High Dimensional Ensemble Kalman Filter

TL;DR

This paper develops high-dimensional Ensemble Kalman Filter methods with consistent estimators, analyzes their theoretical properties, and demonstrates their superior performance over standard methods in complex models.

Contribution

It introduces novel high-dimensional EnKF algorithms with theoretical analysis and shows improved accuracy in complex physical models.

Findings

HD-EnKF outperforms standard EnKF in numerical tests

Theoretical analysis provides error bounds and insights

Methods are effective even with model misspecification

Abstract

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution observations of physical models, some key theoretical aspects of the EnKF are open for investigation. This paper proposes several high dimensional EnKF (HD-EnKF) methods equipped with consistent estimators for the important forecast error covariance and Kalman Gain matrices. It then studies the theoretical properties of the EnKF under both fixed and high dimensional state variables, which provides one-step and multiple-step mean square errors of the analysis states to the underlying oracle states offered by the Kalman Filter and gives the much needed insight to the roles played by the forecast error covariance on the accuracy of the EnKF. The accuracy of the data assimilation under the misspecified physical model is also considered. Numerical studies on the Lorenz-96 and the Shallow Water Equation models illustrate that the proposed HD-EnKF algorithms outperform the standard EnKF and widely used inflation methods.