OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 33 — Nov. 20, 1998
  • pp: 7718–7728

Physics-based visualization of dense natural clouds. I. Three-dimensional discrete ordinates radiative transfer

David H. Tofsted and Sean G. O’Brien  »View Author Affiliations

Applied Optics, Vol. 37, Issue 33, pp. 7718-7728 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (289 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A technique is developed to model radiative transfer in three-dimensional natural clouds with a standard discrete ordinates finite-element method modified to evaluate cell-surface-averaged radiances. A log-least-squares-based scale transformation is used to improve the discrete phase-function model. We handle dense media by assuming constant diffuse radiances over input faces to cubic cells, allowing analytical forms for transmittance factors. Transmission equations are combined with diffuse volumetric single-scattering calculations to support evaluations of cell energy balance. Energy not accounted for volumetrically is treated with surface-based effects. Results produced show accurate flux computations at over 30 optical depths per modeled cell. Comparisons with nonuniform cloud Monte Carlo calculations show less than 1% rms error and correlations greater than 0.999 for cases in which cloud-density fluctuations are resolved.

© 1998 Optical Society of America

OCIS Codes
(010.1110) Atmospheric and oceanic optics : Aerosols
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(010.1320) Atmospheric and oceanic optics : Atmospheric transmittance
(290.1090) Scattering : Aerosol and cloud effects

Original Manuscript: December 11, 1997
Revised Manuscript: June 4, 1998
Published: November 20, 1998

