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Atmospheric radiative transfer codes

Topic: Engineering

 From HandWiki - Reading time: 10 min

An Atmospheric radiative transfer model, code, or simulator calculates radiative transfer of electromagnetic radiation through a planetary atmosphere, such as the Earth's.

Methods

At the core of a radiative transfer model lies the radiative transfer equation that is numerically solved using a solver such as a discrete ordinate method or a Monte Carlo method. The radiative transfer equation is a monochromatic equation to calculate radiance in a single layer of the Earth's atmosphere. To calculate the radiance for a spectral region with a finite width (e.g., to estimate the Earth's energy budget or simulate an instrument response), one has to integrate this over a band of frequencies (or wavelengths). The most exact way to do this is to loop through the frequencies of interest, and for each frequency, calculate the radiance at this frequency. For this, one needs to calculate the contribution of each spectral line for all molecules in the atmospheric layer; this is called a line-by-line calculation. For an instrument response, this is then convolved with the spectral response of the instrument. A faster but more approximate method is a band transmission. Here, the transmission in a region in a band is characterised by a set of pre-calculated coefficients (depending on temperature and other parameters). In addition, models may consider scattering from molecules or particles, as well as polarisation; however, not all models do so.

Applications

Radiative transfer codes are used in broad range of applications. They are commonly used as forward models for the retrieval of geophysical parameters (such as temperature or humidity). Radiative transfer models are also used to optimize solar photovoltaic systems for renewable energy generation.[1] Another common field of application is in a weather or climate model, where the radiative forcing is calculated for greenhouse gases, aerosols, or clouds. In such applications, radiative transfer codes are often called radiation parameterization. In these applications, the radiative transfer codes are used in forward sense, i.e. on the basis of known properties of the atmosphere, one calculates heating rates, radiative fluxes, and radiances.

There are efforts for intercomparison of radiation codes. One such project was ICRCCM (Intercomparison of Radiation Codes in Climate Models) effort that spanned the late 1980s - early 2000s. The more current (2011) project, Continual Intercomparison of Radiation Codes, emphasises also using observations to define intercomparison cases. [2]

Table of models

Name
 Website
 References
 UV
 Visible
 Near IR
 Thermal IR
 mm/sub-mm
 Microwave
 line-by-line/band
 Scattering
 Polarised
 Geometry
 License
 Notes
4A/OP [1] Scott and Chédin (1981)

[3]

No No Yes Yes No No band or line-by-line Yes Yes freeware
6S/6SV1 [2] Kotchenova et al. (1997)

[4]

No Yes Yes No No No band ? Yes non-Lambertian surface
ARTS [3] Eriksson et al. (2011)

[5]

No No No Yes Yes Yes line-by-line Yes Yes spherical 1D, 2D, 3D GPL
BTRAM [4] Chapman et al. (2009)

[6]

No Yes Yes Yes Yes Yes line-by-line No No 1D,plane-parallel proprietary commercial
COART [5] Jin et al. (2006)

[7]

Yes Yes Yes Yes No No Yes No plane-parallel free
CRM [6] No Yes Yes Yes No No band Yes No freely available Part of NCAR Community Climate Model
CRTM [7] No Yes Yes Yes No Yes band Yes ?
DART radiative transfer model [8] Gastellu-Etchegorry et al. (1996)

[8]

No Yes Yes Yes No No band Yes ? spherical 1D, 2D, 3D free for research with license non-Lambertian surface, landscape creation and import
DISORT [9] Stamnes et al. (1988)[9]

Lin et al. (2015)[10]

Yes Yes Yes Yes Yes radar Yes No plane-parallel or pseudo-spherical (v4.0) free with restrictions discrete ordinate, used by others
FARMS [10] Xie et al. (2016)

[11]

λ>0.2 µm Yes Yes No No No band Yes No plane-parallel free Rapidly simulating downwelling solar radiation at land surface for solar energy and climate research
Fu-Liou [11] Fu and Liou (1993)

[12]

No Yes Yes ? No No Yes ? plane-parallel usage online, source code available web interface online at [13]
FUTBOLIN Martin-Torres (2005)

[14]

λ>0.3 µm Yes Yes Yes λ<1000 µm No line-by-line Yes ? spherical or plane-parallel handles line-mixing, continuum absorption and NLTE
GENLN2 [12] Edwards (1992)

