Abstract
The relative number of sunspots represents the longest evidence describing the level of solar activity. As such, its use goes beyond solar physics, e.g. towards climate research. The construction of a single representative series is a delicate task that involves a combination of the observations of many observers. We propose a new iterative algorithm that allows construction of a target series of relative sunspot number of a hypothetical stable observer by optimally combining series obtained by many observers. We show that our methodology provides us with results that are comparable with recent reconstructions of both sunspot number and group number. Furthermore, the methodology accounts for the possible non-solar changes of observers’ time series such as gradually changing observing conditions or slow change in the observers’ vision. It also provides us with reconstruction uncertainties. We apply the methodology to a limited sample of observations by the ČESLOPOL network and discuss its properties and limitations.
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Data Availability
The data are available upon reasonable request to the corresponding author. The compiled database used in this study is available as an example via GitHub repository. https://github.com/michalsvanda/sunspot_numbers.
Code Availability
The code (Švanda, 2022) is available via the GitHub repository. https://github.com/michalsvanda/sunspot_numbers
Notes
The program is available for download from https://www.asu.cas.cz/~sunwatch/cs/stranka/ke-stazeni, however, its interface is in the Czech language.
In principle, the coefficients might be derived with respect to any reasonable description of \(g\) and \(f\). An option other than the SILSO sunspot number would be, for instance, a simple mean as plotted in panel a) in Figure 2. Another option would be to perform the process iteratively: (i) set both \(c_{g}\) and \(c_{f}\) to zero, (ii) perform the optimisation run as described by our methodology, use the resulting series as the reference, (iii) determine \(c_{g}\) and \(c_{f}\) with respect to this new reference and (iv) run a final optimisation.
Note that a set of identifiers \(\beta \) forms a subset of the set of identifiers \(\alpha \). In the prediction period, some of the observers from the set of \(\alpha \)s may be missing (they did not observe). Similarly, there might be observations provided by other observers, for which the coefficients from the previous evaluation period do not exist (they did not observe during the evaluation period). Such an observer is not considered in forming the composite within the given prediction window.
Note that this target series cropping also drops all the values from the initial series.
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Acknowledgments
We would like to dedicate this paper to František Zloch (29. 1. 1949 – 11. 2. 2022), a meticulous solar observer at the Solar patrol of the Astronomical Institute of the Czech Academy of Sciences. He has held the project FOTOSFEREX for a very long time in times when the access to the international observations was close to impossible and a need for the local network of solar observers was pre-eminent. We would also like to thank the anonymous referee, who gave us many comments improving the paper.
Funding
Authors from the Astronomical Institute of the Czech Academy of Sciences were supported by the institution project ASU:67985815.
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MŠ designed the research, wrote the code, processed the data, wrote an initial manuscript draft. MP and BS digitised the observations. JD contributed the methodology from the mathematical point of view. All authors read and contributed to all manuscript versions.
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Švanda, M., Pavelková, M., Dvořák, J. et al. Iterative Construction of the Optimal Sunspot-Number Series. Sol Phys 297, 151 (2022). https://doi.org/10.1007/s11207-022-02080-8
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DOI: https://doi.org/10.1007/s11207-022-02080-8