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An Analytical Solution for Raindrop Evaporation and Its Application to Radar Rainfall Measurements

Xiaowen LiDepartment of the Geophysical Sciences, University of Chicago, Chicago, Illinois

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Ramesh C. SrivastavaDepartment of the Geophysical Sciences, University of Chicago, Chicago, Illinois

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Abstract

An analytical solution for the evaporation of a single raindrop is derived in this paper. Based on this solution, a parameter D* is defined as the diameter of the raindrop that just evaporates completely after falling through a certain distance in a prescribed environment. The parameter D* is then used for studying the modification of raindrop size distribution by evaporation in a steady, still atmosphere. The results for the Marshall–Palmer distribution are used to discuss errors caused by rain evaporation in radar rainfall measurements. Quantitative estimation of these errors, or as an equivalent, estimation of the rain evaporation along the falling path, using both radar reflectivity Z and radar differential reflectivity ZDR techniques, is studied. The results show that, for the detection of rain evaporation, reflectivity is more sensitive than differential reflectivity, whereas for the estimation of rainfall rate R, an empirical ZDR–ZR formula is more robust and accurate than a ZR formula.

Corresponding author address: Ramesh C. Srivastava, University of Chicago, Dept. of the Geophysical Sciences, 5734 S. Ellis Ave., Chicago, IL 60637-1434. srivast@geosci.uchicago.edu

Abstract

An analytical solution for the evaporation of a single raindrop is derived in this paper. Based on this solution, a parameter D* is defined as the diameter of the raindrop that just evaporates completely after falling through a certain distance in a prescribed environment. The parameter D* is then used for studying the modification of raindrop size distribution by evaporation in a steady, still atmosphere. The results for the Marshall–Palmer distribution are used to discuss errors caused by rain evaporation in radar rainfall measurements. Quantitative estimation of these errors, or as an equivalent, estimation of the rain evaporation along the falling path, using both radar reflectivity Z and radar differential reflectivity ZDR techniques, is studied. The results show that, for the detection of rain evaporation, reflectivity is more sensitive than differential reflectivity, whereas for the estimation of rainfall rate R, an empirical ZDR–ZR formula is more robust and accurate than a ZR formula.

Corresponding author address: Ramesh C. Srivastava, University of Chicago, Dept. of the Geophysical Sciences, 5734 S. Ellis Ave., Chicago, IL 60637-1434. srivast@geosci.uchicago.edu

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