Skip to main content

A review of fast radiative transfer techniques

  • Chapter
  • First Online:

Part of the book series: Springer Praxis Books ((ENVIRONSCI))

Abstract

Atmospheric radiative transfer involves gas absorption coupled with molecular Rayleigh scattering, in addition to scattering and absorption by clouds and aerosols. Further, computation of heating rates are dependent on absorption and emission of radiation, processes that have a complex dependence on various quantities. Typically, spectral regions contain several overlapping lines with intensities varying over many orders of magnitude. The most accurate method for computing the radiative terms in a molecular atmosphere involves a detailed line-by-line (LBL) calculation of the absorption coefficient versus wavenumber. However, direct numerical solution of the radiative transfer equation over frequency is in most cases too computationally expensive to be used on a routine basis. Therefore a variety of approximations have been developed to accelerate the computational process. This chapter discusses several of these techniques.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ambartsumian, V. (1936), The effect of the absorption lines on the radiative equilibrium of the outer layers of the stars, Publ. Obs. Astron. Univ. Leningrad, 6, 7–18.

    Google Scholar 

  • Arking, A. A., and K. Grossman (1972), The influence of line shape and band structure on temperatures in planetary atmospheres, J. Atmos. Sci., 29, 937–949.

    Article  Google Scholar 

  • Armbruster, W., and J. Fischer (1996), Improved method of exponential sum fitting of transmissions to describe the absorption of atmospheric gases, Appl. Opt., 35(12), 1931–1941, doi:10.1364/AO.35.001931.

    Article  Google Scholar 

  • Boesche, E., P. Stammes, R. Preusker, R. Bennartz, W. Knap, and J. Fischer (2008), Polarization of skylight in the O2 A band: Effects of aerosol properties, Appl. Opt., 47(19), 3467–3480, doi:10.1364/AO.47.003467.

    Article  Google Scholar 

  • Buchwitz, M., V. V. Rozanov, and J. P. Burrows (2000), A correlated-k distribution scheme for overlapping gases suitable for retrieval of atmospheric constituents from moderate resolution radiance measurements in the visible/near-infrared spectral region, J. Geophys. Res., 105(D12), 15247–15261, doi:10.1029/2000JD900171.

    Article  Google Scholar 

  • Cao, Y., W. Zhang, Y. Zhang, H. Chang, and M. Cong (2011), A new k-interval selection technique for fast atmospheric radiance calculation in remote sensing applications, J. Quant. Spectrosc. Radiat. Transfer, 112(9), 1479–1485, 10.1016/j.jqsrt.2011.03.004.

    Article  Google Scholar 

  • Chandrasekhar, S. (1950), Radiative Transfer, Oxford: Clarendon Press.

    Google Scholar 

  • Chou, M. D., and A. Arking (1980), Computation of infrared cooling rates in the water vapor bands, J. Atmos. Sci., 37, 855–867.

    Article  Google Scholar 

  • Chou, M.-D., W. L. Ridgway, and M. M.-H. Yan (1993), One-parameter scaling and exponential-sum fitting for water vapor and CO2 infrared transmission functions, J. Atmos. Sci., 50(14), 2294–2303, doi:10.1175/1520-0469(1993)050<2294:OPSAES> 2.0.CO;2.

    Google Scholar 

  • Crisp, D. (1997), Absorption of sunlight by water vapor in cloudy conditions: A partial explanation for the cloud absorption anomaly, Geophys. Res. Lett., 24(5), 571–574, doi:10.1029/97GL50245.

    Article  Google Scholar 

  • Duan, M., Q. Min, and J. Li (2005), A fast radiative transfer model for simulating high-resolution absorption bands, J. Geophys. Res., 110, D15201, doi:10.1029/ 2004JD005590.

    Article  Google Scholar 

  • Germogenova, T. A. (1961), On the solution of the transfer equation for a plane layer, Zurnal. Appl. Math. Math. Phys., 1, 1001–1008.

