References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-12-503-2012

Bulk microphysical properties of semi-transparent cirrus from AIRS: a six year global climatology and statistical analysis in synergy with geometrical profiling data from CloudSat-CALIPSO

Guignard

¹ Stubenrauch

C. J.

¹ Baran

A. J.

² Armante

Laboratoire de Météorologie Dynamique, Ecole Polytechnique, Palaiseau, France

Met Office, Fitzroy Road, Exeter, EX1 3PB, UK

10 01 2012

12 1 503 525

This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

This article is available from http://www.atmos-chem-phys.net/12/503/2012/acp-12-503-2012.html

The full text article is available as a PDF file from http://www.atmos-chem-phys.net/12/503/2012/acp-12-503-2012.pdf

This article presents a retrieval method and a statistical analysis of the bulk microphysical properties of semi-transparent ice clouds using the Atmospheric Infrared Sounder (AIRS). The method relies on spectral differences of cirrus emissivities in the 8–12 μm range and is sensitive to the effective ice crystal diameter (De) and ice water path (IWP) of up to 85 μm and 120 g m−2, respectively. An indication of the most frequent ice crystal habit in the cirrus has been obtained by using separately single scattering properties of column-like and aggregate-like ice crystals in the simulations. Uncertainties due to hypotheses on atmospheric parameters and ice crystal single scattering properties are discussed and the cirrus emissivity and temperature range for the applicability of the method are determined. To be sure that the cirrus only includes ice crystals, one has to restrict the cloud temperature range to Tcld<230 K. On a global scale, these semi-transparent ice clouds (cirrus) represent about 25% of all high clouds and are mainly encountered in the midlatitudes during winter and in the tropics, with an average De and IWP of 52 μm and 27 g m−2, respectively. A comparison with bulk microphysical properties from the TIROS-N Operational Vertical Sounder (TOVS) shows an agreement on global mean values. The addition of spectral information revealed improvements at the limits of the cirrus emissivity range. Collocated Radar-Lidar Geometrical Profiling (GEOPROF) data have been used to study the vertical structure of these clouds and to infer average ice water content (IWC) for cirrus with a small vertical extent. This allowed us to compare and contrast parameterizations of De as functions of IWC and IWP, respectively.

