Atmospheric Absorption Models for the Millimeter Wave Range

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(1)Atmospheric Absorption Models for the Millimeter Wave Range. Thomas Kuhn. Universität Bremen 2003.

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(3) Atmospheric Absorption Models for the Millimeter Wave Range. Vom Fachbereich f¨ ur Physik und Elektrotechnik der Universität Bremen. zur Erlangung des akademischen Grades eines. Doktor der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation. von Dipl.-Phys. Thomas Kuhn aus Basel. 1. Gutachter: 2. Gutachter:. Prof. Dr. K. F. K¨ unzi Prof. Dr. J. Bleck-Neuhaus. Eingereicht am: Tag des Promotionskolloquiums:. 07.04.2003 12.05.2003.

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(5) Contents 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 2.1 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Spectral Line Absorption Theory . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Line Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Line Shape Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Absorption Coefficient in the Impact Approximation . . . . . . . . . 2.2.4 Water Vapor Absorption in the Quasi-static Approximation . . . . . 3 Atmospheric Absorption Models 3.1 Oxygen Absorption in the STHz Frequency Range . 3.1.1 Comparison of Oxygen Absorption Models . 3.2 Nitrogen Absorption in the STHz Frequency Range 3.2.1 Common Atmospheric Absorption Models . . 3.3 Summary of the Dry Air Absorption . . . . . . . . . 3.4 Water Vapor Absorption Models . . . . . . . . . . . 3.4.1 Resonant Line Absorption Comparison . . . . 3.4.2 Empirical Far Wing Absorption Comparison 3.4.3 Impact of Model Differences . . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 4 AAM02 – A new Water Vapor Absorption Model 4.1 Water Vapor Absorption Measurements . . . . . . . . . . . . . 4.2 Spectral Line Absorption Contributions . . . . . . . . . . . . . 4.2.1 Rescaling of Pressure Broadening Parameters . . . . . . 4.2.2 Spectral Line Catalogs . . . . . . . . . . . . . . . . . . . 4.3 Continuum Parameter Estimation . . . . . . . . . . . . . . . . 4.3.1 Discussion of the Continuum Parameter Sets . . . . . . 4.4 Parameter Set of the AAM02 Water Vapor Absorption Model i. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . . . . .. . . . . . . .. . . . . . .. 21 21 26 27 28 32 36. . . . . . . . . .. 41 42 46 56 59 60 62 62 64 68. . . . . . . .. 73 75 78 79 79 86 90 98.

(6) 4.5. Comparison of AAM02 with other Models . . . . . . . . . . . . . . . . . . . 100. 5 Comparison of Absorption Models with Atmospheric Measurements 5.1 ARM Ground Based Radiometer Measurements . . . . . . . . . . . . . . . 5.1.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 AMSU-B Data of the Lindenberg Area . . . . . . . . . . . . . . . . . . . . 5.3 POLEX Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. . . . .. 6 Conclusion. 107 107 121 125 130 137. A Physical Constants and Units A.1 Constants . . . . . . . . . . . . . . . . . . . A.2 Unit Conversion . . . . . . . . . . . . . . . A.2.1 Number Density Unit Amagat . . . A.2.2 Lennard-Jones Potential . . . . . . . A.2.3 Mixing Ratios . . . . . . . . . . . . . A.2.4 Absorption Unit Decibel and Neper. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 141 141 141 141 142 143 145. B Atmospheric Structure 147 B.1 Structure of the Model Atmospheres . . . . . . . . . . . . . . . . . . . . . . . 147 B.1.1 ECMWF Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 D.1 Oxygen Absorption Models . . . . . . . . . . . . . . . D.1.1 O2 -MPM93 . . . . . . . . . . . . . . . . . . . . D.1.2 O2 -MPM85-O2 -MPM92 . . . . . . . . . . . . D.1.3 O2 -PWR98 . . . . . . . . . . . . . . . . . . . . D.1.4 O2 -PWR93 . . . . . . . . . . . . . . . . . . . . D.1.5 O2 -PWR88 . . . . . . . . . . . . . . . . . . . . D.2 Water Vapor Absorption Models . . . . . . . . . . . . D.2.1 H2 O-MPM87 Water Vapor Absorption Model D.2.2 H2 O-MPM89 Water Vapor Absorption Model D.2.3 H2 O-MPM93 Water Vapor Absorption Model D.2.4 H2 O-CP98 Water Vapor Absorption Model . . D.2.5 H2 O-PWR98 Water Vapor Absorption Model. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. 157 157 157 159 160 161 161 164 164 166 168 171 172. 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 F.1 ARM Ground Based Radiometer Measurements F.1.1 Population Mean Test . . . . . . . . . . F.1.2 Comparison Test with Westwater et al. F.2 AMSU-B Data of the Lindenberg Area . . . . . F.3 POLEX Campaign . . . . . . . . . . . . . . . . ii. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 187 187 187 188 205 214.

(7) G Bibliography. 225. iii.

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(9) List of Figures 2.1. 2.2. 2.3. 2.4. Einstein coefficients for the induced emission (B21 ) and absorption (B12 ) as well as for the spontaneous emission (A21 ). Elow and Eup denote the energy levels of the transition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22. Radiative transfer along the line of sight (LOS) of the sensor. The Schwarzschild equation considers the radiation budget of a small volume dV = dA · ds at a point P on the line of sight. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24. 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 830 km is assumed. The calculation is performed for different frequencies up to 400 GHz. The intensity unit is thermodynamic brightness temperature TB with the definition Iν (S b ) = Bν (TB ) (see Equation (2.12)). . . . . . . . . . . . . . . . . . . . . .. 25. 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 830 km is assumed. The calculation is performed for different frequencies up to 400 GHz. . . . . . . . . . . . . . . .. 27. 2.5. Example of a Van Vleck–Weisskopf line shape function with cutoff (V V W C(ν, νj )) and without cutoff (V V W (ν, νj )) cutoff. The dashed blue line is the V V W C(ν, νj ) line shape with a cutoff frequency of 750 GHz and the solid red line is the V V W (ν, νj ) line shape. The line center frequency of the 11,0 ← 10,1 transition is νj =556.9 GHz. The atmospheric state is from a zonal mean mid-latitude summer atmosphere around 6 km: T =262 K, Ptot =500 hPa (Kneizys et al., 1996). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35. 2.6. Example of a Van Vleck–Weisskopf (V V W ), Voigt (V ) and Doppler (D) line shape function. The line center frequency of the 11,0 ← 10,1 transition is 556.9 GHz. The atmospheric state is from a mid-latitude summer atmosphere (Kneizys et al., 1996). Plot (a) shows simultaneously the V V W (solid red) and V (dashed blue) profiles around 5 km (T =267 K, Ptot =554 hPa). Plot (b) shows the V V W (solid red), V (dashed blue), and D (dashed-dotted green) profiles around 50 km (T =276 K, Ptot =1 hPa). . . . . . . . . . . . . . . . . .. 36. Far wing line coupling function χ ˆkl for H2 O–H2 O (left plot) and H2 O–N2 (right plot) according to Tipping and Ma (1995). The frequency is relative to the line center frequency of water vapor transitions. (Figures adapted from Tipping and Ma (1995).) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38. Far wing H2 O–N2 absorption features calculated according to Tipping and Ma (1995). (Figure adapted from Tipping and Ma (1995)). . . . . . . . . . . . . .. 39. 2.7. 2.8. v.

