Approximation Methods in Atmospheric 3D Radiative Transfer Part 1: Resolved Variability and Phenomenology

  • A.B. Davis
  • I.N. Polonsky
Part of the Physics of Earth and Space Environments book series (EARTH)


Radiative Transfer Optical Depth Phase Function Diffusion Theory Radiative Transfer Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alcouffe, R.E., R.S. Baker, F.W. Brinkley, D.R. Marr, R.D. O’Dell, and W.F. Walters (1997). DANTSYS: A Diffusion Accelerated Neutral Particle Transport, (UC-705), issued 06/95, revised 03/97. Los Alamos National Laboratory, Los Alamos (NM).Google Scholar
  2. Box, M.A., M. Keevers, and B.H.J. McKellar (1988). On the perturbation series for radiative effects. J. Quant. Spect. Radiat. Trans., 39, 219–223.CrossRefGoogle Scholar
  3. Box, M.A., S.A.W. Gerstl, and C. Simmer (1989). Computation of atmospheric radiative effects via perturbation theory. Beitr. Phys. Atmosph., 62, 193–199.Google Scholar
  4. Box, M.A., I.N. Polonsky, and A.B. Davis (2003). Higher-order perturbation theory applied to radiative transfer in non-plane-parallel media. J. Quant. Spectrosc. Radiat. Transfer, 78, 105–118.CrossRefGoogle Scholar
  5. Cahalan, R.F., L. Oreopoulos, G. Wen, A. Marshak, S.-C. Tsay, and T. DeFelice (2001). Cloud characterization and clear-sky correction from Landsat-7. Remote Sens. Environ., 78, 89–98.CrossRefGoogle Scholar
  6. Cahalan, R.F., L. Oreopoulos, A. Marshak, K.F. Evans, A.B. Davis, R. Pincus, K. Yetzer, B. Mayer, R. Davies, T.P. Ackerman, H.W. Barker, E.E. Clothiaux, R.G. Ellingson, M.J. Garay, E. Kassianov, S. Kinne, A. Macke, W. O’Hirok, P.T. Partain, S.M. Prigarin, A.N. Rublev, G.L. Stephens, F. Szczap, E.E. Takara, T. Várnai, G. Wen, and T.B. Zhuravleva (2005). The international Intercomparison of 3D Radiation Codes (I3RC): Bringing together the most advanced radiative transfer tools for cloudy atmospheres. Bull. Amer. Meteor. Soc., to appear in Sept 2005 issue.Google Scholar
  7. Cannon, C.J. (1970). Line transfer in two dimensions. Astrophys. J., 161, 255–264.CrossRefGoogle Scholar
  8. Case, K.M. and P.F. Zweifel (1967). Linear Transport Theory. Addison-Wesley, Reading (MA).Google Scholar
  9. Caudill, M. and C. Butler (1992). Understanding Neural Networks: Computer Explorations. MIT Press, Cambridge (MA), 2nd edition.Google Scholar
  10. Chu, M.C. and W.S. Churchill (1955). Numerical solution of problems in multiple scattering of electromagnetic radiation. J. Chem. Phys., 59, 855–863.CrossRefGoogle Scholar
  11. Chýlek, P., C. Borel, A.B. Davis, S. Bender, J. Augustine, and G. Hodges (2004). Effect of broken clouds on satellite based columnar water vapor retrieval. IEEE Geosci. and Remote Sens. Lett., 1, 175–179.CrossRefGoogle Scholar
  12. Coakley, J.A. and P. Chýlek (1975). The two-stream approximation in radiative transfer: Including the angle of the incident radiation. J. Atmos. Sci., 32, 409–418.CrossRefGoogle Scholar
  13. Cornet, C., H. Isaka, B. Guillemet, and F. Szczap (2004). Neural network retrieval of cloud parameters of inhomogeneous clouds from multispectral and multiscale radiance data: Feasibility study. J. Geophys. Res., 109, D12203, doi:10.1029/2003JD004186.CrossRefGoogle Scholar
  14. Davies, R. (1978). The effect of finite geometry on the three-dimensional transfer of solar irradiance in clouds. J. Atmos. Sci., 35, 1712–1725.CrossRefGoogle Scholar
  15. Davis, A.B. (2002). Cloud remote sensing with sideways-looks: Theory and first results using Multispectral Thermal Imager (MTI) data. SPIE Pro. Vol. 4725, pp. 397–405.CrossRefGoogle Scholar
  16. Davis, A. and A. Marshak (1997). Lévy kinetics in slab geometry: Scaling of transmission probability. In Fractal Frontiers. M.M. Novak and T.G. Dewey (eds.). World Scientific, Singapore, pp. 63–72.Google Scholar
  17. Davis, A.B. and A. Marshak (2001). Multiple scattering in clouds: Insights from three-dimensional diffusion/P1 theory. Nuclear Sci. and Engin., 137, 251–280.Google Scholar