References 1

Hilton, F., Armante, R., August, T., Barnet, C., Bouchard, A., Camy-Peyret, C., Capelle, V., Clarisse, L., Clerbaux, C., Coheur, P.-F., Collard, A., Crevoisier, C., Dufour, G., Edwards, D., Faijan, F., Fourrié, N., Gambacorta, A., Goldberg, M., Guidard, V., Hurtmans, D., Illingworth, S., Jacquinet-Husson, N., Kerzenmacher, T., Klaes, D., Lavanant, L., Masiello, G., Matricardi, M., McNally, A., Newman, S., Paveli, E., Payan, S., Péquignot, E., Peyridieu, S., Phulpin, T., Remedios, J., Schl�ssel, P., Serio, C., Strow, L., Stubenrauch, C. J., Taylor, J., Tobin, D., Wolf, W., and Zhou, D.: Hyperspectral Earth Observation from IASI, B. Am. Meteor. Soc., http://dx.doi.org/10.1175/BAMS-D-11-00027.1doi:10.1175/BAMS-D-11-00027.1, in press, 2012. \bibitem[Hong et al., 2007] hong07 Hong, G., Yang, P., Gao, B.-C., Baum, B. A., Hu, Y. X., King, M. D., and Platnik, S.: High Cloud Properties from Three Years of MODIS Terra and Aqua Collection-4 Data over the Tropics, J. Appl. Meteorol. Clim., 46, 1840–1856, 2007. \bibitem [Hu and Winker, 2009] hu09 Hu, Y. and Winker, D.: Caliop Cloud Phase Discrimination Algorithm, J. Atmos. Oceanic Technol., 26, 2293–2309, http://dx.doi.org/10.1175/2009JTECHA1280.1doi:10.1175/2009JTECHA1280.1, 2009. \bibitem[Ivanova et al., 2001] ivanova01 Ivanova, D., Mitchell, D. L., Arnotta, W. P., and Poellotb, M.: A GCM parameterization for bimodal size spectra and ice mass removal rates in mid-latitude cirrus clouds, Atmos. Res., 59–60, 89–113, 2001. \bibitem[Kahn et al., 2004] kahn04 Kahn, B. H., Eldering, A., Ghil, M., Bordoni, S., and Clough, S. A.: Sensitivity Analysis of Cirrus Cloud Properties from High-Resolution Infrared Spectra. Part I: Methodology and Synthetic Cirrus, J. Climate, 17, 4856–4870, 2004. \bibitem[Kahn et al., 2007] kahn07 Kahn, B. H., Eldering, A., Braverman, A. J., Fetzer, E. J., Jiang, J. H., Fishbein, E., and Wu, D. L.: Toward the characterization of upper tropospheric clouds using Atmospheric Infrared Sounder and Microwave Limb Sounder observations, J. Geophys. Res., 112, D05202, http://dx.doi.org/10.1029/2006JD007336doi:10.1029/2006JD007336, 2007. \bibitem[Kahn et al., 2008] kahn08 Kahn, B. H., Liang, C. K., Eldering, A., Gettelman, A., Yue, Q., and Liou, K. N.: Tropical thin cirrus and relative humidity observed by the Atmospheric Infrared Sounder, Atmos. Chem. Phys., 8, 1501–1518, http://dx.doi.org/10.5194/acp-8-1501-2008doi:10.5194/acp-8-1501-2008, 2008. \bibitem[Kristjánsson et al., 2000] krist00 Kristjánsson, J. E., Edwards, J. M., and Mitchell, D. L.: Impact of a new scheme for optical properties of ice crystals on climates of two GCMs, J. Geophys. Res., 105, 10063–10079, 2000. \bibitem[Korolev and Isaac, 2003] korolev03 Korolev, A. and Isaac, G.: Roundness and aspects ratios of particles in ice clouds, J. Atmos., 60, 1795–1808, 2003. \bibitem[Korolev and Isaac, 2004] korolev04 Korolev, A. V. and Isaac, G. A.: Shattering during Sampling by OAPs and HVPS. Part I: Snow Particles, J. Atmos. Ocean Tech., 22, 528–542, 2004. \bibitem[Korolev et al., 2001] korolev01 Korolev, A. V., Isaac, G. A., Mazin, I. P., and Barker, H. W.: Microphysical properties of continental clouds from in-situ measurements, Q. J. Roy. Meteor. Soc., 127, 2117–2151, 2001. \bibitem[L'Ecuyer et al., 2006] lecuyer06 L'Ecuyer, T. S., Gabriel, P., Leesman, K., Cooper, S. J., and Stephens, G. L.: Objective assessment of the information content of visible and infrared radiance measurements for cloud microphysical property retrievals over the global oceans. Part I: Liquid clouds, J. Appl. Meteor. Climatol., 