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

Abstract

We screen several algorithms for their ability to produce good predictive models of hourly 40–150 keV electron flux at geostationary orbit (data from GOES‐13) using solar wind, Interplanetary Magnetic Field, and geomagnetic index parameters that would be available for real time forecasting. Value‐predicting models developed using ARMAX (autoregressive moving average transfer function), RNN (recurrent neural network), or stepwise‐reduced regression produced roughly similar results. Including magnetic local time as a categorical variable to describe both the differing levels of flux and the differing influence of parameters improved the models (r as high as 0.814; Heidke Skill Score (HSS) as high as 0.663), however value‐predicting models did a poor job at predicting highs and lows. Diagnostic tests are introduced (cubic fit to observation‐prediction relationship and Lag1 correlation) that better assess predictions of extremes than single metrics such as root mean square error, mean absolute error, or median symmetric accuracy. Classifier models (RNN and logistic regression) were equally able to predict flux rise above the 75th percentile (HSS as high as 0.667). Logistic regression models were improved by the addition of multiplicative interaction and quadratic terms. Only predictors from 1 or 3 hr before were necessary and a detailed description of flux time series behavior was not needed. Stepwise selection of these variables trimmed non‐contributing parameters for a more parsimonious and portable logistic regression model that predicted as well as neural network‐derived models. We provide a logistic regression model (LL3: LogisticLag3) based on inputs measured 3 hr previous, along with optimal probability thresholds, for future predictions.

Comparing Influences of Solar Wind, ULF Waves, and Substorms on 20 eV–2 MeV Electron Flux (RBSP) Using ARMAX Models

“…Pearson correlations, often termed "simple" correlations because each analysis contains only two variables, are performed over 48 hr for just the lower energy flux (20 eV-6 keV) with each parameter. These show reasonably high, statistically significant influences of V, P, B, B z , SME, ULF, and SymH (Figure 2), similar to what has previously been found for 11 keV-2 MeV flux (Simms, Ganushkina, et al, 2022;Simms, Ganushkina, et al, 2023). Nonsignificant correlations (where p > 0.05) lie within the gray areas.…”

“…The time series behavior must be removed (Simms, Engebretson, & Reeves, 2022) or described separately using ARMAX modeling in order to identify the underlying physical relationships. This is not to say that ARMAX models cannot be used to build effective prediction models (Balikhin et al, 2011(Balikhin et al, , 2016Sakaguchi et al, 2013;Sakaguchi et al, 2015;Simms & Engebretson, 2020;Simms, Ganushkina, et al, 2023), and if prediction is the only goal, modeling using such methods as regression, correlation, or neural networks do not need to model time series behavior as a separate influence because the set of variables as a whole, exogenous variables plus intrinsic time behavior, can effectively predict flux. The only caveat is that we cannot make the jump to assuming that uncorrected, highly correlated relationships give any information on the physical drivers.…”

“…Depending on the situation, higher ULF wave activity is thought to both decrease electron flux levels through outward radial diffusion (Katsavrias et al., 2015; Kellerman & Shprits, 2012; Loto'aniu et al., 2010; K. R. Mann et al., 2012; Ozeke et al., 2020; Turner et al., 2012) or enhance levels through inward radial diffusion (Hao et al., 2019; Katsavrias et al., 2019; I. Mann et al., 2004). ULF and VLF waves appear to act in tandem, both additively (Katsavrias et al., 2019; Li et al., 2005; O’Brien & McPherron, 2003; Simms, Engebretson, Clilverd, Rodger, Lessard, et al., 2018, Simms, Ganushkina, et al., 2023) and synergistically, with the presence of one wave type enhancing the effect of the other (Simms et al., 2021). However, we use only ULF waves in the present study because high quality VLF data was not available.…”

Upper Limit on Outer Radiation Belt Electron Flux Based on Dynamical Equilibrium

“…Different methods have been developed for estimating maximum electron fluxes in the outer radiation belt. Empirical models provide estimates of maximum electron fluxes based on solar wind, storm, or substorm activity (Chu et al., 2021; Hua, Bortnik, Chu, Aryan, & Ma, 2022; Ma et al., 2022; Mourenas, Agapitov, et al., 2022; Mourenas et al., 2019; Simms et al., 2023). Theoretical or numerical models estimate upper limits on electron fluxes based on the consequences of chorus wave‐particle interactions on electron fluxes.…”

PEMEM Percentile: New Plasma Environment Specification Model for Surface Charging Risk Assessment

“…There exists another class of empirical models that output average environmental characteristics based on solar wind parameters or geomagnetic activity indices (e.g., Denton et al, 2015;Sillanpää et al, 2017;Stepanov et al, 2021). A subclass within this category employs a machine learning approach for determining plasmaspheric density (Bortnik et al, 2016;Chu et al, 2017;Zhelavskaya et al, 2017;Zhou et al, 2022), and for predicting electron fluxes (Boynton et al, 2016(Boynton et al, , 2019Simms et al, 2022Simms et al, , 2023Swiger et al, 2022). However, these models pose challenges for practical application in risk assessment, as neither the solar wind parameters nor the activity indices are known in advance for future missions.…”