Group Sunspot Number Research Articles

Revisiting Kunitomo’s Sunspot Drawings During 1835 – 1836 in Japan

We revisit the sunspot drawings made by the Japanese astronomer Kunitomo Toubei during 1835-1836 and recount the sunspot group number for each image. There are two series of drawings, preliminary (P, containing 17 days with observations) and summary (S, covering 156 days with observations), all made using brush and ink. S is a compilation of drawings for the period from February 1835, to March 1836. Presently, the P drawings are available only for one month, September 1835; those of other periods have presumably been lost. Another drawing (I) lets us recover the raw group count (RGC) for 25 September 1836, on which the RGC has not been registered in the existing catalogs. We also revise the RGCs from P and S using the Zurich classification and determine that Kunitomo's results tend to yield smaller RGCs than those of other contemporary observers. In addition, we find that Kunitomo's RGCs and spot areas have a correlation (0.71) that is not very different from the contemporary observer Schwabe (0.82). Although Kunitomo's spot areas are much larger than those determined by Schwabe due to skill and instrument limitations, Kunitomo at least captured the growing trend of the spot activity in the early phase of the Solar Cycle 8. We also determine the solar rotation axis to estimate the accurate position (latitude and longitude) of the sunspot groups in Kunitomo's drawings.

The Periodic and Temporal Behaviors of Solar X-Ray Flares in Solar Cycles 23 and 24

Abstract The recent solar cycles 23 and 24 are thought to be unusually quiet with more prolonged periods. Both sunspot groups and solar soft X-ray (SXR) flares show a decline in numbers comparable to cycles 21 and 22. In order to understand the periodic variations and distributions of solar flares with the sunspot group numbers in these cycles, this study investigates the periodicities and distributions of the solar SXR flares, 36354 in total (B (13351) 36.7%, C (20699) 56.9%, M (2141) 5.9%, and X (163) 0.45%) between 1996 July and 2016 December. The continuous wavelet transforms and cross-correlation methods were used to carry out the study. First, we found that the B- class flare number is asynchronous and negatively correlated with the sunspot group numbers. The flare class exhibits deviation when sunspot group numbers rise or fall around 100. The other class flares are in phase, synchronous with the sunspot group numbers. The C-class flares show the highest level of correlation of 0.868 with sunspot group numbers. A different number of short and intermediate periodicities was also noticed among the flare classes. Notable 256-day periodicity is found for B flares, 7, 64, and 300 days for C, 32, 64, and 256 days for M flares, and 40, 32, and 25 days for X flares. The difference in periodic variations of the flare classes could be attributed to the magnetic flux system of sunspot groups producing them.

The Present Special Solar Cycle 24: Casting a Shadow over Periodicity of the North–South Hemispherical Asymmetry

The N-S asymmetry (the north-south hemispheric asymmetry) of sunspot areas for each of the cycles 7-24 have been investigated, and a trend of a long-term characteristic timescale of about eight cycles is inferred, which is confirmed again by studying the fitted lines of the yearly values of the N-S asymmetry of sunspot numbers and sunspot group numbers at solar cycle 24. Then, a periodic behavior of about 12 solar cycles is found in the cumulative counts of yearly sunspot areas for each of the cycles 7-24. Nevertheless, the cumulative counts of sunspot numbers and sunspot group numbers for cycle 24 have different behaviors. Moreover, the dominant hemispheres for cycles 7-23 show a trend of a long-term characteristic timescale of about 12 cycles. However, we cannot determine the dominant hemisphere of cycle 24, as these three parameters give different results for the dominant hemisphere. Cycle 24 is a particular solar activity cycle, as sunspot areas suggest a long characteristic timescale of about 12-cycle length, while sunspot numbers and sunspot group numbers support an eight-cycle period of the N-S asymmetry.