45, 20–41, 2006. \bibitem[Liou et al., 2008] liou08 Liou, K. N., Gu, Y., Yue, Q., and McFarguhar, G.: On the correlation between ice water content and ice crystal size and its application to radiative transfer and general circulation models, Geophys. Res. Lett, 35, L13805, http://dx.doi.org/10.1029/2008GL033918doi:10.1029/2008GL033918, 2008. \bibitem[Luo and Rossow, 2004] luo04 Luo, Z. and Rossow, W. B.: Characterizing Tropical Cirrus Life Cycle, Evolution, and Interaction with Upper-Tropospheric Water Vapor Using Lagrangian, J. Climate, 17, 4541–4563, 2004. \bibitem[Lynch et al., 2002] lynch02 Lynch, D. K., K. Sassen, D. O.-C. Starr, and Stevens, G.: Cirrus, 480 pp., Oxford Univ. Press, New York, 480 pp., 2002. \bibitem[Mace et al., 1998] mace98 Mace, G. G., Sassen, K., Kinne, S., and Ackerman, T. P.: An examinationo f cirrus cloud characteristicsu singd ata from millimeter wave radar and lidar: The 24 April SUCCESS casestudy, Geophys. Res. Lett., 25, 1133–1136, 1998. \bibitem[Mace et al., 2009] mace09 Mace, G. G., Zhang, Q., Vaughan, M., Marchand, R., Stephens, G., Trepte, C., and Winker, D.: A description of hydrometeor layer occurrence statistics derived from the first year of merged Cloudsat and CALIPSO data, J. Geophys. Res., 114, D00A26, http://dx.doi.org/10.1029/2007JD009755doi:10.1029/2007JD009755, 2009. \bibitem [Martins et al., 2011] martins11 Martins, E., Noel, V., and Chepfer, H.: Properties of cirrus and subvisible cirrus from nighttime Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), related to atmospheric dynamics and water vapor, J. Geophys. Res., 116, D02208, http://dx.doi.org/10.1029/2010JD014519doi:10.1029/2010JD014519, 2011. \bibitem[McFarlane et al., 1992] farlane92 McFarlane, N. A., Boer, G. J., Blanchet, J.-P., and Lazare, M.: The canadian climate Centre second-generation general circulation model and its equilibrium climate, J. Climate, 5, 1013–1044, 1992. \bibitem[McFarquhar and Heymsfield, 1996] farquhar96 McFarquhar, G. and Heymsfield, A. J.: Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific experiment, J. Atmos. Sci, 53, 2401–2423, 1996. \bibitem[McFarquhar and Heymsfield, 1997a] farquhar962 McFarquhar, G. and Heymsfield, A. J.: Parameterization of Tropical Cirrus Ice Crystal Size Distributions and Implications for Radiative Transfer: Results from CEPEX, J. Atmos. Sci., 54, 2187–2200, 1997a. \bibitem[McFarquhar and Heymsfield, 1997b] farquhar97 McFarquhar, G. and Heymsfield, A. J.: The Definition and Significance of an Effective Radius for Ice Clouds, J. Atmos. Sci., 55, 2039–2052, 1997b. \bibitem[McFarquhar et al., 2003] farquhar03 McFarquhar, G., Iacobellis, S., and Somerville, C. J.: SCM Simulations of Tropical Ice Clouds Using Observationally Based Parameterizations of Microphysics, J. Climate, 16, 1643–1664, 2003. \bibitem[McFarquhar et al., 2007] farquhar07 McFarquhar, G., Um, J., Freer, M., Baumgardner, D., Kok, G. L., and Mace, G.: Importance of small ice crystals to cirrus properties: Observations from the Tropical Warm Pool International Cloud Experiment (TWP-ICE), Geophys. Res. Lett., 34, L13803, http://dx.doi.org/10.1029/2007GL029865doi:10.1029/2007GL029865, 2007. \bibitem[Mitchell, 2002] mitchell02 Mitchell, D.: Effective Diameter in Radiation Transfer: General Definition, Applications and Limitations, J. Atmos. Sci., 59, 2330–2346, 2002. \bibitem [Mitchell, 2009] mitchell09 Mitchell, D. L.: Inferring cirrus size distributions through satellite remote sensing and microphysical databases, J. Atmos. Sci., 67, 1106–1125, 2009. \bibitem[Mitchell et al., 1996a] mitchell96 