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Atmospheric absorption models for the millimeter wave range [Elektronische Ressource] / von Thomas Kuhn

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Atmospheric Absorption Models for
the Millimeter Wave Range
Thomas Kuhn
Universit at Bremen 2003Atmospheric Absorption Models for
the Millimeter Wave Range
Vom Fachbereich fur Physik und Elektrotechnik
der Universit at Bremen
zur Erlangung des akademischen Grades eines
Doktor der Naturwissenschaften (Dr. rer. nat.)
genehmigte Dissertation
von
Dipl.-Phys. Thomas Kuhn
aus Basel
1. Gutachter: Prof. Dr. K. F. Kun zi
2. Gutachter: Prof. Dr. J. Bleck-Neuhaus
Eingereicht am: 07.04.2003
Tag des Promotionskolloquiums: 12.05.2003Contents
Abstract 3
Zusammenfassung 5
Glossary 7
Prolog 11
Acknowledgment 13
List of Publications 15
1 Introduction 17
2 Theoretical Aspects of Radiative Transfer in the STHz Spectral Range 21
2.1 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Spectral Line Absorption Theory . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Line Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.2 Line Shape Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.3 Absorption Coe cient in the Impact Approximation . . . . . . . . . . 32
2.2.4 Water Vapor Absorption in the Quasi-static Approximation . . . . . . 36
3 Atmospheric Absorption Models 41
3.1 Oxygen Absorption in theSTHz Frequency Range . . . . . . . . . . . . . . . 42
3.1.1 Comparison of Oxygen Absorption Models . . . . . . . . . . . . . . . 46
3.2 Nitrogen Absorption in theSTHz Frequency Range . . . . . . . . . . . . . . 56
3.2.1 Common Atmospheric Absorption Models . . . . . . . . . . . . . . . . 59
3.3 Summary of the Dry Air Absorption . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Water Vapor Absorption Models . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.1 Resonant Line Absorption Comparison . . . . . . . . . . . . . . . . . . 62
3.4.2 Empirical Far Wing Absorption Comparison . . . . . . . . . . . . . . 64
3.4.3 Impact of Model Di erences . . . . . . . . . . . . . . . . . . . . . . . . 68
4 AAM02 – A new Water Vapor Absorption Model 73
4.1 Water Vapor Absorption Measurements . . . . . . . . . . . . . . . . . . . . . 75
4.2 Spectral Line Absorption Contributions . . . . . . . . . . . . . . . . . . . . . 78
4.2.1 Rescaling of Pressure Broadening Parameters . . . . . . . . . . . . . . 79
4.2.2 Spectral Line Catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 Continuum Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 Discussion of the Continuum Parameter Sets . . . . . . . . . . . . . . 90
4.4 Parameter Set of theAAM02 Water Vapor Absorption Model . . . . . . . . 98
i4.5 Comparison of AAM02 with other Models . . . . . . . . . . . . . . . . . . . 100
5 Comparison of Absorption Models with Atmospheric Measurements 107
5.1 ARM Ground Based Radiometer Measurements . . . . . . . . . . . . . . . . . 107
5.1.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 AMSU-B Data of the Lindenberg Area . . . . . . . . . . . . . . . . . . . . . . 125
5.3 POLEX Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6 Conclusion 137
A Physical Constants and Units 141
A.1 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.2 Unit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.2.1 Number Density Unit Amagat . . . . . . . . . . . . . . . . . . . . . . 141
A.2.2 Lennard-Jones Potential . . . . . . . . . . . . . . . . . . . . . . . . . . 142
A.2.3 Mixing Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
A.2.4 Absorption Unit Decibel and Neper . . . . . . . . . . . . . . . . . . . 145
B Atmospheric Structure 147
B.1 Structure of the Model Atmospheres . . . . . . . . . . . . . . . . . . . . . . . 147
B.1.1 ECMWF Pro les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C Line Shape Function 153
C.1 Derivation of the Spectral Density Function . . . . . . . . . . . . . . . . . . . 153
C.1.1 Approximations Used to Derive the Spectral Density Function . . . . 154
