A parametric study of the source rate for outer radiation belt electrons using a Kalman filter

Data assimilation methods have become increasingly popular to describe the outer radiation belt energetic electron environment. We use a Kalman filter with inputs of 1) electron phase space density (PSD) for constant first and second adiabatic invariants, mu = 2083[MeV/G] and K = 0.03[G(1/2)R(E)] respectively, from a five satellite data set (three LANL-GEO, one GPS, and Polar), and 2) a one-dimensional radial diffusion model with loss and source terms included. We augment the Kalman filter to include the intensity of local acceleration in the state vector. The output is an estimate of PSD for the radial range of the outer radiation belt and the time-dependent amplitude parameter of a Gaussian shaped source rate term for given location and width. To further constrain the source rate parameters, a root mean square (RMS) analysis of the observation residual vector (a.k.a. innovation vector) is performed in a parameter space of source location and width. We analyze five storm periods spanning from July 30th to October 24th of 2002, and each period's unique solution in the location-width parameter space is assimilated with the Kalman filter for a continuous reanalysis of the full 87 day period. The source amplitude parameter is analyzed for insight into time periods of enhanced local heating, suppressed loss, or, as the parameter can take negative values, additional loss. The source is found to peak in the recovery phases of the storms where the rate is sufficient to repopulate the radiation belt in approximately one day, suggesting that local heating is a major contributor to the electron radiation belts during the recovery phase.