Mixture Ensembles for Data Assimilation in Dynamic Data-driven Environmental Systems

Many inference problems in environmental DDDAS must contend with high dimensional models and non-Gaussian uncertainties, including but not limited to Data Assimilation, Targeting and Planning. In this this paper, we present the Mixture Ensemble Filter (MEnF) which extends ensemble filtering to non-Gaussian inference using Gaussian mixtures. In contrast to the state of the art, MEnF embodies an exact update equation that neither requires explicit calculation of mixture element moments nor ad-hoc association rules between ensemble members and mixture elements. MEnF is applied to the chaotic Lorenz-63 model and to a chaotic soliton model that allows idealized and systematic studies of localized phenomena. In both cases, MEnF outperforms contemporary approaches, and replaces ad-hoc Gaussian Mixture approaches for non-Gaussian inference.