David H. Tofsted and Sean G. O’Brien, "Physics-based visualization of dense natural clouds. I. Three-dimensional discrete ordinates radiative transfer," Appl. Opt. 37, 7718-7728 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. G. Isaacs, W.-C. Wang, R. D. Worsham, S. Goldenberg, “Multiple scattering lowtran and fascode models,” Appl. Opt. 26, 1272–1281 (1987). [CrossRef] [PubMed]
  2. K. Stamnes, S.-C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988). [CrossRef] [PubMed]
  3. R. M. Welch, B. A. Wielicki, “Stratocumulus cloud field reflected fluxes: the effect of cloud shape,” J. Atmos. Sci. 41, 3085–3103 (1984). [CrossRef]
  4. T. Kobayashi, “Reflected solar flux for horizontally inhomogeneous atmospheres,” J. Atmos. Sci. 48, 2436–2447 (1991). [CrossRef]
  5. J. L. Haferman, W. F. Krajewski, T. F. Smith, A. Sánchez, “Radiative transfer for a three-dimensional raining cloud,” Appl. Opt. 32, 2795–2802 (1993). [CrossRef] [PubMed]
  6. J. Li, D. J. W. Geldart, P. Chylek, “Solar radiative transfer in clouds with vertical internal inhomogeneity,” J. Atmos. Sci. 51, 2542–2552 (1994). [CrossRef]
  7. R. N. Byrne, R. C. J. Somerville, B. Subasilar, “Broken-cloud enhancement of solar radiation absorption,” J. Atmos. Sci. 53, 878–886 (1996). [CrossRef]
  8. G. L. Stephens, “Radiative transfer in spatially heterogeneous, two-dimensional, anisotropically scattering media,” J. Quant. Spectrosc. Radiat. Transf. 36, 51–67 (1986). [CrossRef]
  9. G. L. Stephens, “Radiative transfer through arbitrarily shaped optical media. Part I: a general method of solution,” J. Atmos. Sci. 45, 1818–1836 (1988). [CrossRef]
  10. J. Li, D. J. W. Geldart, P. Chylek, “Perturbation solution for 3D radiative transfer in a horizontally periodic inhomogeneous cloud field,” J. Atmos. Sci. 51, 2110–2122 (1994). [CrossRef]
  11. R. Davies, “The effect of finite geometry on the three-dimensional transfer of solar irradiance in clouds,” J. Atmos. Sci. 35, 1712–1725 (1978). [CrossRef]
  12. Harshvardhan, J. A. Weinman, R. Davies, “Transport of infrared radiation in cuboidal clouds,” J. Atmos. Sci. 38, 2500–2512 (1982).
  13. M. Gube, J. Schmetz, E. Raschke, “Solar radiative transfer in a cloud field,” Contrib. Atmos. Phys. 53, 23–34 (1980).
  14. A. Zardecki, S. A. W. Gerstl, R. E. DeKinder, “Two- and three-dimensional radiative transfer in the diffusion approximation,” Appl. Opt. 25, 3508–3515 (1986). [CrossRef] [PubMed]
  15. T. B. McKee, S. K. Cox, “Scattering of visible radiation by finite clouds,” J. Atmos. Sci. 31, 1885–1892 (1974). [CrossRef]
  16. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  17. B. G. Carlson, K. D. Lathrop, “Transport theory: the method of discrete ordinates,” in Computing Methods in Reactor Physics, H. Greenspan, C. H. Kelber, D. Okrent, eds. (Gordon & Breach, New York, 1968), pp. 171–266.
  18. A. Zardecki, S. A. W. Gerstl, J. F. Embury, “Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation,” Appl. Opt. 22, 1346–1353 (1983). [CrossRef] [PubMed]
  19. S. A. W. Gerstl, A. Zardecki, “Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing,” Appl. Opt. 24, 81–93 (1985). [CrossRef] [PubMed]
  20. W. J. Wiscombe, “The delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977). [CrossRef]
  21. W. A. Fiveland, “The selection of discrete ordinate quadrature sets for anisotropic scattering,” Fundam. Radiat. Heat Trans. (ASME) 160, 89–96 (1991).
  22. N. El Wakil, J. F. Sakadura, “Some improvements of the discrete ordinates method for the solution of the radiative transfer equation in multidimensional anisotropically scattering media,” Dev. Radiat. Heat Trans. (ASME) 203, 119–127 (1992).
  23. J. C. Chai, H. S. Lee, S. V. Patankar, “Improved treatment of scattering using the discrete ordinates method,” Trans. ASME 116, 260–263 (1994). [CrossRef]
  24. R. B. Myneni, A. Marshak, Y. Knyazikhin, G. Asrar, “Discrete ordinates method for photon transport in leaf canopies,” in Photon-Vegetation Interactions, R. B. Myneni, J. Ross, eds. (Springer-Verlag, New York, 1991), pp. 45–110. [CrossRef]
  25. K. F. Evans, “The spherical harmonics discrete ordinates method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429–446 (1998). [CrossRef]
  26. S. G. O’Brien, D. H. Tofsted, “Physics-based visualization of dense natural clouds. II. Cloud-rendering algorithm,” Appl. Opt. 37, 7680–7688 (1998). [CrossRef]
  27. B. H. J. McKellar, M. A. Box, “The scaling group of the radiative transfer equations,” J. Atmos. Sci. 38, 1063–1068 (1981). [CrossRef]
  28. J. F. Potter, “The delta function approximation in radiative transfer,” J. Atmos. Sci. 27, 943–949 (1970). [CrossRef]
  29. J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative reflux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976). [CrossRef]
  30. T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transf. 40, 51–69 (1988). [CrossRef]
  31. J. LeNoble, ed., Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (A. Deepak, Hampton, Va., 1985).
  32. K.-N. Liou, An Introduction to Atmospheric Radiation (Academic, New York, 1980).
  33. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, (Wiley, New York, 1984).
  34. K.-S. Kuo, R. C. Weger, R. M. Welch, S. K. Cox, “The Picard iterative approximation to the solution of the integral equation of radiative transfer—Part II. Three-dimensional geometry,” J. Quant. Spectosc. Radiat. Transf. 55, 195–213 (1996). [CrossRef]
  35. D. H. Tofsted, S. G. O’Brien, “Dense cloud radiative transfer scenarios and model validation,” in Cloud Impacts on DoD Operations and Systems, 1997 Proceedings, PL-TR-97-2112, (Phillips Lab, Hanscom Air Force Base, Mass., 1997), pp. 85–88.
  36. S. G. O’Brien, D. H. Tofsted, “Visualization of dense cloud radiation data in modeling and simulations,” in Modeling, Simulation, and Visualization of Sensory Response for Defense Applications, N. L. Faust, J. D. Illgen, eds., Proc. SPIE3085, 82–93 (1997). [CrossRef]
  37. K.-C. Ng, “Hypernetted chain solutions for the classical one-component plasma up to Γ = 7000,” J. Chem. Phys. 61, 2680–2689 (1974). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited