A quasi-analytic solution of the radiative transfer equation for three-dimensional atmospheres

Journal of Quantitative Spectroscopy and Radiative Transfer

Volumn 103, Issue 2, 2007, Pages 371-393

  Ishida, H ^a   Asano, S ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Discretization of radiative transfer equation; Doubling adding scheme; Horizontal cloud inhomogeneity; Scaling function expansion; Three dimensional radiative transfer

Indexed keywords

RADIATION TRANSFER EQUATION; SCALING-FUNCTION EXPANSION; VECTOR-MATRIX DIFFERENTIAL EQUATION;

CLOUDS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; SOLAR RADIATION; VECTORS;

ATMOSPHERIC RADIATION;

ATMOSPHERE; EQUATION; MATRIX; NUMERICAL MODEL; RADIATIVE TRANSFER; VECTOR;

EID: 33750029361     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2006.05.004     Document Type: Article

References (39)

1. Ramanathan V., Cess R.D., Harrison E.F., Minnis P., Barkstrom B.R., Ahmad E., and Hartmann D. Cloud-radiative forcing and climate: results from the Earth Radiation Budget Experiment. Science 243 (1989) 57-63
2. Wu X., and Moncrieff M.W. Long-term behavior of cloud systems in TOGA COARE and their interactions with radiative and surface processes. Part III: effects on the energy budget and SST. J Atmos Sci 58 (2001) 1155-1168
3. Li Z., and Trishchenko A.P. Quantifying uncertainties in determining SW cloud radiative forcing and cloud absorption due to variability in atmospheric conditions. J Atmos Sci 58 (2001) 376-389
4. Platt C.M.R., Austin R.T., Young S.A., and Heymsfield A.J. LIRAD observations of tropical cirrus clouds in MCTEX. Part II: optical properties and base cooling in dissipating storm anvil clouds. J Atmos Sci 59 (2002) 3163-3177
5. Randall D.A., Harshvardhan, Dazlich D.A., and Corsetti T.G. Interactions among radiation, convection, and large-scale dynamics in a general circulation model. J Atmos Sci 46 (1989) 1943-1970
6. Slingo A. Sensitivity of the Earth radiation budget to changes in low clouds. Nature 343 (1990) 49-51
7. Wu X. Effects of ice microphysics on tropical radiative-convective-oceanic quasi-equilibrium states. J Atmos Sci 59 (2002) 1885-1897
8. Rogers D.P., and Koracin D. Radiative transfer and turbulence in the cloud-topped marine atmospheric boundary layer. J Atmos Sci 49 (1992) 1473-1486
9. Moeng C., Sullivan P.P., and Stevens B. Including radiative effects in an entrainment rate formula for buoyancy-driven PBLs. J Atmos Sci 56 (1999) 1031-1049
10. Boers R.J., Spinhirne D., and Hart W.D. Lidar observations of the fine-scale variability of marine stratocumulus clouds. J Appl Meteor 27 (1988) 797-810
11. Cahalan R.F., and Joseph J.H. Fractal statistics of cloud fields. Mon Weather Rev 11 (1989) 261-272
12. Cahalan R.F., and Snider J.B. Marine stratocumulus structure. Remote Sens Environ 28 (1989) 95-107
13. Barker H.W., and Davies J.A. Cumulus cloud radiative properties and the characteristics of satellite radiance wavenumber spectra. Remote Sens Environ 42 (1992) 51-64
14. Brooks I.M., and Rogers D.P. Aircraft observations of boundary layer rolls off the coast of California. J Atmos Sci 54 (1997) 1834-1849
15. Gayet JF, Asano S, Yamazaki A, Uchiyama A, Sinyuk A, Jourdan O, Auriol F. Two case studies of winter continental-type water and mixed-phase stratocumuli over the sea. 1. Microphysical and optical properties. J Geophys Res 2002;107:4569, doi:10.1029/2001JD001106.
16. Chandrasekhar S. Radiative transfer (1960), Oxford University Press, London
17. Hansen J.E. Multiple scattering of polarized light in planetary atmospheres. Part II: sunlight reflected by terrestrial water clouds. J Atmos Sci 28 (1971) 1400-1426
18. Welch R.M., and Wielicki B.A. Stratocumulus cloud field reflected fluxes: The effect of cloud shape. J Atmos Sci 41 (1984) 3085-3103
19. Coakley Jr. J.A., and Kobayashi T. Broken cloud biases in albedo and surface insolation derived from satellite imagery data. J Clim 2 (1989) 721-730
20. Loeb N.G., Varnai T., and Winker D.M. Influence of subpixel-scale cloud-top structure on reflectances from overcast stratiform cloud layers. J Atmos Sci 55 (1998) 2960-2973
21. Cahalan R.F., Ridgway W., Wiscombe W.J., Gollmer S., and Harshvardhan. Independent pixel and Monte Carlo estimates of stratocumulus albedo. J Atmos Sci 51 (1994) 3776-3790
22. Barker H.W. A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part I: methodology and homogeneous biases. J Atmos Sci 53 (1996) 2289-2303
23. Fu Q., Cribb M.C., Barker H.W., Krueger S.K., and Grossman A. Cloud geometry effects on atmospheric solar absorption. J Atmos Sci 57 (2000) 1156-1168
24. Iwabuchi H., and Hayasaka T. Effects of cloud horizontal inhomogeneity on the optical thickness retrieved from moderate-resolution satellite data. J Atmos Sci 59 (2002) 2227-2242
25. Di Giuseppe F., and Tompkins A.M. Effect of spatial organization on solar radiative transfer in three-dimensional idealized stratocumulus cloud fields. J Atmos Sci 60 (2003) 1774-1794
26. Stephens G.L. Radiative transfer through arbitrarily shaped optical media. Part I: a general method of solution. J Atmos Sci 45 (1988) 1818-1836
27. Gabriel P.M., Tsay S., and Stephens G.L. A Fourier-Riccati approach to radiative transfer. Part I: foundations. J Atmos Sci 50 (1993) 3125-3147
28. Kobayashi T. Reflected solar flux for horizontally inhomogeneous atmospheres. J Atmos Sci 48 (1991) 2436-2447
29. Stephens G.L. Radiative transfer through arbitrarily shaped optical media. Part II: group theory and simple closures. J Atmos Sci 45 (1988) 1837-1848
30. Evans K.F. Two-dimensional radiative transfer in cloudy atmospheres: the spherical harmonic spatial grid method. J Atmos Sci 50 (1993) 3111-3124
31. Evans K.F. The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer. J Atmos Sci 55 (1998) 429-446
32. Chui C, translated by Sakurai A, Arai T. An introduction to wavelets. Tokyo: Tokyo Denki University; 1993 [in Japanese].
33. Sakakibara S. Wavelet: beginners guide. Tokyo: Tokyo Denki University; 1995 [in Japanese].
34. Resnikoff H.L., and Wells Jr. R.O. Wavelet analysis: The scalable structure of information (1998), Springer, New York
35. Nakajima T., and Tanaka M. Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere. JQSRT 35 (1986) 13-21
36. Stamnes K., and Swanson R.A. A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. J Atmos Sci 38 (1981) 387-399
37. Nakajima T., and Tanaka M. Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation. JQSRT 40 (1988) 51-69
38. Stamnes K., and Dale H. A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. II: intensity computations. J Atmos Sci 38 (1981) 2696-2706
39. van de Hulst H.C. Light scattering by small particles (1957), Dover, New York