(10) 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. Energy level triplet structure of molecular oxygen 168 O2 . The molecular rotation angular momentum is denoted by N while J is the total angular momentum including the spin. The solid arrows mark the transitions which build up the 60 GHz band plus the remote line at 118 GHz. The dashed arrows denote the SMMW lines which connect adjacent triplets. Each triplet is labeled by the rotational quantum number N . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42. Influence of line coupling on the 60 GHz band of oxygen. The solid line shows the absorption calculated with line coupling (Yj 6= 0) and the dashed line without line coupling. The absorption is calculated for a pressure of 1000 hPa and a temperature of 293.7 K. The calculation is performed with the updated version of the Rosenkranz (1993) model. . . . . . . . . . . . . . . . . . . . . .. 44. Line strength ratios calculated from theory with the rotational constant of B=43.100543 GHz (Amano and Hirota, 1974). The ratio is calculated with respect to the 3+ and 3− transitions at temperatures of 300 K and 200 K, respectively. The circles and diamonds denote the ratios (SN ∓ /S3∓ ) at a temperature of 300 K and the triangles and squares denote the same ratios at a temperature of 200 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46. Relative difference in total simulated absorption for the frequency range of 40-70 GHz. Considered absorbers are water vapor (H2 O-PWR98, Rosenkranz (1998)), nitrogen (N2 -MPM93, Liebe et al. (1993)), ozone (HITRAN96, Rothman et al. (1998)) and oxygen (O2 -PWR98 as reference model) as atmospheric constituents. Using different oxygen absorption models, the relative difference in total absorption is calculated according to Equation (3.10) with O2 -PWR98 as reference oxygen model. The atmospheric profile used is the mean profile of the reduced ECMWF atmospheric profile sample (see Appendix B and Chevallier (2001)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48. Simulated brightness temperatures, TB , for the AMSU-A channel region around 60 GHz, using different oxygen absorption models. The upper left plot shows the absolute values of TB , considering water vapor (H2 O-PWR98, Rosenkranz (1998)), nitrogen (N2 -MPM93, Liebe et al. (1993)), and oxygen (O2 -MPM93) as atmospheric constituents. The dots and vertical bars show the mean and the two standard deviation margin of TB for the 77 atmospheric profiles (see Appendix B) of the reduced ECMWF profile set of Chevallier (2001). The upper right and the lower two plots show the mean and two standard deviation differences between the TB values using identical H2 O and N2 absorption models in the radiative transfer calculation but different O2 absorption models. O2 -MPM93 is taken as the reference oxygen absorption model. The AMSUA characteristics are neglected in this calculation. The surface emissivity is generally set to 0.95. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50. Relative difference in total simulated absorption for the frequency range of 70300 GHz. Considered absorbers are water vapor (H2 O-PWR98, Rosenkranz (1998)), nitrogen (N2 -MPM93, Liebe et al. (1993)), ozone (HITRAN96 Rothman et al. (1998)) and oxygen (O2 -PWR98 is taken as the reference model) as atmospheric constituents. Using different oxygen absorption models, the relative difference in total absorption is calculated according to Equation (3.10) with O2 -PWR98 as reference oxygen model. The atmospheric profile used is the mean profile of the reduced ECMWF atmospheric profile sample (see Appendix B and Chevallier (2001)). . . . . . . . . . . . . . . . . . . . . . . .. 51. vi.

(11) 3.7. Simulated brightness temperatures, TB , for a ground based radiometer, using different oxygen absorption models. The radiative transfer calculation considers water vapor (H2 O-PWR98, Rosenkranz (1998)), nitrogen (N2 -MPM93, Liebe et al. (1993)) and oxygen (O2 -PWR98, reference model) as atmospheric constituents. The dots and vertical bars show the mean and the two standard deviation margin of the brightness temperature differences, ∆TB , for the 77 atmospheric profiles (see Appendix B) of the reduced ECMWF profile set of Chevallier (2001). The additionally considered oxygen absorption models are O2 -MPM93, O2 -MPM92 (without the cutoff of Equation (3.11)), O2 MPM87, and O2 -PWR88. The radiometer characteristics are neglected in this calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52. Ratio of simulated total absorption around the 118.75 GHz oxygen line for the two O2 -PWR98 and O2 -PWR93 oxygen absorption models (ratio = αtot (O2 -PWR93) / αtot (O2 -PWR98)). The water vapor absorption is calculated with H2 O-PWR98 while the nitrogen absorption is calculated with N2 -MPM93. For the absorption of ozone the HITRAN96 (Rothman et al., 1998) line catalog is used. The 77 atmospheric profiles are taken from the reduced ECMWF sample (Chevallier , 2001) as described in Appendix B. The solid line is the mean ratio while the two grey shaded regions indicate the 1σ and 2σ range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53. Brightness temperatures for the Odin 118 GHz channel, using different oxygen absorption models. The individual plots show the ratio of the calculated brightness temperature with one O2 model to the TB using the reference model of O2 -PWR98. The absorption of water vapor is calculated with H2 O-PWR98 and that of nitrogen with N2 -MPM93 (see below for details). The 77 atmospheric profiles are taken from the reduced ECMWF sample (Chevallier , 2001) as described in Appendix B. The dots are the mean ratios while the bars indicate the 2σ range for the 77 profiles. . . . . . . . . . . . . . . . . . .. 53. 3.10 Line coupling parameter at a temperature of 294 K for the individual lines of the 60 GHz band for three different absorption models (O2 -MPM93, O2 PWR93, and O2 -PWR88). The dry air and water vapor partial pressures are pdry =1013 hPa, and e=24.92 hPa, respectively. These values correspond to a zonal mean mid-latitude summer surface condition. The numbers at the top of the plot are the rotational quantum numbers N ±. The abscissa indicates the individual line center frequency. . . . . . . . . . . . . . . . . . . . . . . .. 55. 3.11 Contributions (in percent) from each oxygen line of the 60 GHz band (αN ) to the effective line absorption αl,tot at a frequency of 625 GHz. Since αl,tot is negative at this frequency, positive percent numbers correspond to negative absorption values and vice versa. The contributions from the SMMW lines are summed up at the N=0 point. Mid-latitude zonal mean atmospheric conditions are selected. The abscissa indicates the rotational quantum number N (Pbranch: N −, R-branch: N +) . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57. 3.8. 3.9. vii.

