Foundations for Statistical–Physical Precipitation Retrieval from Passive Microwave Satellite Measurements. Part II: Emission-Source and Generalized Weighting-Function Properties of a Time-dependent Cloud-Radiation Model

Abstract

We present the second part of a study on the development of a framework for precipitation retrieval from space-based passive microwave measurements using a three-dimensional time-dependent cloud model to establish the microphysical setting. We first develop the theory needed to interpret the vertically distributed radiative sources and the emission-absorption-scattering processes responsible for the behavior of frequency-dependent top-of-atmosphere brightness temperatures T_B's. This involves two distinct types of vertical weighting functions for the T_B's: an emission-source weighing function describing the origin of emitted radiation that eventually reaches a satellite radiometer, and a generalized weighting function describing emitted-scattered radiation undergoing no further interactions prior to interception by the radiometer. The weighting-function framework is used for an analysis of land-based precipitation processes within a hail-storm simulation originally described in Part I. The individual roles of cloud drops, rain drops, graupel particles, ice crystals, and snow aggregates—as well as absorbing gases, the earth's surface, and cosmic background—on generating and modulating the frequency-dependent T_B's are examined in detail. The analysis emphasizes how microwave T_B measurements are highly regulated by mixtures of hydrometeors, with particular emphasis on the importance of the vertical profile structures. We demonstrate how scattering produces sequential, frequency-dependent, vertical “break aways” of the peak amplitudes in the generalized weighting functions, thus explaining how a multichannel radiometer can be used to depth probe a precipitating cloud. We also seek to explain the extent to which 19-, 37-, and 85-GHz T_B's are responding to separate and distinct processes in precipitating cells in an unambiguous fashion, helping to elucidate the two key aspects of these standard satellite frequencies. That is, 1) they are best suited to decipher certain microphysical profile features above the main rain layers and near cloud top, and 2) they are ill suited for directly sensing precipitation intensity information within the main rain layers, particularly the surface rain rates. Finally, a summary of the various components of a hybrid statistical-physical rainfall algorithm used to produce liquid-ice profile information, as well as surface rain rates, is given. The algorithm employs the cloud model to provide a consistent and objectively generated source of detailed microphysical information as the underpinnings to an inversion-based perturbative retrieval scheme.