Variational data assimilation via sparse regularisation

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.

• variational data assimilation
• sparsity
• l₁ regularisation
• wavelet
• discrete cosine transform

6. Acknowledgements

This work has been mainly supported by a NASA Earth and Space Science Fellowship (NESSF-NNX12AN45H), a Doctoral Dissertation Fellowship (DDF) of the University of Minnesota Graduate School to the first author, and the NASA Global Precipitation Measurement award (NNX07AD33G). Partial support by an NSF award (DMS-09-56072) to the third author is also greatly acknowledged. Special thanks also go to Arthur Hou and Sara Zhang at NASA-Goddard Space Flight Center for their support and insightful discussions.