Solar Physics

, 294:24 | Cite as

Neural Network Forecast of the Sunspot Butterfly Diagram

  • Eurico CovasEmail author
  • Nuno Peixinho
  • João Fernandes


Using neural networks as a prediction method, we attempt to demonstrate that forecasting of the Sun’s sunspot time series can be extended to the spatio-temporal case. We employ this machine-learning method to forecast not only in time but also in space (in this case, latitude) on a spatio-temporal dataset representing the solar sunspot diagram extending to a total of 142 years. The analysis shows that this approach seems to be able to reconstruct the overall qualitative aspects of the spatial-temporal series, namely the overall shape and amplitude of the latitude and time pattern of sunspots. This is, as far as we are aware, the first time that neural networks have been used to forecast the Sun’s sunspot butterfly diagram, and although the results are limited in the quantitative prediction aspects, it points to the way to use the full spatio-temporal series as opposed to just the time series for machine-learning approaches to forecasting. Additionally, we use the method to predict that the upcoming Cycle 25 maximum sunspot number will be around \(R_{25}=57 \pm17\). This implies a very weak cycle and, in fact, the weakest cycle on record.


Sunspots Statistics Solar cycle Observations 



We would like to thank Reza Tavakol for very useful conversations regarding forecasting sunspots. We also would like to thank David Hathaway for publishing the data that we used in this article. Finally, we would also like to thank the anonymous referee, whose comments have helped us to improve this article. N. Peixinho acknowledges funding from the Portuguese FCT – Foundation for Science and Technology (ref: SFRH/BGCT/113686/2015). CITEUC is funded by National Funds through FCT – Foundation for Science and Technology (project: UID/Multi/00611/2013) and FEDER – European Regional Development Fund through COMPETE 2020 – Operational Programme Competitiveness and Internationalisation (project: POCI-01-0145-FEDER-006922). J. Fernandes acknowledges funding from the POCH and Portuguese FCT – Foundation for Science and Technology (ref: SFRH/BSAB/143060/2018) and visiting facilities at Niels Bohr Institute (University of Copenhagen).

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.CITEUC – Centre for Earth and Space Science Research of the University of CoimbraGeophysical and Astronomical Observatory of the University of CoimbraCoimbraPortugal
  2. 2.Department of MathematicsUniversity of CoimbraCoimbraPortugal

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