Editorial Type:
Article
Article Type:
Research Article

A Variational Scheme for Retrieving Rainfall Rate and Hail Reflectivity Fraction from Polarization Radar

Robin J. Hogan Department of Meteorology, University of Reading, Reading, United Kingdom

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Print Publication:
01 Oct 2007
DOI:
https://doi.org/10.1175/JAM2550.1
Page(s):
1544–1564
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Abstract

Polarization radar offers the promise of much more accurate rainfall-rate R estimates than are possible from radar reflectivity factor Z alone, not only by better characterization of the drop size distribution, but also by more reliable correction for attenuation and the identification of hail. However, practical attempts to implement retrieval algorithms have been hampered by the difficulty in coping with the inherent noise in the polarization parameters. In this paper, a variational retrieval scheme is described that overcomes these problems by employing a forward model for differential reflectivity Zdr and differential phase shift ϕdp and iteratively refining the coefficient a in the relationship Z = aRb such that the difference between the forward model and the measurements is minimized in a least squares sense. Two methods are used to ensure that a varies smoothly in both range and azimuth. In range, a is represented by a set of cubic-spline basis functions; in azimuth, the retrieval at one ray is used as a constraint on the next. The result of this smoothing is that the retrieval is tolerant of random errors in Zdr of up to 1 dB and in ϕdp of up to 5°. Correction for attenuation is achieved simply and effectively by including its effects in the forward model. If hail is present then the forward model is unable to match the observations of Zdr and ϕdp simultaneously. This enables a first pass of the retrieval to be used to identify the radar pixels that contain hail, followed by a second pass in which the fraction of the Z in those gates that is due to hail is retrieved, this time with the scheme being able to forward-model both Zdr and ϕdp accurately. The scheme is tested on S-band radar data from southern England in cases of rain, spherical hail, oblate hail, and mixtures of rain and hail. It is found to be robust and stable, even in the presence of differential phase shift on backscatter.

Corresponding author address: Robin J. Hogan, Department of Meteorology, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: r.j.hogan@reading.ac.uk

Abstract

Polarization radar offers the promise of much more accurate rainfall-rate R estimates than are possible from radar reflectivity factor Z alone, not only by better characterization of the drop size distribution, but also by more reliable correction for attenuation and the identification of hail. However, practical attempts to implement retrieval algorithms have been hampered by the difficulty in coping with the inherent noise in the polarization parameters. In this paper, a variational retrieval scheme is described that overcomes these problems by employing a forward model for differential reflectivity Zdr and differential phase shift ϕdp and iteratively refining the coefficient a in the relationship Z = aRb such that the difference between the forward model and the measurements is minimized in a least squares sense. Two methods are used to ensure that a varies smoothly in both range and azimuth. In range, a is represented by a set of cubic-spline basis functions; in azimuth, the retrieval at one ray is used as a constraint on the next. The result of this smoothing is that the retrieval is tolerant of random errors in Zdr of up to 1 dB and in ϕdp of up to 5°. Correction for attenuation is achieved simply and effectively by including its effects in the forward model. If hail is present then the forward model is unable to match the observations of Zdr and ϕdp simultaneously. This enables a first pass of the retrieval to be used to identify the radar pixels that contain hail, followed by a second pass in which the fraction of the Z in those gates that is due to hail is retrieved, this time with the scheme being able to forward-model both Zdr and ϕdp accurately. The scheme is tested on S-band radar data from southern England in cases of rain, spherical hail, oblate hail, and mixtures of rain and hail. It is found to be robust and stable, even in the presence of differential phase shift on backscatter.

Corresponding author address: Robin J. Hogan, Department of Meteorology, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. Email: r.j.hogan@reading.ac.uk

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Journal of Applied Meteorology and Climatology

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