Mitchell, D. L., Chai, S. K., and Liu, Y.: Modeling cirrus clouds, I. Treatment of bimodal size spectra and case study analysis, J. Atmos. Sci., 53, 2952–2966, 1996a. \bibitem[Mitchell et al., 1996b] mitchell962 Mitchell, D. L., Macke, A., and Liu, Y.: Modeling cirrus clouds, II, Treatment of radiative properties, J. Atmos. Sci., 53, 2967–2988, 1996b. \bibitem[Mitchell et al., 2006] mitchell06 Mitchell, D. L., Baran, A. J., Arnott, W. P., and Schmitt, C.: Testing and comparing the modified anomalous diffraction approximation, J. Atmos. Sci., 63, 2948–2962, 2006. \bibitem [Mitchell et al., 2011] mitchell11 Mitchell, D. L., Lawson, R. P., and Baker, B.: Understanding effective diameter and its application to terrestrial radiation in ice clouds, Atmos. Chem. Phys., 11, 3417–3429, http://dx.doi.org/10.5194/acp-11-3417-2011doi:10.5194/acp-11-3417-2011, 2011. \bibitem [Ou et al., 1995] ou95 Ou, S. C., Liou, K. N., Takano, Y., Rao, N. X., Fu, Q., Heymsfield, A. J., Miloshevich, L. M., Baum, B., and Kinne, S. A.: Remote sounding of cirrus cloud optical depths and ice crystal sizes from AVHRR data: Verification using FIRE II IFO measurements, J. Atmos. Sci., 52, 4143–4158, 1995. \bibitem [Pavolonis, 2010] pavolonis10 Pavolonis, M. J.: Advances in Extracting Cloud Composition Information from Spaceborne Infrared Radiances-A Robust Alternative to Brightness Temperatures. Part I: Theory, J. Appl. Meteor. Climatol., 49, 1992–2012, 2010. \bibitem [Péquignot et al., 2008] pequignot08 Péquignot, E., Céhdin, A., and Scott, N. A.: Infrared continental surface emissivity spectra retrieved from AIRS hyperspectral sensor, J. Appl. Meteor. Climatol., 47, 1619–1633, 2008. \bibitem [Platnick et al., 2003] platnick03 Platnick, S., King, M. D., Ackerman, S. A., Menzel, W. P., Baum, B. A., Riédi, J. C., and Frey, R. A.: The MODIS Cloud Products: Algorithms and Examples From Terra, IEEE T. Geosci. Remote., 41, 459–473, 2003. \bibitem[Pierangelo et al., 2005] pierangelo05 Pierangelo, C., Mishchenko, M., Balkanski, Y., and Céhdin, A.: Retrieving the effective radius of Saharan dust coarse mode from AIRS, Geophys. Res. Lett., 32, L20813, http://dx.doi.org/10.1029/2005GL023425doi:10.1029/2005GL023425, 2005. \bibitem[Rädel et al., 2003] radel03 Rädel, G., Stubenrauch, C. J., and Holtz, R.: Retrieval of effective ice crystal size in the infrared: Sensitivity study and global measurments from TIROS-N Operationnal Vertical Sounder, J. Geophys. Res., 108, 4281, http://dx.doi.org/10.1029/2002JD002801doi:10.1029/2002JD002801, 2003. \bibitem[Riedi et al., 2010] riedi10 Riedi, J., Marchant, B., Platnick, S., Baum, B. A., Thieuleux, F., Oudard, C., Parol, F., Nicolas, J.-M., and Dubuisson, P.: Cloud thermodynamic phase inferred from merged POLDER and MODIS data, Atmos. Chem. Phys., 10, 11851–11865, http://dx.doi.org/10.5194/acp-10-11851-2010doi:10.5194/acp-10-11851-2010, 2010. \bibitem[Roebeling et al., 2006] roebeling06 Roebeling, R. A., Feijt, A. J., and Stammes, P.: Cloud property retrievals for climate monitoring: Implications of differences between Spinning Enhanced Visible and Infrared Imager (SEVIRI) on METEOSAT-8 and Advanced Very High Resolution Radiometer (AVHRR) on NOAA-17, J. Geophys. Res., 111, D20210, http://dx.doi.org/10.1029/2005JD006990doi:10.1029/2005JD006990, 2006. \bibitem[Rossow and Schiffer, 1999] rossow99 Rossow, W. B. and Schiffer, R. A.: Advances in understanding clouds from ISCCP, B. Am. Meteor. Soc., 80, 2261–2287, 1999. \bibitem[Sassen and Dodd, 1988] sassen88 Sassen, K. and Dodd, G. C.: Homogeneous nucleation rate for highly supercooled