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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/amt-2019-189
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2019-189
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 13 May 2019

Submitted as: research article | 13 May 2019

Review status
This discussion paper is a preprint. A revision of the manuscript is under review for the journal Atmospheric Measurement Techniques (AMT).

A Gaussian Mixture Method for Specific Differential Phase Retrieval at X-band Frequency

Guang Wen, Neil I. Fox, and Patrick S. Market Guang Wen et al.
  • School of Natural Resources, University of Missouri, 332 ABNR Building, Columbia, Missouri, USA, 65201

Abstract. Specific differential phase Kdp is one of the most important polarimetric radar variables, but the variance σ2(Kdp), regarding the errors in the calculation of the range derivative of differential phase shift Φdp, is not well characterized due to the lack of a data generation model. This paper presents a probabilistic method based on Gaussian mixture model for Kdp estimation at X-band frequency. The Gaussian mixture method can not only estimate the expected values of Kdp by differentiating the expected values of Φdp, but also obtain σ2(Kdp) from the product of the square of the first derivative of Kdp and the variance of Φdp. Additionally, ambiguous Φdp 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 Kdp estimates are highly consistent with the gradients of Φdp in the leading edge of the bow echo, and large σ2(Kdp) occurs with high variation of Kdp. Furthermore, the performance is quantitatively assessed by three-year radar-gauge data, and the results are compared to linear regression model. It is clear that Kdp-based rain amounts have good agreement with the rain gauge data, while the Gaussian mixture method gives improvements over linear regression model, particularly for far ranges.

Guang Wen et al.
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Guang Wen et al.
Guang Wen et al.
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Latest update: 20 Sep 2019
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Short summary
In this study, we propose a probabilistic method based on Gaussian mixture model to estimate the slope of a data profile. The Gaussian mixture method (GMM) not only obtains the expected value of the slope by differentiating the conditional expectation of the data, but also yields the variance of the slope regarding the errors in the calculation of the first derivative.
In this study, we propose a probabilistic method based on Gaussian mixture model to estimate the...
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