10-1 100

MODE RRDIUS,,m

(d)

Fig. 1. fco 2 vs mode radius for different CO2 wavelengths and for different aerosol materials: (a)H2 SO4 ; (b) dust; (c) (NH4 )2 SO4 ; (d) water soluble.

from 9.1 to 11.1 m are listed in Table I. Some of thevalues listed in Table I are obtained by linear interpo-lation of the published data. It is obvious that, ingeneral, the refractive index is quite sensitive to thewavelength, especially for water soluble and (NH4 )2 SO4aerosols. At certain wavelengths the refractive indexis much larger than these at adjacent wavelengths [e.g.,(NH 4 )2SO4 at = 9.5 ,im]. Furthermore, for somematerials (e.g., H2SO4), the real parts of the refractiveindices are not monotonic functions of the wavelength.Consequently, errors may be produced by interpolatingthe values given in the literature. It should also benoted that the imaginary parts of the refractive indicesat CO2 wavelengths are quite large, and the absorptionby aerosols at these wavelengths should not be ignoredin any Mie calculation.

In our first set of calculations, we assume aerosol sizesto be lognormal with the geometric mean standard de-

1672 APPLIED OPTICS / Vol. 22, No. 11 / 1 June 1983

"4_ 1111111 1 a I I I I 1 |

H S2S°4

0c 5.1 L M_ / A 9.5 g M

10.0 U M-A/? = 10.6 U M

= 11.1 M M

, , II Ie,1 , ,,,1,,, , ,,,,,,

-4.

1°

1

6<'1>

Co0)

_,, I 1111 ,, ,,,, ,, 1111 1II I

DUST

O = 5.1 M M= 3.5 M M= 10.0 A M

A = 10.6 A M-= 11.1 NM

I .

0I -a

I-.0U

co

F.0

C.)

an0

0C.)1Da

0

0

3

;i

02E

0

-

.a)

4)

0

E

0

2

c

(0a)la

2a)

.(anI-

(NH4 ) 2 S04 0

0?, 5 .1 U 0, 5 =.5 A C)?, 10.0 AL N

0 A /// 6= / 1. AL Nt g O A _jO.O g j

101

101

WATERSOLUBLE -u

0?/DO = 5.1 AL N0I° = 9.5 M N

t ID° = i.0 AL MA1D = 10.6 M N

I fill I = 11.1 N II (liii,1 ,,,,,,,1,i I 1111(11

ls

O o0c0

<C)¢E

| | W x X 1 1 1 1 1 1 1 1 1 l l l 1 1 1 1 1 | r

1i

viation oa,> = 2.0 and mode radii r, varying from 0.05 to5.0 gim. The backscattering function defined by thefollowing expression is calculated for different moderadii, different aerosol materials, and different wave-lengths:

$= X Q(na) dN(r) (1)rl dr

where the size distributiondN(r) A ln2(r/r,,)1

=__ - expl -(2dr r [- 2(lnu,)2] (2)

and Q(n,a) is the backscattering cross section, whichis a function of the complex refractive index n and thesize parameter ce = (22rr)/,N, where r is the particle ra-dius, and X is the wavelength. The normalization factorA is chosen to be (2wx lna.)- /

2 so that the total numberconcentration is unity. The calculated results for 1C02are shown in Fig. 1. These figures illustrate that, forsome common aerosol materials, such as sulfuric acid,with 75% H2SO4 and 25% H2O, and dust, the variationOf /co 2 with CO2 wavelength is relatively small (a factorof less than -3) regardless of the assumed aerosol sizedistribution. However, for other materials such aswater soluble and (NH4 )2 SO4, the variation of co withCO2 wavelength may not only be appreciable but is alsosize dependent.' For lognormal aerosol size distribu-tions with mode radii at -0.7 ,im, the variation is afactor of <2. But, for aerosols with large or small radii,it is possible to get an order of magnitude variation. Itis of interest to note that the variation of fco2 withwavelength for pure (NH4 )2SO4 is similar to that forwater soluble. This is because the main component ofthe water soluble material is (NH4 )2SO4 .

