Limitations in the Hilbert Transform Approach to Locating Solar Cycle Terminators

• Published in: Solar physics 2021-07, Vol.296 (7), Article 108
• Main Author: Booth, R. J.
• Format: Article
• Language: English
• Subjects: Astrophysics and Astroparticles; Atmospheric Sciences; Hilbert transformation; Physics; Physics and Astronomy; Robustness (mathematics); Solar cycle; Solar physics; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Sunspot numbers; Sunspots
• ISSN: 0038-0938; 1573-093X
• DOI: 10.1007/s11207-021-01833-1

This paper studies the method by which Leamon et al. ( Solar Phys. 295 , 36, 2020 ) produces predictions for the so-called “terminator” of solar cycles (in particular Solar Cycle 24), which is a novel way of defining the length of a solar cycle. This method involves use of a Hilbert transform of the data and a derived “phase”. The present paper both replicates and augments methods and results from that paper, but finds that its claim to have identified a mathematically robust signature of terminators in sunspot records is not well founded. In particular, we demonstrate that the results are significantly sensitive to both the starting point of the data and the centralizing constant used to provide a meaningful Hilbert phase. Some realistic parameter choices, including more recently available data, push the predicted terminator back by about 2 years. This has concomitant implications for predictions of the magnitude of the next cycle (25), which depend on the length of the previous cycle. In particular, an increase by 2 years would reduce the predicted 233 maximum sunspot number in McIntosh et al. ( Solar Phys. 295 , 163, 2020 ) to 173.