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-minute 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.
