Foundations for Statistical–Physical Precipitation Retrieval from Passive Microwave Satellite Measurements. Part I: Brightness-Temperature Properties of a Time-dependent Cloud-Radiation Model

A cloud-radiation model is used to investigate the relationship between emerging microwave brightness temperatures (TB's) and vertically distributed mixtures of liquid and frozen hydrometeors as a means to establish the framework for a hybrid statistical–physical rainfall retrieval algorithm. The focus in this study is on the microwave characteristics of an intense hailstorm in which cold-rain microphysics dominate the precipitation process. The TB calculations exhibit a high degree of intercorrelation across a wide frequency range (15–128 GHz) due to the pervasive influence of large ice particles on attenuation of upwelling radiation emerging from the rain layers. When the radiative emission source is near blackbody, fluctuations of the mixing ratios of ice particles are wholly responsible for the TB variations, as opposed to fluctuations in the cloud- or raindrop mixing ratios. Supercooled cloud drops, suspended in the graupel layers, can exert influence on the TB's but only at the higher frequencies. Emission by the large ice particles themselves becomes an important radiative source to the emerging TB's at the top of the atmosphere as the graupel-mixing ratios increase and effectively block the radiative sources from within the liquid layers. Strong relationships are found between the emerging TB's and various rain parameters, but these correlations are misleading in that the TB's are largely controlled by fluctuations in ice-particle mixing ratios, which in turn are highly correlated to fluctuations in liquid-particle mixing ratios. This does not negate the use of empirically based brightness-temperature-rain-rate (TB–RR) algorithms as useful tools for estimating precipitation (i.e., graupel particles ultimately fall out as rain), but it does point to a basic problem that remote-sensing methodology must address. More specifically, the hydrometeor profiles used for TB–RR algorithms must not be specified in an ad hoc fashion. It is argued that a cloud model can overcome the ad hoc assumptions. It is shown that the lowest SSM/I frequency (19 GHz) is actually a better estimator of columnar ice water content than the highest frequency (85 GHz). This is because both cloud-water emission and multiple scattering by ice particles are more prevalent at 85 GHz than at 19 GHz (which tends to be mostly influenced by single scattering). As a consequence, 85 GHz is much more sensitive to the configurational details of the vertical distribution of large ice particles