Group Sunspot Number Research Articles

Daniel Mögling’s Sunspot Observations in 1626–1629: A Manuscript Reference for the Solar Activity before the Maunder Minimum

Abstract The sunspots have been observed since 1610, and their group numbers have been used for evaluating the amplitude of solar activity. Daniel Mögling recorded his sunspot observations for more than 100 days in 1626–1629 and formed a significant data set of sunspot records before the Maunder Minimum. Here we have analyzed his original manuscripts in the Universitäts- und Landesbibliothek Darmstadt to review Mögling’s personal profile and observational instruments and derived the number and positions of the recorded sunspot groups. In his manuscript, we have identified 134 days with an exact sunspot group number and 3 days of additional descriptions. Our analyses have completely revised the observational dates and group numbers, added 19 days of hitherto overlooked observations, and removed 8 days of misinterpreted observations. We have also revisited the sunspot observations of Schickard and Hortensius and revised their data. These results have been compared with the contemporary observations. Moreover, we have derived the sunspot positions from his sunspot drawings and located them at 2°–23° in heliographic latitude in both solar hemispheres. Contextualized with contemporary observations, these results indicate their temporal migration to lower heliographic latitudes and emphasize their location in the declining phase of solar cycle −12 in the 1620s. Mögling’s observations were probably conducted using a pinhole and camera obscura, which likely made him underestimate the sunspot group number by ≥33%–52%. This underestimation should be noted upon comparison with modern data sets.

Active Days around Solar Minimum and Solar Cycle Parameter

Utilizing a new version of the sunspot number and group sunspot number dataset available since 2015, we have statistically studied the relationship between solar activity parameters describing solar cycles and the slope of the linear relationship between the monthly sunspot numbers and the monthly number of active days in percentage (AD). As an effort of evaluating possibilities in use of the number of active days to predict solar activity, it is worthwhile to revisit and extend the analysis performed earlier. In calculating the Pearson’s linear correlation coefficient r, the Spearman’s rank-order correlation coefficient rs, and the Kendall’s τ coefficient with the rejection probability, we have calculated the slope for a given solar cycle in three different ways, namely, by counting the spotless day that occurred during the ascending phase and the descending phase of the solar cycle separately, and during the period corresponding to solar minimum ± 2 years as well. We have found that the maximum solar sunspot number of a given solar cycle and the duration of the ascending phase are hardly correlated with the slope of a linear function of the monthly sunspot numbers and AD. On the other hand, the duration of a solar cycle is found to be marginally correlated with the slope with the rejection probabilities less than a couple of percent. We have also attempted to compare the relation of the monthly sunspot numbers with AD for the even and odd solar cycles. It is inconclusive, however, that the slopes of the linear relationship between the monthly group numbers and AD are subject to the even and odd solar cycles.

Solar Activity of the Past 100 Years Inferred From 10Be in Ice Cores—Implications for Long‐Term Solar Activity Reconstructions

AbstractDifferences between 10Be records from Greenland and Antarctica over the last 100 years have led to different conclusions about past changes in solar activity. The reasons for this disagreement remain unresolved. We analyze a seasonally resolved 10Be record from a firn core (North Greenland Eemian Ice Drilling [NEEM] ice core project) in Northwestern Greenland for 1887–2002. By comparing the NEEM data to 10Be data from the NGRIP and Dye3 ice cores, we find that the Dye3 data after 1958 are significantly lower. These low values lead to a normalization problem in solar reconstructions when connecting 10Be variations to modern observations. Excluding these data strongly reduces the differences between solar reconstructions over the last 2,000 years based on Greenland and Antarctic 10Be data. Furthermore, 10Be records from polar regions and group sunspot numbers do not support a substantial increase in solar activity for the 1937–1950 period as proposed by previous extensions of the neutron monitor data.

