A physical/variational approach to the inversion of precipitation and quantification of the associated errors

A 1D variational (1DVAR) retrieval algorithm, known as the Microwave Integrated Retrieval System (MiRS), has been developed at the NOAA Center for Satellite Applications and Research (STAR) for the simultaneous retrieval of multiple surface and atmospheric parameters, including hydrometeors, from any microwave sounder/imager. At the core of the MiRS is the use of the Community Radiative Transfer Model (CRTM), which provides the forward model and jacobians for the minimization process. The retrieved state vector is composed of temperature, water vapor and hydrometeor (liquid cloud, ice cloud and rain) profiles, as well as surface emissivity and skin temperature. The inclusion of the surface emissivity allows for retrievals globally over all surface types, including ocean, land, snow, ice and mixed scenes such as coastal areas. In this presentation, we will focus on the instantaneous rainfall rate from MiRS and identify the challenges as well as characterize potential sources of error in retrieving rainfall from microwave observations using this 1DVAR approach. MiRS retrieval of the rainfall rate takes advantage of the relationship between the rainfall rate and the retrieved hydrometeor amounts. Because the relationship is not in radiometric space, the rainfall rate estimation is sensor independent. The same methodology is applied to retrieve the hydrometeors themselves, whether from an imager, a sounder, or combination imager/sounder. Fundamentally, the microwave observations must be sensitive to the hydrometeors, and the algorithm must distinguish between the surface and atmospheric signals. For example, we show that in moderately intense rainfall cases, low frequency microwave channels are sensitive to the surface and a 2% error in emissivity could translate to 20-100% error in rainfall rate estimates. Therefore, proper characterization of the surface in rainy conditions, where changes in soil moisture may change the emissivity over land up to 10% or more, is important. Additionally, we present metrics from the MiRS algorithm to further characterize possible errors in the rainfall rate estimation. These include the chi-square (fit to the observation), averaging kernel, contribution functions, and jacobians, which reveal the sensitivity of the observations and model to hydrometeors in precipitating scenes. In the case of the chi-square, we assess the impact of the assumed Radiative Transfer Modeling uncertainty and its impact on rainfall detection and false alarm rates. Finally, we assess the performances of MiRS rainfall rate from individual and composite sensors relative to ground truth references such as the CPC rain-gauge analysis, NCEP Stage IV radar/gauge analysis, and external assessments from the International Precipitation Working Group project.