Identification of Rain-Rate Profiles from Radar Returns at Attenuating Wavelengths Using an Inverse Method: A Feasibility Study

Abstract

Attenuation in rainfall is recognized as one of the most significant limitations in rain-rate estimation from weather radar returns at X- or C-band wavelengths. This paper introduces a radar measurement correction as an inverse problem that accounts for attenuation effects in rainfall. First, a direct theoretical model, relating radar returns at attenuating wavelengths to the rainfall rates between the radar and the point of measurement, is presented. Second, the inverse algorithm used to identify rain-rate estimates from radar returns is described and its application to the attenuation correction is discussed, with the well-known characteristics of the attenuation model (i.e., instability, underdetermination, and nonlinearity) receiving particular attention. Third, a sensitivity analysis is then performed to test the influence of the raindrop size distribution, radar measurement features, and statistical parameters involved in the inverse method. The sensitivity analysis allows for establishing the application conditions of the method. Last, a preliminary evaluation of the method is provided, through simulated radar rainfall measurements and through a limited case study. Various attenuation correction methods are compared with the inverse algorithm. These methods include the standard radar reflectivity?rainfall rate algorithm and two versions of the Hitschfeld?Bordan algorithm. In the simulation exercise, various examples of rainfall field, with different characteristics, are tested. The case study confirms the utility of the proposed method and its ability to provide a robust and stable solution. The method consistently provides better results than the well-known Hitschfeld?Bordan algorithm.