Aspects of the Ensemble Kalman Filter

This dissertation points to a potential flaw in the general framework for semi-deterministic formulations of the EnKF, affecting some but not all such formulations, and a simple mechanical system is described that is of interest to meteorologists as an illustration of the problem of initialisation.

Abstract

The Ensemble Kalman Filter (EnKF) is a data assimilation method designed to provide estimates of the state of a system by blending information from a model of the system with observations. It maintains an ensemble of state estimates from which a single best state estimate and an assessment of estimation error may be calculated. Compared to more established methods it offers advantages of reduced computational cost, better handling of nonlinearity, and greater ease of implementation. This dissertation starts by reviewing different formulations of the EnKF, covering stochastic and semi-deterministic variants. Two formulations are selected for implementation, and the adaptation of their algorithms for better numerical behaviour is described. Next, as a subject for experiments, a simple mechanical system is described that is of interest to meteorologists as an illustration of the problem of initialisation. Experimental results are presented that show some unexpected features of the implemented filters, including ensemble statistics that are inconsistent with the actual error. Explanations