CMX Lunch Seminar

In this talk, I will discuss two novel ensemble data assimilation (DA) methods for improving forecast model statistics.

The first one is the multi-model ensemble Kalman filter (MM-EnKF). The MM-EnKF can combine multiple model ensembles for both DA and forecasting in a flow-dependent manner, using adaptive model error estimation to provide weights for the separate models and the observations. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM-EnKF results in significant probabilistic error reductions compared to the best model, as well as to an unweighted multi-model ensemble. We discuss the potential of the MM-EnKF as a method for incorporating machine learning forecast models into the DA process.

The second is the ensemble Fokker–Planck filter (EnFPF). We consider the problem of filtering dynamical systems, possibly stochastic, using observations of statistics. The task is naturally formulated as an infinite-dimensional filtering problem in the space of densities. However, for the purposes of tractability, we introduce a mean field state space model and, using interacting particle system approximations to this model, we propose an ensemble method. Our numerical experiments show that the EnFPF is able to correct ensemble statistics and to accelerate convergence to a system's invariant density. We discuss applications of the EnFPF to correcting error in the statistical properties of dynamical models.