Sunspot number solar cycle clock based prediction of cycle 26 maximum

The overall level of activity of the solar cycle, as seen in the sunspot number (SSN) record, paces both the amplitude and occurrence rates of extreme space weather events [1] and the state of the ionosphere [2]. Predictions of future solar activity levels can be critical to assess system resilience and for planning. For example, under-prediction of current cycle 25 led to under-estimation of drag in LEO, with significant impact on satellite operations [3,4].  SSN predictions on solar cycle timescales are however challenging as no two past cycles have the same amplitude or duration. One method is that of precursors, that is, the upcoming cycle strength is found to correlate with properties of the preceding cycle [5]. The Hilbert transform of 13 month smoothed SSN since 1749 is used to construct a uniform clock for the Schwabe solar cycle which establishes a clear switch on and off of geomagnetic activity seen at earth [1] and which correlates with the morphology of the solar cycle [6].  Timings from the clock can be mapped back to the observed SSN time-series and used to hindcast each cycle SSN maximum from the properties of its preceding cycle. The last 25 solar cycles are hindcasted with good fidelity by this method. Linear correlation between the cycle maximum and properties of the preceding cycle identified from the solar cycle clock has coefficient of determination exceeding 0.7 and Pearson correlation coefficient exceeding 0.8. This new method is used to predict the maximum of upcoming solar cycle 26.

[1] S. C. Chapman, S. W. McIntosh, R. J. Leamon, N. W. Watkins (2020) Quantifying the solar cycle modulation of extreme space weather, Geophys. Res. Lett. doi:10.1029/2020GL087795

[2] M. A. Cafolla, S. C. Chapman, N. W. Watkins, X. Meng, O. P. Verkhoglyadova (2025) Dynamics of TEC High Density Regions seen in JPL GIMs: Variations with Latitude, Season and Geomagnetic Activity, Space Weather doi:10.1029/2024SW004307

[3] W. S. Shambaugh (2024) Doing battle with the sun: lessons from LEO and operating a satellite constellation in the elevated atmospheric drag environment of solar cycle 25, Proceedings, The 4S Symposium 2024. https://arxiv.org/abs/2406.08342

[4] X. Wang et al., (2025) Premature Reentry of the Binar CubeSats due to underestimation of solar and geomagnetic activities and its implication for importance of medium- and long-term space weather forecasts, Space Weather doi:10.1029/2025SW004619

[5] D. H. Hathaway (2015) The solar cycle, Living Rev. Solar Phys. 12, 4 doi:10.1007/lrsp-2015-4

[6] S. C. Chapman, T. Dudok de Wit (2024) A solar cycle clock for extreme space weather. Scientific Reports doi:10.1038/s41598-024-58960-5