On the consistency of ensemble transform filter formulations

Sebastian Reich; Seoleun Shin

doi:10.3934/jcd.2014.1.177

Article Contents

2014, Volume 1, Issue 1: 177-189. Doi: 10.3934/jcd.2014.1.177

This issue Previous Article Global optimal feedbacks for stochastic quantized nonlinear event systems Next Article Modularity revisited: A novel dynamics-based concept for decomposing complex networks

On the consistency of ensemble transform filter formulations

Sebastian Reich^1, and
Seoleun Shin^2,

1.
Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, D-14469 Potsdam
2.
Korea Institute of Atmospheric Prediction Systems, 4F Korea Computer Bldg., 35 Boramae-ro 5-gil, Dongjak-gu, Seoul 156-849

Received: October 2011

Revised: July 2012

Published: January 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we consider the data assimilation problem for perfect differential equation models without model error and for either continuous or intermittent observational data. The focus will be on the popular class of ensemble Kalman filters which rely on a Gaussian approximation in the data assimilation step. We discuss the impact of this approximation on the temporal evolution of the ensemble mean and covariance matrix. We also discuss options for reducing arising inconsistencies, which are found to be more severe for the intermittent data assimilation problem. Inconsistencies can, however, not be completely eliminated due to the classic moment closure problem. It is also found for the Lorenz-63 model that the proposed corrections only improve the filter performance for relatively large ensemble sizes.

Keywords:

Mathematics Subject Classification: Primary: 93E11, 60G35, 65C05; Secondary: 62M20, 62F15, 65C35.

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