[15]

? ? ? Yes ? ? line-by-line ? ?
KARINE [13] Eymet (2005)

[16]

No No Yes No No ? ? plane-parallel GPL
KCARTA [14] ? ? Yes Yes ? ? line-by-line Yes ? plane-parallel freely available AIRS reference model
KOPRA [15] No No No Yes No No ? ?
LBLRTM [16] Clough et al. (2005)

[17]

Yes Yes Yes Yes Yes Yes line-by-line ? ?
LEEDR [17] Fiorino et al. (2014)

[18]

λ>0.2 µm Yes Yes Yes Yes Yes band or line-by-line Yes ? spherical US government software extended solar & lunar sources;

single & multiple scattering

LinePak [18] Gordley et al. (1994)

[19]

Yes Yes Yes Yes Yes Yes line-by-line No No spherical (Earth and Mars), plane-parallel freely available with restrictions web interface, SpectralCalc
libRadtran [19] Mayer and Kylling (2005)

[20]

Yes Yes Yes Yes No No band or line-by-line Yes Yes plane-parallel or pseudo-spherical GPL
MATISSE [20] Caillault et al. (2007)

[21]

No Yes Yes Yes No No band Yes ? proprietary freeware
MCARaTS [22] GPL 3-D Monte Carlo
MODTRAN [21] Berk et al. (1998)

[23]

ṽ<50,000 cm−1 Yes Yes Yes Yes Yes band or line-by-line Yes ? proprietary commercial solar and lunar source, uses DISORT
MOSART [22] Cornette (2006)

[24]

λ>0.2 µm Yes Yes Yes Yes Yes band Yes No freely available
PUMAS [23] Yes Yes Yes Yes Yes Yes Line-by-line and correlated-k Yes Yes plane-parallel and pseudo-spherical Free/online tool
RADIS [24] Pannier (2018)

[25]

No No Yes No No No No plane-parallel GPL
RFM [25] No No No Yes No No line-by-line No ? available on request MIPAS reference model based on GENLN2
RRTM/RRTMG [26] Mlawer, et al. (1997)

[26]

ṽ<50,000 cm−1 Yes Yes Yes Yes ṽ>10 cm−1 ? ? free of charge uses DISORT
RTMOM [27][[[Link rot dead link}}]]] λ>0.25 µm Yes Yes λ<15 µm No No line-by-line Yes ? plane-parallel freeware
RTTOV [28] Saunders et al. (1999)

[27]

λ>0.4 µm Yes Yes Yes Yes Yes band Yes ? available on request
SASKTRAN [28] Bourassa et al.

(2008)[29]

Zawada et al.

(2015)[30]

Yes Yes Yes No No No line-by-line Yes Yes spherical 1D, 2D, 3D, plane-parallel available on request discrete and Monte Carlo options
SBDART [29] Ricchiazzi et al. (1998)

[31]

Yes Yes Yes ? No No Yes ? plane-parallel uses DISORT
SCIATRAN [30] Rozanov et al. (2005)

,[32] 

Rozanov et al. (2014)

[33]

Yes Yes Yes No No No band or line-by-line Yes Yes plane-parallel or pseudo-spherical or spherical
SHARM Lyapustin (2002)

[34]

No Yes Yes No No No Yes ?
SHDOM [31] Evans (2006)

[35]

? ? Yes Yes ? ? Yes ?
σ-IASI [32] Amato et al. (2002)[36]

Liuzzi et al. (2017)[37]

No No Yes Yes Yes No band Yes No plane-parallel Available on request Semi-analytical Jacobians.
SMART-G [33] Ramon et al. (2019)

[38]

Yes Yes Yes No No No band or line-by-line Yes Yes plane-parallel or spherical free for non-commercial purposes Monte-Carlo code parallelized by GPU (CUDA). Atmosphere or/and ocean options
Streamer, Fluxnet [34][39] Key and Schweiger (1998)

[40]

No No λ>0.6 mm λ<15 mm No No band Yes ? plane-parallel Fluxnet is fast version of STREAMER using neural nets
XRTM [35] Yes Yes Yes Yes Yes Yes Yes Yes plane-parallel and pseudo-spherical GPL
Name Website References UV VIS Near IR Thermal IR Microwave mm/sub-mm line-by-line/band Scattering Polarised Geometry License Notes

Molecular absorption databases

For a line-by-line calculation, one needs characteristics of the spectral lines, such as the line centre, the intensity, the lower-state energy, the line width and the shape.