Sunspot Positions and Areas from Observations by Cigoli, Galilei, Cologna, Scheiner, and Colonna in 1612 – 1614

Digital images of manuscripts stored in the Galilean collection of the Central National Library of Florence are analyzed to obtain sunspot groups, their areas and heliographic positions. Overall, 142 drawings were processed. The way of drawing is usually schematic resulting in area uncertainty which may exceed a factor of two for small sunspots. We suggest that there is an upper limit of a factor of two between sunspot group numbers from the drawings and the actual ones. The computed penumbra-to-umbra ratio is consistent with modern observations. A distribution of sunspot latitudes versus time is reconstructed by means of two methods: exploiting the observation time noted by an observer and minimizing the day-to-day variability of sunspot latitudes.

Evidence for a Causal Relationship between the Solar Cycle and Locust Abundance

Time series of abundance indices for Desert Locusts Schistocerca gregaria (Forskål 1775) and Oriental Migratory Locusts Locusta migratoriamanilensis (Meyen 1835) were analysed independently and in relation to measures of solar activity and ocean oscillation systems. Data were compiled on the numbers of territories infested with swarms of the Desert Locust from 1860–2015 and an inferred series that compensated for poor reporting in the 1860 to 1925 period. In addition, data for 1930 to 2014, when reports are considered to have been consistently reliable were converted to numbers of 1° grid squares infested with swarms and separated according to four different geographical regions. Spectral analysis to test the hypothesis that there are cycles in the locust dynamics revealed periodicities of 7.5 and 13.5 years for the inferred series that were significant according to the Ornstein-Uhlenbeck state-space (OUSS) test. Similar periodicities were evident in the 1° grid square data and in each of the regions but even though these were significantly different from white noise, they were not significant according to the OUSS criterion. There were no significant peaks in the Oriental Migratory Locust results with the OUSS test, but the data were significantly different from white noise. To test hypotheses that long term trends in the locust dynamics are driven by solar activity and/or oceanic oscillation systems (the Southern Oscillation Index (SOI), the North Atlantic Oscillation Index (NAO) and the Indian Ocean Dipole (IOD)), the original locust data series and their Kalman-filtered low frequency (LF) components were tested for causality using both spectral coherence tests and convergent cross mapping. Statistically significant evidence was found that solar activity measured by numbers of sunspot groups drive the dynamics, especially the LF components, of both species. In addition, causal links were inferred between both the SOI and NAO data and Desert Locust dynamics. Spectral coherence was also found between sunspot groups and the NAO, the IOD and LF SOI data. The data were also analysed showing that the LF SOI had causal links with the LF inferred Desert Locust series. In addition, the LF NAO was causally linked to the LF 1° grid square data, with the NAO for December-March being most influential. The results suggest that solar activity plays a role in driving locust abundance, but that the mechanisms by which this happens, and whether they are mediated by fluctuations in oceanic systems, is unclear. Furthermore, they offer hope that information on these phenomena might enable a better early warning forecasting of Desert Locust upsurges.

Temporal Distribution of Solar Cycle 24 Sunspot Groups: Comparison to Cycles 12-23

Abstract We analyze the temporal distribution of sunspot groups for even and odd cycles in the range SC12-SC24. It seems that cycle 24 is a characteristic even cycle, although with low amplitude. The number of large sunspot groups for cycle 24 is relatively smaller than for the average of both even and odd cycles SC12-SC23, and there is a deep decline of the large groups in the middle of the cycle. Temporal evolution of the sunspot groups of the even cycles is non-synchronous such that the northern hemisphere distribution of groups maximizes earlier that the southern hemisphere groups. This leads to a double-peak structure for the average even cycle. On the other hand, the distributions of the sunspot groups of odd cycles maximize simultaneously. We show that this double-peak structure intensifies the Gnevyshev gap (GG) for the even cycles, but is not its primary cause. On the contrary, we show that the GG exists for even and odd cycles, and separately on both hemispheres. We resample all cycles to have equal number of 3945 days and study the difference in the evolution of average total group area and average group area of the even and odd cycles separately. The analysis shows that there is a decline in both total area and average area in the even cycles 1445 days (about four years) after the beginning of the cycle, which is at least 99 % significant for both total and average area. The odd cycles do not have such a clear decline.

