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<p>Ensemble-based data assimilation often suffers from sampling errors in finite ensembles and insufficient observational information, which can lead to long-range spurious correlations and lower analysis accuracy. In this study, we propose a novel data-driven method, ResNet-CL-DA, in which a deep residual network is embedded in the assimilation process to replace traditional covariance localization. The network is designed to adaptively learn the forecast error covariance, preserving its overall structure while reducing the influence of spurious correlations and enhancing the propagation of observational information to unobserved variables. The performance of this method is evaluated using the Lorenz-96 model within the stochastic EnKF framework under multiple experimental scenarios, including varying ensemble sizes and observation dimensions. The promising results show that the ResNet-CL-DA can estimate the forecast error covariance effectively, and the analysis states are closer to the true states compared with traditional approaches using GC-based covariance localization, particularly improving the accuracy of the unobserved variables. This study demonstrates the potential of deep learning to strengthen key components of data assimilation, such as covariance localization, for more accurate analysis states.</p>

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Covariance localization combined with deep learning technology in ensemble kalman filter

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Xiangru Chen,
  • Shan Ma,
  • Chunyu Qiu

摘要

Ensemble-based data assimilation often suffers from sampling errors in finite ensembles and insufficient observational information, which can lead to long-range spurious correlations and lower analysis accuracy. In this study, we propose a novel data-driven method, ResNet-CL-DA, in which a deep residual network is embedded in the assimilation process to replace traditional covariance localization. The network is designed to adaptively learn the forecast error covariance, preserving its overall structure while reducing the influence of spurious correlations and enhancing the propagation of observational information to unobserved variables. The performance of this method is evaluated using the Lorenz-96 model within the stochastic EnKF framework under multiple experimental scenarios, including varying ensemble sizes and observation dimensions. The promising results show that the ResNet-CL-DA can estimate the forecast error covariance effectively, and the analysis states are closer to the true states compared with traditional approaches using GC-based covariance localization, particularly improving the accuracy of the unobserved variables. This study demonstrates the potential of deep learning to strengthen key components of data assimilation, such as covariance localization, for more accurate analysis states.