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 language||English (US)|
|Journal||Tellus, Series A: Dynamic Meteorology and Oceanography|
|State||Published - 2014|
- Discrete cosine transform
- Variational data assimilation