Name Author Description
HITRAN[41] Rothman et al. (1987, 1992, 1998, 2003, 2005, 2009, 2013, 2017) HITRAN is a compilation of molecular spectroscopic parameters that a variety of computer codes use to predict and simulate the transmission and emission of light in the atmosphere. The original version was created at the Air Force Cambridge Research Laboratories (1960's). The database is maintained and developed at the Harvard-Smithsonian Center for Astrophysics in Cambridge MA, USA.
GEISA[42] Jacquinet-Husson et al. (1999, 2005, 2008) GEISA (Gestion et Etude des Informations Spectroscopiques Atmosphériques: Management and Study of Spectroscopic Information) is a computer-accessible spectroscopic database, designed to facilitate accurate forward radiative transfer calculations using a line-by-line and layer-by-layer approach. It was started in 1974 at Laboratoire de Météorologie Dynamique (LMD/IPSL) in France. GEISA is maintained by the ARA group at LMD (Ecole Polytechnique) for its scientific part and by the ETHER group (CNRS Centre National de la Recherche Scientifique-France) at IPSL (Institut Pierre Simon Laplace) for its technical part. Currently, GEISA is involved in activities related to the assessment of the capabilities of IASI (Infrared Atmospheric Sounding Interferometer on board of the METOP European satellite) through the GEISA/IASI database derived from GEISA.

