Nonlinear, Non-Gaussian Ensemble Filters for Data Assimilation

Both the deterministic and perturbed observation ensemble Kalman filters that are used in geophysics are predicated on assumptions that the joint prior distributions of model state variables and observations are Gaussian. Nevertheless, these methods have proved to be successful in situations where the prior is not Gaussian. In this case, these filters still assume that a least squares fit is appropriate for approximating the prior relation between an observation and a state variable.
Two new ensemble filter algorithms are described and tested. The first relaxes the assumptions that the prior observation distribution and the observation likelihood are gaussian. This algorithm is shown to be competitive with existing ensemble methods even when things are nearly Gaussian. The new method facilitates the assimilation of bounded quantities and observations that do not have gaussian observational error distributions.
The second new algorithm also relaxes the assumption that the relation between an observation and a state variable is linear. This algorithm is a hybrid ensemble/particle filter that works for large geophysical assimilation problems. Performance is superior in cases where the relation between observations and state variables is significantly nonlinear. However, the traditional ensemble filters are better for linear or weakly nonlinear applications. Possible directions for further improved ensemble algorithms are outlined.