In our second set of calculations, we use measuredbackground aerosol size distributions as a basis for thecalculation. Three size distributions have been selectedas typical for the free troposphere. They consist of acontinental distribution with a large number of the largeparticles by Cress, spring average, 8 a continental dis-

tribution with fewer large particles by Patterson et al. 9Most aerosol size distributions found in the literaturelie between the limits represented by these three. Plotsof these aerosol size distributions are given in our pre-vious paper.' The calculated variations of co2 withCO2 wavelengths for these three aerosol size distribu-tions are shown in Fig. 2. It can be seen that for theCress spring average size distribution, the variation ofthe backscattering function with CO2 wavelength isalways a factor of <2 regardless of the aerosol material.However, for the Patterson et al. size distributions withfewer large particles the backscattering functions forwater soluble material and (NH4)2SO4 aerosols mayvary by about an order of magnitude with the CO2wavelength; for other common aerosol materials, thevariation is small. Figures 2(b) and (c) also show thatthe maximum of (3co for (NH4 )2 SO4 containing aero-sols is at about X = 9.1 gim. This property can be uti-lized to obtain maximum backscatter signal.

From the analysis mentioned before, we conclude thatthe choice of any specific CO2 wavelength for back-scatter measurements will not effectively change theresult for most common aerosol materials in the atmo-sphere, with the exception of aerosols containing(NH4 )2SO4 , where the number of large aerosols is verysmall. This may occur in the free troposphere over theremote oceans. It may be possible to utilize the largevariation of co with CO2 wavelengths, for (NH 4 )2SO4 ,to detect the presence of (NH4)2SO4 aerosols in suchaerosol populations.

Ill. Effects of Humidity Change on co2

As the ambient humidity increases, water vapor maybe absorbed by aerosol particles suspended in the at-mosphere. Laboratory experiments and theoreticalcalculations have shown that the properties of solidaerosol particles do not change until the ambient hu-midity has reached a threshold value which depends onthe deliquescent property of the aerosol compound

9.5 10.0 10.5WRVE LENGTH, m

(a)

11.0 11.5

10-7

E

5: 10'8

L.)

I I I -s

LD

L- 10-ic

C:F-10

U 10-11:D

3.0 9.S 10.0 10.5 11.0 11.5

WRVE LENGTH, m

(b)

1 0-7 - "|""|" 7 0"PATTERSON ET AL MARINE-

E

108ED

0 H2 S04C) _ o WRTERen SOLUBLELL 0 oDUST

A SOOTz.CLRY, _ NH4 ) 2So4

L)F

c 10-IL

M 3.0 9.5 10.0 10.5 11.0 11.5WRVE LENGTH, pm

(C)

Fig. 2. /co 2 vs CO2 wavelength tor different aerosol materials and for different measured aerosol size distributions: (a) spring average aerosols

reported by Cress8 ; (b) continental aerosols reported by Patterson et al.9; (c) marine aerosols reported by Patterson et al.9

1 June 1983 / Vol. 22, No. 11 / APPLIED OPTICS 1673

10-7

17Q

E

Z 10-a

LL I0-S

LD

LLI- 1 0-10

CEC-)

'I-C-) o1rn

C):

1010

,,,I''' )( 4)|| 5|E- CRESS SPRING AVERAGE

- ° H2504

- u WRTERSOLUBLE

O DUSTA SOOTL CLRY

NHq) 2SO4

- PATTERSON ET AL CONTINENTAL

- o H2S04- ° WRTER- SOLUBLE

DUSTASOOT

- LCLRY(NH4)2SO4

I II I I

.0

10

I

under consideration. The condensed water will changethe optical properties of aerosols in two ways: the firstis to increase the size of the aerosol particles, and thesecond is to change their effective refractive index.

