Variational Data Assimilation via Sparse Regularization

Document Type

Article

Journal/Book Title/Conference

Tellus

Volume

66

Publisher

The International Meteorological Institute in Stockholm

Publication Date

1-1-2013

Abstract

This paper studies the role of sparse regularisation in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable of interest exhibits sparsity in the real or transform domains. We show that in the presence of sparsity, the -norm regularisation produces more accurate and stable solutions than the classic VDA methods. We recast the VDA problem under the -norm regularisation into a constrained quadratic programming problem and propose an efficient gradient-based approach, suitable for large-dimensional systems. The proof of concept is examined via assimilation experiments in the wavelet and spectral domain using the linear advection–diffusion equation.

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