Prediction of Solar Cycle 25

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Latest revision as of 08:58, 19 October 2020

Introduction

The solar cycle is driven by a self-exciting dynamo in the solar interior. This dynamo effectively converts poloidal magnetic fields (basically extending north and south) into azimuthal or toroidal fields that erupt as solar active regions and sunspots. Solar variations across a cycle seem to form a family of curves well-characterized by a single parameter: SN_Max, the maximum smoothed monthly sunspot number. Predicting the amplitude, shape, and duration of the next cycle thus concentrates on predicting SN_Max for the cycle. The many empirical prediction methods that have been tried fall in two broad categories: statistical methods and precursor methods. The former assume that the centuries-long time-series of sunspot numbers carries information about the underlying physics that can be exploited for forecasting. The precursor methods assume that some properties of the recent cycles, perhaps only a part of the most recent ones, have predictive power for the next.

Ref. [1] had suggested (four cycles ago), on assumed physical grounds (the Babcock-Leighton model of the solar dynamo) that the magnetic field in the polar regions near minimum would be a precursor proxy for the amount of sunspot activity in the following cycle. It would provide a 'seed' for the dynamo when advected into the solar interior following the observed cycle-dependent concentration of surface fields in the polar regions. They suggested using the average polar fields during the three-year interval preceding solar minimum as the precursor value to regress against the amplitude of the following cycle (Ref. [2]), and we examine this idea here.

Result

Using the measurements of the Wilcox Solar Observatory of the solar axial magnetic dipole moment (DM, calculated as the difference between the north and south polar fields), we regress SN_Max against the DM for Cycles 21-24, using both 3-year and 2-year averages of DM prior to the solar minma (Figure 1). Two separate regression fits have (likely fortuitously) very high coefficients of determination, R² of 0.99. The resulting predicted SN maximum then comes to 128.

Figure 1: Smoothed monthly maximum sunspot number, SN_Max, for cycles 21-24 regressed against the (absolute) solar dipole moment averaged over three years before solar minimum (blue symbols) and over two years (violet symbols). Symbols of lighter shade are used for the more uncertain Cycle 21. Where symbols completely cover each other, they have been offset slightly for display purposes. The predictions for Cycle 25 is shown with red diamonds.

The earlier predictions of Refs. [2] and [3] had missed by about 6% overall. On top of that, there is uncertainty in how well the sunspot number represents actual solar activity. The modern SILSO sunspot data product lists a typical standard deviation of cycle-maximum of the sunspot number of 6%, for a combined error of 8.5% or 11 sunspot units for a SN of 128. We shall round that to 10 SN-units as even the unit digit is uncertain.

Conclusions

That the art of solar cycle prediction is still in its infancy is well borne out by the extreme range of predictions of Cycle 25 (Ref. [4]). Figure 2 indicates that we have not made much progress since predictions were made of Cycle 24, which showed a similar spread (from half to double of actual value observed). With the wide range (from 50 to 233), some individual one, or even several predictions are bound to be right regardless of the possible correctness of the method used. The many non-overlapping error bars illustrate the folly of even assigning error bars to the predictions or, at least, to believe in them. Our prediction is shown by the yellow circle in the middle of the plot, its diameter being its error bar, and we think that it is in a class by itself.

Figure 2: The 38 predictions of Solar Cycle 25 that had been registered by January 2020 (adapted from Ref. [2] with permission). Our prediction (128+-10) is indicated by the yellow sun in the center of the plot, near the average (123+-21) of the 6 (now 7) precursor methods that seem to be preferred. The overall average is 132+-47 (median 124). None of these numbers are substantially different, so one could perhaps just go with the Wisdom of Crowds (Aristotle, 350 BCE, Politics, III:xi; Ref. [5])

References

[1] "Using Dynamo Theory to predict the sunspot number during Solar Cycle 21"

[2] "Sunspot cycle 24: Smallest cycle in 100 years?"

[3] "Fair space weather for solar cycle 24"

[4] "How Well Can We Predict Solar Cycle 35?"

[5] "Vox Populi"