See also

References

Footnotes
  1. ↑ R.W. Andrews, J.M. Pearce, The effect of spectral albedo on amorphous silicon and crystalline silicon solar photovoltaic device performance, Solar Energy, 91,233–241 (2013). DOI:10.1016/j.solener.2013.01.030 open access
  2. ↑ Continual Intercomparison of Radiation Codes
  3. ↑ Scott, N. A.; Chedin, A. (1981). "A fast line-by- line method for atmospheric absorption computations: The Automatized Atmospheric Absorption Atlas". J. Appl. Meteorol. 20 (7): 802–812. doi:10.1175/1520-0450(1981)020<0802:AFLBLM>2.0.CO;2. Bibcode: 1981JApMe..20..802S. 
  4. ↑ Kotchenova, S. Y.; Vermote, E. F.; Matarrese, R; Klemm, F. J. (2006). "Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: Path Radiance". Applied Optics 45 (26): 6762–6774. doi:10.1364/AO.45.006762. PMID 16926910. Bibcode: 2006ApOpt..45.6762K. 
  5. ↑ Eriksson, P.; Buehler, S. A.; Davis, C.P.; Emde, C.; Lemke, O. (2011). "ARTS, the atmospheric radiative transfer simulator, Version 2". Journal of Quantitative Spectroscopy and Radiative Transfer 112 (10): 1551–1558. doi:10.1016/j.jqsrt.2011.03.001. Bibcode: 2011JQSRT.112.1551E. http://radiativetransfer.org/docs/arts-2-0-paper.pdf. Retrieved 2016-11-02. 
  6. ↑ Chapman, I. M.; Naylor, D. A.; Gom, B. G.; Querel, R. R.; Davis-Imhof, P. (2009). "BTRAM: An Interactive Atmospheric Radiative Transfer Model". The 30th Canadian Symposium on Remote Sensing 30: 22–25. 
  7. ↑ Jin, Z.; Charlock, T.P.; Rutledge, K.; Stamnes, K.; Wang, Y. (2006). "An analytical solution of radiative transfer in the coupled atmosphere-ocean system with rough surface". Appl. Opt. 45 (28): 7443–7455. doi:10.1364/AO.45.007443. PMID 16983433. Bibcode: 2006ApOpt..45.7443S. 
  8. ↑ Gastellu-Etchegorry, JP; Demarez, V; Pinel, V; Zagolski, F (1996). "Modelling radiative transfer in heterogeneous 3-D vegetation canopies". Rem. Sens. Env. 58 (2): 131–156. doi:10.1016/0034-4257(95)00253-7. Bibcode: 1996RSEnv..58..131G. http://hal.ird.fr/ird-00405222/document. 
  9. ↑ Stamnes, Knut; Tsay, S. C.; Wiscombe, W.; Jayaweera, Kolf (1988). "Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media". Appl. Opt. 27 (12): 2502–2509. doi:10.1364/AO.27.002502. PMID 20531783. Bibcode: 1988ApOpt..27.2502S. 
  10. ↑ Lin, Zhenyi; Stamnes, S.; Jin, Z.; Laszlo, I.; Tsay, S. C.; Wiscombe, W. (2015). "Improved discrete ordinate solutions in the presence of an anisotropically reflecting lower boundary: Upgrades of the DISORT computational tool". Journal of Quantitative Spectroscopy and Radiative Transfer 157 (12): 119–134. doi:10.1016/j.jqsrt.2015.02.014. Bibcode: 2015JQSRT.157..119L. 
  11. ↑ Xie, Y.; Sengupta, M.; Dudhia, J. (2016). "A Fast All-sky Radiation Model for Solar applications (FARMS): Algorithm and performance evaluation". Solar Energy 135: 435–445. doi:10.1016/j.solener.2016.06.003. Bibcode: 2016SoEn..135..435X. 
  12. ↑ Fu, Q.; Liou, K.-N (1993). "Parameterization of the radiative properties of cirrus clouds". J. Atmos. Sci. 50 (13): 2008–2025. doi:10.1175/1520-0469(1993)050<2008:POTRPO>2.0.CO;2. Bibcode: 1993JAtS...50.2008F. 
  13. ↑ "Archived copy". Archived from the original on 2010-05-27. https://web.archive.org/web/20100527145310/http://snowdog.larc.nasa.gov/cgi-bin/rose/flp200503/flp200503.cgi. Retrieved 2010-07-07. 
  14. ↑ Martin-Torres, F. J.; Kutepov, A.; Dudhia, A.; Gusev, O.; Feofilov, A.G. (2003). "Accurate and fast computation of the radiative transfer absorption rates for the infrared bands in the atmosphere of Titan". Geophysical Research Abstracts: 7735. Bibcode: 2003EAEJA.....7735M. 
  15. ↑ Edwards, D. P. (1992), GENLN2: A general line-by-line atmospheric transmittance and radiance model, Version 3.0 description and users guide, NCAR/TN-367-STR, National Center for Atmospheric Research, Boulder, Co.
  16. ↑ KARINE: a tool for infrared radiative transfer analysis in planetary atmospheres par V. Eymet. Note technique interne, Laboratoire d'Energétique, 2005.
