Data assimilation: Mathematical and statistical perspectives
Data assimilation: Mathematical and statistical perspectives
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DOI：
10.1002/fld.1698
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发表时间：
2008-03-20
影响因子：
1.8
通讯作者：
Voss, J.
中科院分区：
文献类型：
--
作者：
Apte, A.;Jones, C. K. R. T.;Voss, J.
本文的大部分内容包含了数据同化主题的简明数学概述，突出了三个主要思想：(i)描述了3DVAR、4DVAR和弱约束4DVAR的标准优化方法，并解释了它们的相互关系；（ii）然后引入这些方法的统计类似物，导致滤波（推广3DVAR）和平滑形式（推广4DVAR和弱约束4DVAR），并且优化方法被证明是这些统计方法所隐含的概率分布的最大后验估计；（iii）从一般动力系统的角度来看这个问题，表明拉格朗日数据的结合可以通过对前面概念的直接扩展来处理。我们认为，基于4DVAR和弱约束4DVAR的统计类似物的数据同化平滑方法提供了将时空分布数据同化到模型中的最佳解决方案。得到的最优解是相关函数类（初始条件或精细相关解）上的概率分布。该方法在第一个实例中是有用的，因为它澄清了什么是最优解决方案的概念，从而提供了一个可以评估现有方法的基准。从长远来看，它还提供了创建模型解决方案集成的新方法的潜力，以最佳方式合并可用数据。给出了两个例子来说明这种数据同化方法，两个例子都是在拉格朗日数据的背景下，一个基于统计4DVAR，另一个基于弱约束统计4DVAR。将前者与集成卡尔曼滤波进行了比较，结果表明集成卡尔曼滤波在各种情况下都是不准确的。版权所有(C) 2007约翰威利父子有限公司
The bulk of this paper contains a concise mathematical overview of the subject of data assimilation, highlighting three primary ideas: (i) the standard optimization approaches of 3DVAR, 4DVAR and weak constraint 4DVAR are described and their interrelations explained; (ii) statistical analogues of these approaches are then introduced, leading to filtering (generalizing 3DVAR) and a form of smoothing (generalizing 4DVAR and weak constraint 4DVAR) and the optimization methods are shown to be maximum a posteriori estimators for the probability distributions implied by these statistical approaches; and (iii) by taking a general dynamical systems perspective on the subject it is shown that the incorporation of Lagrangian data can be handled by a straightforward extension of the preceding concepts.We argue that the smoothing approach to data assimilation, based on statistical analogues of 4DVAR and weak constraint 4DVAR, provides the optimal solution to the assimilation of space-time distributed data into a model. The optimal Solution obtained is a probability distribution on the relevant class of functions (initial conditions or fine-dependent solutions). The approach is a useful one in the first instance because it clarifies the notion of what is the optimal Solution, thereby providing a benchmark against which existing approaches can be evaluated. In the longer term it also provides the potential for new methods to create ensembles of solutions to the model, incorporating the available data in an optimal fashion.Two examples are given illustrating this approach to data assimilation, both in the context of Lagrangian data, one based on statistical 4DVAR and the other on weak constraint statistical 4DVAR. The former is compared with the ensemble Kalman filter, which is thereby shown to be inaccurate in a variety of scenarios. Copyright (C) 2007 John Wiley & Sons, Ltd.