Ensemble Kalman filter algorithms are a method of choice for data assimilation 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. A naïve implementation of the method struggles in representing analysis multivariate distributions. Approaches similar to the use of proposal densities for particle filters show promise in addressing this deficiency. There is potential to combine these extended rank histogram methods with particle filters to create methods with the strengths of both that may avoid many of the scaling challenges of the particle filters. The methods are illustrated with low order model examples with varying degrees of nonlinearity.