A theoretical formula for the prediction of cross-polarized signal phase

An approximate theoretical formula for the prediction of cross-polarized signal phase relative to co-polar signal is presented. In the formula, the phase of cross-polarized signal induced by rain is related to rainfall rate or rain-induced attenuation. The relation is derived by calculating the forward scattering amplitudes of the Pruppacher-Pitter type raindrops at 33 frequencies ranging from 3 to 40 GHz. The dependence of the relation on raindrop-size distribution is also discussed.