Better Forecasting of Extreme Geomagnetic Storms Using Non‐Stationary Statistical Models

An assessment of the risk of extreme geomagnetic storms is critically important for modern society. However, current methods mainly focus on using stationary statistical models to analyze extreme geomagnetic events. These models ignore the non‐stationary nature of the data, caused by effects of the solar cycle and the seasons, and thus could provide unreliable estimates of return levels. We propose use of hidden Markov models and generalized additive models, both involving time‐varying parameters, in order to capture these features of the data. We use these models to analyze extreme values of the magnitude of the derivative in the horizontal component R 1 ( t ) ${R}_{1}(t)$ of geomagnetic observations from the Eyrewell geomagnetic observatory in New Zealand. We use residual diagnostics to check for lack‐of‐fit of the models, demonstrate that they can successfully model the effects of both the solar cycle and the seasons, and use the best‐fitting models to provide more reliable estimates of return levels. From our analysis, the 50‐year and 100‐year conditional return levels of the extreme magnitude of the derivative in the horizontal component R 1 ( t ) ${R}_{1}(t)$ at the Eyrewell magnetic observatory are likely to be within the ranges 500–2,600 and 700–4,500 nT/min respectively at solar maximum.