Using ARMAX Models to Determine the Drivers of 40–150 keV GOES Electron Fluxes

Abstract

Geostationary/geosynchronous orbit (GEO) is highly populated with active satellites (http://www.unoosa.org/ oosa/osoindex/) that can experience damaging surface charging due to high energy electrons present in the radiation belts (e.g.,

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).) 4.…”

“…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.…”

Predicting Geostationary 40–150 keV Electron Flux Using ARMAX (an Autoregressive Moving Average Transfer Function), RNN (a Recurrent Neural Network), and Logistic Regression: A Comparison of Models

“…IMF B z , while it does not show as high a correlation as solar wind velocity, may still be a useful addition as it provides further information not present in the solar wind parameters alone. (The southward component of IMF ( B s ) may appear to be a more targeted version of this parameter and therefore likely of more predictive use, but we have found that B s does not correlate better with flux than B z itself, at least in hourly data (Simms, Ganushkina, et al., 2022)).…”

“…Second, as much of the correlation between predictor variables and flux is the result of common cycles (e.g., the diurnal cycle due to satellite position and the 27 day solar cycle; Simms et al ( 2022)), a good predictor may not be a driver at all. (For an investigation into the driving role of various parameters see Simms, Ganushkina, et al, 2022) That the ARMAX models produced no better predictions than models derived by other means (RNN and regression) suggests that the description of the time behavior of flux can be accomplished either with AR and MA parameters or simply by using the co-cycling predictor variables, just so long as we have no reason to separate out the time behavior independent of these other variables. ARMAX modeling, therefore, is best suited to exploring actual physical relationships between flux and possible drivers, but does not give this model type any advantage in producing a predictive model.…”

“…Highly correlated proxies may be sufficient for prediction, and more practical given their real‐time availability. For keV electrons, the strongest solar wind correlates are some combination of velocity, density and pressure (Ganushkina et al., 2019; Simms, Ganushkina, et al., 2022). IMF B z , while it does not show as high a correlation as solar wind velocity, may still be a useful addition as it provides further information not present in the solar wind parameters alone.…”