Predicting Solar Cycle 26 Using the Polar Flux as a Precursor, Spectral Analysis, and Machine Learning: Crossing a Gleissberg Minimum?

Abstract

This study introduces a novel method for predicting the sunspot number (SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document}) of Solar Cycles 25 (the current cycle) and 26 using multivariate machine-learning techniques, the Sun’s polar flux as a precursor parameter, and the fast Fourier transform to conduct a spectral analysis of the considered time series. Using the 13-month running average of the version 2 of the SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document} provided by the World Data Center—SILSO, we are thus able to present predictive results for the SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document} until January 2038, giving maximum peak values of 131.4 (in July 2024) and 121.2 (in September 2034) for Solar Cycles 25 and 26, respectively, with a root mean square error of 10.0. These predicted dates are similar to those estimated for the next two polar flux polarity reversals (April 2024 and August 2034). Furthermore, the values for the SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document} maxima of Solar Cycles 25 and 26 have also been forecasted based on the known correlation between the absolute value of the difference between the polar fluxes of both hemispheres at an SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document} minimum and the maximum SN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathrm{S}_{\\mathrm{N}}$\\end{document} of the subsequent cycle, obtaining similar values to those achieved with the previous method: 142.3 ± 34.2 and 126.9 ± 34.2 for Cycles 25 and 26, respectively. Our results suggest that Cycle 25 will have a maximum amplitude that lies below the average and Cycle 26 will reach an even lower peak. This suggests that Solar Cycles 24 (with a peak of 116.4), 25, and 26 would belong to a minimum of the centennial Gleissberg cycle, as was the case in the final years of the 19th and the early 20th centuries (Solar Cycles 12, 13, and 14).