Lognormal Kalman filter for assimilating phase space density data in the radiation belts

Data assimilation combines a physical model with sparse observations and has become an increasingly important tool for scientists and engineers in the design, operation, and use of satellites and other high-technology systems in the near-Earth space environment. Of particular importance is predicting fluxes of high-energy particles in the Van Allen radiation belts, since these fluxes can damage spaceborne platforms and instruments during strong geomagnetic storms. In transiting from a research setting to operational prediction of these fluxes, improved data assimilation is of the essence. The present study is motivated by the fact that phase space densities (PSDs) of high-energy electrons in the outer radiation belt-both simulated and observed-are subject to spatiotemporal variations that span several orders of magnitude. Standard data assimilation methods that are based on least squares minimization of normally distributed errors may not be adequate for handling the range of these variations. We propose herein a modification of Kalman filtering that uses a log-transformed, one-dimensional radial diffusion model for the PSDs and includes parameterized losses. The proposed methodology is first verified on model-simulated, synthetic data and then applied to actual satellite measurements. When the model errors are sufficiently smaller then observational errors, our methodology can significantly improve analysis and prediction skill for the PSDs compared to those of the standard Kalman filter formulation. This improvement is documented by monitoring the variance of the innovation sequence.