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

Abstract

Although lagged correlations have suggested influences of solar wind velocity (V) and number density (N), Bz, ultralow frequency (ULF) wave power, and substorms (as measured by the auroral electrojet (AE) index) on MeV electron flux at geosynchronous orbit over an impressive number of hours and days, a satellite’s diurnal cycle can inflate correlations, associations between drivers may produce spurious effects, and correlations between all previous time steps may create an appearance of additive influence over many hours. Autoregressive-moving average transfer function (ARMAX) multiple regressions incorporating previous hours simultaneously can eliminate cycles and assess the impact of parameters, at each hour, while others are controlled. ARMAX influences are an order of magnitude lower than correlations uncorrected for time behavior. Most influence occurs within a few hours, not the many hours suggested by correlation. A log transformation accounts for nonlinearities. Over all hours, solar wind velocity (V) and number density (N) show an initial negative impact, with longer term positive influences over the 9 (V) or 27 (N) hr. Bz is initially a positive influence, with a longer term (6 hr) negative effect. ULF waves impact flux in the first (positive) and second (negative) hour before the flux measurement, with further negative influences in the 12–24 hr before. AE (representing electron injection by substorms) shows only a short term (1 hr) positive influence. However, when only recovery and after-recovery storm periods are considered (using stepwise regression), there are positive influences of ULF waves, AE, and V, with negative influences of N and Bz.Plain Language SummaryThe influence of solar wind, waves, and substorms on high energy electrons at geosynchronous orbit can appear to occur over a number of hours and days. However, these long duration correlations may be due to diurnal cycles in satellite data, associations between the driving parameters, or correlations of each variable with itself over previous time steps. These extraneous correlations can be corrected for using autoregressive-moving average multiple regression models including previous hours simultaneously. Once these are controlled, the correlations between possible driving parameters and high energy electrons are both lower and influential only over a few hours.Key PointsAutoregressive-moving average transfer function models show drivers of relativistic electron flux are influential only within a few hours or a day of flux changesContrary to simple correlation findings, influences are lower in magnitude and act more immediatelyStepwise multiple regression shows less cumulative effects of drivers in after-storm periods than simple correlation would suggest