The Approximate Analytical Solution for the Top-Of-Atmosphere Spectral Reflectance of Atmosphere – Underlying Snow System Over Antarctica

The optical signals detected on multiple satellite platforms over snow surfaces are determined by the optical properties of snow surface and atmosphere. The solution of both direct and inverse problems of an atmosphere – underlying snow system requires simple relationships between top-of-atmosphere (TOA) reflectance R and microphysical/optical characteristics of both snow and atmosphere. The task of this paper is to present a simple analytical relationship between the value of R as detected on a satellite with atmosphere/snow properties. Such a relationship can be established using a numerical solution of integro - differential radiative transfer equation (RTE) (Liou, 2022). However, this path is quite complicated and time consuming. The analytical solutions of RTE are needed for the solution of various applied atmospheric and snow optics problems (Cachorro et al., 2022; Mei et al., 2020, 2022; Kokhanovsky, 2021). This is the main driver of this work. To simplify the problem under study we consider the case of Antarctica, where both snow and atmosphere are almost free of pollutants. This work is focused on the simulation of the moderate spectral resolution TOA measurements (1nm or so) and the spectral range 400-1000nm.