(12) 3.12 Contributions of the different interaction terms to the total N2 -N2 collision induced absorption. The unit of the absorption is chosen as [m−1 Pa−2 ], thus it is pressure independent. The calculation is performed at a temperature of 300 K with the program of Borysow (2001). The notation of the interaction terms is as follows: 3220/3202 is the quadrupole-induced dipole transition component via the trace of the molecule’s polarizability tensor, 5440/5404 is the hexadecapole-induced dipole transition component via the trace of the molecule’s polarizability tensor, 3322 is the quadrupole-induced dipole transition component via the anisotropy of the molecule’s polarizability. . . . . . .. 58. 3.13 absorption of the collision induced absorption models of N2 -BF86 (Borysow and Frommhold , 1986a) (solid black lines), N2 -MPM93 (Liebe et al., 1993) (dashed blue lines), and N2 -PWR93 (Rosenkranz , 1993) (dashed-dotted red lines). The calculation is performed for two different atmospheric pressure levels (Ptot =1000 hPa / T =299 K and 10 hPa / T =235 K). The arrows together with the shadowed areas indicate the range of the N2 -PWR98 and N2 -MPM93 models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. 3.14 Relative difference of the collision induced absorption models of N2 -BF86 (Borysow and Frommhold , 1986a), N2 -MPM93 (Liebe et al., 1993), and N2 PWR93 (Rosenkranz , 1993). The calculation is performed for three different atmospheric pressure levels (Ptot =1000 hPa / T =299 K (black lines), Ptot =100 hPa / T =195 K (red lines), and 10 hPa / T =235 K (blue lines)) with the N2 -BF86 model as the reference model. The dotted lines correspond to the N2 -PWR93 model and the dashed lines to the N2 -MPM93. . . . . . .. 61. 3.15 Comparison of the water vapor line intensity parameter b1 (see Equation (3.22) for the exact definition). The JPL01 values are taken from Pickett et al. (2001). Shown are the differences (in percent) with respect to the HITRAN00. HIT value (Rothman et al., 1998): 100 % × (b1,k − bHIT 1,k )/b1,k . The corresponding parameters of the different models and spectral line catalogs are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . .. 65. 3.16 Comparison of the temperature parameters, b2,k , of the water vapor line intensity (see Equation (3.22) for the exact definition). The JPL01 values are taken from Pickett et al. (2001). Shown is the relative difference in percent with respect to the HITRAN00 (Rothman et al., 1998) value: 100 % × (b2,k − HIT bHIT 2,k )/b2,k . The corresponding parameters of the different models and spectral line catalogs are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65. 3.17 Comparison of the foreign pressure broadening parameters, b3,k , of the water vapor absorption models. Shown is the relative difference in percent with respect to the theoretical value predicted within the CRB approach given in Bauer et al. (1989): 100 % × (b3,k − bCRB )/bCRB . The corresponding param3,k 3,k eters of the different models are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . . . . . . . . . . . . . . . . . . . .. 66. 3.18 Comparison of the self pressure broadening parameters, b4,k , of the water vapor absorption models. Shown is the relative difference in percent with respect to the theoretical value predicted within the CRB approach given in Bauer et al. (1989): 100 % × (b4,k − bCRB )/bCRB . The corresponding parameters of the 4,k 4,k different models and spectral line catalogs are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . . . . . . . . . . . .. 66. viii.

(13) 3.19 Comparison of the self pressure broadening temperature parameters, b5,k , of the water vapor absorption models. Shown is the relative difference in percent with respect to the theoretical value predicted within the CRB approach given in Bauer et al. (1989): 100 % × (b5,k − bCRB )/bCRB . The corresponding 5,k 5,k parameters of the different models and spectral line catalogs are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . .. 67. 3.20 Comparison of the self pressure broadening temperature parameters, b6,k , of the water vapor absorption models. Shown is the relative difference in percent with respect to the theoretical value predicted within the CRB approach given in Bauer et al. (1989): 100 % × (b6,k − bCRB )/bCRB . The corresponding 6,k 6,k parameters of the different models and spectral line catalogs are converted to the H2 O-MPM93 parameterization presented in Equation (3.21). . . . . . . .. 67. 3.21 Maximum relative difference between the absorption models H2 O-PWR98, H2 O-MPM87, H2 O-MPM89, and H2 O-MPM93. The reference model is H2 O-PWR98. The atmospheric profiles are taken from the ECMWF profiles of Chevallier (2001) (see Section B.1.1 in Appendix B). Only profiles with a latitude between 0◦ and 30◦ are considered for this calculation. For profile i = 1, · · · , N and pressure level k the maximum relative difference, δi (Pk ), is calculated according to Equation (3.25). From the ensemble {δi (Pk ), i = 1, · · · , N } the mean, mk , and standard deviation, σk is calculated. The dark line in the plot represents the mean value mk and the shaded area indicates the 1 σk range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 70. 3.22 Maximum relative difference between the absorption models H2 O-PWR98, H2 O-MPM87, H2 O-MPM89, and H2 O-MPM93. The reference model is H2 O-PWR98 (only water vapor is considered as absorber). The atmospheric profiles are taken from the ECMWF profiles of Chevallier (2001) (see Section B.1.1 in Appendix B). Only profiles with a latitude between 30◦ and 65◦ are considered for this calculation. For profile i = 1, · · · , N and pressure level k the maximum relative difference, δi (Pk ), is calculated according to Equation (3.25). From the ensemble {δi (Pk ), i = 1, · · · , N } the mean, mk , and standard deviation, σk is calculated. The dark line in the plot represents the mean value mk and the shaded area indicates the 1 σk range. . . . . . . . . .. 71. 3.23 Maximum relative difference between the absorption models H2 O-PWR98, H2 O-MPM87, H2 O-MPM89,and H2 O-MPM93. The reference model is H2 OPWR98. The atmospheric profiles are taken from the ECMWF profiles of Chevallier (2001) (see Section B.1.1 in Appendix B). Only the profiles with a latitude between 65◦ and 90◦ are considered for this calculation. For profile i = 1, · · · , N and pressure level k the maximum relative difference, δi (Pk ), is calculated according to Equation (3.25). From the ensemble {δi (Pk ), i = 1, · · · , N } the mean, mk , and standard deviation, σk is calculated. The dark line in the plot represents the mean value mk and the shaded area indicates the 1 σk range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 72. 4.1. Water vapor spectral line distribution in the STHz range. The line intensities are given in per cent of the 183 GHz line intensity. The HITRAN00 spectral line catalog is used for the frequency and intensity information. The bars indicate the frequency windows (W1,W2,W3) where only few nearby strong H2 O lines are influencing the total water vapor absorption. . . . . . . . . . . ix. 76.