  17. ↑ Clough, S. A.; Shephard, M. W.; Mlawer, E. J.; Delamere, J. S.; Iacono, M. J.; Cady-Pereira, K.; Boukabara, S.; Brown, P. D. (2005). "Atmospheric radiative transfer modeling: a summary of the AER codes". J. Quant. Spectrosc. Radiat. Transfer 91 (2): 233–244. doi:10.1016/j.jqsrt.2004.05.058. Bibcode: 2005JQSRT..91..233C. 
  18. ↑ Fiorino, S. T.; Randall, R. M.; Via, M. F.; Burley, J. L. (2014). "Validation of a UV-to-RF High-Spectral-Resolution Atmospheric Boundary Layer Characterization Tool". J. Appl. Meteorol. Climatol. 53 (1): 136–156. doi:10.1175/JAMC-D-13-036.1. Bibcode: 2014JApMC..53..136F. 
  19. ↑ Gordley, L. L.; Marshall, B. T. (1994). "LINEPAK: Algorithm for Modeling Spectral Transmittance and Radiance". J. Quant. Spectrosc. Radiat. Transfer 52 (5): 563–580. doi:10.1016/0022-4073(94)90025-6. Bibcode: 1994JQSRT..52..563C. 
  20. ↑ Mayer, B.; Kylling, A. (2005). "Technical note: The libRadtran software package for radiative transfer calculations - description and examples of use". Atmospheric Chemistry and Physics 5 (7): 1855–1877. doi:10.5194/acp-5-1855-2005. Bibcode: 2005ACP.....5.1855M. https://hal.archives-ouvertes.fr/hal-00295701/file/acp-5-1855-2005.pdf. 
  21. ↑ Caillaut, K.; Fauqueux, S.; Bourlier, C.; Simoneau, P.; Labarre, L. (2007). "Multiresolution optical characteristics of rough sea surface in the infrared". Applied Optics 46 (22): 5471–5481. doi:10.1364/AO.46.005471. PMID 17676164. Bibcode: 2007ApOpt..46.5471C. 
  22. ↑ "MCARaTS". https://sites.google.com/site/mcarats/home. 
  23. ↑ Berk, A.; Bernstein, L. S.; Anderson, G. P.; Acharya, P. K.; Robertson, D. C.; Chetwynd, J. H.; Adler-Golden, S. M. (1998). "MODTRAN cloud and multiple scattering upgrades with application to AVIRIS". Remote Sensing of Environment 65 (3): 367–375. doi:10.1016/S0034-4257(98)00045-5. Bibcode: 1998RSEnv..65..367B. 
  24. ↑ Cornette, William M. (2006). "Moderate Spectral Atmospheric Radiance and Transmittance (MOSART) Computer Code Version 2.00., Lexington, MA (2006)". Proc. IEEE-GRSS/AFRL Atmospheric Transmission Modeling Conference, Lexington MA. 
  25. ↑ Pannier, E.; Laux, C. (2019). "RADIS: A nonequilibrium line-by-line radiative code for CO2 and HITRAN-like database species". Quantitative Spectroscopy and Radiative Transfer 222-223: 12–25. doi:10.1016/j.jqsrt.2018.09.027. Bibcode: 2019JQSRT.222...12P. https://hal.archives-ouvertes.fr/hal-01904972/file/radis_submitted.pdf. 
  26. ↑ Mlawer, E. J.; Taubman, S. J.; Brown, P. D.; Iacono, M. J.; Claugh, S. A. (1997). "RRTM, a validated correlated-k model for the longwave". J. Geophys. Res. 102 (16): 663–682. doi:10.1029/97JD00237. Bibcode: 1997JGR...10216663M. 
  27. ↑ Saunders, R. W.; Matricardi, M.; Brunel, P. (1999). "An Improved Fast Radiative Transfer Model for Assimilation of Satellite Radiance Observations". Quarterly Journal of the Royal Meteorological Society 125 (556): 1407–1425. doi:10.1256/smsqj.55614. Bibcode: 1999QJRMS.125.1407S. 
  28. ↑ "Welcome to SASKTRAN's documentation! — SASKTRAN 0.1.3 documentation" (in en). https://arg.usask.ca/docs/sasktran/. 
  29. ↑ Bourassa, A.E.; Degenstein, D.A.; Llewellyn, E.J. (2008). "SASKTRAN: A spherical geometry radiative transfer code for efficient estimation of limb scattered sunlight". Journal of Quantitative Spectroscopy and Radiative Transfer 109 (1): 52–73. doi:10.1016/j.jqsrt.2007.07.007. Bibcode: 2008JQSRT.109...52B. 
  30. ↑ Zawada, D. J.; Dueck, S. R.; Rieger, L. A.; Bourassa, A. E.; Lloyd, N. D.; Degenstein, D. A. (2015-06-26). "High-resolution and Monte Carlo additions to the SASKTRAN radiative transfer model". Atmos. Meas. Tech. 8 (6): 2609–2623. doi:10.5194/amt-8-2609-2015. ISSN 1867-8548. Bibcode: 2015AMT.....8.2609Z. 
  31. ↑ Ricchiazzi, P.; Yang, S.; Gautier, C.; Sowle, D. (1998). "SBDART: A Research and Teaching Software Tool for Plane-Parallel Radiative Transfer in the Earth's Atmosphere". Bull. Am. Meteorol. Soc. 79 (10): 2101–2114. doi:10.1175/1520-0477(1998)079<2101:SARATS>2.0.CO;2. Bibcode: 1998BAMS...79.2101R. 
