Skip to main content

Numerical simulation of boundary effects in aerosol and cloud optics


The problem of calculating the brightness coefficient of sunlight reflected from the atmosphere in the presence of spatially local horizontal inhomogeneities (property discontinuity surfaces) of a medium (where one-dimensional mathematical models, traditionally used in such calculations, cannot be applied) is considered. A two-dimensional mathematical model, which makes it possible to obtain the detailed spatial distribution of the brightness coefficient in the vicinity of an inhomogeneity, has been proposed and used to obtain the characteristic distributions in a model problem. It has been proposed to use a quasione-dimensional model to effectively estimate the extension of a subregion including an inhomogeneity, outside of which multidimensional effects in the brightness coefficient can be neglected, and this model has been numerically tested.

This is a preview of subscription content, access via your institution.


  1. K. N. Liou, An Introduction to Atmospheric Radiation (Academic, New York, 2002).

    Google Scholar 

  2. E. N. Aristova and V. Ya. Gol’din, “Calculation of Anisotropic Solar Radiation Scattering in the Atmosphere (Monoenergetic Case),” Mat. Model. 10(9), 13–34 (1998).

    MathSciNet  Google Scholar 

  3. A. A. Kokhanovsky, W. von Hoyningen-Huene, H. Bovensmann, and J. P. Burrows, “The Determination of the Atmospheric Optical Thickness over Western Europe Using Sea WiFS Imagery,” IEEE Trans. Geosci. Remote Sens. 42(4), 824–832 (2004).

    Article  ADS  Google Scholar 

  4. A. A. Kokhanovsky and W. von Hoyningen-Huene, “Optical Properties of a Hurricane,” Atmos. Res. 69(3–4), 165–183 (2004).

    Article  Google Scholar 

  5. A. Marshak, A. Davis, et al., Three-Dimensional Radiative Transfer in Cloudy Atmospheres (Springer-Verlag, 2005).

  6. A. A. Ioltukhovskii, I. V. Mishin, and T. A. Sushkevich, “Solution of Equation of Transport in a Three-dimensional Scattering Layer Using the Method of Characteristics,” Zh. Vychisl. Mat. Mat. Fiz. 24(1), 92–108 (1984).

    MathSciNet  Google Scholar 

  7. T. V. Zhuravleva, Doctoral Dissertation in Mathematical Physics (Novosibirsk, 2008).

  8. G. A. Titov, “Radiative Horizontal Transport and Absorption in Stratocumulus Clouds,” J. Atmos. Sci. 55(15), 2549–2560 (1998).

    Article  ADS  Google Scholar 

  9. T. Varnai and A. Marshak, “Observations of Three-Dimensional Radiative Effects that Influence MODIS Cloud Optical Thickness Retrievals,” J. Atmos. Sci. 59(9), 1607–1618 (2002).

    Article  ADS  Google Scholar 

  10. O. V. Nikolaeva, L. P. Bass, T. A. Germogenova, A. A. Kokhanovsky, V. S. Kuznetsov, and B. Mayer, “The Influence of Neighbouring Clouds on the Clear Sky Reflectance Studied with the 3-D Transport Code RADUGA,” J. Quant. Spectrosc. Radiat. Transfer 94(3–4), 405–424 (2005).

    Article  ADS  Google Scholar 

  11. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957; Inostrannaya Literatura, Moscow, 1961).

    Google Scholar 

  12. O. V. Nikolaeva, “Simplified 1D Model to 2D Transport Equation,” in Proceedings of 20th International Conference on Transport Theory, Obninsk, 2007.

  13. T. Kobayashi, K. Masuda, M. Sasaki, and J. Mueller, “Monte Carlo Simulations of Enhanced Visible Radiance in Clear-Air Fields of View near Clouds,” J. Geophys. Res. 105, 26 569–26 576 (2000).

    ADS  Google Scholar 

  14. A. Marshak, Y. Knyazikhin, A. B. Davis, W. J. Wiscombe, and P. Pilewskie, “Cloud-Vegetation Interaction: Use of Normalized Cloud Index for Estimation of Cloud Optical Thickness,” Geophys. Res. Lett. 27(12), 1695–1698 (2000).

    Article  ADS  Google Scholar 

  15. T. Varnai and A. Marshak, “A Method for Analyzing How Various Parts of Clouds Influence Each Other’s Brightness,” J. Geophys. Res. 108, JD003561 (2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

Original Russian Text © L.P. Bass, T.A. Germogenova, O.V. Nikolaeva, A.A. Kokhanovsky, V.S. Kuznetsov, 2009, published in Optika Atmosfery i Okeana.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bass, L.P., Germogenova, T.A., Nikolaeva, O.V. et al. Numerical simulation of boundary effects in aerosol and cloud optics. Atmos Ocean Opt 22, 102–107 (2009).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI:


  • Solar Zenith Angle
  • Scattered Light Intensity
  • Vertical Boundary
  • Cloud Optical Thickness
  • Cloud Edge