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Estimation of Rainfall Drop Size Distributions from Dual-Frequency Wind Profiler Spectra Using Deconvolution and a Nonlinear Least Squares Fitting Technique

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  • 1 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado
  • | 2 Bureau of Meteorology Research Centre, Melbourne, Australia
  • | 3 Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado
  • | 4 Cooperative Institute for Research in Environmental Sciences, University of Colorado, and NOAA/Aeronomy Laboratory, Boulder, Colorado
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Abstract

This paper compares two different analysis approaches for dual-frequency (VHF and UHF) wind profiler precipitation retrievals. The first technique is based on a general deconvolution process to remove broadening effects from the Doppler spectra due to turbulence and finite radar beamwidth. The second technique is based on a nonlinear least squares fitting approach, where an analytical function that describes the drop size distribution is convolved with a clear air distribution to model the broadening of the observed spectra. These techniques are tested with simulated data, where the true drop size distribution is known and represented by a gamma or exponential distribution, and with observations. The median volume diameter D0, which is based on the third moment of the drop size number distribution, is used to test these retrieval techniques. This parameter is closely related to the rain rate, which is approximately the 3.67th moment of the drop size number distribution.

Methods for extracting D0 from deconvolved and convolved spectra performed equally well up to D0 = 2.25 mm and a spectral width σ of about 0.5 m s−1, while for D0 > 2.25 mm a nonlinear least squares fit to the spectra gave better results. At σ = 1.5 m s−1, a direct retrieval of D0 from the deconvolved spectra, the method of moments applied to the deconvolved spectra, and a nonlinear least squares fit to the convolved spectra gave the best results, with retrieval success rates of about 80% for most D0. At the largest simulated spectral width, σ = 3 m s−1, the deconvolution methods performed best up to about D0 = 2 mm, with a success rate of about 60%, while the nonlinear least squares fit gave better results for D0 > 2 mm. An application of these dual-frequency retrieval techniques to real measurements taken during rain events shows a median absolute error (MAE) of less than 0.15 mm between D0 calculated by deconvolution methods, and D0 calculated by the convolution fitting approach. Comparison of retrieved rain rate and surface rain gauge measurements showed an MAE of less than 1.25 mm h−1 between the retrieval methods and the rain gauge, and less than 0.5 mm h−1 between the dual-frequency retrieval methods. These results suggest that the gamma distribution is a good representation of the drop size distribution during this rain event.

Corresponding author address: Dr. Robert Schafer, University of Colorado, CIRES Bldg., Room 318, Boulder, CO 80309-0216. Email: robert.schafer@colorado.edu

Abstract

This paper compares two different analysis approaches for dual-frequency (VHF and UHF) wind profiler precipitation retrievals. The first technique is based on a general deconvolution process to remove broadening effects from the Doppler spectra due to turbulence and finite radar beamwidth. The second technique is based on a nonlinear least squares fitting approach, where an analytical function that describes the drop size distribution is convolved with a clear air distribution to model the broadening of the observed spectra. These techniques are tested with simulated data, where the true drop size distribution is known and represented by a gamma or exponential distribution, and with observations. The median volume diameter D0, which is based on the third moment of the drop size number distribution, is used to test these retrieval techniques. This parameter is closely related to the rain rate, which is approximately the 3.67th moment of the drop size number distribution.

Methods for extracting D0 from deconvolved and convolved spectra performed equally well up to D0 = 2.25 mm and a spectral width σ of about 0.5 m s−1, while for D0 > 2.25 mm a nonlinear least squares fit to the spectra gave better results. At σ = 1.5 m s−1, a direct retrieval of D0 from the deconvolved spectra, the method of moments applied to the deconvolved spectra, and a nonlinear least squares fit to the convolved spectra gave the best results, with retrieval success rates of about 80% for most D0. At the largest simulated spectral width, σ = 3 m s−1, the deconvolution methods performed best up to about D0 = 2 mm, with a success rate of about 60%, while the nonlinear least squares fit gave better results for D0 > 2 mm. An application of these dual-frequency retrieval techniques to real measurements taken during rain events shows a median absolute error (MAE) of less than 0.15 mm between D0 calculated by deconvolution methods, and D0 calculated by the convolution fitting approach. Comparison of retrieved rain rate and surface rain gauge measurements showed an MAE of less than 1.25 mm h−1 between the retrieval methods and the rain gauge, and less than 0.5 mm h−1 between the dual-frequency retrieval methods. These results suggest that the gamma distribution is a good representation of the drop size distribution during this rain event.

Corresponding author address: Dr. Robert Schafer, University of Colorado, CIRES Bldg., Room 318, Boulder, CO 80309-0216. Email: robert.schafer@colorado.edu

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