Observation-Dependent Posterior Inflation for the Ensemble Kalman Filter
Observation-Dependent Posterior Inflation for the Ensemble Kalman Filter
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DOI：
10.1175/mwr-d-15-0329.1
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发表时间：
2016-07-01
影响因子：
3.2
通讯作者：
Whitaker, Jeffrey S.
中科院分区：
文献类型：
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作者：
Hodyss, Daniel;Campbell, William F.;Whitaker, Jeffrey S.
众所周知，基于集成的卡尔曼滤波(EBKF)算法会产生后验集成，其方差因各种原因(例如，非线性和采样误差)而不正确。文中指出，抽样误差的存在意味着真正的后验误差方差是最新观测值的函数，而不是标准的EBKF，后者的后验方差与观测值无关。此外，在EBKF的集成生成步骤中，传统的集成验证工具“二元化扩散技能”图不能正确识别这一问题，导致人们对后验方差与平方误差之间的关系过于乐观。描述了一种更新的集成验证工具，该工具揭示了均方误差(MSE)和集成方差之间的错误关系，并对EBKF算法的后验方差进行了无偏估计。最后，推导了一种新的通货膨胀方法，它考虑了抽样误差，并正确地产生了依赖于最新观测值的后验误差方差。新方法具有很小的计算开销，不需要访问观测数据，并且易于在任何序列或全局EBKF中使用。
Ensemble-based Kalman filter (EBKF) algorithms are known to produce posterior ensembles whose variance is incorrect for a variety of reasons (e.g., nonlinearity and sampling error). It is shown here that the presence of sampling error implies that the true posterior error variance is a function of the latest observation, as opposed to the standard EBKF, whose posterior variance is independent of observations. In addition, it is shown that the traditional ensemble validation tool known as the "binned spread-skill'' diagram does not correctly identify this issue in the ensemble generation step of the EBKF, leading to an overly optimistic impression of the relationship between posterior variance and squared error. An updated ensemble validation tool is described that reveals the incorrect relationship between mean squared error (MSE) and ensemble variance, and gives an unbiased evaluation of the posterior variances from EBKF algorithms. Last, a new inflation method is derived that accounts for sampling error and correctly yields posterior error variances that depend on the latest observation. The new method has very little computational overhead, does not require access to the observations, and is simple to use in any serial or global EBKF.