论文标题
海啸模型的变异数据同化的二阶伴随灵敏度分析
Second order adjoint sensitivity analysis in variational data assimilation for tsunami models
论文作者
论文摘要
我们从数学上得出了海啸建模的数据同化结果的敏感性，以扰动观测操作员。我们考虑了（i）初始条件重建的一维浅水方程上的变异数据同化方案的结果，以及（ii）Kevlahan等人所示的测深测量检测。 （2019，2020）。我们使用变分方法来得出成本函数的Hessian j表示预测解决方案和观察之间的误差。使用Shutyaev等人概述的Hessian表示和方法。 （2017，2018），我们分别从数学上得出了任意响应函数对案例（i）和（ii）分别对扰动的敏感性。这种分析可能证实了早期工作的结果，在足够的收敛条件下以及传播表面波对测深的重建中的误差的敏感性。这种敏感性分析将说明观察网络的特定要素是否比其他元素更为重要，并有助于最大程度地减少观察收集和预测模型效率的外部成本。
We mathematically derive the sensitivity of data assimilation results for tsunami modelling, to perturbations in the observation operator. We consider results of variational data assimilation schemes on the one dimensional shallow water equations for (i) initial condition reconstruction, and (ii) bathymetry detection as presented in Kevlahan et al. (2019, 2020). We use variational methods to derive the Hessian of a cost function J representing the error between forecast solutions and observations. Using this Hessian representation and methods outlined by Shutyaev et al. (2017, 2018), we mathematically derive the sensitivity of arbitrary response functions to perturbations in observations for case (i) and (ii) respectively. Such analyses potentially substantiate results from earlier work, on sufficient conditions for convergence, and sensitivity of the propagating surface wave to errors in bathymetry reconstruction. Such sensitivity analyses would illustrate whether particular elements of the observation network are more critical than others, and help minimise extraneous costs for observation collection, and efficiency of predictive models.
