FOR THE THERMOMICROWAVE IMAGING OF TEMPERATURE PROFILES OF THE ATMOSPHERE. PART II

Using the apparatus of functional derivatives, we linearize the basic integral equation which is used to find the altitude temperature profile of the atmosphere by thermomicrowave imaging from above (from an aircraft or from outer space). The obtained Hnearized equation differs from the existing (incorrect) linearized equation used for the radar imaging of temperature profiles by wavelengths in the oxygen absorption band k ~ ,5 ram. This existing equation does not take into account the isothermal nature of the atmosphere and the difference between the temperature of the earth's surface Ts, the temperature of the surface atmospheric layer To, and the brightness temperature of the atmosphere Tb(v , 0) (in the case of thermomicrowave imaging from the earth's surface). We distinguish two cases: flight over ground or vegetation, and the flight over a water surface. In the former case, the correction to the regularized temperature ArT(h) = Tr(h) - T(h) [Tr(h) is the reconstructed regularized altitude temperature profile, and T(h) is the linear rms temperature profile] is practically independent of frequency v and of the zenith angle of sensing 0 and depends on the nonisothermicity of the atmosphere and on the difference T s - T 0. For Ts - T o = 10~ the correction can reach 7%. In the latter case for v ~ 53 GHz, the correction is about 10%. 1. This paper is a continuation of [1] (below referred to as I), and its aim is to linearize the fundamental equation used for thermomicrowave imaging. This equation is applied to the imaging of the earth-atmosphere system from above (i.e., from an aircraft or from space). The brightness temperature of the earth-atmosphere system by radar sonding from above is, neglecting sphericity, equal to H,