Visualization of the challenges and limitations of the long-term sunspot number record

The solar cycle periodically reshapes the magnetic structure and radiative output of the Sun and determines its impact on the heliosphere roughly every 11 years. Besides this main periodicity, it shows century-long variations (including periods of abnormally low solar activity called grand minima). The Maunder Minimum (1645-1715) has generated significant interest as the archetype of a grand minimum in magnetic activity for the Sun and other stars, suggesting a potential link between the Sun and changes in terrestrial climate. Recent reanalyses of sunspot observations have yielded a conflicted view on the evolution of solar activity during the past 400 years (a steady increase versus a constant level). This has ignited a concerted community-wide effort to understand the depth of the Maunder Minimum and the subsequent secular evolution of solar activity. The goal of this Perspective is to review recent work that uses historical data to estimate long-term solar variability, and to provide context to users of these estimates that may not be aware of their limitations. We propose a clear visual guide than can be used to easily assess observational coverage for different periods, as well as the level of disagreement between currently proposed sunspot group number series.

Principal component analysis of sunspot cycle shape

Aims. We study the shape of sunspot cycles using the Wolf sunspot numbers and group sunspot numbers of solar cycles 1–23. We determine the most typical “model” cycles and the most asymmetric cycles, and test the validity of the two Waldmeier rules: the anti-correlation between cycle height and the length of its ascending phase (rule 1), and between cycle height and the length of the preceding cycle (rule 2). Methods. We applied the principal component analysis to sunspot cycles and studied the first two components, which describe the average cycle shape and cycle asymmetry, respectively. We also calculated their autocorrelation in order to study their recurrence properties. Results. The best model cycles for Wolf numbers are SC12, SC14, and SC16, the successive even cycles from a long period of rather low overall solar activity. We find that the model cycles in eight different analyses using both sunspot series are almost exclusively even cycles. Correspondingly, the most asymmetric cycles are odd cycles. We find that both Waldmeier rules are valid for the whole Wolf number series of 23 cycles. Waldmeier rule 2 is also valid for group number series although its significance is weaker. Waldmeier rule 1 is not significant for the original group number series, but becomes significant for the proxy series. For separate centuries, Waldmeier rules are not always valid for Wolf numbers and very rarely for group numbers. Conclusions. The preference of even cycles as model cycles supports the Gnevyshev-Ohl rule and the related 22-year alternation of cycle amplitudes and intensities, with even cycles on average being 10–15% lower than odd cycles. Our results also offer a new interpretation for the Gnevyshev gap. In addition to being a local depression of solar activity, the Gnevyshev gap is a separatrix that divides cycles into two parts whose relative intensities determine the cycle asymmetry. The Gnevyshev gap is the zero value time of PC2, located approximately 33–42% into the cycle after its start.

Sunspot observations by Pehr Wargentin in Uppsala in 1747

This article reports on solar observations by Pehr Wargentin made in Uppsala in 1747. Drawings of the sun accompanied by textual annotations are preserved in the archives of the Royal Swedish Academy of Sciences. Numbers of sunspot groups, as well as sunspot numbers, were derived for March 1 to May 13, 1747 (Gregorian), the latter being approximations for some days as the exact number of spots and pores in large groups was not mentioned by Wargentin. Sunspot positions were also derived for the observing period, where reliable ones were obtained from right ascension and declination measurements by Wargentin and less accurate ones were measured in his drawings of the solar disk.

Stable Sunspot Area Level of Debrecen Photoheliographic Data and Multivariate Correction Factor of SOON Data

