Group Sunspot Numbers: A New Reconstruction of Sunspot Activity Variations from Historical Sunspot Records Using Algorithms from Machine Learning

Abstract

Historical sunspot records and the construction of a comprehensive database are among the most sought after research activities in solar physics. Here, we revisit the issues and remaining questions on the reconstruction of the so-called group sunspot numbers (GSN) that was pioneered by D. Hoyt and colleagues. We use the modern tools of artificial intelligence (AI) by applying various algorithms based on machine learning (ML) to GSN records. The goal is to offer a new vision in the reconstruction of sunspot activity variations, i.e. a Bayesian reconstruction, in order to obtain a complete probabilistic GSN record from 1610 to 2020. This new GSN reconstruction is consistent with the historical GSN records. In addition, we perform a comparison between our new probabilistic GSN record and the most recent GSN reconstructions produced by several solar researchers under various assumptions and constraints. Our AI algorithms are able to reveal various new underlying patterns and channels of variations that can fully account for the complete GSN time variability, including intervals with extremely low or weak sunspot activity like the Maunder Minimum from 1645 – 1715. Our results show that the GSN records are not strictly represented by the 11-year cycles alone, but that other important timescales for a fuller reconstruction of GSN activity history are the 5.5-year, 22-year, 30-year, 60-year, and 120-year oscillations. The comprehensive GSN reconstruction by AI/ML is able to shed new insights on the nature and characteristics of not only the underlying 11-year-like sunspot cycles but also on the 22-year Hale’s polarity cycles during the Maunder Minimum, among other results previously hidden so far. In the early 1850s, Wolf multiplied his original sunspot number reconstruction by a factor of 1.25 to arrive at the canonical Wolf sunspot numbers (WSN). Removing this multiplicative factor, we find that the GSN and WSN differ by only a few percent for the period 1700 to 1879. In a comparison to the international sunspot number (ISN) recently recommended by Clette et al. (Space Sci. Rev. 186, 35, 2014), several differences are found and discussed. More sunspot observations are still required. Our article points to observers that are not yet included in the GSN database.

Appendices

Appendix A: Notes on Historical Sunspot Observations

In this appendix, we compile all the available historical observations of sunspots and sunspot activity variations.

In 1995, a table of known observers whose original observations could not be found was compiled (see Table 4 below). The missing observations by Fink are probably the most important. Subsequently, some of these observations have been located. For example, Staudacher’s observations have been found and have been reported by Arlt (2008). Neuhäuser, Arlt, and Richter (2018) recently reported the sunspot positions based on the correspondence of Gottfried Kirch from 1680 – 1709. Hayakawa et al. (2021c) recently compiled all the sunspot observations around 1681 – 1718 from the Eimmart Observatory, St. Petersburg, Russia. Scheiner’s observations (1611 – 1633) have recently been found and reported by Arlt et al. (2016), Carrasco, Gallego, and Vaquero (2020a), Vokhmyanin, Arlt, and Zolotova (2021). Carrasco et al. (2020b) recently re-examined the sunspot observations by William C. Bond between 1847 and 1849 concluding that the counts listed in the GSN database should be reduced by 20%. It is worth pointing out that Bond’s sunspot counts, as published in the GSN database, are already reduced by 25% and in good agreement with Carrasco’s et al. conclusion. We have also added ten new entries in Table 4 of which nine are based on reports in archive newspaper publications, while the one by Alischer is a clarification of Hoyt and Schatten (1998).

Table 4 Sunspot observations that are lost or misplaced and may potentially be found. Most of the entries were compiled in the early 1990s, but newly found missing observers are noted by the text; these are indicated as “entry added in 2021”. Column 1 of this table lists the period covered by the suspected sunspot observations. Column 2 lists our notes.

Table 5 (from 1994) lists observers missed completely or partially by R. Wolf and associates that were used as the basis for the GSN reconstruction. Not all listed observers were used because those with scale factors in the Royal Greenwich Observatory (RGO) above 1.4 in the modern era were discarded. The reconstruction tried to attain at least 10 observers each year, preferably the ones not used in the original Wolf sunspot number (WSN) reconstruction, so as to have as much independence as could reasonably be achieved.

