Variational data assimilation via sparse regularisation
Variational data assimilation via sparse regularisation
复制标题
通过稀疏正则化进行变分数据同化
DOI：
10.3402/tellusa.v66.21789
复制
发表时间：
2013
期刊：
影响因子：
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通讯作者：
E. Foufoula‐Georgiou
中科院分区：
文献类型：
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作者：
A. Ebtehaj;M. Zupanski;Gilad Lerman;E. Foufoula‐Georgiou
本文研究了稀疏正则化在变分数据同化(VDA)问题中的作用。具体地说，它侧重于噪声和下采样观测的数据同化，而感兴趣的状态变量在实域或变换域表现出稀疏性。我们证明了在存在稀疏性的情况下，正则化方法比经典的VDA方法产生了更精确和稳定的解。我们将范数正则化下的VDA问题转化为约束二次规划问题，并提出了一种适用于高维系统的有效的基于梯度的求解方法。通过在小波域和谱域使用线性平流扩散方程的同化实验，检验了概念的证明。
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.