The use of optimal polarizations for studying the microphysics of precipitation: Nonattenuating wavelengths

The objective of this work is to explore relationships between the microphysical properties of precipitation and optimal polarizations. The dependence of three optimal polarization parameters (asymmetry ratio A, optimal tilt tau(sub op), and optimal ellipticity epsilon(sub op) on the reflectivity-weighted mean drop shape, mean canting angle, and standard deviation of a Gaussian canting angle distribution is studied. This is accomplished by using computer simulations that provide the rms scattering matrix for an ensemble of canted drops with a prescribed two-parameter canting angle distribution. Also examined are the effects of propagation on the polarization parameters for nonattenuating wavelengths. The asymmetry ratio A is simply the ratio of the maximal to minimal total backscattered energy (ratio of the largest and smallest eigenvalue of the Graves power matrix G is identically equal to S dagger S). Similar to Z(sub DR), this ratio decreases with increasing mean axial ratio, but unlike Z(sub DR), it is not affected by canting (for a single drop). The dependence of A on the reflectivity-weighted mean drop shape is examined, and a power-law relationship similar to that which exists for Z(sub DR) is established. The asymmetry ratio A can be regarded as a generalization of Z(sub DR) because it requires only a measurement of linear depolarization ratio (in addition to Z(sub DR)), is independent of the propagation phase, and is less sensitive to canting. In a similar manner, the dependence of optimal ellipticity and tilt on the microphysical parameters is studied. In particular, it appears that the rms tilt of the optimal polarization ellipse is proportional to the variance of the canting angle distribution. Several other promising relationships between optimal polarizations and the microphysical variables of an ensemble of hydrometeors are also discussed.