Variational Data Assimilation via Sparse Regularization

TL;DR

This paper explores the use of sparse regularization in variational data assimilation to improve accuracy and stability when the state variable is sparse in a certain basis, demonstrated through experiments in wavelet and spectral domains.

Contribution

It introduces a novel approach applying $ ext{l}_1$-norm regularization in VDA, showing improved results over traditional methods for sparse states.

Findings

Sparse regularization yields more accurate solutions.

Enhanced stability in data assimilation with sparse states.

Effective in wavelet and spectral domain applications.

Abstract

This paper studies the role of sparse regularization 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 transformed domain. We show that in the presence of sparsity, the $\ell_{1}$-norm regularization produces more accurate and stable solutions than the classic data assimilation methods. To motivate further developments of the proposed methodology, assimilation experiments are conducted in the wavelet and spectral domain using the linear advection-diffusion equation.