Accounting for model error from unresolved scales in ensemble Kalman filters by stochastic parametrization

We investigate by numerical experiment the use of discrete-time stochastic parametrization to account for model error due to unresolved scales in ensemble Kalman filters. The parametrization quantifies the model error and produces an improved non-Markovian forecast model, which generates high-quality forecast ensembles and improves filter performance. We compare this with the methods of dealing with model error through covariance inflation and localization (IL), using as example the two-layer Lorenz 96 system. The numerical results show that when the ensemble size is sufficiently large, the parametrization is more effective in accounting for the model error than IL; if the ensemble size is small, IL are needed to reduce sampling error, but the parametrization further improves the performance of the filter. This suggests that in real applications where the ensemble size is relatively small, the filter can achieve better performance than pure IL if stochastic parametrization methods are combined with IL.