This contribution addresses the characterization of the model-error covariance matrix from the new theoretical perspective provided by the parametric Kalman filter method which approximates the covariance dynamics from the parametric evolution of a covariance model. The classical approach to obtain the modified equation of a dynamics is revisited to formulate a parametric modelling of the model-error covariance matrix which applies when the numerical model is dissipative compared with the true dynamics. As an illustration, the particular case of the advection equation is considered as a simple test bed. After the theoretical derivation of the predictability-error covariance matrices of both the nature and the numerical model, a numerical simulation is proposed which illustrates the properties of the resulting model-error covariance matrix.

中文翻译：

---

从参数卡尔曼滤波器角度获得由于离散化方案而导致的模型误差协方差的方法

此贡献从参数卡尔曼滤波方法提供的新理论角度解决了模型误差协方差矩阵的特征，该方法从协方差模型的参数演化近似协方差动态。重新探讨了获得动力学修正方程的经典方法，以建立模型误差协方差矩阵的参数化模型，该模型适用于数值模型与真实动力学相比耗散的情况。作为说明，对流方程的特殊情况被认为是一个简单的试验台。在对自然和数值模型的可预测性-误差协方差矩阵进行理论推导之后，提出了一个数值模拟，说明了所得模型误差-协方差矩阵的性质。