D Common Absorption Models 157
D.1 Oxygen Absorption Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
D.1.1 O -MPM93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1572
D.1.2 O -85-O -MPM92 . . . . . . . . . . . . . . . . . . . . . . . . . 1592 2
D.1.3 O -PWR98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1602
D.1.4 O -PWR93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1612
D.1.5 O -PWR88 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1612
D.2 Water Vapor Absorption Models . . . . . . . . . . . . . . . . . . . . . . . . . 164
D.2.1 H O-MPM87 Water Vapor Absorption Model . . . . . . . . . . . . . 1642
D.2.2 H O-89 Water Vapor Absorption Model . . . . . . . . . . . . . 1662
D.2.3 H O-MPM93 Water Vapor Absorption Model . . . . . . . . . . . . . 1682
D.2.4 H O-CP98 Water Vapor Absorption Model . . . . . . . . . . . . . . . 1712
D.2.5 H O-PWR98 Water Vapor Absorption Model . . . . . . . . . . . . . 1722
E Continuum Parameter Set 175
E.1 Laboratory Measurements of Water Vapor Absorption . . . . . . . . . . . . . 175
E.2 Fit of the Continuum Parameter Sets. . . . . . . . . . . . . . . . . . . . . . . 177
E.3 Comparison of Measurements with Model Calculations . . . . . . . . . . . . . 184
F Comparison of Absorption Models with Data 187
F.1 ARM Ground Based Radiometer Measurements . . . . . . . . . . . . . . . . . 187
F.1.1 Population Mean Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
F.1.2 Comparison Test with Westwater et al. . . . . . . . . . . . . . . . . . 188
F.2 AMSU-B Data of the Lindenberg Area . . . . . . . . . . . . . . . . . . . . . . 205
F.3 POLEX Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
iiG Bibliography 225
iiiivList of Figures
2.1 Einstein coe cients for the induced emission ( B ) and absorption (B ) as21 12
well as for the spontaneous emission (A ). E and E denote the energy21 low up
levels of the transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Radiativetransferalongthelineofsight(LOS)ofthesensor. TheSchwarzschild
equation considers the radiation budget of a small volume dV = dAds at a
pointP on the line of sight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Example of an integrated intensity calculation for a cloud-free mid-latitude
summer atmosphere, consisting of oxygen, nitrogen, and water vapor. A nadir
viewing geometry with a platform altitude of 830km is assumed. The cal-
culation is performed for di erent frequencies up to 400GHz. The inten-
sity unit is thermodynamic brightness temperature T with the de nitionB
I (S )=B (T ) (see Equation (2.12)). . . . . . . . . . . . . . . . . . . . . . 25 b B
2.4 Example of a transmission calculation for a cloud-free mid-latitude summer
atmosphere consisting of oxygen, nitrogen, and water vapor. A nadir viewing
geometry with a platform altitude of 830km is assumed. The calculation is
performed for dierent frequencies up to 400GHz. . . . . . . . . . . . . . . . 27
2.5 ExampleofaVanVleck–Weisskopflineshapefunctionwithcuto ( VVWC(,))j
andwithoutcuto ( VVW(,))cuto . Thedashedbluelineisthe VVWC(,)j j
line shape with a cuto frequency of 750GHz and the solid red line is the
VVW(,) line shape. The line center frequency of the 1 1 transitionj 1,0 0,1
is =556.9GHz. The atmospheric state is from a zonal mean mid-latitudej
summer atmosphere around 6km: T=262K, P =500hPa (Kneizys et al.,tot
1996). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Example of a Van Vleck–Weisskopf (VVW), Voigt (V) and Doppler (D) line
shape function. The line center frequency of the 1 1 transition is1,0 0,1
556.9GHz. The atmospheric state is from a mid-latitude summer atmosphere
(Kneizys et al., 1996). Plot (a) shows simultaneously the VVW (solid red)
and V (dashed blue) pro les around 5km ( T=267K, P =554hPa). Plot (b)tot
shows the VVW (solid red), V (dashed blue), and D (dashed-dotted green)
pro les around 50km ( T=276K, P =1hPa). . . . . . . . . . . . . . . . . . 36tot
