Variational Data Assimilation via Sparse Regularization
The International Meteorological Institute in Stockholm
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.
Ebtehaj, A.M., M. Zupanski, G. Lerman, E. Foufoula-Georgiou (2013), Variational Data Assimilation via Sparse Regularization, Tellus A, 2014, 66, 21789