Development and testing of an efficient, non-Gaussian ensemble filter for data assimilation in geophysics

Ensemble data assimilation strategies are now common practice in geoscience; examples include the ensemble Kalman filter (EnKF) and ensemble/variational hybrids. These methods provide Monte Carlo estimates of a system's probability density conditioned on observations, assuming errors for the model state and observations are independent and Gaussian. A major benefit of Gaussian-based approaches is that they can be constructed to work effectively using relatively small ensembles by treating sampling errors in ensemble-estimated covariances. Nevertheless, these methods may not be the best option as computational resources allow for increasingly larger ensembles that better resolve non-Gaussian errors.

In this talk, we introduce a new ensemble data assimilation approach based on the particle filter (PF) that has potential for nonlinear/non-Gaussian applications in geoscience. PFs make no assumptions regarding the underlying error distribution, allowing them to perform well for most applications provided that the ensemble size is sufficiently large. The proposed method is similar to the PF in that ensemble realizations of the model state are weighted based on the likelihood of observations to approximate posterior probabilities of the system state. The new approach, denoted the local PF, reduces the influence of distant observations on the weight calculations via a localization function. Unlike standard PFs, the local PF provides accurate results using ensemble sizes small enough to be affordable for large models. Comparisons of the local PF and an EnKF using a simplified atmospheric general circulation model (with a 25-member ensemble) demonstrate that the new method is a viable data assimilation technique for large geophysical systems. The local PF also shows substantial benefits over the EnKF when observation networks consist of measurements that relate nonlinearly to the model state—analogous to remotely sensed data used frequently in atmospheric analyses.