2.7 Farwinglinecouplingfunctionˆ forH O–H O(leftplot)andH O–N (rightkl 2 2 2 2
plot)accordingtoTipping and Ma (1995). Thefrequencyisrelativetotheline
center frequency of water vapor transitions. (Figures adapted from Tipping
and Ma (1995).) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.8 Far wing H O–N absorption features calculated according to Tipping and Ma2 2
(1995). (Figure adapted from Tipping and Ma (1995)).. . . . . . . . . . . . . 39
v6
163.1 Energy level triplet structure of molecular oxygen O . The molecular rota-28
tionangularmomentumisdenotedbyNwhileJisthetotalangularmomentum
including the spin. The solid arrows mark the transitions which build up the
60GHz band plus the remote line at 118GHz. The dashed arrows denote the
SMMW lines which connect adjacent triplets. Each triplet is labeled by the
rotational quantum number N. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 In uence of line coupling on the 60GHz band of oxygen. The solid line shows
the absorption calculated with line coupling (Y = 0) and the dashed linej
without line coupling. The absorption is calculated for a pressure of 1000hPa
and a temperature of 293.7K. The calculation is performed with the updated
version of the Rosenkranz (1993) model. . . . . . . . . . . . . . . . . . . . . . 44
3.3 Line strength ratios calculated from theory with the rotational constant of
B=43.100543GHz (Amano and Hirota, 1974). The ratio is calculated with
respect to the 3+ and 3 transitions at temperatures of 300K and 200K,
respectively. The circles and diamonds denote the ratios (S /S ) at aN 3
temperature of 300K and the triangles and squares denote the same ratios at
a temperature of 200K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Relative dierence in total simulated absorption for the frequency range of
40-70GHz. Considered absorbers are water vapor (H O-PWR98, Rosenkranz2
(1998)), nitrogen (N -MPM93, Liebe et al. (1993)), ozone (HITRAN96, Roth-2
manetal.(1998))andoxygen(O -PWR98asreferencemodel)asatmospheric2
constituents. Using di erent oxygen absorption models, the relative dierence
intotalabsorptioniscalculatedaccordingtoEquation(3.10)withO -PWR982
as reference oxygen model. The atmospheric pro le used is the mean pro le of
thereducedECMWFatmosphericpro lesample(seeAppendixBand Cheval-
lier (2001)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Simulatedbrightnesstemperatures,T ,fortheAMSU-AchannelregionaroundB
60GHz, using di erent oxygen absorption models. The upper left plot shows
theabsolutevaluesofT ,consideringwatervapor(H O-PWR98, Rosenkranz2B
(1998)),nitrogen(N -MPM93, Liebe et al.(1993)),andoxygen(O -MPM93)2 2
as atmospheric constituents. The dots and vertical bars show the mean and
the two standard deviation margin of T for the 77 atmospheric pro les (seeB
Appendix B) of the reduced ECMWF pro le set of Chevallier (2001). The
upper right and the lower two plots show the mean and two standard devia-
tion di erences between the T values using identical H O and N absorption2 2B
modelsintheradiativetransfercalculationbutdi erentO absorptionmodels.2
O -MPM93 is taken as the reference oxygen absorption model. The AMSU-2
A characteristics are neglected in this calculation. The surface emissivity is
generally set to 0.95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6 Relative di erence in total simulated absorption for the frequency range of 70-
300GHz. Considered absorbers are water vapor (H O-PWR98, Rosenkranz2
(1998)), nitrogen (N -MPM93, Liebe et al. (1993)), ozone (HITRAN96 Roth-2
man et al.(1998))andoxygen(O -PWR98istakenasthereferencemodel)as2
atmospheric constituents. Using dierent oxygen absorption models, the rel-
ative di erence in total absorption is calculated according to Equation (3.10)
with O -PWR98 as reference oxygen model. The atmospheric pro le used2
is the mean pro le of the reduced ECMWF atmospheric pro le sample (see
Appendix B and Chevallier (2001)). . . . . . . . . . . . . . . . . . . . . . . . 51
vi