Tikhonov regularization is critical for accurately specifying both the background (B) and observational (R) error covariances in four‐dimensional variational data assimilation (4DVar). The ratio of the background and observation error variances (referred to as the B‐R ratio) is the key to ensuring that 4DVar maximizes the information extracted from the observations. However, it is difficult to specify the regularization parameters in a high‐dimensional variational data assimilation (VDA) system for both the single‐ and multiple‐parameter regularization schemes. In this study, we used a maximum likelihood estimation (MLE)‐based inflation scheme that originated from the ensemble Kalman filter (EnKF) community and proposed an alternating direction method (ADM) to minimize the 4DVar cost function with the iterative application of multiple regularization parameters to simultaneously optimize the regularization parameters and model states under the framework of the nonlinear least‐squares 4‐D ensemble variational data assimilation method (NLS‐4DVar). The big‐data‐driven version of NLS‐4DVar (BD‐NLS4DVar) with multiple‐parameter Tikhonov regularization was able to adjust the B‐R ratios more accurately. Several groups of observing system simulation experiments (OSSEs) based on 2‐D shallow‐water equations demonstrated that BD‐NLS4DVar with multiple‐parameter Tikhonov regularization produced a substantial performance improvement over the standard BD‐NLS4DVar method with no regularization.

中文翻译：

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多参数Tikhonov正则化的多维变分数据同化的无伴随交替方向方法

Tikhonov正则化对于准确指定背景（B）和观测（R）误差协方差在多维变异数据同化（4DVar）中至关重要。背景误差与观察误差方差之比（称为B ‐ R比率）是确保4DVar最大化从观测中提取的信息的关键。但是，很难在单参数和多参数正则化方案的高维变异数据同化（VDA）系统中指定正则化参数。在这项研究中，我们使用了基于最大似然估计（MLE）的通货膨胀方案，该方案源自集合卡尔曼滤波器（EnKF）社区，并提出了一种交替方向方法（ADM）以通过多次正则化的迭代应用最小化4DVar成本函数在非线性最小二乘4D集成变分数据同化方法（NLS-4DVar）的框架下同时优化正则化参数和模型状态的参数。B - R比更准确。基于二维浅水方程的几组观测系统仿真实验（OSSE）表明，具有多参数Tikhonov正则化的BD-NLS4DVar与没有正则化的标准BD-NLS4DVar方法相比，具有实质性的性能提升。