    Google Scholar 

  • Germogenova, T. A. (1963), Some formulas to solve the transfer equation in a plane layer problem, in Spectroscopy of Scattering Media, (ed. B. I. Stepanov), Minsk: AN BSSR, 36–41.

    Google Scholar 

  • Goody, R., R. West, L. Chen, and D. Crisp (1989), The correlated-k method for radiation calculations in non homogeneous atmospheres, J. Quant. Spectrosc. Radiat. Transfer, 42, 539–550.

    Article  Google Scholar 

  • Hasekamp, O. P., and A. Butz (2008), Efficient calculation of intensity and polarization spectra in vertically inhomogeneous scattering and absorbing atmospheres, J. Geophys. Res., 113, D20309, doi:10.1029/2008JD010379.

    Article  Google Scholar 

  • Hovenier, J. W. (1971), Multiple scattering of polarized light in planetary atmospheres, Astron. Astrophys., 13, 7–29.

    Google Scholar 

  • Hunt, G., and I. Grant (1969), Discrete space theory of radiative transfer and its application to problems in planetary atmospheres, J. Atmos. Sci., 26, 963–972, doi:10.1175/ 1520-0469(1969)026<0963:DSTORT>2.0.CO;2.

    Google Scholar 

  • Kawabata, K., and S. Ueno (1988), The first three orders of scattering in vertically inhomogeneous scattering-absorbing media, Astrophys. Space Sci., 150, 327–344.

    Article  Google Scholar 

  • Key, J. R., and A. J. Schweiger (1998), Tools for atmospheric radiative transfer: Streamer and FluxNet, Comp. Geosci., 24(5), 443–451, doi:10.1016/S0098-3004(97)00130-1.

    Article  Google Scholar 

  • Kokhanovsky, A. A. (2002), Simple approximate formula for the reflection function of a homogeneous, semi-infinite turbid medium, J. Opt. Soc. Am. A, 19(5), 957–960.

    Article  Google Scholar 

  • Kokhanovsky, A. A., and T. Nauss (2006), Reflection and transmission of solar light by clouds: Asymptotic theory, Atmos. Chem. Phys., 6, 5,537-5,545, doi:10.5194/acp-6- 5537–2006.

    Google Scholar 

  • Kokhanovsky, A. A., and V. V. Rozanov (2003), The reflection function of optically thick weakly absorbing turbid layers: A simple approximation, J. Quant. Spectrosc. Radiat. Transfer, 77, 165–175.

    Article  Google Scholar 

  • Kratz, D. P. (1995), The correlated k-distribution technique as applied to the AVHRR channels, J. Quant. Spectrosc. Radiat. Transfer, 53(5), 501–517, doi:10.1016/0022- 4073(95)00006-7.

    Google Scholar 

  • Kratz, D. P., M.-D. Chou, M. M.-H. Yan, and C.-H. Ho (1998), Minor trace gas radiative forcing calculations using the k distribution method with one-parameter scaling, J. Geophys. Res., 103(D24), 31,647–31,656, doi:10.1029/1998JD200009.

    Google Scholar 

  • Lacis, A. A., and V. Oinas (1991), A description of the correlated k distribution method for modeling non gray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres, J. Geophys. Res., 96, 9027–9063.

    Article  Google Scholar 

  • Lacis, A. A., W. C. Wang, and J. E. Hansen (1979), Correlated k-distribution method for radiative transfer in climate models: Application to effect of cirrus clouds on climate, NASA Conf. Publ., 2076, 309–314.

    Google Scholar 

  • Liu, X., W. L. Smith, D. K. Zhou, and A. Larar (2006), Principal component-based radiative transfer model for hyperspectral sensors: theoretical concept, Appl. Opt., 45(1), 201–209, doi: 10.1364/AO.45.000201.

    Article  Google Scholar 

  • Mano, Y. (1995), Modified ESFT method for application to atmospheric radiation, Papers in Meteorology and Geophysics, 46(1), 1–8.