Table 5 Observers missed completely or partially by R. Wolf that are in our database^a. Columns 1 and 2 of this table list the first and last year that the observer recorded observations. Column 3 lists the number of observing days. Column 4 lists the observer’s name and our notes.

Table 6 (from 1994) lists additional modern observers that were not included in the Zurich publications following R. Wolf. Table 7 lists significant new sunspot observers and added observations from known observers since 1995.

Table 6 Additional modern observers not included in Zurich publication^a. Columns 1 and 2 of this table list the first and last year that the observer recorded data. Column 3 lists the number of observing days. Column 4 lists the name of the observatory/institution and our notes.

Table 7 Significant new sunspot observers and added observations from known observers since 1995. Column 1 of this table lists the period covered by the sunspot observations. Column 2 lists the observer and our notes.

It appears that sunspot Cycles -4 and -3 (i.e., see Figure 5) are controversial; in those, the new estimates by Svalgaard and Schatten (2016) are significantly higher. The reason these estimates are so low in the in the reconstruction by Hoyt and Schatten (1998) is that for sunspots observed prior to 1715 only a single group was reported. Observers seemed quite consistent on this point. Thus, in a hypothetical case, if a sunspot group was observed every day in 1705, the upper limit of solar activity would be about 12.1. Since many days in 1705 had no sunspots, the annual mean for that year must be much less than 12. There is a similar case for 1715, when for the first time two sunspot groups were reported on the Sun during a day, indicating that the Solar Cycle -3 had low solar activity.

Finally, Spörer made detailed drawings of the Sun from 1860 to 1893, which agree fairly well with RGO when they overlap, so that the GSN would appear to be reliable from 1860 to 1880 (i.e., see Cycles 10 and 11 in Figure 5), and not as high as other sunspot reconstructions. Wolf had at least two different sunspot reconstructions and the Hoyt and Schatten (1998) GSN reconstruction agrees well with Wolf’s earlier reconstruction (see Figure 6), before he altered his results using magnetic needle observations (Hoyt, Schatten, and Nesme-Ribes, 1994).

Appendix B: Wavelet Analysis of the Bayesian ML Reconstructed GSN

In Figure 8, we show the wavelet analysis of our Bayesian ML model of the annual GSN (black line) from 1610 to 2020 (Figure 3 in the main text).

Figure 8

Wavelet analysis of (a) our Bayesian ML model of the annual GSN (black line) from 1610 to 2020 shown in Figure 3 of the main text. (b) The global wavelet shown using a black curve; the red dashed line is the 95% red-noise confidence level. (c) The wavelet power spectral density (PSD).

The global wavelet spectral analysis shows that there are three periodicities with a confidence level greater than 95% (i.e., 5.5, 11, and 120 years) as well as three periodicities with a confidence level lower than 95% (i.e., 22, 30, and 60 years). The wavelet PSD in the central panel shows the evolution of each periodicity. This result is similar to that shown in Figure 1, where the original GSN record of Hoyt and Schatten (1998) was analyzed.

Appendix C: Comparison Between Different Reconstructions

Table 8 compares the original GSN record by Hoyt and Schatten (1998) with two possible interpretations of the sunspot number reconstructed by R. Wolf in the eighteenth century in relation to the 1.25 $k$-factor. We show that under the proposal that this correction is unnecessary and probably incorrect, then the sunspot counts for both reconstructions agree to within the difference of 1.2% over the 1700 – 1799 time interval.

Table 8 A comparison of the mean GSN and Wolf sunspot numbers (WSN) for the period 1700 – 1799 divided in two 50-year ranges and the full period, along with the percentage differences. It is unclear if Wolf applied his 1.25 multiplication factor to the WSN in the 1700s, so another column is listed with the 1.25 correction factor removed. It is followed by the percent difference from the GSN. The large differences in the years from 1700 to 1749 is almost exclusively due to the much higher WSN compared to the GSN before 1725. Usoskin et al. (2021b) have recently confirmed that the first two sunspot cycles in the 1700s are in poor agreement with the GSN reconstruction. It is interesting to note that if the 1.25 factor is removed, the sunspot counts for both reconstructions are only 1.2% apart.

