Many solar wind and magnetosphere parameters correlate with relativistic electron flux following storms. These include relativistic electron flux before the storm; seed electron flux; solar wind velocity and number density (and their variation); interplanetary magnetic field B z , AE and Kp indices; and ultra low frequency (ULF) and very low frequency (VLF) wave power. However, as all these variables are intercorrelated, we use multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Using 219 storms (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002), we obtained hourly averaged electron fluxes for outer radiation belt relativistic electrons (>1.5 MeV) and seed electrons (100 keV) from Los Alamos National Laboratory spacecraft (geosynchronous orbit). For each storm, we found the log 10 maximum relativistic electron flux 48-120 h after the end of the main phase of each storm. Each predictor variable was averaged over the 12 h before the storm, the main phase, and the 48 h following minimum Dst. High levels of flux following storms are best modeled by a set of variables. In decreasing influence, ULF, seed electron flux, Vsw and its variation, and after-storm B z were the most significant explanatory variables. Kp can be added to the model, but it adds no further explanatory power. Although we included ground-based VLF power from Halley, Antarctica, it shows little predictive ability. We produced predictive models using the coefficients from the regression models and assessed their effectiveness in predicting novel observations. The correlation between observed values and those predicted by these empirical models ranged from 0.645 to 0.795.

The daily maximum relativistic electron flux at geostationary orbit can be predicted well with a set of daily averaged predictor variables including previous day's flux, seed electron flux, solar wind velocity and number density, AE index, IMF Bz, Dst, and ULF and VLF wave power. As predictor variables are intercorrelated, we used multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Empirical models produced from regressions of flux on measured predictors from 1 day previous were reasonably effective at predicting novel observations. Adding previous flux to the parameter set improves the prediction of the peak of the increases but delays its anticipation of an event. Previous day's solar wind number density and velocity, AE index, and ULF wave activity are the most significant explanatory variables; however, the AE index, measuring substorm processes, shows a negative correlation with flux when other parameters are controlled. This may be due to the triggering of electromagnetic ion cyclotron waves by substorms that cause electron precipitation. VLF waves show lower, but significant, influence. The combined effect of ULF and VLF waves shows a synergistic interaction, where each increases the influence of the other on flux enhancement. Correlations between observations and predictions for this 1 day lag model ranged from 0.71 to 0.89 (average: 0.78). A path analysis of correlations between predictors suggests that solar wind and IMF parameters affect flux through intermediate processes such as ring current (Dst), AE, and wave activity.

Relativistic electron flux at geosynchronous orbit depends on enhancement and loss processes driven by ultralow frequency (ULF) Pc5, chorus, and electromagnetic ion cyclotron (EMIC) waves, seed electron flux, magnetosphere compression, the "Dst effect," and substorms, while solar wind inputs such as velocity, number density, and interplanetary magnetic field Bz drive these factors and thus correlate with flux. Distributed lag regression models show the time delay of highest influence of these factors on log 10 high-energy electron flux (0.7-7.8 MeV, Los Alamos National Laboratory satellites). Multiple regression with an autoregressive term (flux persistence) allows direct comparison of the magnitude of each effect while controlling other correlated parameters. Flux enhancements due to ULF Pc5 and chorus waves are of equal importance. The direct effect of substorms on high-energy electron flux is strong, possibly due to injection of high-energy electrons by the substorms themselves. Loss due to electromagnetic ion cyclotron waves is less influential. Southward Bz shows only moderate influence when correlated processes are accounted for. Adding covariate compression effects (pressure and interplanetary magnetic field magnitude) allows wave-driven enhancements to be more clearly seen. Seed electrons (270 keV) are most influential at lower relativistic energies, showing that such a population must be available for acceleration. However, they are not accelerated directly to the highest energies. Source electrons (31.7 keV) show no direct influence when other factors are controlled. Their action appears to be indirect via the chorus waves they generate. Determination of specific effects of each parameter when studied in combination will be more helpful in furthering modeling work than studying them individually. Citation:Simms, L., Engebretson, M., Clilverd, M., Rodger, C., Lessard, M., Gjerloev, J., & Reeves, G. (2018). A distributed lag autoregressive model of geostationary relativistic electron fluxes: Comparing the influences of waves, seed and source electrons, and solar wind inputs.

1] Long-period ground ULF waves may be controlled by the mean values of solar wind and interplanetary magnetic field (IMF) parameters (velocity, density, and North-South IMF component Bz). We investigated the influence of these parameters on ground ULF power in the Pc5 range (2-7 mHz) during periods of quiet and during coronal mass ejection (CME) and corotating interaction region (CIR) storms from 1991 to 2004. With multiple regression and path analysis, we studied the influence of these hourly parameters as a set rather than individually. This allowed us to determine which factors were most influential and which were only correlated with influential factors. By using multiple regression, we have explained more variation in Pc5 power than has been achieved in previous studies. In both storm types (CME and CIR) and during all storm phases (initial, main phase, recovery, and a 48 h period after recovery) as well as during quiet periods, solar wind velocity and IMF Bz influenced ground Pc5 power directly. These two variables also acted on the ULF Pc5 indirectly through the intermediate parameters of Dst, and the variations in number density and IMF, although at a weaker level. Ground Pc5 power was greater during CME storms during the main phase and recovery but larger during CIR storms in the period after recovery. In addition, the effect of certain independent variables differed depending on storm type. A model such as this offers the possibility of nowcasting Pc5 power by inserting current levels of solar wind and IMF variables as predictors into the regression equation. Citation: Simms, L. E., V. A. Pilipenko, and M. J. Engebretson (2010), Determining the key drivers of magnetospheric Pc5 wave power,

Using data covering the years 2005-2009, we study the linear and nonlinear responses of log 10 relativistic electron flux measured at geosynchronous orbit to ultralow frequency (ULF) Pc5, very low frequency (VLF) lower band chorus, and electromagnetic ion cyclotron (EMIC) waves. We use regression models incorporating a quadratic term and a synergistic interaction term. Relativistic electron fluxes respond to ULF Pc5 and VLF chorus waves both linearly and nonlinearly. ULF Pc5 waves contribute both to electron enhancement (at midrange wave activity) and loss (at high levels of wave activity). Nonlinear effects of VLF chorus are positive (i.e., cause acceleration), adding to the positive linear effects. Synergistic interaction effects between high levels of VLF chorus and midrange values of ULF Pc5 waves result in more electron acceleration than would be predicted by a simpler additive model. Similarly, the negative effect of EMIC waves (losses) is more influential than would be predicted by a linear model when combined with either VLF chorus or ULF Pc5 waves. During disturbed conditions (high Kp), geostationary electron flux responds more strongly to the same levels of ULF Pc5 and VLF chorus waves. This flux also responds more to ULF Pc5 and chorus waves during southward Bz conditions. Unstandardized regression coefficients for models incorporating nonlinear and synergistic effects of waves are presented for use in future modeling.However, the combined effect of several wave types on flux may not be simply a matter of adding their influences together. They could act synergistically, with each factor having more or less influence at varying levels of the other. This can be tested with an interaction term in multiple regression. By multiplying the factors together and entering this new variable into the analysis, the hypothesis that these factors do more than act additively can be tested. Key Points: • Regression analyses of relativistic electron flux (0.7-7.8 MeV) show both linear and nonlinear response to wave activity • High chorus intensity and midrange ULF Pc5 power result in more electron acceleration than would be predicted by an additive model • The negative effect of EMIC waves is greater if combined with either chorus or ULF Pc5 waves