Variational data assimilation using targetted random walks
Variational data assimilation using targetted random walks
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DOI：
10.1002/fld.2510
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发表时间：
2012-02
影响因子：
1.8
通讯作者：
Simon L. Cotter;M. Dashti;Andrew M. Stuart
中科院分区：
文献类型：
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作者：
Simon L. Cotter;M. Dashti;Andrew M. Stuart
数据同化的变异方法是在线预测和重新分析的广泛方法。未知状态的后验分布我们显示，在离线情况下，该后验分布的完整计算探测。链 - 蒙特·卡洛（MCMC）方法，使我们能够直接从有趣的观察值的未知函数上进行贝叶斯后验分布进行采样。在离线重新分析的背景下，使用简单的随机步行型MCMC方法，我们能够仅使用对前向模型的评估来表征问题和数据不匹配。 Lagrangian，在二维周期性几何形状中流入低雷诺数。由于数据不明，并且随着信息的量增加，我们的估计中的不确定性降低了。
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain–Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk‐type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two‐dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. Copyright © 2011 John Wiley & Sons, Ltd.