Table 9 provides a summary of the differences in the correction factors involved in the construction of the sunspot-number record of Clette et al. (2014) and the group sunspot number of Hoyt and Schatten (1998). We note that the correction factors by Hoyt and Schatten (1998) were designed to put all observers on the same scale as the photographic record of RGO. The high values for the correction factors by Clette et al. (2014) for the two early observers causes the solar activity to be overestimated. The low correction factors by Clette et al. (2014) for the two later observers cause the twentieth-century solar activity to be underestimated. Visual observers might miss small spots and transient spots when compared to photographic results. Occasionally, visual observers might confuse two or more sunspot groups that were close together and claimed that one sunspot group was present, thus underestimating the total number of groups. This mistake was slightly more common with earlier observers than with more recent observers. These errors mean that correction factors for most visual observers need to be corrected upwards, giving rise to correction factors greater than one.

Table 9 The correction factors for two different reconstructions of solar activity. The values chosen for the backbone observers of Clette et al. (2014) are compared to those in Hoyt and Schatten (1998).

The GSN calibration factor used for Staudacher is 2.0, using the count of groups provided by Wolf. Svalgaard (2017) re-examined Staudacher’s drawings and concluded that there are 25% more sunspot groups than Wolf reported. If these new counts are incorporated in the GSN reconstruction, the calibration factor does not remain unchanged because then the observer would become inconsistent with overlapping observers. In the case of Staudacher, the new calibration factor would be 25% less and equal to 1.6. The change in Staudacher’s counts affects only one observer and not others. That is how the GSN reconstruction works.

Clette et al. (2014) and Svalgaard (2017) overlooked the previously mentioned issue in their research. This lead them inappropriately to multiply the WSN V1 by 1.25 or a number close to 1.25 for most years before 1879. The exception to this rule is the period from 1849 to 1866, when a 1.43 multiplier was used, indicating that Clette et al. (2014) considered that Schwabe suddenly became a poorer observer in 1849. Leussu et al. (2013) showed that no such discontinuity exists. There are approximately 250 observers between 1700 and 1879. Just because the Staudacher’s count is wrong by 25% does not mean the other 249 observers are also wrong by exactly 25%. Usoskin et al. (2016b) agreed that the GSN reconstruction after 1830 is correct, implying that these authors believe that the 25% correction is not valid.

An example of how a recount and calibration factor are intertwined is the case of W.C. Bond. For Bond, the calibration factor is 0.75, indicating that an overcount of groups was detected in the GSN reconstruction. When Carrasco et al. (2020b) considered Bond’s recount, they found a 20% overcount. With the new count, the new calibration factor becomes about 0.94.

Appendix D: Comparison Between Reconstructions Based on Machine Learning and Cosmogenic ¹⁴C Isotope

Cosmogenic isotopes like ¹⁰Be and ¹⁴C have been used to analyze and reconstruct solar activity, including the creation of proxy records for sunspot activity cycles (see, e.g., Usoskin, 2017; Miyahara et al., 2021). Unfortunately, there is not yet a methodology and/or algorithms that allow a high degree of confidence in reconstructing the sunspot activity cycles, especially during the Maunder minimum.

In Figure 9, we compare our ML reconstructed GSN (blue shaded area) with the reconstructed SSN from the tree-ring isotopic ¹⁴C by Usoskin et al. (2021b) using a black line for sunspot Cycles -12 to 13 (1610 – 1900 time interval). For comparison, we have also added the currently recommended SSN record of Clette et al. (2014) using a red line connected by dots set every year in Figure 9. All three records are put on the canonical Wolf Sunspot Number (V1) scale, vertical axis on the right, as in the comparison shown in Table 3 of the main text.

