The maximum likelihood ensemble smoother for the Kuramoto–Sivashinsky equation
The maximum likelihood ensemble smoother for the Kuramoto–Sivashinsky equation
复制标题
Kuramoto-Sivashinsky 方程的最大似然系综平滑器
DOI：
10.1093/imamat/hxac026
复制
发表时间：
2022
影响因子：
1.2
通讯作者：
Gao, Xinfeng
中科院分区：
文献类型：
--
作者：
Hurst, Christopher;Zupanski, Milija;Gao, Xinfeng
数据同化（DA）的目的是将联合收割机观测/数据与模型相结合，以最大限度地利用信息来获得最佳估计。最大似然集成滤波器（MLEF）是一种顺序DA方法或滤波器类型的方法。滤波方法的缺点是同化时间积分观测值和估计经验参数估计。原因是在这种类型的DA方法中，在分析过程之外采用了正演模型。为了克服这些弱点，MLEF现在扩展为平滑和新的最大似然集成平滑（MLES）的建议。MLES是一种具有变分性质的平滑方法，特别是在成本函数中。MLES可以在选定的时间窗口内包括观测值和正演模型，而不是像MLEF那样使用来自单个时间位置的误差信息来求解最佳分析更新。新提出的DA方法首先验证了一系列严格和彻底的性能测试，使用Lorenz 96模型。然后，由于DA被广泛用于增加气象应用中常见的混沌动力系统的可预测性，本研究演示了MLES与由1D Kuramoto-Sivashinky（KS）方程控制的模型混沌问题。此外，MLES被证明是一种有效的方法，在改善不确定的经验模型参数的估计。MLES和MLEF，然后直接比较，它表明，MLES的性能是足够的，它是一个很好的候选人，增加混沌动力系统的可预测性。未来的工作将集中在MLES的高度湍流的广泛应用。
Data assimilation (DA) aims to combine observations/data with a model to maximize the utility of information for obtaining the optimal estimate. The maximum likelihood ensemble filter (MLEF) is a sequential DA method or a filter-type method. Weaknesses of the filter method are assimilating time-integrated observations and estimating empirical parameter estimation. The reason is that the forward model is employed outside of the analysis procedure in this type of DA method. To overcome these weaknesses, the MLEF is now extended as a smoother and the novel maximum likelihood ensemble smoother (MLES) is proposed. The MLES is a smoothing method with variational-like qualities, specifically in the cost function. Rather than using the error information from a single temporal location to solve for the optimal analysis update as done by the MLEF, the MLES can include observations and the forward model within a chosen time window. The newly proposed DA method is first validated by a series of rigorous and thorough performance tests using the Lorenz 96 model. Then, as DA is known to be used extensively to increase the predictability of the commonly chaotic dynamical systems seen in meteorological applications, this study demonstrates the MLES with a model chaotic problem governed by the 1D Kuramoto–Sivashinky (KS) equation. Additionally, the MLES is shown to be an effective method in improving the estimate of uncertain empirical model parameters. The MLES and MLEF are then directly compared and it is shown that the performance of the MLES is adequate and that it is a good candidate for increasing the predictability of a chaotic dynamical system. Future work will focus on an extensive application of the MLES to highly turbulent flows.