Regularized Data Assimilation and Fusion of non-Gaussian States Exhibiting Sparse Prior in Transform Domain

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Journal/Book Title/Conference

American Geophysical Union


San Francisco, CA

Publication Date



Improved estimation of geophysical state variables in a noisy environment from down-sampled observations and background model forecasts has been the subject of growing research in the past decades. Often the number of degrees of freedom in high-dimensional non-Gaussian natural states is quite small compared to their ambient dimensionality, a property often revealed as a sparse representation in an appropriately chosen domain. Aiming to increase the hydrometeorological forecast skill and motivated by wavelet-domain sparsity of some land-surface geophysical states, new framework is presented that recast the classical variational data assimilation/fusion (DA/DF) problem via L_1 regularization in the wavelet domain. Our results suggest that proper regularization can lead to more accurate recovery of a wide range of smooth/non-smooth geophysical states exhibiting remarkable non-Gaussian features. The promise of the proposed framework is demonstrated in multi-sensor satellite and land-based precipitation data fusion, while the regularized DA is performed on the heat equation in a 4D-VAR context, using sparse regularization in the wavelet domain.; ; Top panel: Noisy observations of the linear advection diffusion equation at five consecutive snapshots, middle panel: Classical 4D-VAR and bottom panel: l_1 regularized 4D-VAR with improved results.

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