The brightness angular structure of the cloudless sky is studied based on the model of the sunlight single scattering. It is shown that the so-called near-horizon maximum of the sky brightness can be described within the framework of this model. Physical mechanism of arising of this maximum is analyzed; dependence of the maximum position on the light wavelength is explained. When the light wavelength increases, the sky brightness maximum "shifts" towards the horizon. It is related to the fact that the atmosphere optical thickness decreases with growth of a wavelength. These model data are compared to the experimental angular characteristics of the sky brightness obtained due to digital imaging of the horizon from the oceanographic platform. Possibility of estimating the atmosphere optical thickness using the angular position of the sky brightness near-horizon maximum is analyzed. Proposed is the algorithm for assessing the given characteristic for a certain value of the light wavelength based on graphical "inversion" of dependence of the angular distribution of the cloudless sky brightness upon the atmosphere optical thickness. The proposed algorithm and the horizon digital images permit to assess the atmosphere optical thickness in the R, G and B spectral ranges. The algorithm "robustness" to the errors in determining the sun azimuth relative to the observer is analyzed. The obtained estimates of the atmosphere optical thicknesses are in agreement with the known results of the nature measurements of the atmosphere analogous characteristics. The described method for reconstructing the values of the atmosphere optical thicknesses makes it possible to develop the applied sky brightness model taking into account multiple light scattering. The obtained values of optical thickness can be used in the models of angular distribution of the cloudless sky brightness to provide possibility of estimating the waves' statistical characteristics by the remote optical method.