An investigation into the application of an ensemble Kalman smoother to high-dimensional geophysical systems

Abstract

We examine the application of ensemble Kalman filter algorithms to the smoothing problem in high-dimensional geophysical prediction systems. The goal of smoothing is to make optimal estimates of the geophysical system state making best use of observations taken before, at, and after the analysis time. We begin by reviewing the underlying probabilistic theory, along with a discussion how to implement a smoother using an ensemble Kalman filter algorithm. The novel contribution of this paper is the investigation of various key issues regarding the application of ensemble Kalman filters to smoothing using a series of Observing System Simulation Experiments in both a Lorenz 1996 model and an Atmospheric General Circulation Model. The results demonstrate the impacts of non-linearities, ensemble size, observational network configuration and covariance localization. The Atmospheric General Circulation model results demonstrate that the ensemble Kalman smoother (EnKS) can be successfully applied to high-dimensional estimation problems and that covariance localization plays a critical role in its success. The results of this paper provide a foundation of understanding which will be useful in future applications of EnKS algorithms.