(14) 4.2. 4.3. 4.4. 4.5. 4.6. 4.7. Ratio of foreign broadening parameters GNf,k2 /Gair f,k for water vapor lines in the STHz range. The data is taken from Bauer et al. (1989) and Gamache et al. (1994). For the theoretically predicted values listed in Bauer et al. (1989), the complex Robert-Bonamy approach (CRB) is used. The dots and solid line at 1.08 are from these predictions while the solid line at 1.11 and the shaded area are from the measurement analysis of Gamache et al. (1994). . . . . . . . . .. 80. Water Vapor self continuum parameter fit result for the full 138-350 GHz data. The H2 O-AAM02 line catalog is used in the line absorption calculation in connection with a Van Vleck–Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91. Water Vapor foreign continuum parameter fit result for the full 138-350 GHz data. The H2 O-AAM02 line catalog is used in the line absorption calculation in connection with a Van Vleck–Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91. Mean and standard deviation of the relative difference between model calculations and measurements. The line catalog used in the line absorption calculation is indicated at the left side. Additionally the line shape is stated in brackets: Van Vleck–Weisskopf (VVW), Van Vleck–Weisskopf with a cutoff of 750 GHz (VVWC). The associated continuum parameter sets for the calculation of the continuum absorption are given in Table 4.6. The symbols indicate the mean value and the horizontal bars the standard deviation of the three subsamples for pure water vapor measurements. The subsamples are defined by the frequency intervals of the laboratory measurements: 130-160 GHz (squares), 170-200 GHz (triangles), and 200-350 GHz (circles). . . . . . . . . .. 94. Mean and standard deviation of the relative difference between model calculations and measurements. The line catalog used in the line absorption calculation is indicated at the left side. Additionally the line shape is stated in brackets: Van Vleck–Weisskopf (VVW), Van Vleck–Weisskopf with a cutoff of 750 GHz (VVWC). The associated continuum parameter sets for the calculation of the continuum absorption are given in Table 4.6. The symbols indicate the mean value and the horizontal bars the standard deviation of the three subsamples for H2 O-N2 measurements. The subsamples are defined by the frequency intervals of the laboratory measurements: 130-160 GHz (squares), 170-200 GHz (triangles), and 200-350 GHz (circles). . . . . . . . . . . . . . . .. 94. Comparison of measured water vapor absorption by Becker and Autler (1946) with different absorption models. The measurements (solid line) are performed for different water vapor densities at normal pressure (1013 hPa) and a temperature of 45◦ C. The absorption models are the three versions of Liebe’s H2 O-MPM model together with the H2 O-PWR98 and H2 O-AAM02 models. The upper four plots show the absolute amount of absorption while the lower four plots show the relative difference between the modeled and measured absorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 x.

(15) 4.8. Mean maximum difference in brightness temperature for six different combinations of three H2 O absorption models (H2 O-MPM93, H2 O-AAM02, H2 OPWR98) and two oxygen absorption models (O2 -PWR98, O2 -MPM93). The atmospheric input is taken from the reduced ECMWF sample of Chevallier (2001) as described in Appendix B. The considered atmospheric constituents are H2 O, N2 , O2 , and O3 (strong O3 at 625.4 GHz is indicated by the arrow). The calculation is performed for the three JEM/SMILES bands (A,B,C) of the planned SMMW limb sounder aboard the international space station ISS (Amano et al., 2001). The instrument’s characteristics are not considered in the calculation of TB . The radiative transfer calculation is performed for four different tangent altitudes from the tropopause up to the stratopause. . . . . 104. 4.9. Mean maximum difference in brightness temperature for six different combinations of three H2 O absorption models (H2 O-MPM93, H2 O-AAM02, H2 OPWR98) and two oxygen absorption models (O2 -PWR98, O2 -MPM93). The atmospheric input is taken from the reduced ECMWF sample of Chevallier (2001) as described in Appendix B. The considered atmospheric constituents are H2 O, N2 , O2 , and O3 . The calculation is performed for band C of MASTER, a polar orbiting MMW/SMMW limb sounder proposed as an ESA Earth Explorer Core Mission (European Space Agency, 2001). The instrument’s characteristics are not considered in the calculation of TB . The radiative transfer calculation is performed for four different tangent altitudes from the tropopause up to the stratopause. A strong water vapor line at 325 GHz lies within this band (indicated by the arrow). The three absorption models use different line broadening parameters for this line. . . . . . . . . . . . . . . 105. 4.10 Mean maximum difference in brightness temperature for six different combinations of three H2 O absorption models (H2 O-MPM93, H2 O-AAM02, H2 OPWR98) and two oxygen absorption models (O2 -PWR98, O2 -MPM93). The atmospheric input is taken from the reduced ECMWF sample of Chevallier (2001) as described in Appendix B. The considered atmospheric constituents are H2 O, N2 , and O2 . The calculation is performed for the five AMSU-B channels (National Oceanic and Atmospheric Administration, 2002; Atkinson, 2001; Saunders et al., 1995) at 89 GHz, 150 GHz, 183.3±1 GHz, 183.3±3 GHz, and 183.3±7 GHz (see Table 5.3). The instrument’s characteristics are not considered in the calculation of TB . The radiative transfer calculation is performed for nadir viewing geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106. 5.1. Comparison of the measured MWR and radiosonde precipitable water vapor (P W V ). The number states the mean and standard deviation of the difference P W V (radiosonde) - P W V (MWR). The filled circles are for the comparison of the corrected radiosonde profiles (see text) while the open triangles are for the original radiosonde profiles. The increase in P W R due to the correction formula is between 6 and 10.5 %. For the estimation of P W V from the MWR data the following formula is used: P W V = 0.0228 + 21.602 · τ23 − 12.804 · τ31 , where τ23 = log ((248.823 − 2.75)/(248.823 − TB (23))) and τ31 = log ((247.813 − 2.75)/(247.813 − TB (31))). . . . . . . . . . . . . . . . . . 109 xi.

