Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indices

SummaryMicrowave rain rate retrieval algorithms have most often been formulated in terms of the raw brightness temperatures observed by one or more channels of a satellite radiometer. Taken individually, single-channel brightness temperatures generally represent a near-arbitrary combination of positive contributions due to liquid water emission and negative contributions due to scattering by ice and/or visibility of the radiometrically cold ocean surface. Unfortunately, for a given rain rate, emission by liquid water below the freezing level and scattering by ice particles above the freezing level are rather loosely coupled in both a physical and statistical sense. Furthermore, microwave brightness temperatures may vary significantly (∼30–70 K) in response to geophysical parameters other than liquid water and precipitation. Because of these complications, physical algorithms which attempt to directly invert observed brightness temperatures have typically relied on the iterative adjustment of detailed microphysical profiles or cloud models, guided by explicit forward microwave radiative transfer calculations.In support of an effort to develop a significantly simpler and more efficient inversion-type rain rate algorithm, the physical information content of two linear transformations of single-frequency, dual-polarization brightness temperatures is studied: thenormalized polarization difference P of Petty and Katsaros (1990, 1992), which is intended as a measure of footprint-averaged rain cloud transmittance for a given frequency; and ascattering index S (similar to the polarization corrected temperature of Spencer et al., 1989) which is sensitive almost exclusively to ice. A reverse Monte Carlo radiative transfer model is used to elucidate the qualitative response of these physically distinct single-frequency indices to idealized 3-dimensional rain clouds and to demonstrate their advantages over raw brightness temperatures both as stand-alone indices of precipitation activity and as primary variables in physical, multichannel rain rate retrieval schemes.As a byproduct of the present analysis, it is shown that conventional plane-parallel analyses of the well-known footprint-filling problem for emission-based algorithms may in some cases give seriously misleading results.