Abstract

We present a new multiscale covariance localisation method for ensemble data assimilation that is based on the estimation of eigenvectors and subsequent projections, together with traditional spatial localisation applied with a range of localisation lengths. In short, we estimate the leading, large-scale eigenvectors from the sample covariance matrix obtained by spatially smoothing the ensemble (treating small scales as noise) and then localise the resulting sample covariances with a large length scale. After removing the projection of each ensemble member onto the leading eigenvectors, the process may be repeated using less smoothing and tighter localizations or, in a final step, using the resulting, residual ensemble and tight localisation to represent covariances in the remaining subspace. We illustrate the use of the new multiscale localisation method in simple numerical examples and in cycling data assimilation experiments with the Lorenz Model III. We also compare the proposed new method to existing multiscale localisation and to single-scale localisation.

摘要

我们提出了一种新的用于集合数据同化的多尺度协方差本地化方法，该方法基于特征向量和后续投影的估计，以及应用了一系列定位长度的传统空间定位。简而言之，我们从样本协方差矩阵中估计领先的大规模特征向量，该样本协方差矩阵是通过对空间进行整体平滑处理（将小尺度作为噪声进行处理）而获得的，然后对具有较大长度尺度的样本协方差进行局部定位。在去除每个集合成员到前导特征向量上的投影之后，可以使用较少的平滑度和更紧密的定位来重复该过程，或者在最后一步中，使用所得的剩余集合和紧密的定位来表示剩余子空间中的协方差。我们在简单的数值示例中以及在用Lorenz Model III进行的循环数据同化实验中说明了新的多尺度定位方法的使用。我们还将提议的新方法与现有的多尺度本地化和单尺度本地化进行了比较。