cirrus cloud droplets, J. Atmos. Sc., 45, 1357–1369, 1988. \bibitem[Scott and Chédin, 1981] scott81 Scott, N. A., and Chédin A.: A fast line-by-line method for atmospheric absorption computations: the 4A Automized Atmospheric Absorption Atlas, J. Appl. Meteor., 20, 801–812, 1981. \bibitem[Seemann et al., 2008] seeman08 Seemann, S. W., Borbas, E. E., Knuteson, R. O., Stephenson, G. R., and Huang, H. L.: Development of a Global Infrared Land Surface Emissivity Database for Application to Clear Sky Sounding Retrievals from Multispectral Satellite Radiance Measurements, J. Appl. Meteor. Climatol., 47, 108–123, http://dx.doi.org/10.1175/2007JAMC1590.1doi:10.1175/2007JAMC1590.1, 2008. \bibitem[Seo and Liu, 2006] seo06 Seo, E. K. and Liu, G.:Determination of 3D Cloud Ice Water Contents by Combining Multiple Data Sources rom Satellite, Ground Radar, and a Numerical Model, J. Appl. Metorol., 45, 1494–1504, 2006. \bibitem[Smith et al., 1979] smith79 Smith, W. L., Woolf, H. M., Hayden, M. C., Wark, D. Q., and McMillin, L. M.: The TIROS-N Operational Vertical Sounder, B. Am. Meteorol. Soc., 60, 1177–1187, 1979. \bibitem[Stamnes et al., 1988] stamnes88 Stamnes, K., Tsay, S., Wiscombe, W., and Jayaweera, K.: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Appl. Optics, 27, 2502–2509, 1988. \bibitem[Stith et al., 2002] stith02 Stith, J. L., Dye, A. E., Bansemer, A., and Heymsfield, J. A.: Microphysical Observations of Tropical Clouds, J. Appl. Metorol., 41, 97–117, 2002. \bibitem[Stephens et al., 2002] stephens02 Stephens, G. L., Vane, D. G., Boain, R. J., Mace, G. G., Sassen, K., Wang, Z., Illingworth, A. J., O'Connor, E. J., Rossow, W. B., Durden, S. L., Miller, S. D., Austin, R. T., Benedetti, A., and Mitrescu, C.: The CloudSat mission and the A-train, B. Am. Meteor. Soc., 83, 1771–1790, 2002. \bibitem[Stubenrauch et al., 1999] stubenrauch99 Stubenrauch, C. J., Holz, R., Chédin, A., Mitchell, D. L., and Baran, A. J: Retrieval of cirrus ice crystal sizes from 8.3 and 11.1 μm emissivities determined by the improved initialization inversion of TIROS-N Operational Vertical Sounder observations, J. Geophys. Res., 104, 793–808, 1999. \bibitem[Stubenrauch et al., 2004] stubenrauch04 Stubenrauch, C. J., Eddounia, F., and Rädel, G.: Correlations between microphysical properties of large-scale semi-transparent cirrus and the state of the atmosphere, Atmos. Res., 72, 403–423, 2004. \bibitem[Stubenrauch et al., 2006] stubenrauch06 Stubenrauch, C. J., Chédin, A., Rädel, G., Scott, N. A., and Serra, S.: Cloud Properties and Their Seasonal and Diurnal Variability from TOVS Path-B, J. Climate, 19, 5531–5553 2006. \bibitem[Stubenrauch et al., 2007] stubenrauch07 Stubenrauch, C. J., Eddouina, F., Edwards, J. M., and Macke, A.: Evaluation of Cirrus Parameterizations for Radiative Flux Computations in Climate Models Using TOVS–ScaRaB Satellite Observations, J. Climate, 20, 4459–4475, http://dx.doi.org/10.1175/JCLI4251.1doi:10.1175/JCLI4251.1, 2007. \bibitem[Stubenrauch et al., 2008] stubenrauch08 Stubenrauch, C. J., Cros, S., Lamquin, N., Armante, R., Chédin, A., Crevoisier, C., and Scott, N. A.: Cloud properties from AIRS and evaluation with CALIPSO, J. Geophys. Res., 113, D00A10, http://dx.doi.org/10.1029/2008JD009928doi:10.1029/2008JD009928, 2008. \bibitem [Stubenrauch et al., 2010] stubenrauch10 Stubenrauch, C. J., Cros, S., Guignard, A., and Lamquin, N.: A 6-year global cloud climatology from the Atmospheric InfraRed Sounder AIRS and a statistical analysis in synergy with CALIPSO and CloudSat, Atmos. Chem. Phys., 10, 