We investigate the spatial and temporal variation of sunspot group areas reported by the Greenwich Photoheliographic Results (GPR), the Solar Optical Observing Network (SOON), the Kislovodsk Mountain Astronomical Station (KMAS), and the Debrecen Photoheliographic Data (DPD) databases. We identify improved correction factors for reconciling these individual records to a common scale. Our results show that the DPD sunspot group areas are stable over the studied interval (1974 – 2014). We find an improved fit between GPR and DPD sunspot group areas when using a correction factor such that $\mathrm{GPR} = 0.975(\pm 0.006) \times \mathrm{DPD}$ , independent of the position of the sunspot group on the solar disk. We also find that the scale of KMAS sunspot group areas fits that of DPD well, but has a small position-dependent trend near the limb. However, in order to set SOON sunspot group area records onto the scale of DPD, we find that there is a need for a multivariate correction factor. This multivariate correction factor has a value ranging between 1.1 and 1.9 and is dependent upon the time of the SOON observation, the distance of the group from disk center, and the observatory within the SOON network. Finally, we provide further context to the systematic bias in SOON sunspot group area observations toward lower values relative to those recorded in the GPR and DPD databases that has previously been reported in the literature. We have identified the two main contributors to the SOON area deficit; some penumbral parts are unobserved, and the spot areas are underestimated. Our analysis is vital for studies that require stable, long-term solar activity records such as solar irradiance models that estimate irradiance reduction from records of sunspot group numbers, areas, and locations.

Sunspot Observations Made by Hallaschka During the Dalton Minimum

We present and analyse the sunspot observations performed by Franz I. C. Hallaschka in 1814 and 1816. These solar observations were carried out during the so-called Dalton minimum, around the maximum phase of the Solar Cycle 6. These records are very valuable because they allow us to complete observational gaps in the collection of sunspot group numbers, improving its coverage for this epoch. We have analysed and compared the observations made by Hallaschka with the records made by other contemporary observers. Unfortunately, the analysis of the sunspot areas and positions showed that they are too inaccurate for scientific use. But, we conclude that sunspot counts made by Hallaschka are similar to those made by other astronomers of that time. The observations by Hallaschka confirm a low level of the solar activity during the Dalton minimum.

A Test of the Active-Day Fraction Method of Sunspot Group Number Calibration: Dependence on the Level of Solar Activity

The method of active day fraction (ADF) was proposed recently to calibrate different solar observers to the standard observational conditions. The result of the calibration may depend on the overall level of solar activity during the observational period. This dependency is studied quantitatively using data of the Royal Greenwich Observatory, by formally calibrating synthetic pseudo-observers to the full reference dataset. It is shown that the sunspot group number is precisely estimated by the ADF method for periods of moderate activity, may be slightly underestimated by 0.5\,--\,1.5 groups ($\leq$10\,\%) for strong and very strong activity, and is strongly overestimated by up to 2.5 groups ($\leq$30\,\%) for weak--moderate activity. The ADF method becomes unapplicable for the periods of grand minima of activity. In general, the ADF method tends to overestimate the overall level of activity and to reduce the long-term trends.

Evolution of the Sunspot Number and Solar Wind B $B$ Time Series

The past two decades have witnessed significant changes in our knowledge of long-term solar and solar wind activity. The sunspot number time series (1700-present) developed by Rudolf Wolf during the second half of the 19th century was revised and extended by the group sunspot number series (1610–1995) of Hoyt and Schatten during the 1990s. The group sunspot number is significantly lower than the Wolf series before ∼1885. An effort from 2011–2015 to understand and remove differences between these two series via a series of workshops had the unintended consequence of prompting several alternative constructions of the sunspot number. Thus it has been necessary to expand and extend the sunspot number reconciliation process. On the solar wind side, after a decade of controversy, an ISSI International Team used geomagnetic and sunspot data to obtain a high-confidence time series of the solar wind magnetic field strength ( $B$ ) from 1750-present that can be compared with two independent long-term (> ∼600 year) series of annual $B$ -values based on cosmogenic nuclides. In this paper, we trace the twists and turns leading to our current understanding of long-term solar and solar wind activity.

