EAKF-Based Parameter Optimization Using a Hybrid Adaptive Method

To effectively reduce model bias and improve assimilation quality, we adopt a hybrid adaptive approach of ensemble adjustment Kalman filter (EAKF) and multigrid analysis (MGA), called EAKF-MGA, to implement parameter optimization as follows. For each assimilation cycle, observations are used to adjust the prior ensembles of both state variables and parameters using the EAKF without inflation. Then, the MGA is adaptively triggered to extract multiscale information from the observational residual to innovate the ensemble mean of the state once again. Results of biased twin experiments consisting of a barotropic spectral model and idealized observation systems show that the proposed EAKF-MGA is insensitive to state variance inflation and localization during the parameter optimization process, compared with the EAKF with adaptive inflation. We also find that computational efficiency is another important advantage of the EAKF-MGA for both state estimation and parameter estimation since extremely small ensemble size is allowed, while the EAKF with adaptive inflation does not work anymore. In essence, the EAKF-MGA is designed to estimate and correct systematic errors jointly with model’s state variables. Through alleviating biases, including the model bias caused by the biased parameter and the analysis bias resulting from the sampling noise given the limited ensemble size, it can be guaranteed that the analysis in the EAKF-MGA will be proceeded onward with the standard assumption of the unbiased model background field in modern data assimilation theory to be met.