Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

Satellite microwave observations have been widely used for estimating rain rate in an attempt to meet the need of a regular basis of precipitation measurements in the atmospheric community, especially over the ocean. However, up to now, there has been a lack of basis for systematically and rigorously charactering uncertainty in currently available retrieval algorithms. Among a number of retrieval methods for rain rate, a Bayesian approach offers a rigorous way of optimally combining actual multichannel observations with our prior knowledge. The success of a Bayesian rain rate retrieval algorithm is determined by how we characterize the prior rain rate distribution and the conditional probability density function that relates microwave signature to precipitation, as well as how we interpret the resulting posterior probability distribution of surface rain rate. This study presents a self-contained Bayesian algorithm whose output is not just a single rain rate, but rather a complete posterior probability distribution of rain rate. In addition to thorough sensitivity tests that demonstrate theoretical benefits and limitations of Bayesian algorithms, we also compare the performance of our new algorithm with other benchmark algorithms against datasets from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager and the Precipitation Radar.