  18. Davis, A.B. and A. Marshak (2002). Space-time characteristics of light transmitted through dense clouds: A Green function analysis. J. Atmos. Sci., 59, 2714–2728.CrossRefGoogle Scholar
  19. Davis, A.B. and A. Marshak (2004). Photon propagation in heterogeneous optical media with spatial correlations: Enhanced mean-free-paths and wider-than-exponential free-path distributions. J. Quant. Spectrosc. Radiat. Transfer, 84, 3–34.CrossRefGoogle Scholar
  20. Davis, A., S. Lovejoy, and D. Schertzer (1993). Supercomputer simulation of radiative transfer in multifractal cloud models. In IRS’92: Current Problems in Atmospheric Radiation. S. Keevallik and O. Kärner (eds.). Deepak Publ., Hampton (VA), pp. 112–115.Google Scholar
  21. Davis, A., A. Marshak, R.F. Cahalan, and W.J. Wiscombe (1997). The LANDSAT scale-break in stratocumulus as a three-dimensional radiative transfer effect, Implications for cloud remote sensing. J. Atmos. Sci., 54, 241–260.CrossRefGoogle Scholar
  22. Davis, A.B., R.F. Cahalan, J.D. Spinhirne, M.J. McGill, and S.P. Love (1999). Offbeam lidar: An emerging technique in cloud remote sensing based on radiative Green-function theory in the diffusion domain. Phys. Chem. Earth (B), 24, pp. 177–185 (Erratum 757-765).Google Scholar
  23. Davis, A.B., D.M. Winker, and M.A. Vaughan (2001). First retrievals of dense cloud properties from off-beam/multiple-scattering lidar data collected in space. In Laser Remote Sensing of the Atmosphere, Selected Papers from the 20th International Conference on Laser Radar. A. Dabas, C. Loth and J. Pelon (eds.). Editions de l’Ècole Polytechnique, Palaiseau (France), pp. 35–38.Google Scholar
  24. Eddington, A.S. (1916). On the radiative equilibrium of stars. Mon. Not. Roy. Ast. Soc., 77, 16–35.Google Scholar
  25. Evans, K.F., R.P. Lawson, P. Zmarzly, D. O’Connor, and W.J. Wiscombe (2003). In situ cloud sensing with multiple scattering lidar: Simulations and demonstration. J. Atmos. and Oceanic Tech., 20, 1505–1522.CrossRefGoogle Scholar
  26. Faure, T., H. Isaka, and B. Guillemet (2001). Neural network analysis of the radiative interaction between neighboring pixels in inhomogeneous clouds. J. Geophys. Res., 106, 14,465–14,484.Google Scholar
  27. Faure, T., H. Isaka, and B. Guillemet (2002). Neural network retrieval of clouds parameters from high-resolution multi-spectral radiometric data. Remote Sens. Environ., 80, 285–296.CrossRefGoogle Scholar
  28. Fermi, E. (1941). Cosmic ray theory. Rev. Modern Phys., 13, 240.CrossRefGoogle Scholar
  29. Gabriel, P.M. and K.F. Evans (1996). Simple radiative transfer methods for calculating domain-averaged solar fluxes in inhomogeneous clouds. J. Atmos. Sci., 53, 858–877.CrossRefGoogle Scholar
  30. Gabriel, P.M., S.M. Lovejoy, A. Davis, D. Schertzer, and G.L. Austin (1990). Discrete angle radiative transfer II: Renormalization approach for homogeneous and fractal clouds. J. Geophys. Res., 95, 11,717–11,728.CrossRefGoogle Scholar
  31. Galinsky, V.L. (2000). 3D radiative transfer in weakly inhomogeneous media, Part II: Discrete ordinate method and effective algorithm for its inversion. J. Atmos. Sci., 57, 1635–1645.CrossRefGoogle Scholar
  32. Galinsky, V.L. and V. Ramanathan (1998). Three-dimensional radiative-transfer in weakly inhomogeneous media, Part I: Diffusive approximation. J. Atmos. Sci., 55, 2946–2959.CrossRefGoogle Scholar
  33. Giovanelli, R.G. (1959). Radiative transfer in non-uniform media. Aust. J. Phys., 12, 164–170.Google Scholar
  34. Gu, Y. and K.-N. Liou (2001). Radiation parameterization for three-dimensional inhomogeneous cirrus clouds: Application to climate models. J. Climate, 14, 2443–2457.CrossRefGoogle Scholar
  35. Henderson, B.G. and P. Chýlek (2005). The effect of spatial resolution on satellite aerosol optical depth retrieval. IEEE Trans. Geosci. and Remote Sens., in press.Google Scholar
