Bayesian estimation of the observation‐error covariance matrix in ensemble‐based filters
Bayesian estimation of the observation‐error covariance matrix in ensemble‐based filters
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DOI：
10.1002/qj.2803
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发表时间：
2016-07
影响因子：
8.9
通讯作者：
G. Ueno;Nagatomo Nakamura
中科院分区：
文献类型：
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作者：
G. Ueno;Nagatomo Nakamura
我们开发了一种贝叶斯技术，用于估计集合数据同化的观测噪声协方差矩阵Rt中的参数。我们利用集合近似似然和Wishart先验分布设计了一个后验分布，并给出了一个参数估计的迭代算法。Rt的时间平滑度可以通过适当选择先验分布的两个参数来控制，即协方差矩阵S和自由度ν。可以通过最大化边际似然来估计ν参数。本形式主义可以处理的情况下，数据点或数据位置的数量随时间而变化，其中前者是在实验中举例说明。本文在以下假设下，给出了一个大气-海洋耦合模式的应用：Rt是固定矩阵的标量倍数（Rt=αt，其中αt是标量参数，α t是固定矩阵），Rt是对角矩阵，Rt具有固定的特征向量或Rt没有特定的结构。我们验证了所提出的算法工作良好，只有有限的迭代次数是必要的。当Rt具有上述结构之一时，通过假设S是先前的估计，我们得到Rt的贝叶斯估计，与最大似然估计相比，它随时间平滑变化。当Rt没有特定结构时，我们需要正则化S以保持正定性。通过孪生实验，我们发现Rt的最佳估计值通常是通过无结构Rt和锥形S的组合获得的，使用模型海洋盆地大小一半的去相关长度。从使用真实的观测的实验中，我们发现，与无结构的Rt相比，结构化Rt的估计导致数据的过拟合。
We develop a Bayesian technique for estimating the parameters in the observation‐noise covariance matrix Rt for ensemble data assimilation. We design a posterior distribution by using the ensemble‐approximated likelihood and a Wishart prior distribution and present an iterative algorithm for parameter estimation. The temporal smoothness of Rt can be controlled by an adequate choice of two parameters of the prior distribution, the covariance matrix S and the number of degrees of freedom ν. The ν parameter can be estimated by maximizing the marginal likelihood. The present formalism can handle cases in which the number of data points or data positions varies with time, the former of which is exemplified in the experiments. We present an application to a coupled atmosphere–ocean model under each of the following assumptions: Rt is a scalar multiple of a fixed matrix (Rt=αtΣ, where αt is the scalar parameter and Σ is the fixed matrix), Rt is diagonal, Rt has fixed eigenvectors or Rt has no specific structure. We verify that the proposed algorithm works well and that only a limited number of iterations are necessary. When Rt has one of the structures mentioned above, by assuming S to be the previous estimate we obtain a Bayesian estimate of Rt that varies smoothly in time compared with the maximum‐likelihood estimate. When Rt has no specific structure, we need to regularize S to maintain the positive‐definiteness. Through twin experiments, we find that the best estimate of Rt is, in general, obtained by a combination of structure‐free Rt and tapered S using decorrelation lengths of half the size of the model ocean basin. From experiments using real observations, we find that the estimates of the structured Rt lead to overfitting of the data compared with the structure‐free Rt.