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

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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 precipitation indicator (PPI) polar data. The scaling exponents for the hourly Cartesian case, the instantaneous polar case using the 1° C-band radar, and the instantaneous polar case using the 1.6° S-band radar data were estimated as 0.024, 0.10, and 0.22, respectively.