Variational Rainfall Fusion and Downscaling via 1-Regularization in the Wavelet Domain

Document Type


Journal/Book Title/Conference

American Geophysical Union


San Francisco, CA

Publication Date



resolution estimate of a state variable of interest is sought from a set of coarse-scale and noisy observations. Following recent developments in regularization of inverse problems in transform domains, this work proposes a new variational approach for rainfall data fusion and/or downscaling. From a statistical standpoint, the proposed framework can be interpreted as a maximum a posteriori (MAP) estimator, which explicitly accounts for the non-Gaussian and sparse pdf of the state variable in the transform domain. This MAP estimator yields an improved estimate of rainfall and properly regularizes the intrinsically ill-posed DFD problem in a noisy environment. Efficient solution methods for large scale problems are discussed and the results of synthetic and real case studies for simultaneous fusion and downscaling of the ground-based NEXRAD and TRMM-PR are presented, denoting superior performance of the proposed framework compared to the classical least squares methods.op panel: TRMM-PR snapshot 06/28/1996 at 18:13:00 UTC(TX), middle panel: NEXRAD coincidental snapshot and lower panel: fused product using variational methods with L_1 regularization in the wavelet domain.

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