Parameter estimation of the geomagnetic activity model by non-linear least squares

Geomagnetic disturbances during coronal mass ejections (CMEs), which are powerful plasma ejections from Sun’s corona, pose significant challenges for space weather forecasting. In this study, we propose an improvement to the O’Brien-McPherron model [1] for forecasting the storm-time disturbance index Dst, a key parameter reflecting geomagnetic storm intensity during CMEs, in terms of solar wind parameters. By optimizing the parameters of the O’Brien-McPherron model with respect to the sunspot number, we enhanced the model’s performance for both very low and high solar activity.

We have analysed 48 CME-induced geomagnetic storms from 1996 to 2020 and grouped them in four different solar activity levels based on the mean number of sunspots during each storm. We derived the new optimal values for three model parameters for each activity level by employing a non-linear least squares approach, specifically utilizing the Levenberg-Marquardt algorithm.

By taking into account the number of sunspots during a geomagnetic storm, we successfully mitigated the model’s tendency to consistently overestimate the intensity of very weak geomagnetic storms in the very low solar activity level. While the average difference between the forecasted maximum storm intensity and the observed intensity for the regular O’Brien-McPherron model is 17 nT, the optimized model demonstrates a notably reduced difference of 2 nT. Simultaneously, we expanded the model’s applicability to include hazardous superstorms (Dst < -150 nT) occurring during high solar activity, effectively preventing the substantial underestimation of their intensity. The O’Brien-McPherron model is not suited for superstorms and exhibits deviations of about 100 nT in forecasting their maximum intensity, whereas the optimized model underestimates it on average by only 25 nT.

Geomagnetic superstorms can induce very strong electrical currents in power grids, navigation and communication systems and satellites. Underestimating their impact can lead to insufficient shielding and permanent damage of these systems. Enhancing our ability to forecast these events with greater precision, as demonstrated by the improved performance of the optimized model, is crucial in minimizing disruptions and safeguarding infrastructure and technology.

[1] O'Brien, T. P., and R. L. McPherron (2000), An empirical phase space analysis of ring current dynamics: Solar wind control of injection and decay, J. Geophys. Res., 105(A4), 7707–7719, doi:10.1029/1998JA000437.