Generalized Canonical Transform method for radio occultation sounding with improved retrieval in the presence of horizontal gradients

Abstract. By now, a series of advanced Wave Optical (WO) approaches to the processing of Radio Occultation (RO) observations are widely used. In particular, the Canonical Transform (CT) method and its further developments need to be mentioned. The latter include the Full Spectrum Inversion (FSI) method, the Geometric Optical (GO) Phase Matching (PM) method, and the general approach based on the Fourier Integral Operators (FIOs), also referred to as the CT type 2 (CT2) method. The general idea of these methods is the application of a canonical transform that changes the coordinates in the phase space from time and Doppler frequency to impact parameter and bending angle. For the spherically symmetric atmosphere, the impact parameter, being invariant for each ray, is a unique coordinate of the ray manifold. Therefore, the derivative of the phase of the wave field in the transformed space is directly linked to the bending angle, as a single-valued function of the impact parameter. However, in the presence of horizontal gradients, this approach may not work. Here we introduce a further generalization of the CT methods in order to reduce the errors due to horizontal gradients. We describe, in particular, the modified CT2 method denoted CT2A, which complements the former with one more affine transform: a new coordinate that is a linear combination of the impact parameter and bending angle. The linear combination coefficient is a tunable parameter. We derive the explicit formulas for the CT2A and develop the updated numerical algorithm. For testing the method, we performed statistical analyses based on COSMIC RO retrievals and (collocated) ECMWF analysis profiles. We demonstrate that it is possible to find a reasonably optimal value of the new tunable CT2A parameter that mitigates systematic errors in the lower troposphere and allows the practical realization of the improved capability to cope with horizontal gradients.