A comparison of the hybrid Ensemble Transform Kalman Filter-3D variational analysis scheme (ETKF)—3DVAR and the pure Ensemble Square Root Filter (EnSRF) Analysis Schemes

Recent studies on assimilating a large set of real atmospheric observations with up-to-date pure ensemble filters show competitive but not superior results with the operational 3D variational (3DVAR) scheme. While a further comparison of fully developed ensemble filter and 3DVAR schemes within operational environment is still needed, it would be appealing to have an alternative algorithm that can benefit from the flow-dependent information that ensembles provide and also can easily fit in the current operational 3DVAR framework without incurring much extra cost. In this study, we revisit the hybrid ensemble-3DVAR scheme, in particular, the Ensemble Transform Kalman Filter (ETKF)-3DVAR scheme, and explore its potential skill by comparing with the pure Ensemble Square Root Filter (ENSRF) within both perfect model and imperfect model environments.

Experiments are run with a dry, global, two-layer primitive equation model, where the assumed true state is a series of forecast simulations. Observational network considered is a set of equally spaced interface heights observations, whose values are given by truth states plus random noise. The types of models considered include a perfect model and a model with resolution errors. For the hybrid ETKF-3DVAR, the background error statistics for updating the ensemble mean are estimated from a linear combination of the 3DVAR covariances and the ensemble covariances, and initial perturbations are generated by updating the background ensemble perturabtions with a transformation matrix. For the ENSRF, observations are assimilated serially with the background error statistics estimated purly from the ensemble with covariance localization applied. For the perfect model experiment, a uniform adaptive covariance inflation based on innovation statistics is used to avoid filter divergence due to sampling error. For the truncation model error experiment, two methods and the combination of them are used to parameterize the model error. One is the additive noise method where random samples drawn from a pool of differences between high-resolution and low-resolution forecasts are added to the dynamic ensemble. The other is to inflate the dynamic ensemble perturbations with latitude-dependent adaptive inflation based on innovation statistics to account for possible flow-dependent non-uniform growth of model error.

In general for both the perfect and imperfect model experiments, it is found that the hybrid scheme with the optimal linear combination of the ensemble covariance and the 3DVAR covariance has similar skill with the ENSRF and outperforms the 3DVAR scheme. For the perfect model experiment, the hybrid scheme performs the best when the background error covariance is estimated largely from the ensemble whereas for the imperfect model experiment, the 3DVAR background covariance is weighted largely in order to get the best performance. For the imperfect model experiment, the hybrid scheme with latitude-dependent inflation method to represent model error is competitive with the ENSRF with additive noise. The hybrid scheme is improved further with the additive noise included. The computational cost of the ETKF-3DVAR scheme amounts to perform approximately one 3DVAR analysis and to compute ETKF initial perturbations which was previously shown not expensive with ensemble size in order of hundreds. The results in this study thus indicate that the ETKF-3DVAR scheme could be worth considering as an operational scheme for data assimilation and ensemble forecasting.