Chinese sunspot drawings and their digitization – (III) quasi-biennial oscillation of the hand-drawn sunspot records

Quasi-biennial Oscillations (QBOs) of the Sun have a significant meaning as a benchmark of solar cycle, not only for understanding the dynamo action but also in terms of space weather prediction. In this paper, the hand-drawn sunspot images recorded from the Purple Mountain Observatory are used to investigate the solar QBOs and the Gnevyshev gap of the sunspot relative numbers (Rs) and group sunspot numbers (Rg) during the period 1954–2011. The main results are as follows: (1) both the Rs and Rg exhibit similar periods including the 22-year magnetic cycle, the 11-year Schwabe cycle, and the QBOs modes; (2) the reconstructed QBOs of both data sets exhibit coherent behavior and tend to have a high amplitude during the maximum phase of each solar cycle; (3) the Gnevyshev gap is produced by the superposition of the QBOs and the 11-year Schwabe cycle, and the Rs is better to study the variation of the Gnevyshev gap rather than the Rg.

Reanalyses of the sunspot observations of Fogelius and Siverus: two ‘long-term’ observers during the Maunder minimum

ABSTRACT The solar activity during the Maunder minimum (MM; 1645–1715) has been considered significantly different from the one captured in modern observations, in terms of sunspot group number and sunspot positions, whereas its actual amplitudes and distributions are still under active discussions. In its core period (1650/1660–1700), Martin Fogelius and Heinrich Siverus have formed significant long-term series in the existing data bases. With numerous spotless days, they have been considered as the 13th and 7th most active observers before the end of the MM. In this study, we have analysed their original archival records, revised their data, have removed significant contaminations of the apparent ‘spotless days’ in the existing data bases, and cast caveats on the potential underestimation of the solar-cycle amplitude in the core MM. Still, they reported at best one sunspot group throughout their observational period and confirm the significantly suppressed solar cycles during the MM. This is also supported from the contemporary observations of Hook and Willoughby, analysed in this study. Based on their revised data, we have also derived positions of notable sunspot groups, which Siverus recorded in 1671 (≈N7.5° ± 2.5°), in comparison with those of Cassini's drawings (≈N10° ± 1°). Their coincidence in position and chronology in corrected dates indicates these sunspot groups were probably the same recurrent active region (AR) and its lifespan was significantly long (≥35 d) even during the MM.

Revisiting the Amplitude of Solar Cycle 9: The Case of Sunspot Observations by W.C. Bond

William Cranch Bond, director of the Harvard College Observatory in mid-19th century, carried out detailed sunspot observations during the period 1847-1849. We highlight Bond was the observer with the highest daily number of sunspot groups observed in Solar Cycle 9 recording 18 groups on 26 December 1848 according to the current sunspot group database. However, we have detected significant mistakes in these counts due to the use of sunspot position tables instead of solar drawings. Therefore, we have revisited the sunspot observations made by Bond, establishing a new group counting. Our new counts of the sunspot groups from Bond's drawings indicate that solar activity was previously overestimated. Moreover, after this new counting, Bond would not be the astronomer who recorded the highest daily group number for Solar Cycle 9 but Schmidt with 16 groups on 14 February 1849. We have also indicated the new highest annual group numbers recorded by any observer for the period 1847-1849 in order to correct those values applied in the "brightest star" method, which is used as a rough indicator of the solar activity level. Furthermore, a comparison between Bond's sunspot records and the sunspot observations made by Schwabe and Wolf is shown. We conclude that the statistics of Wolf and Bond are similar regarding to the group count. Additionally, Schwabe was able to observe smaller groups than Bond.

Sunspot Records by Antonio Colla Just After the Dalton Minimum

Antonio Colla was a meteorologist and astronomer who made sunspot observations at the Meteorological Observatory of the Parma University (Italy). He carried out his sunspot records from 1830 to 1843, just after the Dalton Minimum. We have recovered 71 observation days for this observer. Unfortunately, many of these records are qualitative and we could only obtain the number of sunspot groups and/or single sunspots from 25 observations. However, we highlight the importance of these records because Colla is not included in the sunspot group database as an observer and, therefore, neither his sunspot observations. According to the number of groups, the sunspot observations made by Colla are similar as several observers of his time. For common observation day, only Stark significantly recorded more groups than Colla. Moreover, we have calculated the sunspot area and positions from Colla's sunspot drawings concluding that both areas and positions recorded by this observer seem unreal. Therefore, Colla's drawings can be interpreted such as sketches including reliable information on the number of groups but the information on sunspot areas and positions should not be used for scientific purposes.