Iwahashi Zenbei’s Sunspot Drawings in 1793 in Japan

Three Japanese sunspot drawings associated with Iwahashi Zenbei (1756-1811) are shown here from contemporary manuscripts and woodprint documents with the relevant texts. We revealed the observational date of one of the drawings to be 26 August 1793, and the overall observations lasted for over a year. Moreover, we identified the observational site for the dated drawing at Fushimi in Japan. We then compared his observations with group sunspot number and raw group count from Sunspot Index and Long-term Solar Observations (SILSO) to reveal its data context, and concluded that these drawings filled the gaps in understanding due to the fragmental sunspots observations around 1793. These drawings are important as a clue to evaluate astronomical knowledge of contemporary Japan in the late 19 th century and are valuable as a non-European observation, considering that most sunspot observations up to mid-19 th century are from Europe.

Critical frequencies of the ionospheric [formula omitted] and [formula omitted] layers during the last four solar cycles: Sunspot group type dependencies

The long term solar activity dependencies of ionospheric F1 and F2 regions’ critical frequencies (f0F1 and f0F2) are analyzed for the last four solar cycles (1976–2015). We show that the ionospheric F1 and F2 regions have different solar activity dependencies in terms of the sunspot group (SG) numbers: F1 region critical frequency (f0F1) peaks at the same time with the small SG numbers, while the f0F2 reaches its maximum at the same time with the large SG numbers, especially during the solar cycle 23. The observed differences in the sensitivity of ionospheric critical frequencies to sunspot group (SG) numbers provide a new insight into the solar activity effects on the ionosphere and space weather. While the F1 layer is influenced by the slow solar wind, which is largely associated with small SGs, the ionospheric F2 layer is more sensitive to Coronal Mass Ejections (CMEs) and fast solar winds, which are mainly produced by large SGs and coronal holes. The SG numbers maximize during of peak of the solar cycle and the number of coronal holes peaks during the sunspot declining phase. During solar minimum there are relatively less large SGs, hence reduced CME and flare activity. These results provide a new perspective for assessing how the different regions of the ionosphere respond to space weather effects.

The Ratio Between the Number of Sunspot and the Number of Sunspot Groups

Data from three solar observatories, Learmonth, Holloman, and San Vito, are used to study the variations in the average number of sunspots per sunspot group. It is found that the different types of sunspot groups and the number of sunspots in these groups have different solar cycle and cycle to cycle variations. The varying ratio between the average number of sunspots and the number of sunspot groups is shown to be a real feature and not a result of changing observational instruments, observers experience, calculation schemes, etc., and is a result of variations in the solar magnetic fields. Therefore, the attempts to minimize the discrepancies between the sunspot number and sunspot group series are not justified, and lead to the loss of important information about the variability of the solar dynamo.

The Waldmeier Effect for Two Sunspot Populations

This paper continues our studies in which we showed that sunspot groups form two populations differing by physical properties—populations of small and large groups. The known Waldmeier effect has been individually considered for these populations. Two formulations of this effect were verified: the classical one, which connects the solar activity index at the maximum of the 11-year cycle with the length of the ascending phase of a cycle, and the modified one, connecting the index value at the cycle maximum with the highest rate of the index change along the ascending branch. We used the data from the Greenwich Observatory and the Kislovodsk Mountain Astronomical Station for the solar activity cycles from 12 to 24 to construct the series of indices for the areas and the numbers of sunspot groups. It has been shown that the Waldmeier effect works more strictly for the population of large sunspot groups than for that of small groups. The results of this analysis may find an application in the dynamo theory.

