Ensemble Kalman filter for nonconservative moving mesh solvers with a joint physics and mesh location update,Quarterly Journal of the Royal Meteorological Society

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Ensemble Kalman filter for nonconservative moving mesh solvers with a joint physics and mesh location update
Quarterly Journal of the Royal Meteorological Society ( IF 3.0 ) Pub Date : 2021-01-21 , DOI: 10.1002/qj.3980
Christian Sampson ₁ , Alberto Carrassi _{2,

3} , Ali Aydogdu ₄ , Chris K.R.T Jones ₁

Affiliation

Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing important or unresolved physics. The adaptation can be informed by the model state or external information, or made to depend on the model physics. In this latter case, one can think of the mesh configuration as part of the model state. If observational data are to be assimilated into the model, the question of updating the mesh configuration with the physical values arises. Adaptive meshes present significant challenges when using popular ensemble data assimilation (DA) methods. We develop a novel strategy for ensemble‐based DA, for which the adaptive mesh is updated along with the physical values. This involves including the node locations as a part of the model state itself, allowing them to be updated automatically at the analysis step. This poses a number of challenges, which we resolve to produce an effective approach that promises to apply with some generality. We evaluate our strategy with two testbed models in one dimension (1‐d), comparing them with a strategy we previously developed that does not update the mesh configuration. We find that updating the mesh improves the fidelity and convergence of the filter. An extensive analysis on the performance of our scheme beyond just the root‐mean‐squared error (RMSE) is also presented.

中文翻译：

具有联合物理特性和网格位置更新的适用于非保守运动网格求解器的Ensemble Kalman滤波器

使用自适应网格的数值求解器可以将计算能力集中在模型域的重要区域上，从而捕获重要的或未解决的物理问题。可以通过模型状态或外部信息来告知适应性，也可以取决于模型的物理性质。在后一种情况下，可以将网格配置视为模型状态的一部分。如果要将观测数据同化到模型中，则会出现用物理值更新网格配置的问题。当使用流行的集成数据同化（DA）方法时，自适应网格提出了重大挑战。我们针对基于集合的DA开发了一种新颖的策略，针对该策略，自适应网格与物理值一起更新。这涉及将节点位置作为模型状态本身的一部分包括在内，从而允许它们在分析步骤中自动更新。这带来了许多挑战，我们决心产生一种有效的方法，有望在某种程度上得到普遍应用。我们使用一维（1-d）中的两个测试平台模型评估我们的策略，并将它们与我们先前开发的不更新网格配置的策略进行比较。我们发现更新网格可以提高滤波器的保真度和收敛性。不仅对均方根误差（RMSE），还对我们的方案的性能进行了广泛的分析。

更新日期：2021-01-21

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