Number of sunspot groups from the Galileo–Scheiner controversy revisited

ABSTRACT We revise the sunspot observations made by Galileo Galilei and Christoph Scheiner in the context of their controversy regarding the nature of sunspots. Those of their sunspot records not included in the current sunspot group database, used as a basis to calculate the sunspot group number, are analysed. Within the documentary sources consulted in this work, we can highlight the sunspot observations by Scheiner included in the letters sent under the pseudonym Apelles to Marcus Welser and the first sunspot observations made by Galileo, which can be consulted in Le opere di Galileo Galilei. These sunspot observations would extend the temporal coverage for these two observers and fill some gaps in the current group database in the earliest period, where the data available are sparse. Moreover, we have detected changes in the quality of the sunspot drawings made by Galileo and Scheiner in their observation series, affecting the number of groups recorded by the two observers. We also compare these records with sunspot observations made by other astronomers of that time. According to this comparison and regarding the same observation days, Scheiner was generally the astronomer who reported more sunspot groups, while Harriot, Cigoli and Galileo recorded a similar number of groups. We conclude that these differences are mainly because of the observational methods used by the observers.

Sunspot Observations by Barnaba Oriani (1778 – 1779)

We present the sunspot observations made by Barnaba Oriani in 1778 and 1779 at the Brera Observatory (Milan, Italy). We have computed the number of sunspot groups and individual sunspots and extracted the positions of all individual sunspots recorded by Oriani. It must be highlighted that the observations made by Oriani in 1779 are not included in the current sunspot-group number database. The observations made in 1778 were already included, but we have found important deficiencies in these values that underestimated the true level of solar activity. The highest daily number of groups recorded by Oriani was 12 (24 August 1778). Only Horrebow in Solar Cycle 2 observed a higher daily number of groups (up to 16 groups in 1769) in the second half of the 18th century. We have compared the sunspot observations made by Oriani and Staudacher for the common dates. In general, Oriani observed a few more groups than Staudacher, while Staudacher recorded more individual sunspots than Oriani. Furthermore, the sunspot positions recorded by both observers are similar, but some significant differences can be found. Finally, we want to highlight that the sunspot records made in the 18th century will help us to understand better the behavior of the long-term solar activity. Therefore, we need to improve the observational coverage of the sunspot records carried out in that century.

Comparison of the shape and temporal evolution of even and odd solar cycles

Aims. We study the difference in the shape of solar cycles for even and odd cycles using the Wolf sunspot numbers and group sunspot numbers of solar cycles 1−23. We furthermore analyse the data of sunspot area sizes for even and odd cycles SC12−SC23 and sunspot group data for even and odd cycles SC8−SC23 to compare the temporal evolution of even and odd cycles. Methods. We applied the principal component analysis (PCA) to sunspot cycle data and studied the first two components, which describe the average cycle shape and cycle asymmetry. We used a distribution analysis to analyse the temporal evolution of the even and odd cycles and determined the skewness and kurtosis for even and odd cycles of sunspot group data. Results. The PCA confirms the existence of the Gnevyshev gap (GG) for solar cycles at about 40% from the start of the cycle. The temporal evolution of sunspot area data for even cycles shows that the GG exists at least at the 95% confidence level for all sizes of sunspots. On the other hand, the GG is shorter and statistically insignificant for the odd cycles of aerial sunspot data. Furthermore, the analysis of sunspot area sizes for even and odd cycles of SC12−SC23 shows that the greatest difference is at 4.2−4.6 years, where even cycles have a far smaller total area than odd cycles. The average area of the individual sunspots of even cycles is also smaller in this interval. The statistical analysis of the temporal evolution shows that northern sunspot groups maximise earlier than southern groups for even cycles, but are concurrent for odd cycles. Furthermore, the temporal distributions of odd cycles are slightly more leptokurtic than distributions of even cycles. The skewnesses are 0.37 and 0.49 and the kurtoses 2.79 and 2.94 for even and odd cycles, respectively. The correlation coefficient between skewness and kurtosis for even cycles is 0.69, and for odd cycles, it is 0.90. Conclusions. The separate PCAs for even and odd sunspot cycles show that odd cycles are more inhomogeneous than even cycles, especially in GSN data. Even cycles, however, have two anomalous cycles: SC4 and SC6. The variation in the shape of the early sunspot cycles suggests that there are too few and/or inaccurate measurements before SC8. According to the analysis of the sunspot area size data, the GG is more distinct in even than odd cycles. This may be partly due to sunspot groups maximizing earlier in the northern than in the southern hemisphere for even cycles. We also present another Waldmeier-type rule, that is, we find a correlation between skewness and kurtosis of the sunspot group cycles.

