Yes / A workshop was recently held at Nagoya University (31 October – 02 November 2017), sponsored by the Center for International Collaborative Research, at the Institute for Space-Earth Environmental Research, Nagoya University, Japan, to quantitatively compare the performance of today’s operational solar flare forecasting facilities. Building upon Paper I of this series (Barnes et al. 2016), in Paper II (Leka et al. 2019) we described the participating methods for this latest comparison effort, the evaluation methodology, and presented quantitative comparisons. In this paper we focus on the behavior and performance of the methods when evaluated in the context of broad implementation differences. Acknowledging the short testing interval available and the small number of methods available, we do find that forecast performance: 1) appears to improve by including persistence or prior flare activity, region evolution, and a human “forecaster in the loop”; 2) is hurt by restricting data to disk-center observations; 3) may benefit from long-term statistics, but mostly when then combined with modern data sources and statistical approaches. These trends are arguably weak and must be viewed with numerous caveats, as discussed both here and in Paper II. Following this present work, we present in Paper IV a novel analysis method to evaluate temporal patterns of forecasting errors of both types (i.e., misses and false alarms; Park et al. 2019). Hence, most importantly, with this series of papers we demonstrate the techniques for facilitating comparisons in the interest of establishing performance-positive methodologies. / We wish to acknowledge funding from the Institute for Space-Earth Environmental Research, Nagoya University for supporting the workshop and its participants. We would also like to acknowledge the “big picture” perspective brought by Dr. M. Leila Mays during her participation in the workshop. K.D.L. and G.B. acknowledge that the DAFFS and DAFFS-G tools were developed under NOAA SBIR contracts WC-133R-13-CN-0079 (Phase-I) and WC-133R-14-CN-0103 (PhaseII) with additional support from Lockheed-Martin Space Systems contract #4103056734 for Solar-B FPP Phase E support. A.E.McC. was supported by an Irish Research Council Government of Ireland Postgraduate Scholarship. D.S.B. and M.K.G were supported by the European Union Horizon 2020 research and innovation programme under grant agreement No. 640216 (FLARECAST project; http://flarecast.eu). MKG also acknowledges research performed under the A-EFFort project and subsequent service implementation, supported under ESA Contract number 4000111994/14/D/ MPR. S. A. M. is supported by the Irish Research Council Postdoctoral Fellowship Programme and the US Air Force Office of Scientific Research award FA9550-17-1-039. The operational Space Weather services of ROB/SIDC are partially funded through the STCE, a collaborative framework funded by the Belgian Science Policy Office.

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yes / A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e. g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

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