A POD reduced-order 4D-Var adaptive mesh ocean modelling approach
A POD reduced-order 4D-Var adaptive mesh ocean modelling approach
复制标题
POD降阶4D-Var自适应网格海洋建模方法
DOI：
10.1002/fld.1911
复制
发表时间：
2008
影响因子：
1.8
通讯作者：
Fang F
中科院分区：
文献类型：
--
作者：
Fang F
本文提出了一种新的适用于自适应网格海洋模式（Imperial College Ocean Model）的本征正交分解（POD）逆模式。新的POD模型进行了验证，使用蒙克环流测试的情况下，它反转的初始条件。优化的速度场表现出整体良好的协议与完整的模型所产生的。在大部分区域内，反演速度与真实速度之间的相关性为80-98%。采用误差估计方法对降阶自适应网格模型的质量进行了评价。在POD基更新后，成本函数比原始值降低了20%，进一步降低了70%。在这项研究中，减少伴随模型是直接从离散化的减少正演模型。整个优化过程完全在减小的空间中进行。四维变分（4D-Var）数据同化的计算成本显着降低（在这里的测试情况下减少了70%），通过减少控制空间的尺寸，在向前和伴随模式。计算效率进一步提高，因为这两个减少的前向和伴随模型是由一系列的时间无关的子矩阵。简化的前向和伴随模型可以重复运行，计算成本可以忽略不计。采用自适应POD 4D-Var来更新POD基，因为最小化推进和失去控制，因此POD基的自适应更新是必要的。以前开发的数值方法方等人。(Int. J. Numer。Meth. Fluids 2008）的使用，以准确地代表地转平衡，提高效率的POD模拟。版权所有q 2008约翰威利父子有限公司。
A novel proper orthogonal decomposition (POD) inverse model, developed for an adaptive mesh ocean model (the Imperial College Ocean Model, ICOM), is presented here. The new POD model is validated using the Munk gyre flow test case, where it inverts for initial conditions. The optimized velocity fields exhibit overall good agreement with those generated by the full model. The correlation between the inverted and the true velocity is 80–98% over the majority of the domain. Error estimation was used to judge the quality of reduced-order adaptive mesh models. The cost function is reduced by 20% of its original value, and further by 70% after the POD bases are updated. In this study, the reduced adjoint model is derived directly from the discretized reduced forward model. The whole optimization procedure is undertaken completely in reduced space. The computational cost for the four-dimensional variational (4D-Var) data assimilation is significantly reduced (here a decrease of 70% in the test case) by decreasing the dimensional size of the control space, in both the forward and adjoint models. Computational efficiency is further enhanced since both the reduced forward and adjoint models are constructed by a series of time-independent sub-matrices. The reduced forward and adjoint models can be run repeatedly with negligible computational costs. An adaptive POD 4D-Var is employed to update the POD bases as minimization advances and loses control, thus adaptive updating of the POD bases is necessary. Previously developed numerical approaches Fang et al.(Int. J. Numer. Meth. Fluids 2008) are employed to accurately represent the geostrophic balance and improve the efficiency of the POD simulation. Copyright q 2008 John Wiley & Sons, Ltd.