Nudging, ensemble, and nudging ensembles for data assimilation in the presence of model error

Nudging approaches perform relatively better with increased model error; use of poor ensemble covariance estimates when model error is large harms the nudging-ensemble performance. Consequently, nudging-ensemble methods always produce error levels between the objective ensemble filters and empirical nudging, and can never provide analyses or short-range forecasts with lower errors than both. As long as the nudged state and the ensemble-filter state are close enough, the ensemble statistics are useful for the nudging, and fully coupling the ensemble and nudging by centering the ensemble on the nudged state is not necessary.

An ensemble smoother produces the overall smallest errors except for with very large model errors. Results are qualitatively independent of tuning parameters such as covariance inflation and localization.