Maximal growth rate of the ascending phase of a sunspot cycle for predicting its amplitude

¹ Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, Bld. 1, 121205 Moscow, Russia
e-mail: t.podladchikova@skoltech.ru
² University of Graz, Institute of Physics, Universitätsplatz 5, 8010 Graz, Austria
³ University of Graz, Kanzelhöhe Observatory for Solar and Environmental Research, Kanzelhöhe 19, 9521 Treffen, Austria
⁴ Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia
⁵ World Data Center SILSO, Royal Observatory of Belgium, Avenue Circulaire 3, 1180 Brussels, Belgium

Received: 9 March 2022
Accepted: 31 May 2022

Abstract

Context. Forecasting the solar cycle amplitude is important for a better understanding of the solar dynamo as well as for many space weather applications. Different empirical relations of solar cycle parameters with the peak amplitude of the upcoming solar cycle have been established and used for solar cycle forecasts, as, for instance, the Waldmeier rule relating the cycle rise time with its amplitude, the polar fields at previous minimum, and so on. Recently, a separate consideration of the evolution of the two hemispheres revealed even tighter relations.

Aims. We aim to introduce the maximal growth rate of sunspot activity in the ascending phase of a cycle as a new and reliable precursor of a subsequent solar cycle amplitude. We also intend to investigate whether the suggested precursor provides benefits for the prediction of the solar cycle amplitude when using the sunspot indices (sunspot numbers, sunspot areas) derived separately for the two hemispheres compared to the total sunspot indices describing the entire solar disc.

Methods. We investigated the relationship between the maximal growth rate of sunspot activity in the ascending phase of a cycle and the subsequent cycle amplitude on the basis of four data sets of solar activity indices: total sunspot numbers, hemispheric sunspot numbers from the new catalogue from 1874 onwards, total sunspot areas, and hemispheric sunspot areas.

Results. For all the data sets, a linear regression based on the maximal growth rate precursor shows a significant correlation. Validation of predictions for cycles 1–24 shows high correlations between the true and predicted cycle amplitudes reaching r = 0.93 for the total sunspot numbers. The lead time of the predictions varies from 2 to 49 months, with a mean value of 21 months. Furthermore, we demonstrated that the sum of maximal growth rate indicators determined separately for the north and the south hemispheric sunspot numbers provides more accurate predictions than that using total sunspot numbers. The advantages reach 27% and 11% on average in terms of rms and correlation coefficient, respectively. The superior performance is also confirmed with hemispheric sunspot areas with respect to total sunspot areas.

Conclusions. The maximal growth rate of sunspot activity in the ascending phase of a solar cycle serves as a reliable precursor of the subsequent cycle amplitude. Furthermore, our findings provide a strong foundation for supporting regular monitoring, recording, and predictions of solar activity with hemispheric sunspot data, which capture the asymmetric behaviour of the solar activity and solar magnetic field and enhance solar cycle prediction methods.