Variational data assimilation via sparse regularisation - Ardeshir M. Ebtehaj; Milija Zupanski; Gilad Lerman; Efi Foufoula-Georgiou (Tellus: Series A, Dynamic Meteorology and Oceanography, 2014)
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 l1-norm regularisation produces more accurate and stable solutions than the classic VDA methods. We recast the VDA problem under the l1-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.