7197–7214, http://dx.doi.org/10.5194/acp-10-7197-2010doi:10.5194/acp-10-7197-2010, 2010. \bibitem[Susskind et al., 2003] susskind03 Susskind, J., Barnet C., and Blaisdell J.: Retrieval of atmospheric and surface parameters from AIRS/AMSU/HSB data in the presence of clouds, IEEE T. Geosci. Remote, 41, 390–409, 2003. \bibitem[Susskind et al., 2006] susskind06 Susskind, J., Barnet, C., Blaisdell, J., Iredell, L., Keita, F., Kouvaris, L., Molnar, G., and Chahine, M.: Accuracy of geophysical parameters derived from AIRS/AMSU as a function of fractional cloud cover, J. Geophys. Res., 111, D09S17, http://dx.doi.org/10.1029/2005JD006272doi:10.1029/2005JD006272, 2006. \bibitem[Tobin et al., 2006] tobin06 Tobin, D. C., Revercomb, H. E., Knuteson, R. O., Lesht, B. M., Strow, L. L., Hannon, S. E., Feltz, W. F., Moy, L. A., Fetzer, E. J., and Cress, T. S.: Atmospheric Radiation Measurement site atmospheric state best estimates for Atmmospheric Infrared Sounder temperature and water vapour retrieval validation, J. Geophys. Res., 111, D09S14, http://dx.doi.org/10.1029/2005JD006103doi:10.1029/2005JD006103, 2006. \bibitem[Wang et al., 2000] wang00 Wang, J., Rossow, W. B., and Zhang, Y.: Cloud Vertical Structure and its Variations from a 20-Yr Global Rawinsonde Dataset, J. Climate, 13, 3041–3056, 2000. \bibitem[Winker et al., 2003] winker03 Winker, D. M., Pelon, J. R., and McCormick, M. P.: The CALIPSO mission: Spaceborne lidar for observation of aerosols and clouds, Proceedings of SPIE, 4893, 1–11, 2003. \bibitem[Winker et al., 2007] winker07 Winker, D. M., Hunt, W. H., and McGill, M. J.:Initial performance assessment of CALIOP, Geophys. Res. Lett., 34, L19803, http://dx.doi.org/10.1029/2007GL030135doi:10.1029/2007GL030135, 2007. \bibitem[Winker et al., 2008] winker08 Winker, D., Getzewitch, B., and Vaughan, M.: Evaluation and Applications of Cloud Climatologies from CALIOP, Proc. Int. Laser Radar Conference (ILRC), 2008. \bibitem[Winker et al., 2009] winker09 Winker, D. M., Vaughan, M. A., Omar, A., Hu, Y., and Powell, K. A.: Overview of the CALIPSO mission and CALIOP data processing algorithms, J. Atmos. Ocean. Tech., 26, 2310–2323, 2009. \bibitem[Wylie and Menzel, 1994] wylie94 Wylie, D. and Menzel, W. P: Four Years of Global Cirrus Cloud Statistics Using HIRS, J. Climate, 7, 1972–1986, 1994. \bibitem[Wylie and Menzel., 1999] wylie99 Wylie, D. and Menzel, W. P: Eight Years of High Cloud Statistics Using HIRS, J. Climate, 12, 170–184, 1999. \bibitem[Wylie et al., 2005] wylie04 Wylie, D., Jackson, D. L., Menzel, W. P., and Bates, J. J.: Trends in Global Cloud Cover in Two Decades of HIRS Observations, J. Climate, 18, 3021–3031, 2005. \bibitem[Wyser and Yang, 1998] wyser98 Wyser, K. and Yang, P.: Average ice crystal size and bulk short-wave single-scattering properties of cirrus clouds, Atmos. Res., 49, 315–335, 1998. \bibitem [Yang et al., 2002] yang02 Yang, P., Weia, H.-L., and Baumb, B. A.: The spectral signature of mixed-phase clouds composed of non-spherical ice crystals and spherical liquid droplets in the terrestrial window region, J. Quant. Spectrosc. Ra., 79–80, 1171–1188, 2002. \bibitem[Yue and Liou, 2009] Yue09 Yue, Q. and Liou, K. N.: Cirrus cloud optical and microphysical properties determined from AIRS infrared spectra, Geophys. Res. Lett., 36, L05810, http://dx.doi.org/10.1029/2008GL036502doi:10.1029/2008GL036502, 2009. \bibitem[Yue et al., 2007] yue07 Yue, Q., Liou, K. N., Ou, S. C., Kahn, B. H., Yang, P., and Mace, G.: Interpretation of AIRS data in thin cirrus atmospheres based on a fast radiative transfer model, J. Atmos. Sci., 64, 3827–3842, 2007.