Representation errors and retrievals in linear and nonlinear data assimilation
Representation errors and retrievals in linear and nonlinear data assimilation
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DOI：
10.1002/qj.2464
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发表时间：
2015-07
影响因子：
8.9
通讯作者：
P. V. van Leeuwen
中科院分区：
文献类型：
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作者：
P. V. van Leeuwen
本文介绍了如何从贝叶斯定理出发来表述表示问题。本文的目的是提高人们对形式解决方案的认识，以便将近似放在适当的上下文中。在似然中出现了表示误差，讨论了在模型和观测中表示真实的不同可能性，包括非线性表示概率密度函数。具体地说，讨论了在通常的过程中将表示误差协方差加到观测值的误差协方差中所需的假设，并且表明，当存在多个子网格观测值时，它们的平均值仍然具有表示误差；所谓的“超级遮挡”不能解决问题。与离线或在线反演问题相联系，为同化线性反演与原始观测的等价性提供了一种新的简单证明。此外，还展示了如何在不损失信息的情况下同化非线性反演。最后，我们讨论了如何在贝叶斯框架下一致地处理观测算子模型中的错误，并与该领域的前人工作相联系。
This article shows how one can formulate the representation problem starting from Bayes' theorem. The purpose of this article is to raise awareness of the formal solutions, so that approximations can be placed in a proper context. The representation errors appear in the likelihood, and the different possibilities for the representation of reality in model and observations are discussed, including nonlinear representation probability density functions. Specifically, the assumptions needed in the usual procedure to add a representation error covariance to the error covariance of the observations are discussed, and it is shown that, when several sub‐grid observations are present, their mean still has a representation error; so‐called ‘superobbing’ does not resolve the issue. Connection is made to the off‐line or on‐line retrieval problem, providing a new simple proof of the equivalence of assimilating linear retrievals and original observations. Furthermore, it is shown how nonlinear retrievals can be assimilated without loss of information. Finally we discuss how errors in the observation operator model can be treated consistently in the Bayesian framework, connecting to previous work in this area.