  32. ↑ Rozanov, A.; Rozanov, V.; Buchwitz, M.; Kokhanovsky, A.; Burrows, J. P. (2005). "SCIATRAN 2.0-A new radiative transfer model for geophysical applications in the 175-2400 nm spectral region". Advances in Space Research 36 (5): 1015–1019. doi:10.1016/j.asr.2005.03.012. Bibcode: 2005AdSpR..36.1015R. 
  33. ↑ Rozanov, V.; Rozanov, A.; Kokhanovsky, A.; Burrows, J. P. (2014). "Radiative transfer through terrestrial atmosphere and ocean: Software package SCIATRAN". Journal of Quantitative Spectroscopy and Radiative Transfer 133: 13–71. doi:10.1016/j.jqsrt.2013.07.004. Bibcode: 2014JQSRT.133...13R. 
  34. ↑ Lyapustin, A. (2002). "Radiative transfer code SHARM-3D for radiance simulations over a non-Lambertian nonhomogeneous surface: intercomparison study". Applied Optics 41 (27): 5607–5615. doi:10.1364/AO.41.005607. PMID 12269559. Bibcode: 2002ApOpt..41.5607L. https://zenodo.org/record/1235634. 
  35. ↑ Evans, K. F. (1998). "The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer". Journal of the Atmospheric Sciences 55 (3): 429–446. doi:10.1175/1520-0469(1998)055<0429:TSHDOM>2.0.CO;2. Bibcode: 1998JAtS...55..429E. 
  36. ↑ Amato, U.; Masiello, G.; Serio, C.; Viggiano, M. (2002). "The σ-IASI code for the calculation of infrared atmospheric radiance and its derivatives". Environmental Modelling & Software 17 (7): 651–667. doi:10.1016/S1364-8152(02)00027-0. 
  37. ↑ Liuzzi, G.; Masiello, G.; Serio, C.; Meloni, D.; Di Biagio, C.; Formenti, P. (2017). "Consistency of dimensional distributions and refractive indices of desert dust measured over Lampedusa with IASI radiances". Atmospheric Measurement Techniques 10 (2): 599–615. doi:10.5194/amt-10-599-2017. Bibcode: 2017AMT....10..599L. 
  38. ↑ Ramon, D. (2019). "Modeling polarized radiative transfer in the ocean-atmosphere system with the GPU-accelerated SMART-G Monte Carlo code". Journal of Quantitative Spectroscopy and Radiative Transfer 222-223: 89–107. doi:10.1016/j.jqsrt.2018.10.017. Bibcode: 2019JQSRT.222...89R. 
  39. ↑ FluxNet
  40. ↑ Key, J.; Schweiger, A. J. (1998). "Tools for atmospheric radiative transfer: Streamer and FluxNet". Computers & Geosciences 24 (5): 443–451. doi:10.1016/S0098-3004(97)00130-1. Bibcode: 1998CG.....24..443K. 
  41. ↑ HITRAN Site
  42. ↑ GEISA Site
General
  • Bohren, Craig F. and Eugene E. Clothiaux, Fundamentals of atmospheric radiation: an introduction with 400 problems, Weinheim : Wiley-VCH, 2006, 472 p., ISBN:3-527-40503-8.
  • Goody, R. M. and Y. L. Yung, Atmospheric Radiation: Theoretical Basis. Oxford University Press, 1996 (Second Edition), 534 pages, ISBN:978-0-19-510291-8.
  • Liou, Kuo-Nan, An introduction to atmospheric radiation, Amsterdam ; Boston : Academic Press, 2002, 583 p., International geophysics series, v.84, ISBN:0-12-451451-0.
  • Mobley, Curtis D., Light and water: radiative transfer in natural waters; based in part on collaborations with Rudolph W. Preisendorfer, San Diego, Academic Press, 1994, 592 p., ISBN:0-12-502750-8
  • Petty, Grant W, A first course in atmospheric radiation (2nd Ed.), Madison, Wisconsin : Sundog Pub., 2006, 472 p., ISBN:0-9729033-1-3
  • Preisendorfer, Rudolph W., Hydrologic optics, Honolulu, Hawaii : U.S. Dept. of Commerce, National Oceanic & Atmospheric Administration, Environmental Research Laboratories, Pacific Marine Environmental Laboratory, 1976, 6 volumes.
  • Stephens, Graeme L., Remote sensing of the lower atmosphere : an introduction, New York, Oxford University Press, 1994, 523 p. ISBN:0-19-508188-9.
  • Thomas, Gary E. and Knut Stamnes, Radiative transfer in the atmosphere and ocean, Cambridge, New York, Cambridge University Press, 1999, 517 p., ISBN:0-521-40124-0.
  • Zdunkowski, W., T. Trautmann, A. Bott, Radiation in the Atmosphere. Cambridge University Press, 2007, 496 pages, ISBN:978-0-521-87107-5

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