多次散射辐射传输计算中的相函数处理

在实际大气中,分子和粒子不仅遭受单次散射,还遭受多次散射。本文首先计算了多次散射在总散射量中的贡献。结果表明当光学厚度大于0.1时,多次散射在总散射量中的贡献将超过10%,因此必须考虑多次散射的作用。在多次散射辐射传输计算时,一般需把散射相函数展开为勒让德(Legendre)函数的多项式。有些介质如云或气溶胶粒子,散射相函数前向非常尖锐。展开的Legendre多项式需数百项甚至上千项才能收敛,而计算时间与展开项数的3次方成正比。本文介绍了在辐射传输计算时对尖锐相函数的δ-M和δ-fit处理方法,比较了两种方法的计算结果。当计算用的流数相同时,δ-fit方法的计算结果比δ-M方法的计算结果要精确得多;当计算结果精确度相同时,δ-fit方法的流数比δ-M方法的流数少得多,运算速度也快很多。δ-fit方法是目前处理散射相函数的理想方法,可以大大提高计算的精度以及缩减运算时间。

The Treatment of Scattering Phase Function in the Multi-Scattering Radiative Transfer Calculation

In the real atmosphere,light is scattered by the molecules or particles not only once,but many times.This paper firstly computes the percentage of the multi-scattering to the total scattering for various optical depth and single-scattering albedo.The results show that multi-scattering percentage is greater than 10% when the optical depth is larger than 0.1.Thus,the multi-scattering must be considered.The scattering phase function is usually expanded using Legendre polynomial series during the multi-scattering computations.The scattering phase function of some medium such as cloud droplets and aerosol particles is strongly forward peaked.The Legendre polynomial series will not converge until the number of terms of expansion is up to hundreds or thousands,and the computing time is proportional to the third power of the number of terms.This paper introduces a treatment of phase function expansion by using the δ-M and δ-fit methods for forward peaked scattering phase function in the radiative transfer calculation.Comparisons are made between the two methods.Given a fixed stream,the results by δ-fit are more accurate than by δ-M;For a fixed accuracy,the needed number of stream for δ-fit is fewer than for δ-M.Thus the computing time is much less using the δ-fit method.Up to now,δ-fit is a perfect method for phase function expansion in multi-scattering computation.The method can improve the accuracy and reduce the computing time greatly.