Development of a mathematical model of microstructure of hail clouds by remote sensing

The article is devoted the problem of developing mathematical models for determining the microstructure of hail clouds by results of measurements of radar reflectivity from the hail clouds. Determination of microstructure of hail clouds by radar characteristics is reduced to solving integral equation of Fredholm 1 kind that belongs to the class of inverse problems of scattering theory and is an ill-posed problem. Based on the method of solving ill-posed problems proposed by A. N. Tikhonov, a mathematical model and the algorithm, allowing by results of the radar reflectivity at different wavelengths, to find the distribution function of the hail particles. The results of calculation of distribution functions for three, four and five wavelengths. It is shown that the proposed mathematical model and algorithm has sufficient accuracy and stability and can serve as an effective tool for approximate solution of the problem of finding the spectrum of hail particle size measurement of radar reflectivity.