A Bayesian Optimization Approach to Multimodel Ensemble Kalman Filter with a Low-Order Model

Abstract

ultimodel ensemble data assimilation may account for uncertainties of numerical models due to different dynamical cores and physics parameterizations. In the previous studies, the ensemble sizes for each model are prescribed subjectively, for example, uniformly distributed to each model. In this study, a Bayesian filter approach to a multimodel ensemble Kalman filter is adopted to objectively estimate the optimal combination of ensemble sizes for each model. An effective inflation method to make the discrete Bayesian filter work without converging to a single imperfect model was developed.As a first step, the proposed approach was tested with the 40-variable Lorenz-96 model. Different values of the model parameter F are used to mimic the multimodel ensemble. The true F is first chosen to be , and the observations are generated by adding independent Gaussian noise to the true time series. When the multimodel ensemble consists of , 7, 8, 9, and 10, the Bayesian filter finds the true model and converges to quickly. When , 7, 9, and 10, the closest two models, and F = 9, are selected. When the true F has a periodic variation about with a time scale much longer than the observation frequency, the proposed system follows the temporal change, and the error becomes less than that of the time-invariant optimal combination. Sensitivities to several parameters in the proposed system were also investigated, and the system was found to show improvements in a wide range of parameters.