Ensemble Kalman filter implementations based on shrinkage covariance matrix estimation
Ensemble Kalman filter implementations based on shrinkage covariance matrix estimation
复制标题
基于收缩协方差矩阵估计的集成卡尔曼滤波器实现
DOI：
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发表时间：
2015
期刊：
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通讯作者：
Adrian Sandu
中科院分区：
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作者：
Elías D. Nino;Adrian Sandu
本文开发了基于收缩协方差估计的高效集成卡尔曼滤波器（EnKF）实现。每一步的预测集合成员都用于通过 Rao-Blackwell Ledoit 和 Wolf 估计器来估计背景误差协方差矩阵，该估计器是专门为使用少量样本来近似高维协方差矩阵而开发的。考虑两种实现方式：在 EnKF 全空间 (EnKF-FS) 方法中，同化过程在模型空间中执行，而 EnKF 缩减空间 (EnKF-RS) 公式在集合成员跨越的子空间中执行分析。在EnKF-RS的背景下，从背景集合均值和估计的背景协方差矩阵描述的正态分布中获取额外的样本，以增加集合的大小并减少滤波器的采样误差。集合大小的增加是在不运行正向模型的情况下获得的。在同化步骤之后，额外的样本被丢弃，并且仅基于模型的集合成员被进一步传播。讨论了在 EnKF-FS 和 EnKF-RS 实现的背景下减少虚假相关性和低估样本方差影响的方法。还讨论了 EnKF-RS 的无伴随四维扩展。 Lorenz-96模型和准地转模型的数值实验表明，使用收缩协方差矩阵估计可以减轻同化过程中杂散相关的影响。
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the Rao-Blackwell Ledoit and Wolf estimator, which has been specifically developed to approximate high-dimensional covariance matrices using a small number of samples. Two implementations are considered: in the EnKF full-space (EnKF-FS) approach, the assimilation process is performed in the model space, while the EnKF reduce-space (EnKF-RS) formulation performs the analysis in the subspace spanned by the ensemble members. In the context of EnKF-RS, additional samples are taken from the normal distribution described by the background ensemble mean and the estimated background covariance matrix, in order to increase the size of the ensemble and reduce the sampling error of the filter. This increase in the size of the ensemble is obtained without running the forward model. After the assimilation step, the additional samples are discarded and only the model-based ensemble members are propagated further. Methodologies to reduce the impact of spurious correlations and under-estimation of sample variances in the context of the EnKF-FS and EnKF-RS implementations are discussed. An adjoint-free four-dimensional extension of EnKF-RS is also discussed. Numerical experiments carried out with the Lorenz-96 model and a quasi-geostrophic model show that the use of shrinkage covariance matrix estimation can mitigate the impact of spurious correlations during the assimilation process.