Comparison of Ensemble Kalman Filters under Non-Gaussianity

Abstract

Recently various versions of ensemble Kalman filters (EnKFs) have been proposed and studied. This work concerns, in a mathematically rigorous manner, the relative performance of two major versions of EnKF when the forecast ensemble is non-Gaussian. The approach is based on the stability of the filtering methods against small model violations, using the expected squared L 2 distance as a measure of the deviation between the updated distributions. Analytical and experimental results suggest that both stochastic and deterministic EnKFs are sensitive to the violation of the Gaussian assumption, while the stochastic filter is relatively more stable than the deterministic filter under certain circumstances, especially when there are wild outliers. These results not only agree with previous empirical studies, but also suggest a natural choice of a free parameter in the square root Kalman filter algorithm.

Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization

“…It uses an ensemble of random samples, also called particles, to approximate the forecast and analysis distributions by Gaussian distributions whose means and covariances are given by ensemble means and covariances. Among various EnKF algorithms, we choose to consider only the version with perturbed observations, introduced in (Burgers et al 1998;Houtekamer and Mitchell 1998), and we refer to (Lei et al 2010) for a comparison of different versions of EnKF algorithms.…”

Bridging the ensemble Kalman and particle filters

“…One can also adjust the first two moments systematically by a deterministic affine correction of the forecast particles, which leads to the class of so-called ensemble square root filters (Anderson, 2001;Whitaker & Hamill, 2002;Tippett et al, 2003). Here, we focus on the stochastic version, for two reasons: first, the representation (1) is crucial for our developments; second, the stochastic ensemble Kalman filter is known to be more robust than the deterministic variants in nonlinear and/or non-Gaussian situations that are of interest to us (Lawson & Hansen, 2004;Lei et al, 2010).…”

Ensemble Kalman filtering without the intrinsic need for inflation

“…It is assumed that the members of the ensemble are independently drawn from a multivariate Gaussian distribution of mean state x b and covariance matrix B. As argued in the introduction this assumption leads to an approximation, since the ensemble members are rather samples of a (more or less) non-Gaussian distribution (Bocquet et al, 2010;Lei et al, 2010). There is no point in modelling higher-order moments of the statistics prior to the analysis, since the analysis of the Kalman filter only uses the first-and second-order moments.…”