A comparison of error subspace Kalman filters

By Lars Nerger, Wolfgang Hiller, J. Schröter. 2005

115 citations recorded by the source corpus.

Three advanced filter algorithms based on the Kalman filter are reviewed and presented in a unified notation. They are the well-known ensemble Kalman filter (EnKF), the singular evolutive extended Kalman (SEEK) filter, and the less common singular evolutive interpolated Kalman (SEIK) filter. For comparison, the mathematical formulations of the filters are reviewed in relation to the extended Kalman filter as error subspace Kalman filters. The algorithms are presented in their original form and possible variations are discussed. A comparison of the algorithms shows their theoretical capabilities for efficient data assimilation with large-scale non-linear systems. In particular, problems of the analysis equations are apparent in the original EnKF algorithm due to the Monte Carlo sampling of ensembles. Theoretically, the SEIK filter appears to be a numerically very efficient algorithm with high potential for use with non-linear models. The superiority of the SEIK filter is demonstrated on the basis of identical twin experiments using a shallow-water model with non-linear evolution. Identical initial conditions for all three filters allow for a consistent comparison of the data assimilation results. These show how choices of particular state ensembles and assimilation schemes lead to significant variations of the filter performance. This is related to different qualities of the predicted error subspaces, as is demonstrated in an examination of the predicted state covariance matrices.

Subfields: Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/b813cfb290f9efdb301208b5aa222d596e875fa2

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In Atmospheric Science

In Global and Planetary Change

Citations in the corpus

Beyond Gaussian Statistical Modeling in Geophysical Data Assimilation (2010, background): “Such filters work only in subspaces of the complete error space (Lermusiaux and Robinson 1999; Nerger et al. 2005).”
Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF (2015, background): “…typical oceanic and atmospheric data assimilation applications where the rank of the observational error covariance matrixR is much larger than the size of the ensemble (or the number of ensemble members), since in this case R will be strongly undersampled (Nerger et al. 2005; Altaf et al. 2014).”
A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation (2008, methodology): “Information on the error statistics may be obtained using differences between forecasts with different initialization times as in the National Meteorological Center (NMC) method (Parrish and Derber 1992) or ensemble methods based on a perturbed forecast-analysis system.”