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We present two new empirical models of radiation belt electron flux at geostationary orbit. GOES-15 measurements of 0.8 MeV electrons were used to train a Nonlinear Autoregressive with Exogenous input (NARX) neural network for both modeling GOES-15 flux values and an upper boundary condition scaling factor (BF). The GOES-15 flux model utilizes an input and feedback delay of 2 and 2 time steps (i.e., 5 min time steps) with the most efficient number of hidden layers set to 10. Magnetic local time, Dst, Kp, solar wind dynamic pressure, AE, and solar wind velocity were found to perform as predicative indicators of GOES-15 flux and therefore were used as the exogenous inputs. The NARX-derived upper boundary condition scaling factor was used in conjunction with the Versatile Electron Radiation Belt (VERB) code to produce reconstructions of the radiation belts during the period of July-November 1990, independent of in-situ observations. Here, Kp was chosen as the sole exogenous input to be more compatible with the VERB code. This Combined Release and Radiation Effects Satellite-era reconstruction showcases the potential to use these neural network-derived boundary conditions as a method of hindcasting the historical radiation belts. This study serves as a companion paper to another recently published study on reconstructing the radiation belts during Solar Cycles 17-24 (Saikin et al., 2021, ), for which the results featured in this paper were used.
We present a reconstruction of the dynamics of the radiation belts from solar cycles 17 to 24 which allows us to study how radiation belt activity has varied between the different solar cycles. The radiation belt simulations are produced using the Versatile Electron Radiation Belt (VERB)-3D code. The VERB-3D code simulations incorporate radial, energy, and pitch angle diffusion to reproduce the radiation belts. Our simulations use the historical measurements of Kp (available since solar cycle 17, i.e., 1933) to model the evolution radiation belt dynamics between L* = 1-6.6. A nonlinear auto regressive network with exogenous inputs (NARX) neural network was trained off GOES 15 measurements (January 2011-March 2014) and used to supply the upper boundary condition (L* = 6.6) over the course of solar cycles 17-24 (i.e., 1933-2017). Comparison of the model with long term observations of the Van Allen Probes and CRRES demonstrates that our model, driven by the NARX boundary, can reconstruct the general evolution of the radiation belt fluxes. Solar cycle 24 (January 2008-2017) has been the least active of the considered solar cycles which resulted in unusually low electron fluxes. Our results show that solar cycle 24 should not be used as a representative solar cycle for developing long term environment models. The developed reconstruction of fluxes can be used to develop or improve empirical models of the radiation belts.