REPAD: An Empirical Model of Pitch-angle Distributions for Energetic Electrons in the Earth\textquoterights Outer Radiation Belt

We have recently conducted a statistical survey on pitch angle distributions of energetic electrons trapped in the Earth\textquoterights outer radiation belt, and a new empirical model was developed based upon survey results. This model\textemdashrelativistic electron pitch angle distribution (REPAD)\textemdashaims to present statistical pictures of electron equatorial pitch angle distributions, instead of the absolute flux levels, as a function of energy, L shell, magnetic local time, and magnetic activity. To quantify and facilitate this statistical survey, we use Legendre polynomials to fit long-term in situ directional fluxes observed near the magnetic equator from three missions: CRRES, Polar, and LANL-97A. As the first of this kind of model, REPAD covers the whole outer belt region, providing not only the mean and median pitch angle distributions in the area but also error estimates of the average distributions. Preliminary verification and validation results demonstrate the reliable performance of this model. Usage of REPAD is mainly to predict the full pitch angle distribution of fluxes along a given magnetic field line, or even on a given drift shell, based upon one single unidirectional or omnidirectional flux measurement anywhere on that field line. This can be particularly useful for data assimilation, which usually has large tolerance on data errors. In addition, relatively small variations in pitch angle distributions measured at L shell between ~ 4 and 5 justify the assumption of fixed pitch angle distributions at GPS equatorial crossings (L ~ 4.2) used in our previous studies.