Solution of atmosphere refraction and radiometry inverse problems determination of the path delay

Considers inverse problems of atmosphere remote sensing by measurements of refraction and thermal radio emission. Among the various problems it is possible to note two: the problem of the refraction index height profile retrieval by ground-based measurements of the radio refraction at positive elevation angles and the problem of the atmosphere temperature profile retrieval by satellite measurements of the brightness temperatures in the oxygen spectral lines centered at 60 GHz. Both problems consist in the solution of the integral Fredholm equation of the 1-st kind. Statistical and nonstatistical (Tikhonov´s) methods are used to solve refraction inverse problem. the retrieved profile is used to determine the path delay of radio waves in the atmosphere. Only statistical methods have been used elsewhere to solve the corresponding incorrect integral Fredholm equation of the 1-st kind. They are inconsistent in the regions outside meteorological network as well as in a height interval above sounding level (ordinary about 30-35 km). The nonstatistical method based on the Tikhonov´s theory has been worked out to solve the problem