在集合卡尔曼滤波中考虑由未解析尺度导致的模型误差
Accounting for model error due to unresolved scales within ensemble Kalman filtering
AI总结：
针对集合变换卡尔曼滤波中未解析尺度导致的模型误差问题，提出时不变和时变两种基于历史再分析增量的误差处理方法，经低阶混沌系统验证，其滤波性能更优、参数调优更少且易实现。
摘要：
我们提出了一种在集合变换卡尔曼滤波（ETKF）框架下处理由未解析尺度引发的模型误差的方法。该方法将近期针对变分方案和扩展卡尔曼滤波器探索的确定性模型误差公式，拓展应用至这类算法范畴。分析更新所需的模型误差统计量，通过历史再分析增量和合适的模型误差演化律进行估计。本文描述了该方法的两种不同版本：一种是时不变模型误差处理方式，即采用的模型误差统计描述不随时间变化；另一种是时变处理方式，即假设的模型误差统计量在每个分析步骤随机采样。我们将这两种方法与通过膨胀和局地化处理模型误差的标准方法进行对比，并在一个呈现混沌动力学的低阶非线性系统上开展数值模拟以验证结果。结果表明，所提出的模型误差处理方式显著提升了滤波性能，且两种方法所需的参数调优工作量远少于标准方法。此外，该方法在已有的基于集合的方案中易于实现。本文还讨论了在ETKF这类平方根滤波器框架下应用所提方法的普遍意义。
英文摘要：
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently explored for variational schemes and extended Kalman filter. The model error statistic required in the analysis update is estimated using historical reanalysis increments and a suitable model error evolution law. Two different versions of the method are described; a time-constant model error treatment where the same model error statistical description is time-invariant, and a time-varying treatment where the assumed model error statistics is randomly sampled at each analysis step. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low order nonlinear system exhibiting chaotic dynamics. The results show that the filter skill is significantly improved through the proposed model error treatments, and that both methods require far less parameter tuning than the standard approach. Furthermore, the proposed approach is simple to implement within a pre-existing ensemble based scheme. The general implications for the use of the proposed approach in the framework of square-root filters such as the ETKF are also discussed.
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