Thaddäus Derfflinger’s Sunspot Observations during 1802–1824: A Primary Reference to Understand the Dalton Minimum

Abstract As we are heading toward the next solar cycle, presumably with a relatively small amplitude, it is of significant interest to reconstruct and describe the past secular minima on the basis of actual observations at the time. The Dalton Minimum is often considered one of the secular minima captured in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group number vary significantly, and the existing butterfly diagrams have a large data gap during the period. This is partially because most long-term observations at that time have remained unexplored in historical archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two series of Thaddäus Derfflinger’s observational records spanning 1802–1824 (a summary manuscript and logbooks), as well as his Brander’s 5.5 feet azimuthal quadrant preserved in the Kremsmünster Observatory. We have revised the existing Derfflinger’s sunspot group number with Waldmeier classification, and eliminated all the existing “spotless days” to remove contaminations from solar elevation observations. We have reconstructed the butterfly diagram on the basis of his observations and illustrated sunspot distributions in both solar hemispheres. Our article aims to revise the trend of Derfflinger’s sunspot group number and to bridge a data gap of the existing butterfly diagrams around the Dalton Minimum. Our results confirm that the Dalton Minimum is significantly different from the Maunder Minimum, both in terms of cycle amplitudes and sunspot distributions. Therefore, the Dalton Minimum is more likely a secular minimum in the long-term solar activity, while further investigations for the observations at that time are required.

Duffing Oscillator Model of Solar Cycles

Abstract We propose that the solar cycle variability could be described in the framework of an external quasi-sinusoidal influence on an oscillator with cubic nonlinearity and linear damping (Duffing oscillator). To demonstrate this, we compare the empirical amplitude–frequency dependence with the theoretical one obtained by the Krylov–Bogolyubov averaging method. The empirical data are a composite time series of 2.0 version of sunspot number series, which starts in 1700, and the sunspot group number series by Svalgaard & Schatten, scaled to sunspot number, for 1610–1699 interval. We find that while this interpretation of solar cycle is a mathematical approximation, it explains several properties of solar cycle variability.

Variations of interplanetary magnetic field on various long time-scales

ABSTRACT The IDV index of geomagnetic activity is used by many researchers as a proxy of the interplanetary magnetic field (IMF) strength B. Using the original multiscale regression (MSR) method based on wavelet transformation, we obtained a long series of B values starting from 1845. Then, based on the new 2.0 versions of the sunspot number and group sunspot number and using MSR method and this series as a reference, we reconstructed IMF strength B starting from 1610. Further extension of the reconstruction is associated with radiocarbon reconstructions of solar activity at a time-scale of up to several millennia. It is shown that in the last 3200 yr the IMF strength has been experiencing a downward trend of −(0.39 ± 0.17) · 10−3 nT· yr−1.

