A Gaussian mixture method for specific differential phase retrieval at X-band frequency

Wen, Guang; Fox, Neil I.; Market, Patrick S.

The specific differential phase inline-formulaKdp is one of the most important polarimetric radar variables, but the variance inline-formulaσ2(Kdp), regarding the errors in the calculation of the range derivative of the differential phase shift inline-formulaΦdp, is not well characterized due to the lack of a data generation model. This paper presents a probabilistic method based on the Gaussian mixture model for inline-formulaKdp estimation at X-band frequency. The Gaussian mixture method can not only estimate the expected values of inline-formulaKdp by differentiating the expected values of inline-formulaΦdp, but also obtain inline-formulaσ2(Kdp) from the product of the square of the first derivative of inline-formulaKdp and the variance of inline-formulaΦdp. Additionally, the ambiguous phase and backscattering differential phase shift are corrected via the mixture model. The method is qualitatively evaluated with a convective event of a bow echo observed by the X-band dual-polarization radar in the University of Missouri. It is concluded that inline-formulaKdp estimates are highly consistent with the gradients of inline-formulaΦdp in the leading edge of the bow echo, and large inline-formulaσ2(Kdp) occurs with high variation of inline-formulaKdp. Furthermore, the performance is quantitatively assessed by 2-year radar–gauge data, and the results are compared to linear regression model. It is clear that inline-formulaKdp-based rain amounts have good agreement with the rain gauge data, while the Gaussian mixture method gives improvements over the linear regression model, particularly for far ranges.

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Wen, Guang / Fox, Neil I. / Market, Patrick S.: A Gaussian mixture method for specific differential phase retrieval at X-band frequency. 2019. Copernicus Publications.

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