Hydro-meteorological inverse problems via sparse regularization: advanced frameworks for rainfall spaceborne estimation

Abstract

The past decades have witnessed a remarkable emergence of new spaceborne and ground-based sources of multiscale remotely sensed geophysical data. Apart from applications related to the study of short-term climatic shifts, availability of these sources of information has improved dramatically our real-time hydro-meteorological forecast skills. Obtaining improved estimates of hydro-meteorological states from a single or multiple low-resolution observations and assimilating them into the background knowledge of a prognostic model have been a subject of growing research in the past decades. In this thesis, with particular emphasis on precipitation data, statistical structure of rainfall images have been thoroughly studied in transform domains (i.e., Fourier and Wavelet). It is mainly found that despite different underlying physical structure of storm events, there are general statistical signatures that can be robustly characterized and exploited as a prior knowledge for solving hydro-meteorological inverse problems such rainfall downscaling, data fusion, retrieval and data assimilation. In particular, it is observed that in the wavelet domain or derivative space, rainfall images are sparse. In other words, a large number of the rainfall expansion coefficients are very close to zero and only a small number of them are significantly non-zero, a manifestation of the non-Gaussian probabilistic structure of rainfall data. To explain this signature, relevant family of probability models including Generalized Gaussian Density (GGD) and a specific class of conditionally linear Gaussian Scale Mixtures (GSM) are studied. Capitalizing on this important but overlooked property of precipitation, new methodologies are proposed to optimally integrate and improve resolution of spaceborne and ground-based precipitation data. In particular, a unified framework is proposed that ties together the problems of downscaling, data fusion and data assimilation via a regularized variational approach, while taking into account the underlying sparsity in an appropriately chosen transform domain. This framework seeks solutions beyond the paradigm of the classic least squares by imposing a proper regularization. The results suggest that sparsity-promoting regularization can reduce uncertainty of estimation in hydro-meteorological inverse problems of downscaling, data fusion, and data assimilation. In continuation of the proposed methodologies, we also introduce a new data driven framework for multisensor spaceborne rainfall retrieval problem and present some preliminary and promising results.