Bayesian retrieval of complete posterior PDFs of rain rate from satellite passive microwave observations

Jui-Yuan C Chiu, Purdue University

Abstract

This dissertation presents a new Bayesian rain rate retrieval algorithm for the TRMM Microwave Imager (TMI), along with associated error analysis of synthetic sensitivity tests and real-world applications. The Bayesian approach offers a rigorous way of optimally combining the actual multichannel observations with prior knowledge. It has been applied in many studies to retrieve instantaneous rain rates from microwave radiances. However, this is believed to be the first self-contained algorithm whose output is not just a single rain rate, but rather continuous posterior probability distributions of the rain rate. The success of the Bayesian algorithm depends on the accuracy of both the conditional probability density function (pdf) of microwave observations and the prior pdf of rain rate, as well as on the interpretation of the posterior probability distribution of rain intensities. The current study presents explicit functions to reasonably approximate the physical relationships between rain rates and microwave radiance based on both model simulations and observations from TMI and TRMM Precipitation Radar (PR). The prior distribution is lognormal based on PR rainfall measurements. Two common statistical estimators are tested for converting the posterior pdf of the retrieved rain rate to a single rain rate estimate for a pixel. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity tests are conducted using two synthetic datasets for which the “true” physical model and the prior distribution are known. Sensitivity results have demonstrated that even when the prior and conditional likelihoods have been applied perfectly, an apparent bias in retrieval at high surface rain rate occurs. In addition, the tests suggest that the choice of the estimators and the prior information are both crucial to the retrieval. In this study, the new Bayesian algorithm has also been applied to real TMI data over the ocean. Its estimates are validated against independent datasets and the performance of the new Bayesian algorithm is compared with that of other bench mark algorithms. The results are satisfactory in that our algorithm has comparable performance to other algorithms while having the additional advantage of providing posterior rain rate probability distribution.

Degree

Ph.D.

Advisors

Petty, Purdue University.

Subject Area

Atmosphere

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