Periodicity of sunspot group number during the Maunder Minimum

Applying the Hilbert-Huang Transform (HHT) method to the yearly average sunspot group (SG) number reconstructed by Svalgaard& Schatten, we investigate the periodicity of SG number from 1610 to 2015. Our main findings are summarized below. Periodicities of 3.56 +/- 0.24 (Quasi-Triennial Oscillations), 9.22 +/- 0.13 (Schwabe Cycle), 16.91 +/- 0.99 (Hale Cycle), 49.25 +/- 0.96, 118.64 +/- 2.52 (Centennial Gleissberg Cycle), and 206.32 +/- 4.60 yr are statistically significant in the SG numbers. During the Maunder Minimum (MM), the occurrences of the Schwabe Cycle and the Hale Cycle, extracted from SG numbers, are suspended; before and after the MM, Schwabe Cycle and the Hale Cycle, extracted from SG numbers, all exist. The results of applying the Morlet Wavelet Analysis to the SG number confirm that, for SG number, the occurrence of the Schwabe Cycle is suspended during the MM, and, before and after the MM, the Schwabe Cycle all exist. Then we investigate the periodicity in the annual Be-10 data from 1391 to 1983, which are given in a supplementary file to McCracken & Beer, using HHT and the Morlet wavelet transform. We find that, for the Be-10 data, the Schwabe Cycle and the Hale Cycle persist throughout the MM. Our results support the suggestion that the Schwabe Cycle is too weak to be detected in the sunspot data.

Sunspot activity and influenza pandemics: a statistical assessment of the purported association.

Since 1978, a series of papers in the literature have claimed to find a significant association between sunspot activity and the timing of influenza pandemics. This paper examines these analyses, and attempts to recreate the three most recent statistical analyses by Ertel (1994), Tapping et al. (2001), and Yeung (2006), which all have purported to find a significant relationship between sunspot numbers and pandemic influenza. As will be discussed, each analysis had errors in the data. In addition, in each analysis arbitrary selections or assumptions were also made, and the authors did not assess the robustness of their analyses to changes in those arbitrary assumptions. Varying the arbitrary assumptions to other, equally valid, assumptions negates the claims of significance. Indeed, an arbitrary selection made in one of the analyses appears to have resulted in almost maximal apparent significance; changing it only slightly yields a null result. This analysis applies statistically rigorous methodology to examine the purported sunspot/pandemic link, using more statistically powerful un-binned analysis methods, rather than relying on arbitrarily binned data. The analyses are repeated using both the Wolf and Group sunspot numbers. In all cases, no statistically significant evidence of any association was found. However, while the focus in this particular analysis was on the purported relationship of influenza pandemics to sunspot activity, the faults found in the past analyses are common pitfalls; inattention to analysis reproducibility and robustness assessment are common problems in the sciences, that are unfortunately not noted often enough in review.

New reconstruction of the sunspot group numbers since 1739 using direct calibration and “backbone” methods

Group sunspot number (GSN) series constitute the longest instrumental astronomical database providing information on solar activity. It is a compilation of observations by many individual observers, and their inter-calibration has usually been performed using linear rescaling. There are multiple published series that show different long-term trends for solar activity. We aim at producing a GSN series, with a non-linear non-parametric calibration. The only underlying assumptions are that the differences between the various series are due to different acuity thresholds of the observers, and that the threshold of each observer remains constant throughout the observing period. We use a daisy chain process with backbone (BB) observers and calibrate all overlapping observers to them. The calibration of each individual observer is performed with a probability distribution function (PDF) matrix, constructed considering all daily values for the overlapping period with the BB. The calibration of the BBs is done in a similar manner. Propagation of errors is modelled with Monte Carlo simulations. The final series extends back to 1739 and includes data from 314 observers. It suggests moderate activity during the 18th and 19th century, which is significantly lower than the high level of solar activity predicted by other recent reconstructions applying linear regressions. The new series provides a robust reconstruction, based on modern and non-parametric methods, of sunspot group numbers since 1739, and it confirms the existence of the Modern grand maximum of solar activity in the second half of the 20th century.

