论文标题
使用选择Kalman模型的时空反转
Spatio-temporal Inversion using the Selection Kalman Model
论文作者
论文摘要
代表时空现象的模型中的数据同化构成了挑战，特别是如果变量的空间直方图以多种模式出现。传统的卡尔曼模型基于高斯初始分布以及高斯线性动态和观察模型。该模型包含在高斯分布的类别中，因此在分析上可以进行分析。但是，它不适合表示多模式。我们定义了基于选择高斯初始分布以及高斯线性动态和观察模型的选择Kalman模型。选择高斯分布可以看作是高斯分布的概括，可能代表多模态，偏度和峰值。此选择Kalman模型包含在选择高斯分布的类别中，因此在分析上可以进行分析。指定了用于评估选择卡尔曼模型的有效递归算法。由污染监测的启发的最初状态的时空反转的合成案例研究，其中包含极端事件，这表明选择Kalman模型在重建不连续的初始状态时，使用Kalman模型与传统的Kalman模型相比提供了显着改善。
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 dynamic 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 dynamic 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, containing an extreme event suggests that the use of the selection Kalman model offers significant improvements compared to the traditional Kalman model when reconstructing discontinuous initial states.
