Application of Scaling in Radar Reflectivity for Correcting Range-Dependent Bias in Climatological Radar Rainfall Estimates

Abstract This paper presents a method to correct for the range-dependent bias in radar reflectivity that is a result of partial beam filling and of the increase in observation volume with range. The scaling behavior of reflectivity fields as a function of range from the radar was explored in this study. It was found that a simple scaling paradigm was applicable, and a scale transformation function was proposed to ensure uniformity in the probability distributions of reflectivity at both near and far range. The scaling exponents of the power-law transformation function were estimated using a 6-month sequence of reflectivity maps in a Cartesian grid and two sets of instantaneous reflectivity maps in polar coordinates from 1° C-band and 1.6° S-band radars at Sydney, Australia. The averaging process that transforms the instantaneous polar reflectivity into the hourly Cartesian grid data leads to a lower scaling exponent of the hourly Cartesian reflectivity data compared with the instantaneous plan precipitati...