Updated sunspot group number reconstruction for 1749–1996 using the active day fraction method

Sunspot number series are composed from observations of hundreds of different observers that requires careful normalization of the observers to the standard conditions. Here we present a new normalized series of the number of sunspot groups for the period 1749-1996. The reconstruction is based on the active day fraction (ADF) method, which is slightly updated with respect to the previous works, and a revised database of sunspot group observations. Stability of some key solar observers has been evaluated against the composite series. The Royal Greenwich Observatory dataset appears fairly stable since the 1890s but is about 10% too low before that. A declining trend of 10-15% in the quality of Wolfer's observation is found between the 1880s and 1920s, suggesting that using him as the reference observer may lead to additional uncertainties. Wolf (small telescope) appears fairly stable between the 1860s and 1890s, without any obvious trend. The new reconstruction reflects the centennial variability of solar activity as evaluated using the singular spectrum analysis method. It depicts a highly significant feature of the Modern grand maximum of solar activity in the second half of the 20th century, being a factor 1.33-1.77 higher than during the 18-19th centuries. The new series of the sunspot group numbers with monthly and annual resolution, available also in the electronic format, is provided forming a basis for new studies of the solar variability and solar dynamo for the last 250 years.

Sunspot number recalibration: The ~1840–1920 anomaly in the observer normalization factors of the group sunspot number

We analyze the normalization factors (k ′-factors) used to scale secondary observers to the Royal Greenwich Observatory (RGO) reference series of the , ) group sunspot number (GSN). A time series of these k ′-factors exhibits an anomaly from 1841 to 1920, viz. , the average k ′-factor for all observers who began reporting groups from 1841 to 1883 is 1.075 vs. 1.431 for those who began from 1884 to 1920, with a progressive rise, on average, during the latter period. The 1883–1884 break between the two subintervals occurs precisely at the point where Hoyt and Schatten began to use a complex daisy-chaining method to scale observers to RGO. The 1841–1920 anomaly implies, implausibly, that the average sunspot observer who began from 1841 to 1883 was nearly as proficient at counting groups as mid-20th century RGO (for which k ′ = 1.0 by definition) while observers beginning during the 1884–1920 period regressed in group counting capability relative to those from the earlier interval. Instead, as shown elsewhere and substantiated here, RGO group counts increased relative to those of other long-term observers from 1874 to ~1915. This apparent inhomogeneity in the RGO group count series is primarily responsible for the increase in k ′-factors from 1884 to 1920 and the suppression, by 44% on average, of the Hoyt and Schatten GSN relative to the original Wolf sunspot number (WSN) before ~1885. Correcting for the early “learning curve” in the RGO reference series and minimizing the use of daisy-chaining rectifies the anomalous behavior of the k ′-factor series. The resultant GSN time series (designated GSN*) is in reasonable agreement with the revised WSN (S N *; ) and the backbone-based group sunspot number (R GS ; ) but significantly higher than other recent reconstructions (Friedli, personal communication, 2016; , ; ). This result is substantiated by a “correction-factor” (CF) time series defined as the ratio of annual group counts of the , ) series to the average raw (unscaled) group counts of all observers, as well as by a comparison of the GSN and GSN* time series with a recent reconstruction of solar wind B from 1845 to the present. The ~1840–1920 k ′-factor anomaly and its impact on the Hoyt and Schatten GSN are discussed in the context of the ongoing effort to recalibrate the sunspot number time series.

Temporal variations of different solar activity indices through the solar cycles 21-23

Here, we compare the sunspot counts and the number of sunspot groups (SGs) with variations of total solar irradiance (TSI), magnetic activity, Ca II K-flux, faculae and plage areas. We applied a time series method for extracting the data over the descending phases of solar activity cycles (SACs) 21, 22 and 23, and the ascending phases 22 and 23. Our results suggest that there is a strong correlation between solar activity indices and the changes in small (A, B, C and H-modified Zurich Classification) and large (D, E and F) SGs. This somewhat unexpected finding suggests that plage regions substantially decreased in spite of the higher number of large SGs in SAC 23 while the Ca II K-flux did not decrease by a large amount nor was it comparable with SAC 22 and relates with C and DEF type SGs. In addition to this, the increase of facular areas which are influenced by large SGs, caused a small percentage decrease in TSI while the decrement of plage areas triggered a higher decrease in the magnetic field flux. Our results thus reveal the potential of such a detailed comparison of the SG analysis with solar activity indices for better understanding and predicting future trends in the SACs.