The Approximate Analytical Solution for the Top-of-Atmosphere Spectral Reflectance of Atmosphere—Underlying Snow System over Antarctica

Abstract

The analytical solutions of the radiative transfer equation are needed for the solution of various applied atmospheric and snow optics problems. In this paper, we propose a simple analytical equation for the top-of-atmosphere (TOA) spectral reflectance. 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 (1 nm or so) and the spectral range 400–1000 nm. The values of the coefficient of variance (CV) between the measured by the Ocean and Land Colour Instrument (OLCI) on board Sentinel-3A and modelled spectra are smaller than 10% for most cases in Antarctica. There are regions in Eastern Antarctica, where the values of CV are smaller than 5%. The areas with larger deviations between measured and retrieved spectra could be due to the presence of clouds or structures on the snow surface not captured by the proposed model.