Using ARMAX models to determine the drivers of 40-150 keV GOES electron fluxes

Abstract

We investigate the drivers of 40-150 keV hourly electron flux at geostationary orbit (GOES 13) using ARMAX (autoregressive moving average transfer function multiple regression) models which remove the confounding effect of diurnal cyclicity and allow assessment of each parameter independently. By taking logs of the variables, we create nonlinear models. While many factors show high correlation with flux in single variable analysis (substorms, ULF waves, solar wind velocity (V ), pressure (P ), number density (N ) and electric field (E y ), IMF Bz, Kp, and SymH), ARMAX models show substorms are the dominant influence at 40-75 keV and over 20-12 MLT, with little difference seen between disturbed and quiet periods. The Ey influence is positive post-midnight, negative post-noon. Pressure shows a negative influence, strongest at 150 keV. ULF waves are a more modest influence than suggested by single variable correlation. Kp and SymH show little effect when other variables are included. Using path analysis, we calculate the summed direct and indirect influences through the driving of intermediate parameters. Pressure shows a summed direct and indirect influence nearly half that of the direct substorm effect. N , V , and B z , as indirect drivers, are equally influential. While simple correlation or neural networks can be used for flux prediction, neither can effectively identify drivers. Instead, consideration of physical influences, removing cycles that artificially inflate correlations, and controlling the effects of other parameters gives a clearer picture of which are most influential in this system.

Determining the Timing of Driver Influences on 1.8–3.5 MeV Electron Flux at Geosynchronous Orbit Using ARMAX Methodology and Stepwise Regression

“…If determining the combined, additive influence of both V and Bz is desired, a better approach is to include both in a single multiple regression analysis. (Although it may seem that vXBs would be a more targeted form of this function, we have found in the past that Bs is even less correlated with flux than Bz is (Simms, Ganushkina, et al., 2022). )…”

“…If determining the combined, additive influence of both V and Bz is desired, a better approach is to include both in a single multiple regression analysis. (Although it may seem that vXBs would be a more targeted form of this function, we have found in the past that Bs is even less correlated with flux than Bz is (Simms, Ganushkina, et al., 2022). ) Over all hours, with cycles removed, the strongest ULF influences are in the first (positive) and second (negative) hour before the flux measurement, with further negative influences in the 12–24 hr before.…”

“…However, common cycles and trends that inflate correlations can be dealt with by describing the time behavior with autoregressive (AR) and moving average (MA) terms (Simms, Engebretson et al., 2022, Simms, Ganushkina, et al., 2022). Using these ARMA terms (as well as differencing: subtracting previous observations) methods, we have previously found correlations, while statistically significant, much lower than those seen in uncorrected lagged correlations.…”