The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model
The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model
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用于有效计算灵敏度的独立集摄动方法及其在数据同化和有限元浅水模型中的应用
DOI：
10.1016/j.compfluid.2013.01.025
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发表时间：
2013
影响因子：
2.8
通讯作者：
Fang F
中科院分区：
文献类型：
--
作者：
Fang F
利用独立集摄动（ISP,[40]）灵敏度分析，建立了二维Galerkin/ Petrov-Galerkin有限元浅水（S-W）模型的伴随模型。通过与自动微分方法（TAMC）导出的伴随模型（用于优化初始条件）进行比较，评估了其在具有有限面积浅水方程模型的全4-D Var设置中的性能。结果表明，ISP灵敏度分析提供了一种非常简单的方法来形成离散正演模型（甚至复杂的控制方程，离散化方法和非线性参数化）的伴随码/梯度/微分，并使用图着色方法结合微扰方法实现。重要的是，伴随符会随着前向代码的继续开发而自动更新。实验结果表明，基于ISP灵敏度分析的伴随模型可以达到传统的自动微分法（TAMC）[31]伴随模型的精度。进一步的比较表明，使用ISP敏感性分析运行伴随模型所需的CPU时间远少于自动微分衍生伴随模型所需的CPU时间，因为ISP衍生伴随模型所需的CPU时间与问题规模成线性关系。将ISP敏感性分析进一步应用于高度非线性的Petrov-Galerkin有限元模型。然后优化使用ISP灵敏度分析方法推导切线模型时使用的扰动大小，并使用所得方法吸收稀疏（更真实）和密集的观测数据以优化初始条件。建立了一个简单的一阶公式来计算每个变量在每个节点和时间水平上的扰动大小。通过将ISP敏感性方法应用于中等复杂模型（浅水模型），本文概述了将该方法应用于涉及现实复杂模型的数据同化（DA）问题的步骤。
An adjoint model for a 2D Galerkin/Petrov–Galerkin finite element (FE) shallow water (S-W) model is developed using the Independent Set Perturbation (ISP, [40]) sensitivity analysis. Its performance in a full 4-D Var setup with a limited area shallow water equations model is assessed by comparing with the adjoint model derived by the automatic differentiation approach (TAMC), where it is used for optimising the initial conditions. It is shown that the ISP sensitivity analysis provides a very simple approach of forming the adjoint code/gradients/differentiation of discrete forward models (even complex governing equations, discretization methods and non-linear parameterizations) and is realised using a graph colouring approach combined with a perturbation method. Importantly, the adjoint is automatically updated as the forward code continues to be developed. In the test cases, it is shown that the adjoint model using the ISP sensitivity analysis can achieve the accuracy of traditional adjoint models derived by the automatic differentiation method (TAMC) [31]. Further comparison shows that the CPU time required for running the adjoint model using the ISP sensitivity analysis is much less than that required for the automatic differentiation derived adjoint model since the ISP derived adjoint CPU time scales linearly with the problem size. The ISP sensitivity analysis is further applied to a highly non-linear Petrov–Galerkin FE model. The perturbation size used in deriving the tangent linear model with the ISP sensitivity analysis method is then optimised and the resulting approach used to assimilate both sparse (more realistic) and dense observational data for optimising the initial conditions. A simple first order formula is developed to calculate the perturbation size for each variable, at each node and time level. By applying the ISP sensitivity method to an intermediate complexity model (a shallow water model) this paper outlines steps towards applying the approach to data assimilation (DA) problems involving realistic complex models.
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影响因子：
1.2
作者：
D. Cacuci;C. Weber;E. Oblow;J. Marable
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DOI：
10.3402/tellusa.v45i5.15060
发表时间：
1993-10
期刊：
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DOI：
--
发表时间：
2003
期刊：
影响因子：
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作者：
R. Giering;T. Kaminski
通讯作者：
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DOI：
10.1007/978-3-540-68942-3
发表时间：
2008-07
期刊：
--
影响因子：
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