Abstract-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.

[1] Downscaling of remotely sensed precipitation images and outputs of general circulation models has been a subject of intense interest in hydrometeorology. The problem of downscaling is basically one of resolution enhancement, that is, appropriately adding details or high frequency features onto a low-resolution observation or simulated rainfall field. Invoking the property of rainfall self similarity, this mathematically ill-posed problem has been approached in the past within a stochastic framework resulting in ensemble of possible high-resolution realizations. In this work, we recast the rainfall downscaling into an ill-posed inverse problem and introduce a class of nonlinear estimators to properly regularize it and obtain the best high-resolution estimate in an optimal sense. This regularization capitalizes on two main observations: (1) precipitation fields are sparse when transformed into an appropriately chosen domain (e.g., wavelet), and (2) small-scale organized precipitation features tend to recur within and across different storm environments. We demonstrate the promise of the proposed methodology through downscaling and error analysis of level III precipitation reflectivity snapshots provided by the ground-based next generation Doppler weather radars in a ground validation sites of the Tropical Rainfall Measuring Mission.

Satellites are playing an ever‐increasing role in estimating precipitation over remote areas. Improving satellite retrievals of precipitation requires increased understanding of its passive microwave signatures over different land surfaces. Snow‐covered surfaces are notoriously difficult to interpret because they exhibit both emission from the land below and scattering from the ice crystals. Using data from the Global Precipitation Measurement (GPM) satellite, we demonstrate that microwave brightness temperatures of rain and snowfall transition from a scattering to an emission regime from summer to winter, due to expansion of less emissive snow cover. Evidence suggests that the combination of low‐ (10–19 GHz) and high‐frequency (89–166 GHz) channels provides the maximum amount of information for snowfall detection. The results demonstrate that, using a multifrequency matching method, the probability of snowfall detection can even be higher than rainfall—chiefly because of the information content of the low‐frequency channels that respond to the (near) surface temperature.