Ensemble data assimilation techniques for electron phase space density in the radiation belts

Accurate predictions of the effects of hazardous energetic solar plasma events on the near-Earth space environment are invaluable to prepare for and potentially prevent harmful implications to humans and technology in space and on the ground. In order to obtain accurate predictions despite uncertainties in the associated model and the observations, novel data assimilation methods have become increasingly popular. The associated inference problem is particularly challenging when wave activity and mixed diffusion are taken into account, such that the underlying system becomes non-linear. In this case, robust techniques for high dimensional settings are asked for. The class of ensemble Kalman filters has shown to be one of the most promising filtering tools for non-linear and high dimensional systems in the context of terrestrial weather prediction, but has been barely used in the context of electron phase space density for the outer radiation belt. In this study, we adapt traditional ensemble based methods to reduce uncertainties in the estimation of electron phase space density. We use a one-dimensional radial diffusion model, a standard Kalman filter (KF ) and synthetic data to set up the framework for one-dimensional ensemble data assimilation. Furthermore, with the split-operator technique, we develop a total of three split-operator Ensemble Kalman filter approaches for electron phase space density in the radiation belts. The capabilities and properties of the proposed filter approaches are verified on Van Allen Probe and GOES data. Additionally, we compare the performance, computational feasibility and output of these three split-operator Ensemble Kalman filters with the simulations of a full 3D-Ensemble Kalman filter (including mixed terms).