(16) 5.2. Jacobi matrix of the water vapor for selected radiosonde profiles with high and low precipitable water vapor. The H2 O profile of the radiosonde is corrected according to the correction formula Equation (5.1). The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to (Pardo et al., 2001b). The temperature dependence of the foreign water vapor continuum term in AAM02 is set to zero. The frequencies correspond to the dual channel MWR radiometer. For the calculation of the Jacobi matrix elements a local increase of 100 % in H2 O volume mixing ratio is assumed. . . 110. 5.3. Comparison of the measured MWR brightness temperature with the Arts model calculation, using radiosonde data input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The numbers state the mean and standard deviation of the brightness temperature difference ∆TB = TB (calc.) − TB (MWR) for the profiles with less than 1 cm precipitable water vapor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. 5.4. Correlation plot for the two MWR channels. The symbols indicate the mean difference ∆TB = TB (calc.) − TB (MWR). The horizontal and vertical bars indicate the standard deviation of the mean ∆TB . The threshold in precipitable water vapor and cloud liquid water are 1.00 cm and 0.0001 cm. The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). In case of AAM02 the foreign continuum temperature coefficient, xair , is set to 1.33 (top), 0.60 (middle), and 0.00 (bottom). The different values for the same symbol are caused by different oxygen absorption models. The number of data points to calculate the means and standard deviations is n = 16. The grey shaded area indicate the assumed calibration uncertainty of 0.3 K. . . . . . . 112. 5.5. Jacobi matrix of the water vapor for selected radiosonde profiles with high and low precipitable water vapor. The H2 O profile of the radiosonde is corrected according to the correction formula Equation (5.1). The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The temperature dependence of the foreign water vapor continuum term in AAM02 is set to zero. The frequencies correspond to the MIR radiometer channels. The left plots show the Jacobi matrix and the right plots show the corresponding H2 O VMR and the altitude grid of the radiosonde profile for the lowermost 5 km. For the calculation of the Jacobi matrix the perturbation is linearly decreasing in altitude. . . . . . . . . . . . 117. 5.6. Comparison of the measured 183.3±1, 3, 7 GHz MIR channel brightness temperatures with the Arts model calculation, using radiosonde data input for the temperature and relative humidity profiles. The absorption models used in the radiative transfer calculation are H2 O-AAM02, updated version of Rosenkranz (1993) (O2 -PWR98), and Liebe et al. (1993) (N2 -MPM93, scaled by 1.29). The numbers state the mean and standard deviation of the brightness temperature difference ∆TB = TB (calc.) − TB (MIR) for the profiles with less than 0.25 cm precipitable water vapor. . . . . . . . . . . . . . . . . . . . . . . . . . 118 xii.

(17) 5.7. Comparison of the measured 220 GHz and 340 GHz MIR brightness temperatures with model calculations, using radiosonde data input for the temperature and relative humidity profiles. The absorption models used in the radiative transfer calculation are H2 O-AAM02, updated version of Rosenkranz (1993) (O2 -PWR98), and Liebe et al. (1993) (N2 -MPM93, scaled by 1.29). The foreign continuum temperature coefficient is set to xf =0.6 in H2 O-AAM02. The numbers state the mean and standard deviation of the brightness temperature difference ∆TB = TB (calc.) − TB (MIR) for the profiles with less than 0.4 cm precipitable water vapor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119. 5.8. Correlation plot for the 220 GHz and 340 GHz MIR channels. The symbols indicate the mean difference ∆TB = TB (calc.) − TB (MIR). The horizontal and vertical bars indicate the standard deviation of the mean ∆TB . The thresholds in precipitable water vapor and cloud liquid water are 0.25 cm and 0.001 mm. The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b) (SN 2 = 1.29). In case of AAM02 the foreign continuum temperature coefficient, xair , is set to 1.33 (top), 0.60 (middle), and 0.00 (bottom). The different values for the same symbol are caused by different oxygen absorption models. The number of data points to calculate the means and standard deviations is n = 12. The grey shaded areas indicate the assumed resulting standard deviation in TB of 3 K. . . . . . . . . . . . . . . . . . . . . . . . . . 123. 5.9. Same as Figure 5.8 but without scaling of the nitrogen absorption (SN 2 = 1.00).124. 5.10 Comparison of the measured AMSU-B channel 16 (top) and 17 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are H2 O-AAM02 (with the corresponding continuum parameters stated in Table 4.9), updated version of Rosenkranz (1993) (O2 -PWR98), and Liebe et al. (1993) (N2 -MPM93). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The calculation for H2 O-AAM02 is performed with a Van Vleck– Weisskopf line shape without cutoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.11 Comparison of the measured AMSU-B channel 18 (top), 19 (middle), and 20 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are H2 O-AAM02 (with the corresponding continuum parameters stated in Table 4.9), updated version of Rosenkranz (1993) (O2 -PWR98), and Liebe et al. (1993) (N2 -MPM93). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The calculation for H2 O-AAM02 is performed with a Van Vleck– Weisskopf line shape without cutoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.12 Comparison of the measured AMSU-B brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are H2 O-AAM02, the updated version of Rosenkranz (1993) (O2 -PWR98), and Liebe et al. (1993) (N2 -MPM93). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The x-axis is the difference of the calculated and measured brightness temperatures and the y-axis the measured brightness temperatures. The numbers state the mean and the standard deviation of ∆TB .129 xiii.

(18) 5.13 Humidity and temperature profiles of the two selected MARSS flights within the POLEX campaign. The left plot shows the water vapor volume mixing ratio, the middle plot the relative humidity with respect to liquid water and the right plot shows the temperature profile. The measured atmospheric profiles are topped by a zonal mean profile of Kneizys et al. (1996) up to 90 km. The additionally shown profiles are from nearby radiosonde launches, these are for the flight A827.1: Ny-˚ Alesund (78.55◦ N/11.56◦ E, 12:00 UTC), Danmarkshavn (76.77◦ N/18.66◦ W, 11:00 and 23:00 UTC), Scoresbysund (70.48◦ N/21.95◦ W, 11:00 and 23:00 UTC) and for the flight 829.7: Bodø (67.25◦ N/14.37◦ E, 12:00 and 23:00 UTC), Ny-˚ Alesund (78.55◦ N/11.56◦ E, 12:00 UTC), Ørland ◦ ◦ (63.70 N/9.60 E, 11:00 UTC). . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.14 Comparison of the measured MARSS brightness temperatures (flight A827.1, filled circles) with those calculated with Arts (lines), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . . . . 133 5.15 Comparison of the measured MARSS brightness temperatures (flight A829.7, filled circles) with those calculated with Arts (lines), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . . . . 133 5.16 Brightness temperatures for the different components of the atmospheric absorption models. The TB calculation is for each absorber individually calculated, ignoring all other absorbers. For the three water vapor absorption components, (lines, self continuum, and foreign continuum) the AAM02 model is used. For the oxygen and nitrogen absorption the updated version of Rosenkranz (1993) (O2 ) and Liebe et al. (1993) (N2 ) is used. The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The atmospheric conditions are taken from the flight A829.7 . . . . . . . . . . . . . . . 134 5.17 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 135 5.18 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 135 A.1 Individual Lennard-Jones potential for different molecular species. The functional form is given in Equation (A.4) and the individual potential parameters are listed in Table A.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 xiv.

