Spherical harmonics method in the problem of radiative transfer in the atmosphere-surface system.

Details Spherical harmonics method in the problem of radiative transfer in the atmosphere-surface system. Spherical harmonics method in the problem of radiative transfer in the atmosphere-surface system.

Feb 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jqsrt..61..393m&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 61, issue 3, pp. 393-404

Statistics

Computation

9

Radiative Transfer: Numerical Methods

Scientific paper

A correction function method designed for calculating the angular dependence of radiance is described. It allows one to correct the solution of the spherical harmonics method so that the single scattering contribution is calculated exactly regardless of the order of approximation PN. AS a consequence, a smoothed intensity of high accuracy is obtained at a lower N compared to other smoothing methods, which results in the decrease of computational time. Besides, the new method by itself is at least twice as fast as the conventional method of the source function integration. Based on the new method of smoothing, the authors found an empirical formula to predict the minimal order of the spherical harmonics method necessary to provide the accuracy of radiance calculations at the level of 0.2-0.3% for any given scattering function, except for extremely asymmetric ones. The use of this formula makes calculation automatically as it frees the user from the tedious procedure of trial and error while looking for the appropriate order of approximation in each specific case.

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