Non-Gaussian, Nonlinear Extensions for Ensemble Filter Data Assimilation with a Marginal Correction Rank Histogram Filter

Ensemble Kalman filter algorithms have become a method of choice for data assimilation applications in geosciences. While the first two moments of the ensemble are used in basic ensemble Kalman filters, the ensembles contain additional information about non-Gaussian and nonlinear characteristics of the prior model distributions. Serial implementations of ensemble Kalman filters can be extended to exploit non-Gaussian prior probability distributions and observation likelihoods and nonlinear relations between state variables and observed quantities.

An extension of a scalar non-parametric ensemble data assimilation technique, the rank histogram filter, to a multivariate method is described. The method extends serial ensemble Kalman filters so that they can accurately represent any non-Gaussian distribution. In addition, the method can represent many, but not all, nonlinear aspects of atmospheric data assimilation. This method can be implemented for a small additional cost and is particularly applicable for the assimilation of trace constituents. For instance, it maintains non-negativity in a theoretically supported manner. The method will be described and results compared to those from more traditional methods. Examples will focus on data assimilation for trace constituents being advected by dynamical flows.