This paper introduces a new Bayesian approach to the inverse problem of passive microwave rainfall retrieval. The proposed methodology [called the shrunken locally linear embedding algorithm for retrieval of precipitation (ShARP)] relies on a regularization technique and makes use of two joint dictionaries of coincident rainfall profiles and their corresponding upwelling spectral radiative fluxes. A sequential detection-estimation strategy is adopted, which basically assumes that similar rainfall intensity values and their spectral radiances live close to some sufficiently smooth manifolds with analogous local geometry. The detection step employs a nearest neighbor classification rule, whereas the estimation scheme is equipped with a constrained shrinkage estimator to ensure the stability of retrieval and some physical consistency. The algorithm is examined using coincident observations of the active precipitation radar and the passive microwave imager onboard the TRMM satellite. We present promising results of instantaneous rainfall retrieval for some tropical storms and mesoscale convective systems over ocean, land, and coastal zones. We provide evidence that the algorithm is capable of properly capturing different storm morphologies including high-intensity rain cells and trailing light rainfall, particularly over land and coastal areas. The algorithm is also validated at an annual scale for calendar year 2013 versus the standard (version 7) radar (2A25) and radiometer (2A12) rainfall products of the TRMM satellite.

We present a multi-sensor Bayesian passive microwave retrieval algorithm for flood inundation mapping at high spatial and temporal resolutions. The algorithm takes advantage of observations from multiple sensors in optical, short-infrared, and microwave bands, thereby allowing for detection and mapping of the sub-pixel fraction of inundated areas under almost all-sky conditions. The method relies on a nearest-neighbor search and a modern sparsity-promoting inversion method that make use of an a priori dataset in the form of two joint dictionaries. These dictionaries contain almost overlapping observations by the Special Sensor Microwave Imager and Sounder (SSMIS) on board the Defense Meteorological Satellite Program (DMSP) F17 satellite and the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua and Terra satellites. Evaluation of the retrieval algorithm over the Mekong Delta shows that it is capable of capturing to a good degree the inundation diurnal variability due to localized convective precipitation. At longer timescales, the results demonstrate consistency with the ground-based water level observations, denoting that the method is properly capturing inundation seasonal patterns in response to regional monsoonal rain. The calculated Euclidean distance, rank-correlation, and also copula quantile analysis demonstrate a good agreement between the outputs of the algorithm and the observed water levels at monthly and daily timescales. The current inundation products are at a resolution of 12.5 km and taken twice per day, but a higher resolution (order of 5 km and every 3 h) can be achieved using the same algorithm with the dictionary populated by the Global Precipitation Mission (GPM) Microwave Imager (GMI) products.