Title: Addressing the nonlinear problem of low order clustering in deterministic filters by using mean-preserving non-symmetric solutions of the ETKF

Authors: Javier Amezcua (University of Maryland, College Park)
Eugenia Kalnay (University of Maryland, College Park)
Kayo Idea (University of Maryland, College Park)

In previous studies (Lawson and Hansen, 2004; Anderson, 2010), a pathological effect has been observed to occur when using deterministic versions of the Ensemble Kalman Filter in cases in which the nonlinearity of a prediction model becomes important. While the filter does not diverge, the quality of the ensemble is degraded: one member becomes an outlier while the rest cluster together resulting in an effective two-member ensemble. Consequently, the higher order moments of the ensemble and diagnostics such as rank histograms are deeply affected. In this work, an analysis of this phenomenon is provided and it is shown that the use of mean-preserving non-symmetric solutions of the Ensemble Transform Kalman Filter (Bishop et al, 2001; Wang et al, 2004; Livings et al, 2007) can ameliorate this problem without representing further computational expense. Furthermore, it can be considered a form of ensemble resampling. The procedure to construct this type of solution and its application are illustrated with both a simple univariate quadratic model and the Lorenz 1963 model.

References:
J. Anderson, A non-Gaussian ensemble filter update for data assimilation, Mon. Wea. Rev. 138 (2010) 4186-4198.
C. Bishop, B. Etherton and S. Majumdar, Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects, Mon. Wea. Rev. 129 (2001) 420–436.
W. Lawson and J. Hansen, Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth, Mon. Wea. Rev. 132 (2004) 1966-1981.
D. Livings, S. Dance and N. Nichols, Unbiased ensemble square root filters, Phys. D 237 (2008) 1021-1028.
X. Wang, C. Bishop and S. Julier, Which is better, and ensemble of positive-negative pairs or a centered spherical ensemble?, Mon. Wea. Rev. 132 (2004), 1590-1605.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: March 1 2011