The variation of the size of aerosol particles withambient humidity can be modeled in several ways. Theeasiest way is to utilize the published growth factorswhich relate the change of aerosol size to relative hu-midity.10 Unfortunately, most of the published dataon growth factors are limited to certain types of aerosolin the boundary layer. Furthermore, the variation ofthese growth factors with temperature is usually notavailable. In this study, we assume the aerosol particlesto be pure H2 SO4, (NH 1 )2 SOI, or NaCl and use thefollowing method to determine the growth factor atdifferent temperatures. It should be kept in mind thatour modeling results represent only the upper limit ofwhat we should observe in the atmosphere, since growthcurves for natural aerosols generally show smaller sizechange with relative humidity than those observed forpure salt solution.'I

Since the mass of solute in an aerosol droplet, beforeand after changes of ambient humidity, should be thesame, we have

Vpx = V'p'x',

5-

Li

enco(I)Lii

en0.Cc

0 20 40 60PERCENT OF SOLUTE

80 100

100 .X

UC-J

CE_

60 >_

40

20

-Jbi00•

Fig. 3. Water vapor pressures of H2 SO4, (NH4 )2SO4, and NaCl at25 and 15'C vs the weight percentage of the solute.

2.0

z

U-

LL

a:

(3)

where V is the volume of one aerosol particle, p is itsdensity, and x is the weight percentage of solute in thesolution. The symbols without and with primes referto the initial and final conditions, respectively.

From Eq. (3), we have

vspx_=_, ~~~~~~~~~(4)

and for the growth factorf, defined as the ratio of radiiafter and before the change of ambient conditions,

f r = p'x' *3 (5)

The new density p' is a function of x', and the newcomposition x' can be estimated by requiring the am-bient water vapor pressure to be in equilibrium with thewater vapor pressure above the surface of the dropletsolution with composition x'.

The variation of water vapor pressure with the com-position of aerosol solution at a given temperature isgiven in standard references. In this study, the ther-modynamic properties of (NH1)2SO4 and NaCl aretaken from the International Critical Tables, 2 andthat of H2 SO,, is taken from the report by Gmitro andVermeulen.1' The variations of water vapor pressuresabove the surfaces of H2SO4 , (NH) 2 SO4, and NaClsolutions at 25 and 15'C vs the weight percentage ofsolute in the solution are shown in Fig. 3.

In general, the growth factor f is a function of theradius of the aerosol particles if we consider the curva-ture effect. However, for these aerosol particles in theatmosphere that contribute to the total backscatteringfunction, their radii should be >0.01 gm, and the cur-vature effect for these particles can be totally ignored.Consequently, the growth factor depends only on the

1 .5

1 .0

) l I lI I I II

o H2S04(NH4)2 S04

0 NoCI

0

I III I0 20 40 60 80

PERCENT OF SOLUTE100

Fig. 4. Variation of the real parts of the indices of refraction forH 250,, (NH4)2SO,, and NaCl at X = 10.6 ,4m as a function of the

weight percentage of the solute.

initial and final composition. The effect of changingthe ambient humidity is just to shift the position of thewhole aerosol size spectrum, plotted on a log-log scale,without changing its shape. If the initial size distri-bution is lognormal, as expressed in Eq. (2), the final sizedistribution n'(r) is also lognormal with the mode radiusbeing shifted from rm to frm:

r ( 2([n)2(The change of ambient humidity will also change the

aerosol composition, resulting in a change in its effectiveindex of refraction. The variation of refractive indexwith relative humidity is given by the following equation(Hanel' 0):

n = n,, + (no-n,,) X (1 +--) (p1t, m0e

where n is the real or imaginary part of the complexindex of refraction of the aerosols at the relative hu-midity under consideration; n, p, and m with subscriptsrefer to the real or imaginary part of the complex indexof refraction, density, and mass, respectively; subscriptw refers to water; and subscript 0 refers to the puresubstance at 0% relative humidity. The values of m,and mo are functions of the ambient humidity, and they


(7)

can be determined once the value of x' has been foundusing the method described earlier. The values of noand nt,, are given in Table I.

Figure 4 shows the real part of the index of refractionas a function of the weight percentage of the solute forthe three aerosol materials H2SO4, (NH4)2SO4, andNaCl under consideration. The relatively larger vari-ation of the real part of the index of refraction for(NH 4 )2 SO4 and H2 SO4 is obvious from this illustra-tion.

