Atmospheric radiative transfer codes

An Atmospheric radiative transfer model, code, or simulator calculates radiative transfer of electromagnetic radiation through a planetary atmosphere.

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		Scott and Chédin (1981) [3]	No	No	Yes	Yes	No	No	band or line-by-line	Yes	Yes		freeware
6S/6SV1		Kotchenova et al. (1997) [4]	No	Yes	Yes	No	No	No	band	?	Yes			non-Lambertian surface
ARTS		Eriksson et al. (2011) [5]	No	No	No	Yes	Yes	Yes	line-by-line	Yes	Yes	spherical 1D, 2D, 3D	GPL
BTRAM		Chapman et al. (2009) [6]	No	Yes	Yes	Yes	Yes	Yes	line-by-line	No	No	1D,plane-parallel	proprietary commercial
COART		Jin et al. (2006) [7]	Yes	Yes	Yes	Yes	No	No		Yes	No	plane-parallel	free
CRM			No	Yes	Yes	Yes	No	No	band	Yes	No		freely available	Part of NCAR Community Climate Model
CRTM			No	Yes	Yes	Yes	No	Yes	band	Yes	?
DART radiative transfer model		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		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		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		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		Edwards (1992) [15]	?	?	?	Yes	?	?	line-by-line	?	?
KARINE		Eymet (2005) [16]	No	No	Yes		No	No		?	?	plane-parallel	GPL
KCARTA			?	?	Yes	Yes	?	?	line-by-line	Yes	?	plane-parallel	freely available	AIRS reference model
KOPRA			No	No	No	Yes	No	No		?	?
LBLRTM		Clough et al. (2005) [17]	Yes	Yes	Yes	Yes	Yes	Yes	line-by-line	?	?
LEEDR		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		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		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		Caillault et al. (2007) [21]	No	Yes	Yes	Yes	No	No	band	Yes	?		proprietary freeware
MCARaTS	[22]												GPL	3-D Monte Carlo
MODTRAN		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		Cornette (2006) [24]	λ>0.2 µm	Yes	Yes	Yes	Yes	Yes	band	Yes	No		freely available
MSCART		Wang et al. (2017)[25] Wang et al. (2019)[26]	Yes	Yes	Yes	No	No	No		Yes	Yes	1D, 2D, 3D	available on request
PUMAS			Yes	Yes	Yes	Yes	Yes	Yes	Line-by-line and correlated-k	Yes	Yes	plane-parallel and pseudo-spherical	Free/online tool
RADIS		Pannier (2018) [27]	No	No	Yes		No	No		No	No	1D	GPL
RFM			No	No	No	Yes	No	No	line-by-line	No	?		available on request	MIPAS reference model based on GENLN2
RRTM/RRTMG		Mlawer, et al. (1997) [28]	ṽ<50,000 cm^−1	Yes	Yes	Yes	Yes	ṽ>10 cm^−1		?	?		free of charge	uses DISORT
RTMOM			λ>0.25 µm	Yes	Yes	λ<15 µm	No	No	line-by-line	Yes	?	plane-parallel	freeware
RTTOV		Saunders et al. (1999) [29]	λ>0.4 µm	Yes	Yes	Yes	Yes	Yes	band	Yes	?		available on request
SASKTRAN	[30]	Bourassa et al. (2008)[31] Zawada et al. (2015)[32]	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		Ricchiazzi et al. (1998) [33]	Yes	Yes	Yes	?	No	No		Yes	?	plane-parallel		uses DISORT
SCIATRAN		Rozanov et al. (2005) ,[34] Rozanov et al. (2014) [35]	Yes	Yes	Yes	No	No	No	band or line-by-line	Yes	Yes	plane-parallel or pseudo-spherical or spherical
SHARM		Lyapustin (2002) [36]	No	Yes	Yes	No	No	No		Yes	?
SHDOM		Evans (2006) [37]	?	?	Yes	Yes	?	?		Yes	?
σ-IASI		Amato et al. (2002)[38] Liuzzi et al. (2017)[39]	No	No	Yes	Yes	Yes	No	band	Yes	No	plane-parallel	Available on request	Semi-analytical Jacobians.
SMART-G		Ramon et al. (2019) [40]	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	[41]	Key and Schweiger (1998) [42]	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			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[43]	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[44]	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

• Discrete dipole approximation codes
• Codes for electromagnetic scattering by cylinders
• Codes for electromagnetic scattering by spheres
• Optical properties of water and ice

