Influence of the Neglect of Non-Lambertian Earth Surface Reflectance on the Error in Its Retrieval from Satellite Data

Acquisition of high-quality satellite information is important for solving a wide range of problems in monitoring the Earth surface, such as estimation of forest health, agricultural productivity, and others. To perform accurate atmospheric correction (elimination of the distorting influence of the atmosphere) of satellite images of the Earth surface, it is crucial to consider various factors that influence received signals, including non-Lambertian surface reflectance (the difference between surface reflection and Lambert’s law according to which radiation is equally reflected in all directions and depends only on the irradiance of the surface and the reflectance). In some algorithms, non-Lambertian reflection is taken into account after solving a problem in the Lambertian reflection approximation. In this case, the assumption is used that the adjacency effect (i.e., the effect of received radiation reflected from surface areas adjacent to the observed one and scattered in the atmosphere) is formed only by Lambertian surfaces. Our calculations show that at meteorological range of visibility SM ≤ 6 km, neglect of contribution of non-Lambertian reflection produces an error in the reflectance of no higher than 20.3%; neglect of non-Lambertian reflection into the adjacency effect and additional illumination results in an error of no more than 12%; and neglect of non-Lambertian reflection in additional illumination, of no more than 1.4%. For a more transparent atmosphere (SM ≥ 6 km), the maximal errors for similar models do not exceed 92, 14, and 1.2%, respectively. For the solar zenith angles θsun ≤ 60° and the angles of the optical axis of a receiving system θd ≤ 60°, the errors do not exceed 30, 7.5, and 1%, respectively. The results prove the possibility of considering non-Lambertian reflection after taking into account the adjacency effect and additional illumination of the Earth surface in the Lambertian reflection approximation.