The prediction of the strength of future solar cycles is of interest because of its practical significance for space weather and as a test of our theoretical understanding of the solar cycle. The Babcock-Leighton mechanism allows predictions by assimilating the observed magnetic field on the surface. Since the emergence of sunspot groups has random properties, making it impossible to accurately predict the solar cycle and strongly limiting the scope of cycle predictions, we develop a scheme to investigate the predictability of the solar cycle over one cycle. When a cycle has been ongoing for more than three years, the sunspot group emergence can be predicted along with its uncertainty during the rest time of the cycle. The method for this prediction is to start by generating a set of random realizations that obey the statistical relations of the sunspot emergence. We then use a surface flux transport model to calculate the possible axial dipole moment evolutions. The correlation between the axial dipole moment at cycle minimum and the subsequent cycle strength and other empirical properties of solar cycles are used to predict the possible profiles of the subsequent cycle. We apply this scheme to predict the large-scale field evolution from 2018 to the end of cycle 25, whose maximum strength is expected to lie in the range from 93 to 155 with a probability of 95%.

Context. The tilt angle of sunspot groups is crucial in the Babcock-Leighton (BL) type dynamo for the generation of the poloidal magnetic field. Some studies have shown that the tilt coefficient, which excludes the latitudinal dependence of the tilt angles, is anti-correlated with the cycle strength. If the anti-correlation exists, it will be shown to act as an effective nonlinearity of the BL-type dynamo to modulate the solar cycle. However, some studies have shown that the anti-correlation has no statistical significance. Aims. We aim to investigate the causes behind the controversial results of tilt angle studies and to establish whether the tilt coefficient is indeed anti-correlated with the cycle strength. Methods. We first analyzed the tilt angles from Debrecen Photoheliographic Database (DPD). Based on the methods applied in previous studies, we took two criteria (with or without angular separation constraint Δs > 2.​​°5) to select the data, along with the linear and square-root functions to describe Joy’s law, and three methods (normalization, binned fitting, and unbinned fitting) to derive the tilt coefficients for cycles 21–24. This allowed us to evaluate different methods based on comparisons of the differences among the tilt coefficients and the tilt coefficient uncertainties. Then we utilized Monte Carlo experiments to verify the results. Finally, we extended these methods to analyze the separate hemispheric DPD data and the tilt angle data from Kodaikanal and Mount Wilson. Results. The tilt angles exhibit an extremely wide scatter due to both the intrinsic mechanism for its generation and measurement errors, for instance, the unipolar regions included in data sets. Different methods to deal with the uncertainties are mainly responsible for the controversial character of the previous results. The linear fit to the tilt-latitude relation of sunspot groups with Δs > 2.​​°5 of a cycle carried out without binning the data can minimize the effect of the tilt scatter on the uncertainty of the tilt coefficient. Based on this method the tilt angle coefficient is anti-correlated with the cycle strength with strong statistical significance (r = −0.85 at 99% confidence level). Furthermore, we find that tilts tend to be more saturated at high latitudes for stronger cycles. The tilts tend to show a linear dependence on the latitudes for weak cycles and a square-root dependence for strong cycles. Conclusions. This study disentangles the cycle dependence of sunspot group tilt angles from the previous results that were shown to be controversial, spurring confusion in the field.

Here we report our recent prediction of the solar cycle 25 based on a newly developed scheme, which is used to investigate the predictability of the solar cycle over one cycle. The scheme is a combination of the empirical properties of solar cycles and a surface flux transport model to get the possible axial dipole moment evolution at a few years before cycle minimum, by which to get the subsequent cycle strength based on the correlation between the axial dipole moment at cycle minimum and the subsequent cycle strength. We apply this scheme to predict the large-scale field evolution since 2018 onwards. The results show that the northern polar field will keep on increasing, while the southern polar field almost keeps flat by the end of cycle 24. This leads to the cycle 25 strength of 125 ± 32, which is about 10% stronger than cycle 24 according to the mean value.