Correction of radar reflectivity and differential reflectivity for rain attenuation at x band. Part I: Theoretical and empirical basis

In this two-part paper, a correction for rain attenuation of radar reflectivity (Z(H)) and differential reflectivity (Z(DR)) at the X-band wavelength is presented. The correction algorithm that is used is based on the self-consistent method with constraints proposed by Bringi et al., which was originally developed and evaluated for C-band polarimetric radar data. The self- consistent method is modified for the X-band frequency and is applied to radar measurements made with the multiparameter radar at the X-band wavelength (MP-X) operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan. In this paper, characteristic properties of relations among polarimetric variables, such as A(H)-K-DP, A(DP)-A(H), A(H)-Z(H), and Z(DR)-Z(H), that are required in the correction methodology are presented for the frequency of the MP-X radar (9.375 GHz), based on scattering simulations using drop spectra measured by disdrometers at the surface. The scattering simulations were performed under conditions of three different temperatures and three different relations for drop shapes, in order to consider variability of polarimetric variables for these conditions. For the X-band wavelength, the A(H)-K-DP and A(DP)-A(H) relations can be assumed to be nearly linear. The coefficient alpha of the A(H)-K-DP relation varies over a wide range from 0.139 to 0.335 dB (degrees)(-1) with a mean value of 0.254 dB (degrees)(-1). The coefficient gamma of the A(DP)-A(H) relation varies from 0.114 to 0.174, with a mean value of 0.139. The exponent b of the AH-ZH relation does not depend on drop shapes and is almost constant for a given temperature (about 0.78 at the temperature of 15 degrees C). The Z(DR)-Z(H) relation depends primarily on drop shape, and does not vary with temperature.