期刊名称：Tellus A: Dynamic Meteorology and Oceanography
电子版ISSN：1600-0870
出版年度：2014
卷号：66
页码：1-17
DOI：10.3402/tellusa.v66.21789
语种：English
摘要：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.
关键词：variational data assimilation; sparsity; l1 regularisation; wavelet; discrete cosine transform