To examine the effect of water vapor on the back-scattering function, we have calculated P, the per-centage change of the backscattering function underdifferent ambient conditions for different initial aerosolsize distributions and different aerosol materials. Inthis study, the initial aerosol size distributions are firstassumed to be lognormal with geometrical standarddeviation g = 2.0 and mode radii equal to 0.05, 0.5, and5.0 gAm. The ambient temperatures are assumed to be15 and 250C. The ambient relative humidities are as-sumed to be 20, 60, and 90%.

Some plots of the calculated percentage changes inbackscattering function for X = 10.6 gim vs the per-centage change in relative humidity are shown in Fig.5. These figures illustrate that, in general, an increasein ambient humidity will increase the aerosol back-scattering function due to the increase in backscatteringcross section. These figures also show that the changeof backscattering function due to a change in ambientcondition is negligibly small at low relative humidities.However, when the relative humidity is 90% or higher,the change in the backscattering function may reachmore than 100% for a few percent increase in relativehumidity. The plotted curves also demonstrate thatthe change in backscattering function is size dependent;the smaller the aerosol particles, the larger the back-

scattering change corresponding to the same ambienthumidity change. Our results also show that the changein backscattering function depends on the aerosol ma-terial under consideration, in general, the change forNaCl is larger than that for (NH4 )2 SO4 under the sameconditions.

To examine the occurrence of high relative humidityin the atmosphere, we have studied the relative hu-midities reported by Cress.8 The result is plotted inFig. 6 where each dot in the height vs relative humidityplane represents a value reported by Cress. Also plot-ted in Fig. 6 are the median for the Cress data and theprofiles of humidity in January and July reported by

20 I l l l l l l l l l

- rm- 0.05 pn

rm 0.5 pm

10LUJ

n-

0•00LUj

F--

CEU

cc -10 2504

-20 1 1 1 1 1 1 1 1 1 1 1I-12-10-8-6-4-2 0 2 4 6 8 1012

RELATIVE HUMIDITY CHANGE (7.)

(a)

30

. 20

10

0

-10

-20

LUCD

C-)

0•_LUJI--

C)U)C)

U)

-12-10-8-6-4-2 0 2 4 6 8 1012

RELATIVE HUMIDITY CHANGE (7)

(b)

170 I I I160 150 - rm .05,O p140 --- r,0.5pm:130 _n __m5.0 pmDn

1201101009080706050 o0 15C4 0 0 25°C3020 NaCI

20

-10-20 -30-40-6-5-4 -3 -2-1 0 1 2 3 4 5 6

RELATIVE HUMIDITY CHANGE ()

(C)

-

LUj

Z

CC

ccC:

LUJ

C:)U)C)cc

110100

50

80

70

60

-60

40

30

20

10

0

-10

-20-30

-6-5-4-3-2-1 0 1 2 3 4 5 6RELATIVE HUMIDITY CHANGE (%)

(d)

Fig. 5. Percentage 0(fo2 change vs relative humidity change for lognormal aerosol size distributions with mode radii equal to 0.05, 0.5, and5.0 ,um at temperatures 15 and 25 0C: (a) H2SO4 aerosols at an initial relative humidity of 20%; (b) H 2SO4 aerosols at an initial relative humidity

of 60%; (c) NaCl aerosols at an initial relative humidity of 90%; (d) (NH4 )2SO 4 aerosols at an initial relative humidity of 90%.


/ R.H. - 20%a 0 15C

0 25°C

LU

WCDccC)

LU

LL

--ccU)C)U)

nrBy

) I I I I I I I I I I I .- r. QO05pm

--- rim0.5 ,im

rm 50 pm

)1_/ 42504_R.H. = 60%

0 15C

° 25°C

r

7

6

g

ID

5

4

3

2

-sEDIAN (CRESS)--- 40°N JAN (NEWELL)-- 40 N JULY (NEWELL)

MEDIAN

- I\\

*\ *. *

20 40 60 80 100HUMIDITY %

Fig. 6. Humidities at different heights as reported by Cress8 andNewell et al. 1 Each dot represents an ambient condition reportedby Cress, and the solid line is the median value for the data set. Theshort- and long-dashed lines are the 40'N Jan. and July values pre-

sented by Newell et al.,'l respectively.