Figure 9

A comparison of our ML reconstructed GSN (blue area) with the SSN reconstruction based on tree-ring ¹⁴C isotope by Usoskin et al. (2021b) using a black line and the SSN record of Clette et al. (2014) using a red line connected with dots for the 1610 – 1900 time interval. All three records are put on the canonical Wolf Sunspot Number (V1) scale (in blue on the right vertical axis) as in the comparison in Table 3 of the main text. The International Sunspot Number (V2) scale is also shown in the left vertical axis (in black).

We would like to highlight here the complexity involved in adequately reconstructing not only the phase of the sunspot cycles but also the amplitude of these cycles, both during the Maunder minimum and during the entire interval from 1700 to 1900 using the ¹⁴C record. Particularly, one of the main problems to be solved are the negative values of sunspot counts. In contrast, our ML reconstructed GSN fully accounts for both phases and the amplitudes of these sunspot activity cycles. In addition, the comparison with the recommended SSN record by Clette et al. (2014), in turn, suggests the potential application of AI/ML in the reconstruction of SSN or $R_{z}$, especially before 1700 using the cosmogenic isotope records as the input for training and calibration steps outlined in Section 2.6.2.

Appendix E: Comparison Between the GSN by Hoyt and Schatten (1998) and the Updated Sunspot Group Counts from Debrecen Photoheliographic Data (DPD)

In Table 10 we tabulate the yearly mean GSN calculated by Hoyt and Schatten (1998), the updated GSN calculated using the sunspot group counts from Debrecen Photoheliographic Data (DPD), the Solar Optical Observing Network (SOON) database operated by the US Air Force, the ML GSN computed in this article, the canonical Wolf Sunspot Numbers (V1 from SILSO) calculated up to 2013/2014 (point at which they ceased being tabulated; this is labeled as Wolf), and their replacement called the International Sunspot Number (ISN V2) multiplied by 0.6 to put it on the same scale as the other four tabulations.

Table 10 Yearly means of six sunspot number tabulations.

For the years of overlap, 1977 to 1995, the mean values for the five-time series are 83.9 (HS98), 86.3 (DPD), 81.6 (SOON), 83.6 (ML), 84.3 (Wolf V1), and 69.5 (ISN V2), respectively. If the Waldmeier Jump of 20% is removed from ISN V2, the corresponding mean would be 83.4, in good agreement with the other four series.

For the years of overlap, 1977 to 2013, the means are 73.2 (DPD), 64.9 (SOON), 71.4 (ML), 67.1 (Wolf V1), and 56.9 (ISN V2). Again removing the Waldmeier Jump, the ISN V2 mean becomes 68.3, in reasonable agreement with the other three series.

The values from Debrecen Photoheliographic Data tend to be slightly higher than the other time series, particularly during the last two solar minima. The reason for this difference is still under investigation, but it may be caused by the use of the observations by the Solar and Heliospheric Observatory/Michelson Doppler Imager (SOHO/MDI) for those days when there were no ground-based observations. It should be noted that the DPD time series is based solely on photographic images and computer analysis of the images (but using their accurate checking by eye after the computer procedures and comparison with magnetograms), so it is likely to be the most homogeneous sunspot group record currently available (Baranyi, Győri, and Ludmány, 2016; Győri, Ludmány, and Baranyi, 2017). Unfortunately, the last complete year of observations for DPD is 2017.

Finally, for an additional perspective, we have further included our ML reconstructed GSN values to Table 10 to compare them with the original GSN by Hoyt and Schatten (1998) and the GSN derived from DPD values in Figure 10. As previously stated, the three records are in reasonable agreement and we intend to extend the original GSN records by Hoyt and Schatten (1998) indefinitely in the future using our algorithms.

Figure 10

Comparison between the three GSN records: the original GSN by Hoyt and Schatten (1998) (blue line), the GSN derived from DPD (red solid line), and Bayesian ML probabilistic GSN values (purple dotted line plus the cyan shaded area) from 1974 to 2020.