Spatio-temporal Inversion using the Selection Kalman Model

TL;DR

This paper introduces the selection Kalman model, an extension of the traditional Kalman filter that can handle multimodal, skewed, and peaked distributions in spatio-temporal data assimilation, demonstrated through pollution monitoring case studies.

Contribution

The paper proposes the selection Kalman model, a new framework that generalizes the Gaussian assumption to better represent complex distributional features in data assimilation.

Findings

Selection Kalman model outperforms traditional Kalman in reconstructing discontinuous states.

The model effectively captures multimodality, skewness, and peakedness in distributions.

Synthetic case study shows significant improvements in pollution monitoring scenarios.

Abstract

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.