参数化的多次散射激光雷达方程和它的反演理论 Ⅰ:方程

Parameterized Lidar Equation of Multiple Scattering and its Retrieval Theory,I:Equations

本文提出了一个参数化的多次散射激光雷达方程,该方程基于本文引出的四个因子,即几何消光因子、消光分布因子、前向散射因子和后向散射因子.前两个因子表征多次散射成分对大气消光系数分布、激光的发散角和接收视场角以及接收孔径的依赖关系,后两个因子表征多次散射成分对散射相函数的依赖关系.这个参数化多次散射雷达方程在241个数值试验中得以检验,这些试验包含很宽的大气条件和雷达几何参数,包括14个大气散射相函数,均匀和不均匀的大气消光系数分布,0.5至1之间变化的一次散射反照率,地基和空间站激光雷达两种情形.数值试验表明,在小于4的光学厚度内参数化的解和Monte-Carlo解之间的标准偏差小于27％,而本模式的计算时间比Monte-Carlo方法偏小4个数量级左右.本模式不仅适合于研究多次散射对激光回波信号和激光大气遥感的效应,而且对于考虑多次散射的激光大气探测而言,是一个合适的应用模式.

In this paper, a parameterized lidar equation including multiple scattering is developed . This model is based on four factors, a geometry - extinction factor , an extinction distribution factor, a forward scatter factor and a backward scatter factor . The first two factors characterize the dependence of the multiple scatter component on the extinction coefficient distribution , laser beam divergence and the field of view of the receiver as well as the diameter of the receiver. The last two factors are introduced to denote the dependence of the multiple scatter component on the scattering phase function .This approximation is tested in 241 numerical experiments for ground based and space (or air ) - borne lidars. These experiments cover very wide atmospheric conditions, including 14 atmospheric scattering phase functions . homogeneous and mhomogeneous atmospheric extinction coefficient distributions , and different single scatter albedos ranging from 1 to 0. 5 , and two cases of the ground - based lidar and spaceborne lidar . For multiply scattered lidar returns the standard deviation of the parameterized solution from our Monte Carlo solution is less than 27% in the optical depth range of less than 4 for all experiments . The computing time by our method is only about one-ten thousandth of the one by the Monte Carlo method . The present model is an adequate numerical model to describe multiply scattered lidar returns and to use the returns for determining aerosol or cloud optical properties .