POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation
POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation
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DOI：
10.1016/j.jcp.2015.04.030
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
R. Stefanescu;Adrian Sandu;Ionel M. Navon
中科院分区：
文献类型：
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作者：
R. Stefanescu;Adrian Sandu;Ionel M. Navon
本文研究了用降阶模式加速大尺度非线性动力模式变分同化问题的方法。结果表明，一个成功的降阶解的一个关键要求是，降阶Karush-Kuhn-Tucker条件准确地代表他们的全阶同行。特别是，准确的降阶近似需要的前向和伴随动力学模型，以及为减少梯度。本文提出了一种新的降阶基构造策略，用于本征正交分解（POD）ROM数据同化，并分别采用Galerkin和Petrov-Galerkin投影。首次将POD、张量POD和离散经验插值方法（DEIM）应用于地球物理流场模式（二维浅水方程）的简化数据同化系统。数值实验证实了伽辽金投影的理论框架。在Petrov-Galerkin投影的情况下，降阶模型必须考虑镇定策略。新的简化浅水数据同化系统在十分之一的计算时间内提供了与全分辨率数据同化系统类似的分析。
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.