(19) B.1 Upper plot: Annual mean tropical temperature profile of Kneizys et al. (1996) for a latitude of 15◦ N. Middle plot: mid-latitude temperature profiles of Kneizys et al. (1996) for a latitude of 45◦ N. The solid red line is the mean temperature for July and the dashed blue line the mean temperature for January. Lower plot: sub-arctic temperature profiles of Kneizys et al. (1996) for a latitude of 60◦ N. The solid red line is the mean temperature for July and the dashed blue line the mean temperature for January. The green shadowed area in the plots indicate the range of the annual variability of the temperature according to the COSPAR International Reference Atmosphere 1986 (CIRA86) (Rees, 1988). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 B.2 water vapor and ozone volume mixing ratio profiles for the five different atmospheric scenarios of Kneizys et al. (1996). . . . . . . . . . . . . . . . . . . . . 149 B.3 Temperature profiles of the ECMWF reduced subsample of 60L-SDr. The red dots indicate the mean profile and the vertical bars one standard deviation of the subsample. The solid blue lines represent the minimum and maximum profile out of the 77 profiles while the three generic profiles are indicated by the dashed lines (minimum, maximum, and mean). The data is taken from Chevallier (2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B.4 Ozone volume mixing ratio profiles of the ECMWF reduced subsample of 60LSDr. The red dots indicate the mean profile and the vertical bars one standard deviation of the subsample. The solid blue lines represent the minimum and maximum profile out of the 77 profiles while the three generic profiles are indicated by the dashed lines (minimum, maximum, and mean). The data is taken from Chevallier (2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B.5 Water vapor volume mixing ratio (top) and relative humidity (bottom) profiles of the ECMWF reduced subsample of 60L-SDr. The red dots indicate the mean profile and the vertical bars one standard deviation of the subsample. The solid blue lines represent the minimum and maximum profile out of the 77 profiles while the three generic profiles are indicated by the dashed lines (minimum, maximum, and mean). The data is taken from Chevallier (2001). . . . . . . . 152 C.1 Illustration of the intermolecular interaction effect on the energy levels of the optically active molecule. At different intermolecular distances (R0 , · · · , R3 ) the effect on the energy levels is different. Thus the transition frequencies change with R. At R → ∞ the energy levels tend to their unperturbed positions.156 E.1 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The HITRAN00 line catalog is used in the line absorption calculation in connection with a Van Vleck– Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval.. 178. E.2 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The MMHIT-A line catalog is used in the line absorption calculation in connection with a Van Vleck– Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval.. 179. xv.

(20) E.3 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The MMHIT-B line catalog is used in the line absorption calculation in connection with a Van Vleck– Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval.. 180. E.4 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The AAM02 line catalog is used in the line absorption calculation in connection with a Van Vleck–Weisskopf line shape plus a cutoff of 750 GHz (VVWC). The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval. . . . . . . 181 E.5 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The PWR98 absorption model is used to calculate the line absorption. The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval. . . . . . . . . . . . 182 E.6 Water Vapor self continuum (upper plot) and foreign continuum (lower plot) parameter fit for the full 138-350 GHz data. The MPM93 absorption model is used to calculate the line absorption. The solid line is the best fit to the data and the dotted lines indicate the 0.95 confidence interval. . . . . . . . . . . . 183 F.1 Correlation plot for the two MWR channels. The symbols indicate the mean difference ∆TB = TB (calc.) − TB (MWR). The horizontal and vertical bars indicate the standard deviation of ∆TB . The threshold in precipitable water vapor and cloud liquid water are 1.00 cm and 0.0001 cm. The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). In case of AAM02 the foreign continuum temperature coefficient, xair , is set to 1.33 (top), 0.60 (middle), and 0.00 (bottom). The different values for the same symbol are caused by different oxygen absorption models. The number of data points to calculate the means and standard deviations is n = 12. . . . . . . . . . . . . . 203 F.2 Correlation plot for the two MWR channels. The symbols indicate the mean difference ∆TB = TB (calc.) − TB (MWR). The horizontal and vertical bars indicate the standard deviation of ∆TB . The threshold in precipitable water vapor and cloud liquid water are 1.00 cm and 0.0001 cm. The nitrogen absorption is not scaled for these plots. In case of AAM02 the foreign continuum temperature coefficient, xair , is set to 1.33 (top), 0.60 (middle), and 0.00 (bottom). The different values for the same symbol are caused by different oxygen absorption models. The number of data points to calculate the means and standard deviations is n = 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 F.3 Comparison of the measured AMSU-B channel 16 (top) and 17 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . . . . . . 206 F.4 Comparison of the measured AMSU-B channel 18 (top), 19 (middle), and 20 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . 206 xvi.

(21) F.5 Comparison of the measured AMSU-B brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The x-axis is the difference of the calculated and measured brightness temperatures and the y-axis the measured brightness temperatures. The numbers state the mean and the standard deviation of ∆TB .207 F.6 Comparison of the measured AMSU-B channel 16 (top) and 17 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe et al. (1993) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . . . . . . 208 F.7 Comparison of the measured AMSU-B channel 18 (top), 19 (middle), and 20 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe et al. (1993) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . 208 F.8 Comparison of the measured AMSU-B brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe et al. (1993) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The x-axis is the difference of the calculated and measured brightness temperatures and the y-axis the measured brightness temperatures. The numbers state the mean and the standard deviation of ∆TB .209 F.9 Comparison of the measured AMSU-B channel 16 (top) and 17 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe (1989) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . . . . . . 210 F.10 Comparison of the measured AMSU-B channel 18 (top), 19 (middle), and 20 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe (1989) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . . . . . . 210 F.11 Comparison of the measured AMSU-B brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe (1989) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The x-axis is the difference of the calculated and measured brightness temperatures and the y-axis the measured brightness temperatures. The numbers state the mean and the standard deviation of ∆TB . . . . . . . . 211 xvii.