  36. Joseph, J.H., W.J. Wiscombe, and J.A. Weinman (1976). The delta-Eddington approximation for radiative flux transfer. J. Atmos. Sci., 33, 2452–2459.CrossRefGoogle Scholar
  37. Khairoutdinov, M.F. and D.A. Randall (2001). A cloud-resolving model as a cloud parameterization in the NCAR Community Climate System Model: Preliminary results. Geophys. Res. Lett., 28, 3617–3620.CrossRefGoogle Scholar
  38. King, M.D., L.F. Radke, and P.V. Hobbs (1990). Determination of the spectral absorption of solar radiation by marine Streatocumulus clouds from airborne measurements within clouds. J. Atmos. Sc., 47, 894–907.CrossRefGoogle Scholar
  39. Kobayashi, T., K. Masuda, M. Sasaki, and J.-P. Mueller (2000). Monte Carlo simulations of enhanced visible radiance in clear-air satellite fields of view near clouds. J. Geophys. Res., 105, 26569–26576.CrossRefGoogle Scholar
  40. Kokhanovsky, A.A. (2003). The influence of horizontal inhomogeneity on radiative characteristics of clouds: An aysmptotic case study. IEEE Trans. Geosci. and Remote Sens., 41, 817–825.CrossRefGoogle Scholar
  41. Li, J., J.W. Geldart, and P. Chýlek (1994). Perturbation solution for 3D radiative transfer in horizontally periodic inhomogeneous cloud field. J. Atmos. Sci., 51, 2110–2122.CrossRefGoogle Scholar
  42. Li, J., J.W. Geldart, and P. Chýlek (1995). Second order perturbation solution for radiative transfer in clouds with a horizontally arbitrary periodic inhomogeniety. J. Quant. Spectrosc. Radiat. Transfer, 53, 445–456.CrossRefGoogle Scholar
  43. Love, S.P., A.B. Davis, C. Ho, and C.A. Rohde (2001). Remote sensing of cloud thickness and liquid water content with Wide-Angle Imaging Lidar (WAIL). Atmos. Res., 59–60, 295–312.CrossRefGoogle Scholar
  44. Lovejoy, S., A. Davis, P. Gabriel, D. Schertzer, and G. Austin (1990). Discrete angle radiative transfer I: Scaling and similarity, universality and diffusion. J. Geophys. Res., 95, 11,699–11,715.Google Scholar
  45. Lyapustin, A. and Y.J. Kaufman (2001). Role of adjacency effect in the remote sensing of aerosol. J. Geophys. Res., 106, 11909–11916.CrossRefGoogle Scholar
  46. Marshak, A., A. Davis, W.J. Wiscombe, and R.F. Cahalan (1995). Radiative smoothing in fractal clouds. J. Geophys. Res., 100, 26,247–26,261.CrossRefGoogle Scholar
  47. Marshak, A., A. Davis, R.F. Cahalan, and W.J. Wiscombe (1998). Nonlocal Independent Pixel Approximation: Direct and Inverse Problems. IEEE Trans. Geosc. and Remote Sens., 36, 192–205.CrossRefGoogle Scholar
  48. Marshak, A., Yu. Knyazikhin, A.B. Davis, W.J. Wiscombe, and P. Pilewskie (2000). Cloud-vegetation interaction: Use of normalized difference cloud index for estimation of cloud optical thickness. Geophys. Res. Lett., 27, 1695–1698.CrossRefGoogle Scholar
  49. Meador, W.E. and W.R. Weaver (1980). Two-stream approximations to radiative transfer in planetary atmospheres: A unified description of existing methods and a new improvement. J. Atmos. Sci., 37, 630–643.CrossRefGoogle Scholar
  50. Min, Q.-L. and L.C. Harrison (1999). Joint statistics of photon pathlength and cloud optical depth. Geophys. Res. Lett., 26, 1425–1428.CrossRefGoogle Scholar
  51. Morse, P.M. and H. Feshbach (1953). Methods of Theoretical Physics, 2 vols. McGraw-Hill, New York (NY).Google Scholar
  52. Polonsky, I.N. and A.B. Davis (2004). Lateral photon transport in dense scattering and weakly-absorbing media of finite thickness: Asymptotic analysis of the Green functions. J. Opt. Soc. Amer. A, 21, 1018–1025.CrossRefGoogle Scholar
  53. Polonsky, I.N., M.A. Box, and A.B. Davis (2003). Radiative transfer through inhomogeneous turbid media: Implementation of the adjoint perturbation approach at the first-order. J. Quant. Spectrosc. Radiat. Transfer, 78, 85–98.CrossRefGoogle Scholar
