An Interpretation of Circular Polarization Measurements Affected by Propagation Differential Phase Shift

Abstract

Circularly polarized waves are created by adding horizontally and vertically linearly polarized waves of equal magnitude with a phase difference of 90°. As a transmitted wave propagates through precipitation, which is usually not spherical, the relative phase between the horizontal and vertical components of the forward scattered wave from each particle is shifted slightly from 90°. The addition to the transmitted wave of the forward scattered waves from all the particles causes the net propagating wave to become more and more elliptically polarized. This propagation differential phase shift leads to biases in parameters estimated as though the polarization were still circular and can therefore obscure the correct interpretation of the observations in terms of the characteristics of the precipitation. In this paper, a method is developed for recovering unbiased circular polarization parameters from measurements biased by propagation differential phase shift. This is accomplished by first expressing the circular polarization quantities as functions of the linear polarization parameters. These equations are combined to eliminate terms affected by propagation differential phase shift. The resulting expressions are then solved to determine the linear polarization parameters. Finally, the circular polarization quantities can be recomputed from these estimates of the linear polarization parameters. An advantage of this approach is that even when circular polarization measurements are biased by propagation differential phase shift, they can still be transformed into linear polarization parameters unaffected by propagation. These unbiased linear quantities can then be used to characterize the precipitation. It is shown that the standard circular polarization parameters of depolarization ratio (Γ) and the complex cross-correlation function (?c) provide estimates of the linear polarization differential reflectivity (?) and the magnitude (?L) of the linear cross-correlation function (?L) which are free of propagation phase effects. The ?L may not only lead to improved rainfall estimates from differential reflectivity, but also helps clarify some puzzling aspects of polarization measurements in the melting layer. If a radar has the additional capability of switching rapidly between right- and left-handed circular polarizations, the cross-correlation function (?RL) can be computed between the resulting two copolarizations. It is then shown that even when a propagation differential phase shift is occurring, {?c, Γ, Re(?RL)} can be transformed into {?L, ?, L} where L is the linear depolarization ratio and Re(?RL) is the real part of ?RL. This transformation is particularly useful since it provides the measurements necessary for estimating the variance of particle canting.