(22) F.12 Comparison of the measured AMSU-B channel 16 (top) and 17 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe and Layton (1987) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . 212 F.13 Comparison of the measured AMSU-B channel 18 (top), 19 (middle), and 20 (bottom) brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe and Layton (1987) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 F.14 Comparison of the measured AMSU-B brightness temperatures with those calculated with Arts, using Lindenberg radiosonde data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Liebe and Layton (1987) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The x-axis is the difference of the calculated and measured brightness temperatures and the y-axis the measured brightness temperatures. The numbers state the mean and the standard deviation of ∆TB .213 F.15 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM87 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 215 F.16 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM89 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 215 F.17 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM93 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 216 F.18 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM93 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 216 xviii.

(23) F.19 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 217 F.20 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are PWR98 (H2 O), Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 218 F.21 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 218 F.22 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 219 F.23 Comparison of the measured and calculated absorption (flight A827.1), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 219 F.24 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM87 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 220 F.25 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM89 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 220 F.26 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM93 (H2 O), Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . . . 221 xix.

(24) F.27 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are MPM93 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 221 F.28 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), Rosenkranz (1988) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . 222 F.29 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . . . . . . . . 223 F.30 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are Rosenkranz (1998) (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz.223 F.31 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Liebe et al. (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 224 F.32 Comparison of the measured and calculated absorption (flight A829.7), using atmospheric data as input for the temperature and relative humidity profiles. The absorption models used in Arts are AAM02 (H2 O), updated version of Rosenkranz (1993) (O2 ), and Liebe et al. (1993) (N2 ). The nitrogen absorption is scaled by 1.29 according to Pardo et al. (2001b). The center frequencies of the channels 16 to 20 are 89, 157, 183.3±1, 183.3±3, 183.3±7 GHz. . . . . . . 224. xx.

(25) List of Tables 3.1. 3.2. 4.1. 4.2. 4.3. total, continuum, and Line absorption of oxygen at three different frequencies and four different altitudes. The resulting line absorption αl,tot is according to Equation (3.13) divided into two terms which gives the positive and negative fractional line absorption. The subtraction of SR2 and SR1 gives always 1. The total oxygen absorption is denoted by αtot and the continuum absorption term by αc . For each frequency the calculation (using O2 -PWR93) is repeated for four altitudes between the ground and 30 km. The atmospheric input is taken from a mid-latitude summer scenario. . . . . . . . . . . . . . . . . . . .. 56. Values of commonly used continuum parameter sets. The parameters Cso and o and x are for the H O-air term in xs are for the H2 O-H2 O term while Cda da 2 Equation (3.24). The last line (H2 O-MPM93∗ ) represents an approximation of the pseudo-line continuum of MPM93 in the form of Equation (D.32). . .. 68. List of considered absorption measurements for the present investigation of continuum parameter sets. Except for the 138.2 and 137.8 GHz data which were performed at the National Telecommunications and Information Administration (NTIA), all measurements were performed with the same laboratory setup at Université des Sciences et Technologies de Lille (USTL). The first column states the frequency window, the second the measurement frequency. The gas mixtures in the absorption cell and the reference are stated in the subsequent columns. All measurements were performed with Fabry-Pérot interferometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75. Comparison of experimentally determined foreign broadening parameters for air and molecular nitrogen with theoretically predicted values for different water vapor lines. The measurements are taken from Liebe and Dillon (1969), Bauer et al. (1989), Goyette et al. (1993), Colmont et al. (1999), and Gasster et al. (1988) while the calculated values are from Bauer et al. (1989). . . . . .. 80. List of additional pressure broadening information used in connection with the line catalogs MMHIT-A, MMHIT-B, and AAM02. The references are the following: 1: Bauer et al. (1989), 2: Gamache et al. (1994), 3: Liebe and Dillon (1969), 4: Goyette and de Lucia (1990), 5: Goyette et al. (1993), 6: Colmont et al. (1999), 7: Bauer et al. (1987), 8: Markov (1994), 9: Gasster et al. (1988). The values from ref. 1 are with the exception of the 183.3 GHz line theoretical predictions, calculated with the complex Robert-Bonamy formalism (CRB). Different sources for one particular line are indicated by small letters. The reference temperature is To =300 K. The numbers in parentheses state the error of the corresponding last digits. . . . . . . . . . . . . . . . . . . . . . . .. 85. xxi.

(26) 4.4. 4.5. 4.6. 4.7. List of H2 O spectral line widths (To =300 K) for a mixture of H2 O-N2 . The first column states the quantum numbers of the transition (JKa ,Kc ← JKa ,Kc ) and the second column the transition frequency in GHz. The notation for the next three columns is as follows: ”BK” indicates results of Benedict and Kaplan (1959), ”GD” indicates results of Gamache and Davies (1983), and ”CRB” indicates calculations within the complex Robert-Bonamy formalism reported by Bauer et al. (1989); Colmont et al. (1999); Bauer et al. (1987). The last column states laboratory measurements reported in a: Liebe and Dillon (1969), b: Bauer et al. (1989) and ref. therein, c: Bauer et al. (1987) and ref. therein, d: Goyette et al. (1993), e: Colmont et al. (1999), f: Krupnov et al. (2000), g: Gamache et al. (1994) Table 7, h: Gasster et al. (1988), i: Kasuga et al. (1978), j: Goyette and de Lucia (1990). The numbers in parentheses state the error of the corresponding last digits of the measurement. If the reported value is not given at To , the temperature exponent of Bauer et al. (1989) is used to calculate the line width at To . . . . . . . . . . . . . . . . . .. 86. Values of the fitted parameters Cbso , x ˆs , Cbfo , and x ˆf . The used line shape function is either a Van Vleck–Weisskopf with cutoff (VVWC) or without cutoff (VVW) of 750 GHz. The 153.0-350.3 GHz laboratory measurements (USTL data) are used for the parameter estimation. For a conversion from dB/km to m−1 one has to multiply the above values of Cbso and Cbfo by 2.3026 · 10−4 (see Appendix A.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89. Values of the fitted parameters Cbso , x ˆs , Cbfo , and x ˆf . The used line shape function is either a Van Vleck–Weisskopf with cutoff (VVWC) or without cutoff (VVW) of 750 GHz. The 137.8-350.3 GHz laboratory measurements (USTL and NTIA) are used for the parameter estimation. For a conversion from dB/km to m−1 one has to multiply the above values of Cbso and Cbfo by 2.3026 · 10−4 (see Appendix A.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89. List of other continuum parameter sets. The theoretical model of Ma and Tipping (1990) predicts a temperature coefficient for the self term for the frequency range of 30-360 GHz. The temperature dependence increases with increasing frequency. The measurements of Becker and Autler (1946) are around the 22 GHz line of water vapor. For the estimation of Cso the data at ν =34.8 and 40.2 GHz are taken. Since the dry air contribution to the total absorption is only a few percent, the listed absorption coefficients are not corrected for this effect. The different versions of Liebe’s H2 O-MPM model are based on several different absorption measurements and water vapor line catalogs. The H2 O-MPM93 is approximated to the continuum absorption parameterization of Equation (4.1). The approximation is described in Appendix D. The parameter set of Katkov (1997) incorporates some measurements of Russian groups in the free atmosphere in the MMW and SMMW range. In the models of Katkov (1997), Ma and Tipping (1990), Ma and Tipping (2002b), and Liebe et al. (1993) the frequency dependence is not quadratic. For a comparison o values are multiplied with the continuum parameter sets in Table 4.6 the Cair by 1.08 according to the same ratio for the pressure broadening parameters discussed above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 96. xxii.