Sunspot observations by Hisako Koyama: 1945–1996

ABSTRACT Sunspot records are the only observational tracer of solar activity that provides a fundamental, multicentury reference. Its homogeneity has been largely maintained with a succession of long-duration visual observers. In this article, we examine observations of one of the primary reference sunspot observers, Hisako Koyama. By consulting original archives of the National Museum of Nature and Science of Japan (hereafter, NMNS), we retrace the main steps of her solar-observing career, from 1945 to 1996. We also present the reconstruction of a full digital data base of her sunspot observations at the NMNS, with her original drawings and logbooks. Here, we extend the availability of her observational data from 1947–1984 to 1945–1996. Comparisons with the international sunspot number (Version 2) and with the group sunspot number series show a good global stability of Koyama's observations, with only temporary fluctuations over the main interval 1947–1982. Identifying drawings made by alternate observers throughout the series, we find that a single downward baseline shift in the record coincides with the partial contribution of replacement observers mostly after 1983. We determine the correction factor to bring the second part (1983–1996) to the same scale with Koyama's main interval (1947–1982). We find a downward jump by 9 per cent after 1983, which then remains stable until 1995. Overall, the high quality of Koyama's observations with her life-long dedication leaves a lasting legacy of this exceptional personal achievement. With this comprehensive recovery, we now make the totality of this legacy directly accessible and exploitable for future research.

Uncertainty Quantification in Sunspot Counts

Abstract Observing and counting sunspots constitutes one of the longest-running scientific experiments, with first observations dating back to Galileo (around 1610). Today the sunspot number (SN) time series acts as a benchmark of solar activity in a large range of physical models. An appropriate statistical modeling, adapted to the time series’ complex nature, is, however, still lacking. In this work, we provide the first comprehensive uncertainty quantification analysis of sunspot counts. We study three components: the number of sunspots (N s ), the number of sunspot groups (N g ), and the composite N c , defined as . Those are reported by a network of observatories around the world and are corrupted by errors of various types. We use a multiplicative framework to provide, for these three components, an estimation of their error distribution in various regimes (short-term, long-term, minima of solar activity). We also propose a robust estimator for the underlying solar signal and fit density distributions that take into account intrinsic characteristics such as overdispersion, excess of zeros, and multiple modes. The estimation of the solar signal underlying the composite N c may be seen as a robust version of the International Sunspot Number (ISN), widely used as a proxy of solar activity. Therefore, our results on N c may help characterize the uncertainty on ISN as well. Our results pave the way for a future monitoring of the observatories in quasi-real time, with the aim of alerting the observers when they start deviating from the network and preventing large drifts from occurring.

The effect of telescope aperture, scattered light and human vision on early measurements of sunspot and group numbers

ABSTRACT Early telescopic observations of sunspots were conducted with instruments of relatively small aperture. These instruments also suffered from a higher level of scattered light, and the human eye served as a ‘detector’. The eye’s ability to resolve small details depends on image contrast, and on average intensity variations smaller than ≈3 per cent contrast relative to background are not detected even if they are resolved by the telescope. Here we study the effect of these three parameters (telescope aperture, scattered light and detection threshold of human vision) on sunspot number, group number and area of sunspots. As an ‘ideal’ dataset, we employ white-light (pseudo-continuum) observations from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory, and we model the appearance of sunspots by degrading the HMI images to corresponding telescope apertures with added scattered light. We discuss the effects of different parameters on sunspot counts and derive functional dependences, which could be used to normalize historical observations of sunspot counts to a common denominator.

Eric Strach: Four Decades of Detailed Synoptic Solar Observations (1969‐2008)

AbstractEric H. Strach (1914‐2011) studied medicine at University of Prague and graduated in 1938. Strach dedicated a great part of his life to astronomy becoming a consistent and meticulous observer. He joined the Liverpool Astronomical Association and British Astronomical Association during the 1960s and obtained two recognitions as proof of his great work in solar physics: the BAA's Merlin Medal and Gift in 1999 and Walter Goodacre Medal and Gift, 10 years later. Strach recorded four decades (1969‐2008) of systematic solar records in his observation notebooks although he started his observations from the late 1950s. In this work, we document the valuable effort made by Strach in getting four decades of solar records and the importance of this kind of long observation series for studies of space weather and climate. We present the sunspot group number series according to Strach's data and a long observation series of prominences recorded by Strach.