datasheet1_Spatio-Temporal Inversion Using the Selection Kalman Model.zip

Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial distribution and Gauss-linear forward and observation models. This model is contained in the class of Gaussian distribution and is therefore analytically tractable. It is however unsuitable for representing multimodality. We define the selection Kalman model that is based on a selection-Gaussian initial distribution and Gauss-linear forward and observation models. The selection-Gaussian distribution can be seen as a generalization of the Gaussian distribution and may represent multimodality, skewness and peakedness. This selection Kalman model is contained in the class of selection-Gaussian distributions and therefore it is analytically tractable. An efficient recursive algorithm for assessing the selection Kalman model is specified. The synthetic case study of spatio-temporal inversion of an initial state, inspired by pollution monitoring, suggests that the use of the selection Kalman model offers significant improvements compared to the traditional Kalman model when reconstructing discontinuous initial states.

在表征时空现象的模型中进行数据同化是一项挑战，尤其是在变量的空间直方图出现多个峰值时。传统的卡尔曼模型基于高斯初始分布，并采用高斯线性的前向和观测模型。该模型属于高斯分布类，因此具有解析可处理性。然而，它不适合表征多模态现象。我们定义了一种选择卡尔曼模型，该模型基于选择-高斯初始分布和高斯线性的前向和观测模型。选择-高斯分布可视作高斯分布的推广，可能表征多模态、偏态和峰态。此选择卡尔曼模型属于选择-高斯分布类，因此也具有解析可处理性。我们还指定了一种评估选择卡尔曼模型的有效递归算法。受污染监测启发的合成案例研究，对初始状态的空间时间反演进行了探讨，表明在重构不连续初始状态时，与传统的卡尔曼模型相比，使用选择卡尔曼模型能够带来显著的改进。