标题： 变分数据一致同化 显示英文标题

标题： Variational Data-Consistent Assimilation

摘要： 这项工作介绍了一类基于数据一致反演（DCI）理论的四维变分数据同化（4D-Var）方法的新类别。 这些方法通过引入可预测性感知的正则化项来扩展经典4D-Var。 第一个提出的的方法称为数据一致4D-Var（DC-4DVar），然后使用加权均方误差（WME）感兴趣量图来构建DC-WME 4D-Var方法。 虽然DC和DC-WME代价函数都包含一个可预测性感知的正则化项，但DC-WME函数对模型-数据不匹配进行了修改，从而提高了非线性和部分观测动力系统中的估计精度、鲁棒性和理论一致性。 提供了证明，以建立最小值的存在性和唯一性，并分析了在DCI框架中常见的可预测性假设如何有助于促进解的稳定性。 在基准动力系统（Lorenz-63和Lorenz-96）以及浅水方程（SWE）上进行了数值实验。 在基准动力系统中，DC-WME 4D-Var公式被证明在减少误差和偏差方面始终优于标准4D-Var，同时在高观测噪声和短同化窗口下保持鲁棒性。 尽管引入了适度的计算开销，DC-WME 4D-Var在估计性能和预报技巧上有所提高，展示了其在高维数据同化问题中的潜在实用性和可扩展性。 显示英文摘要

摘要： This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware regularization term. The first method formulated is referred to as Data-Consistent 4D-Var (DC-4DVar), which is then enhanced using a Weighted Mean Error (WME) quantity-of-interest map to construct the DC-WME 4D-Var method. While the DC and DC-WME cost functions both involve a predictability-aware regularization term, the DC-WME function includes a modification to the model-data misfit, thereby improving estimation accuracy, robustness, and theoretical consistency in nonlinear and partially observed dynamical systems. Proofs are provided that establish the existence and uniqueness of the minimizer and analyze how a predictability assumption that is common within the DCI framework helps to promote solution stability. Numerical experiments are presented on benchmark dynamical systems (Lorenz-63 and Lorenz-96) as well as for the shallow water equations (SWE). In the benchmark dynamical systems, the DC-WME 4D-Var formulation is shown to consistently outperform standard 4D-Var in reducing both error and bias while maintaining robustness under high observation noise and short assimilation windows. Despite introducing modest computational overhead, DC-WME 4D-Var delivers improvements in estimation performance and forecast skill, demonstrating its potential practicality and scalability for high-dimensional data assimilation problems.