物理学报2017，Vol.66Issue(18)：1-12,12.DOI:10.7498/aps.66.180201
改进的单次散射相函数解析表达式
Modified analytic expression for the single-scattering phase function
摘要
Abstract
In electromagnetic radiative transfer calculation,the accuracy and the computation time are usually determined by the representation of single-scattering phase function.Accurate calculation is time consuming even for spherical particle,thus,an analytic representation is commonly adopted to approximate the exact phase function and then accelerate the calculation.Most widely used single-scattering phase functions are the Henyey-Greenstein phase function and modified Henyey-Greenstein phase function (Henyey-Greenstein*).Although the Henyey-Greenstein phase function and the Henyey-Greenstein* phase function can represent the forward-scattering peak of Mie-scattering phase function well,they fail to reproduce the backscattering behavior,limiting the accuracy of the calculation.In order to better fit exact calculations and simulate the backward-scattering peak,we develop a new analytic expression based on the fundamental theory of electromagnetic scattering and radiation transmission.This phase function is an algebraic expression with one single free parameter (asymmetry factor),and can be expanded into Legendre polynomials.The new phase function converges to the Rayleigh phase function when the asymmetry factor approximates to 0,and it can approach to the Henyey-Greenstein phase function as the asymmetry factor is about 1.We compare the Henyey-Greenstein phase function,the Henyey-Greenstein* phase function,and the new phase function for different asymmetry factors,and find that the new phase function provides a more realistic description for the unpolarized light scattering from small particles.Furthermore,the calculated value for the ratio of the scattering intensity at 90 degree to that in the backward direction is more reasonable.We also investigate the effectiveness by approximating the scattering from polydispersed particles through comparing the new phase function,the Henyey-Greenstein* phase function,and the Mie-scattering phase function for three types of Derimendjian's polydispersions.Results show that the new phase function fits the Mie-scattering phase function much better than the Henyey-Greenstein* phase function.For the new phase function,the root-mean-square error is small for 73.3％ data.By contrast,only 26.7％ data fit the Mie-scattering phase function well for the Henyey-Greenstein* phase function.Similarly,the effectiveness of new function is most significant when calculating the ratio of the scattering intensity at 90 degree to that in the backward direction.In summary,the new Henyey-Greenstein* phase function provides a more accurate calculation for the scattering intensity in the backward direction,and is conducive to electromagnetic radiative transfer calculation.Furthermore,because the proposed phase function has the same basic form as the Heny-Greenstein phase function,reformatting radiative transfer model in terms of the new phase function should require relatively little effort.关键词
散射/相函数/Henyey-Greenstein相函数/新的Henyey-Greenstein相函数Key words
scattering/phase function/Henyey-Greenstein phase function/new Henyey-Greenstein phase function引用本文复制引用
程晨,史泽林,崔生成,徐青山..改进的单次散射相函数解析表达式[J].物理学报,2017,66(18):1-12,12.基金项目
气象专项课题(批准号:GYHY201106002-03)和国家自然科学基金(批准号:41576185)资助的课题.Project supported by the China Special Fund for Meteorological Research in the Public Interest (Grant No.GYHY201106002-03) and the National Natural Science Foundation of China (Grant No.41576185). （批准号:GYHY201106002-03）