(27) 4.8. List of simultaneously measured absorption proportional to water vapor partial pressure squared and foreign perturber pressure compared to pure water vapor. The measurement frequency and temperature for all mixtures are 239.4 GHz and 296 K, respectively. The buffer gas partial pressure is in the case of bν (T ) 1000 hPa. For an explanation of the coefficients aν and a ˆν (T ) see Equations (4.33) and (4.34). The values of aν (T ) are taken from Bauer and Godon (2001) and the value of a ˆν is from Bauer et al. (1995) The ratio of Pwbc /PH2 O is calculated for PX =1000 hPa and PH2 O =10 hPa which are common pressure values of these measurements. For the uncertainty range of a ˆν /aν an individual uncertainty of 10 % is assumed Bauer and Godon (2001).. 98. 4.9. List of H2 O-AAM02 water vapor absorption model parameters. The values for the center frequency, line intensity, and lower state energy are taken from HITRAN00. The line broadening parameters are from Table 4.3. The parameters are given for pure nitrogen as well as for dry air in the table. At the end of the table the continuum parameter sets for a VVW line shape with and without cutoff in the line absorption term are given. The continuum parameter sets are taken from Table 4.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100. 5.1. Comparison of measured MWR and calculated brightness temperature for the 23 GHz and 31 GHz channels. A general threshold of PWV<1.0 cm and CLW<0.001 mm is applied for this comparison. The first three columns state the absorption models used. In the case of nitrogen the scaling factor is additionally given. For each channel the five columns state the data sample size, mean and standard deviation of ∆ TB = TB (calc.) − TB (M W R) as well as two statistical tests. The column ”H0” indicates if the hypothesis is accepted (=0) or rejected (=1) that the ∆ TB distribution of the data sample agrees with a population mean value of ∆ TB = 0 K. The column labeled with ”comp.” gives the statistical compatibility of the Westwater et al. (2000a) analysis with the present investigation (0=agree, 1=disagree). The three sub-columns stands for the analysis with H2 O-MPM87, H2 O-PWR98, and H2 O-MPM93 water vapor absorption models in Westwater et al. (2000a). Both tests are calculated on a 95 % significance level. The details of the statistical test can be found in Appendix F.1. In the calculations denoted by AAM02 1 and AAM02 2 the temperature coefficient of the foreign continuum term is modified to xf = 0.60 and xf =0.00, respectively (nominal value is xf =1.33). . . . . . . . . . . . . . . 115 xxiii.

(28) 5.2. Comparison of measured MIR and calculated brightness temperature for the 183.3±1,3,7 GHz channels. A general threshold of PWV<0.25 cm is applied for this comparison. The first three columns state the absorption models used. In the case of nitrogen the scaling factor is additionally given. For each channel the three columns present the data sample size and the mean and standard deviation of the ∆ TB = TB (calc.) − TB (MIR) distribution. In the case of the 183.3±7 GHz channel the additional columns state if the hypothesis is accepted (=0) or rejected (=1) that the ∆ TB distribution of the data sample agrees with a population mean value of ∆ TB = 0 K (”H0”). The column labeled with ”comp.” gives the statistical compatibility of the Westwater et al. (2000a) analysis with the present investigation (0=agree, 1=disagree). The three subcolumns stand for the calculation with H2 O-MPM87, H2 O-PWR98, or H2 OMPM93 water vapor absorption model in Westwater et al. (2000a). Both tests are calculated on a 95 % significance level. The details of the statistical test can be found in Appendix F.1. In the calculations denoted by AAM02 1 and AAM02 2 the temperature coefficient of the foreign continuum term is modified to xf = 0.60 and xf = 0.00, respectively (nominal value is xf = 1.33). For a full list see Table F.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120. 5.3. Description of the AMSU-B aboard the NOAA-15 satellite. The bandwidth is for a single passband. All these channels have two pass bands. NE∆T is the noise equivalent temperature and is evaluated from the variability of the internal calibration target views of the channel. Nominal spacecraft altitude of NOAA-15 is 833 km (Atkinson, 2001). . . . . . . . . . . . . . . . . . . . . . 126. 5.4. Analysis of the mean and standard deviation of ∆ TB = TB (Arts) − TB (data) for the AMSU-B channels 16 and 17. The calculation for H2 O-AAM02 (with xf = 1.33) is performed with a Van Vleck–Weisskopf line shape without cutoff. The oxygen and nitrogen absorption is modeled in all the cases in the same way (O2 -PWR98 and N2 -MPM93). . . . . . . . . . . . . . . . . . . . . . . . 127. 5.5. Analysis of the mean and standard deviation of ∆ TB = TB (Arts) − TB (data) for the AMSU-B channels 18 to 20. The calculation for H2 O-AAM02 (with the corresponding continuum parameters stated in Table 4.9) is performed with a Van Vleck–Weisskopf line shape without cutoff. The oxygen and nitrogen absorption is modeled in all the cases in the same way (O2 -PWR98 and N2 MPM93). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127. 5.6. Description of the MARSS radiometer channels, valid for the POLEX campaign. The beam width is given as FWHM of the antenna mainlobe. The integration time was 100 ms for all channels (Hewison, 2002; McGrath and Hewison, 2001). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130. A.1 Frequently used physical constants taken from Mohr and Taylor (2000); Trenberth (1995). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.2 SI units are meter, kilogram, second, and Kelvin. This table gives a short conversion scheme to other units commonly used in atmospheric absorption calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 A.3 van der Waals coefficients for some molecules of interest. The values are taken from McQuarrie and Simon (1997); Lide (1994). . . . . . . . . . . . . . . . . 143 xxiv.