  54. Pomraning, G.C. (1989). Diffusion theory via asymptotics. Transp. Theory and Stat. Phys., 18, 383–428.Google Scholar
  55. Qu, Z. (1999). On the Transmission of Ultraviolet Radiation in Horizontally Inhomogeneous Atmospheres: A Three-Dimensional Approach Based on the Delta-Eddington’s Approximation, Ph.D. Thesis. University of Chicago, Department of Geophysical Sciences, Chicago (IL).Google Scholar
  56. Roache, P.J. (1998). Verification and Validation in Computational Science and Engineering. Hermosa, Albuquerque (NM).Google Scholar
  57. Romanova, L.M. (1975). Radiative transfer in a horizontally inhomogeneous scattering medium. Izv. Acad. Sci. USSR Atmos. Oceanic Phys., 11, 509–513.Google Scholar
  58. Rossow, W.B., C. Delo, and B. Cairns (2002). Implications of the observed mesoscale variations of clouds for the earth’s radiation budget. J. Climate, 15, 557–585.CrossRefGoogle Scholar
  59. Savigny, C. von, O. Funk, U. Platt, and K. Pfeilsticker (1999). Radiative smoothing in zenith-scattered sky light transmitted through clouds to the ground. Geophys. Res. Lett., 26, 2949–2952.CrossRefGoogle Scholar
  60. Schuster, A. (1905). Radiation through a foggy atmosphere. Astrophys. J., 21, 1–22.CrossRefGoogle Scholar
  61. Schwarzschild, K. (1906). Über das Gleichgewicht der Sonnenatmosphere (in German, English title: On the equilibrium of the Sun’s atmosphere). Gottingen Nachrichten, 41, 1–24.Google Scholar
  62. Serber, R. and R. Rhodes (1992). The Los Alamos Primer: The First Lectures on How to Build an Atomic Bomb, annotated by Robert Serber, edited with an introduction by Richard Rhodes. University of California Press, Berkeley (CA).Google Scholar
  63. Siddal, R.G. and N. Selçuk (1979). Evaluation of a new six-flux model for radiative transfer in recangular enclosures. Trans. Inst. Chem. Eng., 57, 163–169.Google Scholar
  64. Siegel, R. and J.R. Howell (1981). Thermal Radiation Heat Transfer. McGraw-Hill, New York (NY), 2nd edition.Google Scholar
  65. Stephens, G.L. (1986). Radiative transfer in spatially heterogeneous, two-dimensional anisotropically scattering media. J. Quant. Spectrosc. Radiat. Transfer, 36, 51–67.CrossRefGoogle Scholar
  66. Tikhonov, A.N. (1977). Solutions of Ill-Posed Problems. Winston, New York (NY).Google Scholar
  67. Várnai, T. (2000). Influence of three-dimensional radiative effects on the spatial distribution of shortwave cloud reflection. J. Atmos. Sci., 57, 216–229.CrossRefGoogle Scholar
  68. Várnai, T. and R. Davies (1999). Effects of cloud heterogeneities on shortwave radiation: Comparison of cloud-top variability and internal heterogeneity. J. Atmos. Sci., 56, 4206–4224.CrossRefGoogle Scholar
  69. Várnai, T. and A. Marshak (2003). A method for analyzing how various parts of clouds influence each other’s brightness. J. Geophys. Res., 108, 4706, doi:10.1029/2003JD003561.CrossRefGoogle Scholar
  70. Weinman, J.A. and P.N. Swartztrauber (1968). Albedo of a striated medium of isotropically scattering particles. J. Atmos. Sci., 34, 642–650.Google Scholar
  71. Wen, G., R.F. Cahalan, S.-C. Tsay, and L. Oreopoulos (2001). Imapct of cumulus cloud spacing on Landsat atmospheric correction and aerosol retrieval. J. Geophys. Res., 106, 12,129–12,138.CrossRefGoogle Scholar
  72. Wyser, K., W. O’Hirok, C. Gautier, and C. Jones (2002). Remote sensing of surface solar irradiance with corrections for 3-D cloud effects. Remote Sens. Environ., 80, 272–284.CrossRefGoogle Scholar
  73. Wyser, K., W. O’Hirok, and C. Gautier (2005). A simple method for removing 3-D radiative effects in satellite retrievals of surface irradiance. Remote Sens. Environ., 94, 335–342.CrossRefGoogle Scholar
  74. Yodh, A. and B. Chance (1995). Spectroscopy and imaging with diffusing light. Phys. Today, 48, 34–40.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • A.B. Davis
  • I.N. Polonsky

There are no affiliations available

Personalised recommendations