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A Comparison of Gamma and Lognormal Distributions for Characterizing Satellite Rain Rates from the Tropical Rainfall Measuring Mission

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  • 1 Department of Atmospheric Sciences, Texas A&M University, College Station, Texas
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Abstract

This study investigates the spatial characteristics of nonzero rain rates to develop a probability density function (PDF) model of precipitation using rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The minimum χ2 method is used to find a good estimator for the rain-rate distribution between the gamma and lognormal distributions, which are popularly used in the simulation of the rain-rate PDF. Results are sensitive to the choice of dynamic range, but both the gamma and lognormal distributions match well with the PDF of rainfall data. Comparison with sample means shows that the parametric mean from the lognormal distribution overestimates the sample mean, whereas the gamma distribution underestimates it. These differences are caused by the inflated tail in the lognormal distribution and the small shape parameter in the gamma distribution. If shape constraint is given, the difference between the sample mean and the parametric mean from the fitted gamma distribution decreases significantly, although the resulting χ2 values slightly increase. Of interest is that a consistent regional preference between two test functions is found. The gamma fits outperform the lognormal fits in wet regions, whereas the lognormal fits are better than the gamma fits for dry regions. Results can be improved with a specific model assumption depending on mean rain rates, but the results presented in this study can be easily applied to develop the rainfall retrieval algorithm and to find the proper statistics in the rainfall data.

Corresponding author address: Dr. Hye-Kyung Cho, Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77845-3150. hkc@ariel.met.tamu.edu

Abstract

This study investigates the spatial characteristics of nonzero rain rates to develop a probability density function (PDF) model of precipitation using rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The minimum χ2 method is used to find a good estimator for the rain-rate distribution between the gamma and lognormal distributions, which are popularly used in the simulation of the rain-rate PDF. Results are sensitive to the choice of dynamic range, but both the gamma and lognormal distributions match well with the PDF of rainfall data. Comparison with sample means shows that the parametric mean from the lognormal distribution overestimates the sample mean, whereas the gamma distribution underestimates it. These differences are caused by the inflated tail in the lognormal distribution and the small shape parameter in the gamma distribution. If shape constraint is given, the difference between the sample mean and the parametric mean from the fitted gamma distribution decreases significantly, although the resulting χ2 values slightly increase. Of interest is that a consistent regional preference between two test functions is found. The gamma fits outperform the lognormal fits in wet regions, whereas the lognormal fits are better than the gamma fits for dry regions. Results can be improved with a specific model assumption depending on mean rain rates, but the results presented in this study can be easily applied to develop the rainfall retrieval algorithm and to find the proper statistics in the rainfall data.

Corresponding author address: Dr. Hye-Kyung Cho, Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77845-3150. hkc@ariel.met.tamu.edu

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