50

40

30W -_ID

ow 20

I0

0

0

I-

4n

m

10 20 30 40 50 60 70 80 90 100 110RELATIVE HUMIDITY (%)

Fig. 7. Histogram of the percentage of cases of a given relative hu-midlity at an altitude of 1 km reported by Cress. The curves representthe ratio of o(1o2 at a given relative humidity to 1co2 at 0% relative

humidity.

Newell et al. " It can be seen that the higher the alti-tude the less the chance of occurrence of high humidity.At high altitudes there still exist some cases where therelative humidity is close to 100%. Consequently, theeffect of humidity on backscatter should not be ignored,especially for aerosols near the ground.

The percentage occurrence of humidity at 1 km isplotted in the form of histogram in Fig. 7. Also plottedin Fig. 7 are the ratios of backscattering function at agiven relative humidity to the backscattering functionat 0% relative humidity, using the Cress spring averageaerosol size distribution with two aerosol materials:(NH i)2S&1X and NaCl. The deliquescence starts at arelative humidity equal to -77 and 82% for NaCl and

(NH4j)2S0 4, respectively. The ratio of the backscat-tering functions for (NH4 )2 SO4 drops down to <1 beforeit increases and gradually reaches values of >1 at a rel-ative humidity of >95%. This surprising phenomenonis due to the fact that the refractive index of dry(NH 4 )2 SO4 is -1.98, but that of H2 0 is only -1.18.Although the absorption of water after passing thedeliquescent point increases the cross section of theparticles, the decrease in refractive index plays a moredominant role, resulting in a decrease in backscatteringfunction. The behavior of NaCl aerosols is less unex-pected, showing a large change in backscattering func-tion following the same change in relative humidity ina humid environment.

IV. Effects of Temperature Change on Co 2

When the ambient temperature changes, the originalequilibrium between the water vapor pressure above thesurface of the liquid aerosols and the ambient watervapor pressure is destroyed. Water vapor will evapo-rate or condense until a new equilibrium has been es-tablished. In this study, we have used the variation ofwater vapor pressure with temperature above the sur-face of (NH4 )2SO4 and NaCl solution as given by theInternational Critical Tables' 2 and interpolated, be-tween the temperature points given there, using theClausius-Clapeyron equation. The variation of watervapor pressure above H2SO4 solution is given by thefollowing expression:

p=exp[A( n 298.15B (x)+ C + DT TC x T1I

(8)

where A (x), B (x), C (x), and D (x) are coefficients andare functions of composition x only. The numericalvalues of these coefficients for thirty-six values of x arelisted by Gmitro and Vermeulen.13 If the initial am-bient humidity and temperature are given, the com-position of the sulfuric acid aerosols can be obtained bysolving the implicit function of x in Eq. (8). If theambient temperature has been charged from T to T',the ambient water concentration remains the same, thenew composition x' can be obtained by solving theequation

P' = exp[A(x)ln 298.15+ + C + D(x)T'X

where p' is given by the ideal gas law

p' = p(T'/T).

(9)

(10)

After the composition of aerosols at new temperatureT' has been determined, the growth factor f can easilybe calculated by Eq. (5). In a similar manner to theeffect of ambient humidity change, the effect of tem-perature change on the aerosol is to shift the positionof the whole aerosol size spectrum without changing itsshape.

The change of ambient temperature not only affectsthe aerosol size but the index of refraction as well. Thedependence of refractive index on temperature is givenby the Lorentz-Lorenz formula5


= constant, (11)(n2 + 2)p

where the density p is a function of both aerosol com-position and temperature. For a slight change intemperature, the corresponding change in index of re-fraction is negligibly small.

