Data assimilation for nonlinear systems with a hybrid nonlinear Kalman ensemble transform filter

Ensemble Kalman filters are widely used for data assimilation applications in the geosciences. While they are remarkably stable even with nonlinear systems, it is known that they are not optimal in this case. The alternative particle filters are fully nonlinear, but difficult to apply with high-dimensional models. To combine the strengths of both filter types, a hybrid filter is introduced that combines the local ensemble transform Kalman filter (LETKF) with the nonlinear ensemble transform filter (NETF). Three variants of the hybrid filter are formulated. The hybridization is controlled by a hybrid weight. Different hybrid weights are examined and a new adaptive approach based on the ensemble skewness and kurtosis is introduced. The different hybrid filters and the schemes to compute the hybrid weight are assessed in numerical experiments with the nonlinear Lorenz-63 and Lorenz-96 models at different degrees of nonlinearity. A hybrid variant that first applies the NETF followed by the LETKF yields the best results. For the Lorenz-96 model, error reductions by up to 21.5% compared with the LETKF are obtained for the same ensemble size. Computing the hybrid weight based on skewness and kurtosis combined with the effective sample size yields the lowest estimation errors and the overall highest stability of the hybrid filter. The new hybrid filter applies localization and inflation and is hence also usable with high-dimensional models and can potentially provide a robust way to account for leading nonlinearity with small ensembles in nonlinear data assimilation applications.

Automated summary

The study introduces a hybrid filter combining LETKF and NETF with the performance improved by adjusting the hybrid weight. Results show that a hybrid variant applying NETF followed by LETKF yields the best results in complex nonlinear models. Calculating the hybrid weight based on skewness, kurtosis, and effective sample size reduces estimation errors and enhances stability of the hybrid filter.