Effect of Nonuniform Beam Filling on the Propagation of Radar Signals at X-Band Frequencies. Part II: Examination of Differential Phase Shift

Abstract

An analysis of the effects of nonuniform beam filling on the measurement of the propagation phase shift for X-band radar is presented. An analytical expression is derived for the measured differential phase shift. It is shown that the phase measurement is weighted by the reflectivities and the attenuation within the sampling volume and that this may lead to negative values in the retrieved specific differential phase shift KDP. These effects are compared with those due to the influence of the backscattering phase shift δ. Both effects are quantified using numerical simulations. A very simple rain model with one cell is used to analyze and understand the problem. Comparison of X and S bands shows that the effects of azimuthal gradients are stronger at X band. The problem is also illustrated with radar measurements carried out with an X-band coherent polarimetric radar. For practical purposes, the problem appears to be small for beamwidths of less than 1° and the cell sizes considered here, or if the differential phase shift is evaluated over a long path. This study illustrates some of the practical problems that may be encountered using rain measurement algorithms based on KDP at X band, even though the high values of KDP at X band compared to longer wavelengths make its use attractive for rain estimation, especially for lower rain rates.