Stochastic approach to the results of simultaneous solution of emission transfer and thermal conductivity equations

Abstract

A stochastic theory of the temperature distribution and thermal radio emission of a medium (half-space) is developed on the basis of the results of simultaneous solution of thermal emission transfer and thermal conductivity equations. Expressions for the covariance functions of the temperature profile and brightness temperature as functions of the statistical parameters of the half- space surface temperature, which is considered a random function of time, are found. Estimates of a temperature regression by thermal emission are analyzed using the expressions obtained.