    Article  Google Scholar 

  • Meadows, V. S., and D. Crisp (1996), Ground-based near-infrared observations of the Venus nightside: The thermal structure and water abundance near the surface, J. Geophys. Res., 101(E2), 4595–4622, doi:10.1029/95JE03567.

    Article  Google Scholar 

  • Moncet, J.-L., G. Uymin, A. E. Lipton, and H. E. Snell (2008), Infrared radiance modeling by Optimal Spectral Sampling, J. Atmos. Sci., 65, 3917–3934, doi:10.1175/ 2008JAS2711.1.

    Article  Google Scholar 

  • Natraj, V., X. Jiang, R.-L. Shia, X. Huang, J. S. Margolis, and Y. L. Yung (2005), Application of principal component analysis to high spectral resolution radiative transfer: A case study of the O2 A band, J. Quant. Spectrosc. Radiat. Transfer, 95(4), 539–556, doi:10.1016/j.jqsrt.2004.12.024.

    Article  Google Scholar 

  • Natraj, V., R.-L. Shia, and Y. L. Yung (2010), On the use of principal component analysis to speed up radiative transfer calculations, J. Quant. Spectrosc. Radiat. Transfer, 111(5), 810–816, doi:10.1016/j.jqsrt.2009.11.004.

    Article  Google Scholar 

  • Natraj, V., and R. J. D. Spurr (2007), A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering–absorbing media, J. Quant. Spectrosc. Radiat. Transfer, 107(2), 263–293, doi:10.1016/j.jqsrt.2007.02.011.

    Article  Google Scholar 

  • Nauss, T., and A. A. Kokhanovsky (2011), Retrieval of warm cloud optical properties using simple approximations, Remote Sens. Environ., 115(6), 1,317–1,325, doi:10.1016/ j.rse.2011.01.010.

    Google Scholar 

  • O’Dell, C. W. (2010), Acceleration of multiple-scattering, hyperspectral radiative transfer calculations via low-streams interpolation, J. Geophys. Res., 115, D10206, doi:10.1029/2009JD012803.

    Article  Google Scholar 

  • Schwander, H., A. Kaifel, A. Ruggaber, and P. Koepke (2001), Spectral radiative-transfer modeling with minimized computation time by use of a neural-network technique, Appl. Opt., 40(3), 331–335, doi:10.1364/AO.40.000331.

    Article  Google Scholar 

  • Sobolev, V. V. (1984), Integral relations and asymptotic expressions in the theory of radiative transfer, Astrofizika, 20, 123–132.

    Google Scholar 

  • Spurr, R. J. D. (2002), Simultaneous derivation of intensities and weighting functions in a general pseudo-spherical discrete ordinate radiative transfer treatment, J. Quant. Spectrosc. Radiat. Transfer, 75(2), 129–175, doi: 10.1016/S0022-4073(02)00014-6.

    Article  Google Scholar 

  • Takenaka, H., T. Y. Nakajima, A. Higurashi, A. Higuchi, T. Takamura, R. T. Pinker, and T. Nakajima (2011), Estimation of solar radiation using a neural network based on radiative transfer, J. Geophys. Res., 116, D08215, doi:10.1029/2009JD013337.

    Article  Google Scholar 

  • van de Hulst, H. C. (1980), Multiple Light Scattering: Tables, Formulas and Applications, New York: Academic Press.

    Google Scholar 

  • West, R, D. Crisp, and L. Chen (1990), Mapping transformations for broadband atmospheric radiation calculations, J. Quant. Spectrosc. Radiat. Transfer, 43, 191–199.

    Article  Google Scholar 

  • Wiscombe, W. J., and J. W. Evans (1977), Exponential-sum fitting of radiative transmission functions, J. Comp. Phys., 24, 416–444, doi:10.1016/0021-9991(77)90031-6.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vijay Natraj .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Natraj, V. (2013). A review of fast radiative transfer techniques. In: Kokhanovsky, A. (eds) Light Scattering Reviews 8. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32106-1_10

Download citation

Publish with us

Policies and ethics