Interpretation of the Autocovariances and Cross-Covariance from a Polarization Diversity Radar

Abstract

A theory is presented for interpretation of the autocovariances and cross-covariance derivable from coherent polarization diversity radars. At zero lag time these quantities yield the ?main? received power, the depolarization ratio, the cross-correlation, and the cross-variance amplitude ratio, which have been used previously to deduce shape, orientation, and differential propagation effects. The significance of the covariances at nonzero lag times is developed here in terms of traditional models of the backscattering and propagation media. In particular, the autocovariance of the ?depolarized? signal and the cross-covariance of the two received signals are shown to yield Doppler velocity means and variances which can be compared to the mean and variance derived from the ?main? backscattered signal. If the velocity means and variances thus derived differ from one another, they can then be interpreted jointly to identify variations in the shapes and orientations of the scatterers across the Doppler velocity domain. The interpretation is illustrated by model calculations for rain and mixed rain and ice-phase scattering media and by a radar observation of mixed-phase precipitation.