Assessing Structural Differences in Error Analysis Covariance between Ensemble Kalman Filters and Local Particle Filters

From a Bayesian perspective, ensemble data assimilation seeks samples from a posterior probability distribution of a dynamical system state conditioned on observations. This can then be used to initialize ensemble forecasts. Ensemble Kalman Filters (EnKFs) use ensemble forecasts to estimate background error-covariance, and have shown great promise for high-dimensional applications such as numerical weather prediction. While EnKFs are versatile, they are suboptimal when errors are non-Gaussian, which can occur for nonlinear measurement and model operators and when observations have non-Gaussian errors. As such, there is a benefit to developing data assimilation schemes that utilize ensemble statistics in the presence of non-Gaussian errors. Particle Filters (PFs) are one potential strategy, but require ensemble sizes that scale exponentially with the observed degrees of freedom in the dynamical system. This makes implementation in the geosciences difficult. While similar restrictions exist for EnKFs, covariance localization provides a heuristic means of modulating ensemble-estimated error dependence across state variables, which permits its use in large applications using small ensemble sizes. Likewise, localization has been successfully applied to PFs. Previous assessments of the Poterjoy (2022) localized PF (LPF) show that this technique can be as skillful as EnKFs at producing accurate ensemble mean predictions, but with more reliable probabilistic predictions. However, this property of the LPF has not yet been fully explained. As such, this research investigates structural differences in posterior and forecast error covariance between LPFs and EnKFs to determine key differences in how multivariate uncertainty is treated by the two techniques. We utilize 5-day ensemble forecasts from the Hurricane Analysis and Forecast System (HAFS) over the Atlantic basin to compare changes in ensemble growth between EnKFs and LPFs, with a plan to expand to a global model domain in the future.