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This paper presents a multi-parameter global statistical model of extreme horizontal geomagnetic field fluctuations (dBH/dt), which are a useful input to models assessing the risk of geomagnetically induced currents in ground infrastructure. Generalised Pareto (GP) distributions were fitted to 1-min measurements of |dBH/dt| from 125 magnetometers (with an average of 28 years of data per site) and return levels (RL) predicted for return periods (RP) between 5 and 500 years. Analytical functions characterise the profiles of maximum-likelihood GP model parameters and the derived RLs as a function of corrected geomagnetic latitude, λ. A sharp peak in both the GP shape parameter and the RLs is observed at |λ| = 53° in both hemispheres, indicating a sharp equatorward limit of the auroral electrojet region. RLs also increase strongly in the dayside region poleward of the polar cusp (|λ| > 75°) for RPs > 100 years. We describe how the GP model may be further refined by modelling the probability of occurrences of |dBH/dt| exceeding the 99.97th percentile as a function of month, magnetic local time, and the direction of the field fluctuation, dBH, and demonstrate that these patterns of occurrence align closely to known patterns of auroral substorm onsets, ULF Pc5 wave activity, and (storm) sudden commencement impacts. Changes in the occurrence probability profiles with the interplanetary magnetic field (IMF) orientation reveal further details of the nature of the ionospheric currents driving extreme |dBH/dt| fluctuations, such as the changing location of the polar cusp and seasonal variations explained by the Russell-McPherron effect.

We analyse the response of different ionospheric equivalent current modes to variations in the interplanetary magnetic field (IMF) components By and Bz. Each mode comprises a fixed spatial pattern whose amplitude varies in time, identified by a month‐by‐month empirical orthogonal function separation of surface measured magnetic field variance. Here we focus on four sets of modes that have been previously identified as DPY, DP2, NBZ and DP1. We derive the cross‐correlation function of each mode set with either IMF By or Bz for lags ranging from ‐10 to +600 mins with respect to the IMF state at the bow shock nose. For all four sets of modes, the average correlation can be reproduced by a sum of up to three linear responses to the IMF component, each centered on a different lag. These are interpreted as the statistical ionospheric responses to magnetopause merging (15‐20 mins lag) and magnetotail reconnection (60 mins lag), and to IMF persistence. Of the mode sets, NBZ and DPY are the most predictable from a given IMF component, with DP1 (the substorm component) the least predictable. The proportion of mode variability explained by the IMF increases for the longer lags, thought to indicate conductivity feedbacks from substorms. In summary, we confirm the postulated physical basis of these modes and quantify their multiple reconfiguration timescales.

Relativistic electron flux at geosynchronous orbit depends on enhancement and loss processes driven by ULF Pc5, chorus, and EMIC waves, seed electron flux, magnetosphere compression, the "Dst effect", and substorms, while solar wind inputs such as velocity, number density, and IMF Bz drive these factors and thus correlate with flux. Distributed lag regression models show the time delay of highest influence of these factors on log10 high energy electron flux (0.7 – 7.8 MeV, LANL 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 EMIC waves is less influential. Southward Bz shows only moderate influence when correlated processes are accounted for. Adding covariate compression effects (pressure and IMF 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 modelling work than studying them individually.

We describe a method of producing high-resolution models of the Earth’s combined external and induced magnetic field (EIMF) using the method of Empirical Orthogonal Functions (EOFs) applied to the SuperMAG archive of ground-based magnetometer data. EOFs partition the variance of a system into independent modes, allowing us to extract the spatiotemporal patterns of greatest dynamical importance without applying the a priori assumptions of other methods (such as spherical harmonic analysis, parameterised averaging, or multi-variate regression). We develop an approach based on that of Beckers and Rixen [2003] and use the EOF modes to infill missing data in a self-consistent manner. Applying our method to a north polar case study spanning February 2001 (chosen for its proximity to solar maximum and good data coverage), we demonstrate that 41.7% and 9.4% of variance is explained by the leading two modes, respectively describing the temporal variations of the Disturbance Polar types 2 and 1 (DP2 and DP1) patterns. A further 14.1% of variance is explained by four modes that describe separate aspects of the motion of the DP1 and DP2 systems. Thus, collectively over 65% of variance is described by the leading 6 modes and is attributable to DP1 and DP2. This attribution is based on inspection of the spatial morphology of the modes, and analysis of the temporal variation of the mode amplitudes with respect to solar wind measures and substorm occurrence. This study is primarily a demonstration of the technique and a prelude to a model spanning the full solar cycle.