Variational data assimilation via sparse regularisation

Ardeshir M. Ebtehaj, Milija Zupanski, Gilad Lerman, Efi Foufoula-Georgiou

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7 Scopus citations


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.

Original languageEnglish (US)
Article number21789
JournalTellus, Series A: Dynamic Meteorology and Oceanography
Issue number1
StatePublished - 2014


  • Discrete cosine transform
  • Sparsity
  • Variational data assimilation
  • Wavelet

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