Generalized Canonical Transform Method
Presenter:
M.E. Gorbunov (1,2)
(1) A.M.Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia, (2) Wegener Center for Climate and Global Change, University of Graz, Graz, Austria
(2) Wegener Center for Climate and Global Change, University of Graz, Graz, Austria, (3) Danish Meteorological Institute, Copenhagen, Denmark
Invited talk
By now, a series of advanced Wave Optical (WO) approaches to the processing of Radio Occultation (RO) observation 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 (FIO), also referred to as the CT of type 2 (CT2) method. All these methods have a common basis. The wave field directly measured in the RO experiments is subjected to a transformation into a different more adequate representation by means of a FIO. The general idea 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. The reason is that in this situation, the ray impact parameter is no longer a ray invariant, and its dynamic equation includes the horizontal gradient of refractivity. This results in retrieval errors. In this work, we propose a further generalization of the CT method, termed CT2A, in order to reduce the errors due to horizontal gradients. In CT2A, we enhance the CT2 method with one more affine transform: the new coordinate is a linear combination of the impact parameter and bending angle. The linear combination coefficient is used as a tunable parameter. We derive the explicit formulas for the CT2A and present 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 differences in the lower troposphere.
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