The fluctuation theory of radio occultation signals: geometric optical approximation of the Canonical Transform method

Abstract

The Canonical Transform (CT) method in different modifications is widely employed for processing radio occultation data. The leading idea of the method consists in the transformation of the measured wave field into the diffractionless representation, where the CT amplitude is only defined by the horizontal gradient of the atmospheric refractivity field. In this paper, we develop the theory of the fluctuation of the CT amplitude in the framework of the geometric optics (GO). The GO approximation is based on the Hamilton form of the ray equations, transformed into the representation of the ray impact parameter. The variations of the CT amplitude are defined by the variation of the ray tube cross-section. We derive the expression for the CT amplitude fluctuation spectrum as an operator on the 3-D fluctuation spectrum of the atmospheric refractivity described by the Kolmogorov turbulence model. We perform the numerical simulation using the split-step method, which indicates that the expression for the spectrum is in a good agreement with the simulated amplitude fluctuation. We estimate of the diffraction limit of the GO approximation.