| Scopus记录号: | 2-s2.0-85043700464
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| 论文题名: | What is the correct cost functional for variational data assimilation? |
| 作者: | Bröcker J.
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| 刊名: | Climate Dynamics
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| ISSN: | 9307575
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| 出版年: | 2019
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| 卷: | 52, 期:2019-01-02 | | 起始页码: | 389
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| 结束页码: | 399
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| 语种: | 英语
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| 英文关键词: | Onsager–Machlup functional
; Stochastic differential equations
; Variational data assimilation
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| 英文摘要: | Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and the resulting optimal trajectories may have a probabilistic interpretation, for instance by linking data assimilation with maximum aposteriori (MAP) estimation. This is possible in particular if the unknown trajectory is modelled as the solution of a stochastic differential equation (SDE), as is increasingly the case in weather forecasting and climate modelling. In this situation, the MAP estimator (or “most probable path” of the SDE) is obtained by minimising the Onsager–Machlup functional. Although this fact is well known, there seems to be some confusion in the literature, with the energy (or “least squares”) functional sometimes been claimed to yield the most probable path. The first aim of this paper is to address this confusion and show that the energy functional does not, in general, provide the most probable path. The second aim is to discuss the implications in practice. Although the mentioned results pertain to stochastic models in continuous time, they do have consequences in practice where SDE’s are approximated by discrete time schemes. It turns out that using an approximation to the SDE and calculating its most probable path does not necessarily yield a good approximation to the most probable path of the SDE proper. This suggest that even in discrete time, a version of the Onsager–Machlup functional should be used, rather than the energy functional, at least if the solution is to be interpreted as a MAP estimator. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. |
| 资源类型: | 期刊论文
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| 标识符: | http://119.78.100.158/handle/2HF3EXSE/122461
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| Appears in Collections: | 气候变化事实与影响
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作者单位: | School of Mathematical and Physical Sciences, University of Reading, Reading, United Kingdom
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| Recommended Citation: | |
Bröcker J.. What is the correct cost functional for variational data assimilation?[J]. Climate Dynamics,2019-01-01,52(2019-01-02)
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