Bayesian optimization of multi-model ensemble data assimilation for a low-order model

Multi-model ensemble data assimilation has been studied to account for uncertainties of numerical models, using different dynamical cores and/or physics parameterizations. In the previous studies, the ensemble size for each model is prescribed subjectively, for example, uniformly distributed to each model. In this study, we adopt the Bayesian filter in multi-model ensemble Kalman filter to find the optimal combination of ensemble sizes for each model in the multi-model ensemble. As a first step, we test the proposed approach with the Lorenz 40-variable model.

Different values of the model parameter F are used to mimic the multi-model ensemble. The true F is chosen to be 8, and the observations are generated by adding independent Gaussian noise to the true time series. When the multi-model ensemble consists of F = 6, 7, 8, 9, 10, the Bayesian filter finds the true model and converges to F = 8 quickly. When F = 6, 7, 9, 10 (i.e., the multi-model ensemble does not contain the true model), the closest two models F = 7 and 9 are selected. We developed an effective inflation method to make the Bayesian filter work without converging to a single imperfect model.