The distribution of the sunspot group size (area) and its dependence on the level of solar activity is studied. It is shown that the fraction of small groups is not constant but decreases with the level of solar activity so that high solar activity is largely defined by big groups. We study the possible influence of solar activity on the ability of a realistic observer to see and report the daily number of sunspot groups. It is shown that the relation between the number of sunspot groups as seen by different observers with different observational acuity thresholds is strongly non-linear and cannot be approximated by the traditionally used linear scaling ($k-$factors). The observational acuity threshold [$A_{\rm th}$] is considered to quantify the quality of each observer, instead of the traditional relative $k-$factor. A nonlinear $c-$factor based on $A_{\rm th}$ is proposed, which can be used to correct each observer to the reference conditions. The method is tested on a pair of principal solar observers, Wolf and Wolfer, and it is shown that the traditional linear correction, with the constant $k-$factor of 1.66 to scale Wolf to Wolfer, leads to an overestimate of solar activity around solar maxima.
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 sun…
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 which involves a combination of observation of many observers. We propose a new iterative algorithm that allows to construct 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 recon…
We show that the Active-Day-Fraction calibration method (Willamo et al. [2017]) fails for Gustav Spörer's sunspot group observations. Spörer was labeled a 'perfect observer' on account of his 'observational threshold SS area' being determined to be equal to zero, based on the assumption that the observer can see and report all the groups with the area larger than SS, while missing all smaller groups. So, Spörer could apparently, according to the ADF calibration method, see and report all groups, regardless of size and should never miss any. This suggests a very direct test: compute the yearly …
R. C. Carrington, C. H. F. Peters, and W. de la Rue observed the sunspots in the second half of the 19th century, determining their heliographic positions between 1853 and 1870, before the establishment of the solar program of the Royal Greenwich Observatory. The large tables of sunspot positions included in the catalogues published by these observers have recently been converted to a machine readable format. The present work analyses this data by calculating the sunspot group velocities for each observer. These results are then fitted with a differential rotation law to compare the data of th…
We identify several pairs of 'equivalent' observers defined as observers with equal or nearly equal 'observational threshold' areas of sunspots on the solar disk as determined by the 'Active Days Fraction' method [e.g. Willamo et al., 2017]. For such pairs of observers, the ADF-method would be expected to map the actually observed sunspot group numbers for the individual observers to two reconstructed series that are very nearly equal and (it is claimed) represent 'real' solar activity without arbitrary choices and deleterious, error-accumulating 'daisy-chaining'. We show that this goal has no…
We revise the sunspot observations made by Galileo Galilei and Christoph Scheiner in the context of their controversy on the nature of sunspots. Their sunspot records not included in the current sunspot group database, used as a basis to calculate the sunspot group number, are analyzed. 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 observat…
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 is still under active discussions. In its core period (1650/1660 -- 1700), Martin Fogelius and Henrich Siverus have formed significant long-term series in the existing databases with numerous spotless days, as the 13th and 7th most active observers before the end of the MM. In this study, we have analysed their original archival records, r…
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…
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…
Waldmeier [1971] found a very tight relationship between the F10.7 solar radio flux and the sunspot number and suggested using the flux for an objective calibration of the sunspot number. He suggested that if this relationship changed later on, the sunspot number should be re-calibrated, assuming that the calibration must have drifted with time. I repeat his analysis using data up to the present and it is, indeed, clear that the relationship has changed significantly. This could be due to a drift of the calibration or to a secular change in the visibility of sunspots, or both.
