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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1
1.5
2
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nte
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nit)
Frequency Offset (Arb. Unit)
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Frequency Offset (Arb. Unit)
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.