Lecture 10. Temperature Lidar (1)

How to measure temperature?

Review of Techniques for TemperatureMeasurements

Doppler Technique for Temperature andWind Measurements

Resonance Fluorescence Na Doppler Lidar

Summary

How to Measure Temperature ?

Doppler Technique - Doppler broadening (not only for Na,K, and Fe, but also for Rayleigh scattering, as long asDoppler broadening dominate and can be detected)

Boltzmann Technique - population ratio (not only for Fe,but also for molecular spectroscopy in optical remotesensing and rotational Raman lidar)

Integration Technique (Rayleigh or Raman) - integrationlidar technique using ideal gas law and assuming hydrostaticequilibrium (not only for modern lidar, but also for cwsearchlight and rocket falling sphere - some way tomeasure atmosphere number density)

Rotational Raman Technique - temperature dependenceof population ratio, similar to Boltzmann technique

Use temperature-dependent effects or phenomena

Doppler Technique

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Doppler Spectrum (Width and Shift) Temperature and Radial Wind

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= 1vRc

=

vR

= 0 =

r k

r v = 0

v cos

cDrms = 0

c

kBT

M=1

0

kBT

M=

kBT

M 02

Boltzmann Technique

Atomic Fe Energy Level

z5F0

a5D

3d64s4p

3d6 4s2

J'=1J'=2J'=3J'=4

J'=5

J=0J=1J=2J=3

J=4

372nm

100%

374nm

91%

368nm

9%

E 416cm 1

[Gelbwachs, 1994; Chu et al., 2002]

P2(J = 3)

P1(J = 4)=

Fe (374)

Fe (372)

=g2g1exp( E kBT )

Maxwell-Boltzmann Distributionin Thermal-dynamic Equilibrium

T =E / kB

lng2g1

P1P2

P1, P2 -- Fe populationsg1, g2 -- DegeneracykB -- Boltzmann constantT -- Temperature

Population Ratio Temperature

Rayleigh Integration Technique

T(z0) - Seeding Temperature; - number densityR - gas constant for dry air; g - gravitational acceleration

Lidar Backscatter Ratio Relative Density Temperature (at different altitudes) (Rayleigh)

+

Hydrostatic Equation

dP = gdz

T (z) = T (zo)(zo)

(z) +

1

R g(r)drz

zo (r)

(z)

Seeding

Temperature

Relative

Density

Ideal Gas Law

RTP =

Rotation Raman Technique

Temperature can be derived from the ratio of two pureRotational Raman line intensities. This is essentially the sameprinciple as Boltzmann temperature technique!

V=0, J=0

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20

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60

80

100

120

MSIS90 Temperature

Temperature (K)

Alt

itude

(km

)

Troposphere

Stratosphere

Mesosphere

Thermosphere

Mesopause

Stratopause

Tropopause

Airglow & Meteoric LayersOH, O, Na, Fe, K, CaPMC

OzonePSC

Temperature Techniques 75-120km: resonance

fluorescence Dopplertechnique (Na, K, Fe) &Boltzmann technique (Fe,OH, O2)

30-90km: Rayleighintegration technique &Rayleigh Doppler technique

Below 30 km: scatteringDoppler technique andRaman (Boltzmann andintegration) technique

Boundary layer: DIAL,HSRL, Rotational Raman

AerosolsClouds

Doppler Technique to MeasureTemperature and Wind

Doppler effect is commonly experienced by movingparticles, such as atoms, molecules, and aerosols. It is theapparent frequency change of radiation or wave that isperceived by the particles moving relative to the source ofthe radiation or wave. This is called Doppler shift.

Doppler frequency shift is proportional to the radialvelocity along the line of sight (LOS) of the radiation -

= 0

r k

r v

where 0 is the radiation frequency at rest, is the shiftedfrequency, k is the wave vector of the radiation (k=2 / ), andv is the particle velocity.

= 0 =

r k

r v = 0

v cos

c

Doppler Technique to MeasureTemperature and Wind

exp(Mvz

2

2kBT)dvz = exp

Mc2( 0)2

2 02kBT

c

0

d

Due to particles’ thermal motions in the atmosphere, thedistribution of perceived frequencies for all particles mirrorstheir velocity distribution. According to the Maxwellianvelocity distribution, the perceived frequencies by movingparticles has a Gaussian lineshape, given by

The peak is at = 0 and the rmswidth is give by

rms = 0

c

kBT

M=1

0

kBT

M

Doppler Shift For Wind Measurement

Same direction

- red shift

Opposite direction

- blue shift

= 0 =

r k

r v = 0

v cos

c

r v

r v

r k

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The velocity measurements of lidar, radar, and sodar allbase on the Doppler shift principle !

Doppler Broadening For Temperature

rms = 0

c

kBT

M=1

0

kBT

M

T rms

M rms

0

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AerosolScattering

MolecularScattering

3-30 MHz

1 GHz

Doppler Effect in Na D2 LineResonance Fluorescence

Na D2 absorption linewidthis temperature dependent

Na D2 absorption peak freqis wind dependent

Na Atomic Energy Levels

Na Atomic Parameters

Na Spectroscopy

a b c

c =( a+ b)/2

Metrics: Scanning Technique

NNa( ,z ) =PL( ) t

hc

eff ( )nNa(z ) z( )

A

4 z 2

( )Ta

2( )E2( ,z )G(z )( )

NR ( ,zR ) =PL ( ) t

hc

R ( , )nR (zR ) z( )

A

zR2

( )Ta

2( ,zR )G(zR )( )

eff ( ,z ) =C(z )

E2( ,z )

NNa( ,z )

NR( ,zR )

C(z ) = R( , )nR(zR )

nNa(z )

4 z 2

zR2where

Scanning Na Lidar Results

Metrics: 2-Frequency Technique

Metrics: 3-Frequency Technique

Na Doppler Lidar Calibration

Summary The key point to measure temperature and wind is to find

and use temperature-dependent and wind-dependent effectsand phenomena to make measurements.

Doppler technique utilizes the Doppler effect (frequencyshift and linewidth broadening) by moving particles to inferwind and temperature information.

It is widely applied in lidar, radar and sodar technique aswell as passive optical remote sensing.

Resonance fluorescence Doppler lidar technique appliesscanning or ratio technique to infer the temperature andwind from the Doppler spectroscopy, while the Dopplerspectroscopy is inferred from intensity ratio at differentfrequencies.