A Gaussian‐mixture ensemble transform filter

Abstract

AbstractWe generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian‐mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three‐dimensional Lorenz‐63 model). It is demonstrated that the EGMF is capable of tracking systems with non‐Gaussian uni‐ and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society