Some of the calculated percentage changes in back-scattering function, for X = 10.6 gm, vs the change inambient temperature are plotted in Fig. 8. For NaCland (NH 4 )2 SO4 , the range of temperature change islimited to ±1 0 C. This is because in some cases a largertemperature change may produce supersaturation re-sulting in an unlimited growth of aerosol particles.These figures illustrate that, in general, a decrease intemperature will increase the aerosol backscatteringfunction due to the increase in backscattering cross

20

CD

E

w

EDU2

(/)

E

10

0

-10

section. These figures also show that the change ofbackscattering function due to a change in ambientcondition is negligibly small at low relative humidities.However, when the relative humidity is 90% or higher,the change in the backscattering function may reachmore than 100% for a merely 10 C change in tempera-ture. This is, of course, arising because a small tem-perature change under these conditions brings the at-mosphere close to 100% relative humidity when almostunlimited growth may occur. The plotted curves alsodemonstrate that the smaller the aerosol particles andthe lower the initial ambient temperature, the larger thebackscatter change corresponding to the same ambienttemperature change. The change of backscatter alsodepends on the optical and physical properties of theaerosol material under consideration.

TEMPERATURE CHANGE (DEG)

(a)

90 I I I I I I I I I I I0

80 - rmQ 05 pm

70 --- rm=0.5 pm _rm 50 Lm

60

50

410

30

20

10

-10 R.H. 60%0 15'C

-20 0 25 C 8-30 _ I I I I I I I I

-6 -5 -4 -3 -2 - 0 1 2 3 4 5 6TEMPERATURE CHANGE (DEG)

(b)

270 - I I I250 0 -_ -230 _- r 5 p _

>210 - --- rm=5. pm -

-190 - \

tD 170 ° 15'CLoCE 150 0 251C

A 130

a 110

c: 30E 70L-)CO 5Q

C-) 30E NaCIM 10

R.H. 90%

-30 -

-50-2 -1 0 1 2

TEMPERATURE CHANGE (DEG)

(c)

310290

270~~~~~~~~~r, _ 0 m .05 pm _270- m.5

if

250 --- rm, 05_ 2 3 0 _ l - r 5.0 pm

210CD10- 0 0151C

E 170 0 25C

(2 150

1 30

-110 -

-0 -50

-2 )2 S 14(2~~~~~~d

1 0 R.H. 90%-10-30-50

-2 -1 0 1 2TEMPERATURE CHANGE (DBEG)

(d)

Fig. 8. Percentage /3 co2 change vs temperature change for lognormal aerosol size distributions with mode radii equal to 0.05, 0.5, and 5.0,4m at initial temperatures of 15 and 250 C: (a) H2 SO4 aerosols at relative humidity 20%; (b) H2SO4 aerosols at relative humidity 60%; (c) NaCl

aerosols at relative humidity 90%; (d) (NH4 )2 SO4 aerosols at relative humidity 90%.


IV. Conclusions

The effects of changes in CO2 wavelength, ambienthumidity, and temperature on the backscatteringfunction have been examined in detail. It has beenfound that, except for the important case of (NH4)2SO4containing aerosols, the variation of the backscatteringfunction co2 with CO2 wavelength is not significant.For (NH,1)2SOt containing aerosols, a change in CO2wavelength may cause an order of magnitude change in1C02 for aerosols consisting of relatively large numbersof small particles. It is, therefore, expected that thewater soluble component of tropospheric aerosols maybe identified by the strong CO2 wavelength dependenceof the dCo0. A stronger backscatter signal from theseaerosols can be obtained if we choose wavelengths of thelaser beam close to the lower end of the CO, laserwavelength range.

The effect of ambient humidity and temperaturechanges on the backscattering function depends mainlyon the relative humidity. At low humidities, less thanthat required for deliquescence, the change of ambienttemperature and humidity has no effect on dCo2.However, at high relative humidities, both temperatureand humidity can influence the atmospheric back-scatter. The smaller the aerosol size, the lower theambient temperature, and the higher the ambient hu-midity, the larger will be the change in backscatteringfunction produced in response to the same set ofchanges in ambient conditions. Consequently, even inthe absence of fogs and clouds, a relatively large tem-poral and spatial variation of co2 can be observed inthe first few kilometers above the surface of the earthdue to the large variations both in aerosol characteristicsand ambient conditions. This modeling conclusion is

in agreement with the characteristics of 13 co for the firstfew kilometers of the atmosphere as presented in ourprevious paper.

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This work was supported by NASA Marshall SpaceFlight Center under contract NAS8-34427. We aregrateful to J. D. Bilbro, W. D. Jones, and E. A. Weaverof NASA-MSFC for discussions on various aspects ofthis work.

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