Abstract

The paper studies the properties of the previously proposed method for assimilating observational data into a hydrodynamic model, which is an author’s version of the generalized Kalman filter. This method generalizes the well-known ensemble Kalman filter method. The equations of the generalized Kalman filter are extended to the case when the initial hydrodynamic model is biased relative to the observations, that is, it has a systematic error. In addition, the problem of estimating the confidence limits of the model variables (analysis) constructed after assimilation is considered. The corresponding Fokker–Planck–Kolmogorov equation for these estimates is given. For a special case, which is usually encountered in practice, an analytical solution of this equation is given by the perturbation theory method. Numerical examples are also carried out for a specific dynamic model, and an analysis is discussed of these calculations.

中文翻译：

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一种数据同化方法的系统误差校正和置信限估计

摘要

本文研究了先前提出的将观测数据同化为流体动力学模型的方法的特性，该模型是广义卡尔曼滤波器的作者版本。该方法推广了众所周知的集成卡尔曼滤波方法。广义卡尔曼滤波器的方程扩展到初始流体动力学模型相对于观测值有偏差时的情况，也就是说，它具有系统误差。另外，考虑了估计同化后构造的模型变量（分析）的置信极限的问题。给出了对应于这些估计的Fokker-Planck-Kolmogorov方程。对于在实践中通常会遇到的特殊情况，通过微扰理论方法给出了该方程的解析解。