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. Bibcode:1981JApMe..20..802S. doi:10.1175/1520-0450(1981)020<0802:AFLBLM>2.0.CO;2.
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. Bibcode:2006ApOpt..45.6762K. CiteSeerX 10.1.1.488.9804. doi:10.1364/AO.45.006762. PMID 16926910.
5. Eriksson, P.; Buehler, S. A.; Davis, C.P.; Emde, C.; Lemke, O. (2011). "ARTS, the atmospheric radiative transfer simulator, Version 2" (PDF). Journal of Quantitative Spectroscopy and Radiative Transfer. 112 (10): 1551–1558. Bibcode:2011JQSRT.112.1551E. doi:10.1016/j.jqsrt.2011.03.001. 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. Bibcode:2006ApOpt..45.7443S. doi:10.1364/AO.45.007443. hdl:2060/20080015519. PMID 16983433. S2CID 39305812.
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. Bibcode:1996RSEnv..58..131G. doi:10.1016/0034-4257(95)00253-7.
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. Bibcode:1988ApOpt..27.2502S. doi:10.1364/AO.27.002502. PMID 20531783.
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. Bibcode:2015JQSRT.157..119L. doi:10.1016/j.jqsrt.2015.02.014.
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. Bibcode:2016SoEn..135..435X. doi:10.1016/j.solener.2016.06.003.
12. Fu, Q.; Liou, K.-N (1993). "Parameterization of the radiative properties of cirrus clouds". J. Atmos. Sci. 50 (13): 2008–2025. Bibcode:1993JAtS...50.2008F. doi:10.1175/1520-0469(1993)050<2008:POTRPO>2.0.CO;2.
13. "Archived copy". Archived from the original on 2010-05-27. Retrieved 2010-07-07.CS1 maint: archived copy as title (link)
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. Bibcode:2005JQSRT..91..233C. doi:10.1016/j.jqsrt.2004.05.058. hdl:2027.42/142162.
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. Bibcode:2014JApMC..53..136F. doi:10.1175/JAMC-D-13-036.1.
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. Bibcode:1994JQSRT..52..563C. CiteSeerX 10.1.1.371.5401. doi:10.1016/0022-4073(94)90025-6.
20. Mayer, B.; Kylling, A. (2005). "Technical note: The libRadtran software package for radiative transfer calculations - description and examples of use" (PDF). Atmospheric Chemistry and Physics. 5 (7): 1855–1877. Bibcode:2005ACP.....5.1855M. doi:10.5194/acp-5-1855-2005.
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. Bibcode:2007ApOpt..46.5471C. doi:10.1364/AO.46.005471. PMID 17676164.
22. "MCARaTS". sites.google.com. Retrieved 2016-04-01.
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. Bibcode:1998RSEnv..65..367B. doi:10.1016/S0034-4257(98)00045-5.
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. Wang, Zhen; Cui, Shengcheng; Yang, Jun; Gao, Haiyang; Liu, Chao; Zhang, Zhibo (2017). "A novel hybrid scattering order-dependent variance reduction method for monte carlo simulations of radiative transfer in cloudy atmosphere". Journal of Quantitative Spectroscopy and Radiative Transfer. 189: 283–302.
26. Wang, Zhen; Cui, Shengcheng; Zhang, Zhibo; Yang, Jun; Gao, Haiyang; Zhang, Feng (2019). "Theoretical extension of universal forward and backward Monte Carlo radiative transfer modeling for passive and active polarization observation simulations". Journal of Quantitative Spectroscopy and Radiative Transfer. 235: 81–94. doi:10.1016/j.jqsrt.2019.06.025.
27. Pannier, E.; Laux, C. (2019). "RADIS: A nonequilibrium line-by-line radiative code for CO2 and HITRAN-like database species" (PDF). Quantitative Spectroscopy and Radiative Transfer. 222–223: 12–25. Bibcode:2019JQSRT.222...12P. doi:10.1016/j.jqsrt.2018.09.027.
28. 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. Bibcode:1997JGR...10216663M. doi:10.1029/97JD00237. S2CID 54031652.
29. 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. Bibcode:1999QJRMS.125.1407S. doi:10.1256/smsqj.55614.
30. "Welcome to SASKTRAN's documentation! — SASKTRAN 0.1.3 documentation". arg.usask.ca. Retrieved 2018-04-11.
31. 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. Bibcode:2008JQSRT.109...52B. doi:10.1016/j.jqsrt.2007.07.007.
32. 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. Bibcode:2015AMT.....8.2609Z. doi:10.5194/amt-8-2609-2015. ISSN 1867-8548.
33. 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. Bibcode:1998BAMS...79.2101R. doi:10.1175/1520-0477(1998)079<2101:SARATS>2.0.CO;2. S2CID 55800532.
34. 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. Bibcode:2005AdSpR..36.1015R. doi:10.1016/j.asr.2005.03.012.
35. 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. Bibcode:2014JQSRT.133...13R. doi:10.1016/j.jqsrt.2013.07.004.
36. 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. Bibcode:2002ApOpt..41.5607L. doi:10.1364/AO.41.005607. PMID 12269559.
37. 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. Bibcode:1998JAtS...55..429E. CiteSeerX 10.1.1.555.9038. doi:10.1175/1520-0469(1998)055<0429:TSHDOM>2.0.CO;2.
38. 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.
39. 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. Bibcode:2017AMT....10..599L. doi:10.5194/amt-10-599-2017.
40. 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. Bibcode:2019JQSRT.222...89R. doi:10.1016/j.jqsrt.2018.10.017.
41. FluxNet
42. Key, J.; Schweiger, A. J. (1998). "Tools for atmospheric radiative transfer: Streamer and FluxNet". Computers & Geosciences. 24 (5): 443–451. Bibcode:1998CG.....24..443K. doi:10.1016/S0098-3004(97)00130-1. hdl:2060/19980018471.
43. HITRAN Site
44. 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

External links

• ITWC for radiative transfer