An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

在集成变分数据同化框架内提出了一种用于有效定位误差协方差的原始图聚类方法。在这里，本地化术语非常通用，指的是将全局同化分解为子问题的想法。这种基于线性状态观测测量的无监督定位技术是通用的，并且不依赖于任何先验信息，例如相关空间尺度、经验截止半径或同质性假设。定位是通过图论来执行的，图论是数学的一个分支，正在成为计算地球科学中捕获复杂且高度互连的地球和环境系统的强大方法。这种新颖的方法自动将状态变量和观测变量分离在最佳数量的簇中，并且更适合可扩展的数据同化。该方法的应用不需要先验协方差矩阵的基础块对角线结构。为了解决集群间连接问题，提出了两种替代数据适应方法。一旦定位完成，就会在每个簇内执行协方差诊断和调整，其贡献将按顺序集成到整个协方差矩阵中。数值孪生实验测试表明，与全局协方差调整相比，该方法降低了成本并增加了灵活性，并且观察误差和背景误差参数调整都产生了更准确的结果。