In data assimilation, the description of the model error uncertainty is of the utmost importance because, when incorrectly defined, it may lead to information loss about the real state of the system. In this work, we proposed a novel approach that finds the optimal distribution for describing the model error uncertainty within a particle filtering framework. The method was applied to nonlinear waves in compressible flows. We investigated the influence of observation noise statistics, resolution of the numerical model, smoothness of the solutions, and sensor location. The results showed that in almost all situations the Pearson Type I is preferred, but with different curve-shape characteristics, namely, skewed, nearly symmetric, ∩-, ∪-, and J-shaped. The distributions became, in most cases, ∪-shaped when the sensors were located near the discontinuities.

中文翻译：

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使用 Pearson 系统进行模型误差估计并应用于可压缩流中的非线性波

在数据同化中，模型误差不确定性的描述至关重要，因为如果定义不正确，可能会导致系统真实状态的信息丢失。在这项工作中，我们提出了一种新颖的方法，可以找到描述粒子滤波框架内模型误差不确定性的最佳分布。该方法适用于可压缩流中的非线性波。我们研究了观测噪声统计、数值模型的分辨率、解的平滑度和传感器位置的影响。结果表明，几乎在所有情况下，Pearson I 型曲线都是首选，但具有不同的曲线形状特征，即倾斜、近对称、∩-、∪- 和 J 形。在大多数情况下，当传感器位于不连续点附近时，分布会变成∪形。