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Different modeling methodologies possess different strengths and weakness. For instance, data based models may provide superior accuracy but have a limited spatial coverage while physics based models may provide lower accuracy but provide greater spatial coverage. This study investigates the coupling of a data based model of the electron fluxes at geostationary orbit (GEO) with a numerical model of the radiation belt region to improve the resulting forecasts/pastcasts of electron fluxes over the whole radiation belt region. In particular, two coupling methods are investigated. The first assumes an average value for L* for GEO, namely LGEO* L-GEO* = 6.2. The second uses a value of L* that varies with geomagnetic activity, quantified using the Kp index. As the terrestrial magnetic field responds to variations in geomagnetic activity, the value of L* will vary for a specific location. In this coupling method, the value of L* is calculated using the Kp driven Tsyganenko 89c magnetic field model for field line tracing. It is shown that this addition can result in changes in the initialization of the parameters at the Versatile Electron Radiation Belt model outer boundary. Model outputs are compared to Van Allen Probes MagEIS measurements of the electron fluxes in the inner magnetosphere for the March 2015 geomagnetic storm. It is found that the fixed LGEO* L-GEO* coupling method produces a more realistic forecast.
In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012-2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat-top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two-step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni-directional flux observations and is applicable to low-PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni- or omnidirectional measurement at off-equatorial latitudes. The model can be used for converting the long-term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics-based modeling in the form of boundary conditions, and for data assimilation purposes.