The Waldmeier Effect is the observation that the rise time of a sunspot cycle varies inversely with the cycle amplitude: strong cycles rise to their maximum faster than weak cycles. The shape of the cycle and thus the rise time does not depend on the scale factor of the sunspot number and can thus be used to verify the constancy of the scale factor with time as already noted by Wolfer (1902) and Waldmeier (1978). We extend their analysis until the present using the new SILSO sunspot number (version 2) and group number and confirm that the scale factors have not varied significantly the past 25…
Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day f…
The sunspot record is the only observational tracer of solar activity that provides a fundamental, multi-century reference. Its homogeneity has been largely maintained with a succession of long-duration visual observers. In this paper, 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 database of her sunspot observations at …
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 ($…
We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups $R_B$ above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of $R_B$ are then re-scaled to the observed RGO group number $R_A$ using a variety of regression techniques. It is found that a very high correlation between $R_A$ and $R_B$ ($r…
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 co…
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. T…
The solar program of the Astronomical Observatory of Madrid started in 1876. For ten solar cycles, observations were made in this institution to determine sunspot numbers and areas. The program was completed in 1986. The resulting data have been published in various Spanish scientific publications. The metadata allowed four periods of this program (with different observers and instruments) to be identified. In the present work, the published data were retrieved and digitized. Their subsequent analysis showed that most of these data can be considered reliable given their very high correlation w…
We present a few newly found old sunspot observations from the years AD 1708, 1709, and 1710, which were obtained by Peter Becker from Rostock, Germany. For 1709, Becker gave a detailed drawing: he observed a sunspot group made up of two spots on Jan 5, 6, and 7, and just one of the two spots was observed on Jan 8 and 9. We present his drawing and his explanatory text. We can measure the latitude and longitude of these two spots and estimate their sizes for all five days. While the spots and groups in 1708 and the spot on four of the five days in January 1709 were known before from other obser…
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…
The sunspot number is analyzed by using detailed sunspot data, including aspects of observability, sunspot sizes, and proper identification of sunspot groups as discrete entities of the solar activity. The tests show that besides the subjective factors there are also objective causes of the ambiguities in the series of sunspot numbers. To introduce an alternative activity measure the physical meaning of the sunspot number has to be reconsidered. It contains two components whose numbers are governed by different physical mechanisms, this is one source of the ambiguity. This article suggests an …
Because of the lack of reliable sunspot observation, the quality of sunspot number series is poor in the late 18th century, leading to the abnormally long solar cycle (1784--1799) before the Dalton minimum. Using the newly recovered solar drawings by the 18--19th century observers Staudacher and Hamilton, we construct the solar butterfly diagram, i.e. the latitudinal distribution of sunspots in the 1790's. The sudden, systematic occurrence of sunspots at high solar latitudes in 1793--1796 unambiguously shows that a new cycle started in 1793, which was lost in traditional Wolf's sunspot series.…
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 Se…
We have examined the more than 1100 drawings of the solar disk made by the German astronomy amateur Johann Caspar Staudach during 1749-1799 and counted the spots on each image. Using the modern perception of how to group spots into active regions we regrouped the spots as a modern observer would. The resulting number of groups was found to be on average 25% higher than the first count of groups performed by Wolf in 1857, and used by Hoyt and Schatten in their construction of the Group Sunspot Number. Compared to other observers at the time, Staudach's drawings have a very low average number, ~…
Waldmeier in 1947 introduced a weighting (on a scale from 1 to 5) of the sunspot count made at Zurich and its auxiliary station Locarno, whereby larger spots were counted more than once. This counting method inflates the relative sunspot number over that which corresponds to the scale set by Wolfer and Brunner. Svalgaard re-counted some 60,000 sunspots on drawings from the reference station Locarno and determined that the number of sunspots reported were 'over counted' by 44% on average, leading to an inflation (measured by a weight factor) in excess of 1.2 for high solar activity. In a double…
We have reconstructed the sunspot group count, not by comparisons with other reconstructions and correcting those where they were deemed to be deficient, but by a re-assessment of original sources. The resulting series is a pure solar index and does not rely on input from other proxies, e.g. radionuclides, auroral sightings, or geomagnetic records. 'Backboning' the data sets, our chosen method, provides substance and rigidity by using long-time observers as a stiffness character. Solar activity, as defined by the Group Number, appears to reach and sustain for extended intervals of time the sam…
Sunspot numbers are important tracers of historical solar activity. They are important in the prediction of oncoming solar maximum, in the design of lifetimes of space assets, and in assessing the extent of solar-radiation impact on the space environment. Sunspot numbers were obtained visually from sunspot drawings. The availability of digital images from the US Air Force Improved Solar Optical Observing Network (ISOON) prototype telescope concurrent to observer-dependent sunspot numbers recorded at the National Solar Observatory (NSO) has provided a basis for comparing sunspot numbers determi…
We review the evidence for the argument that Rudolf Wolf's calibration of the Sunspot Number is likely to be correct and that Max Waldmeier introduced an upwards jump in the sunspot number in 1945. The combined effect of these adjustments suggests that there has been no secular change in the sunspot number since coming out of the Maunder Minimum ~1700.
We compare four sunspot-number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International sunspot number [$R_{ISNv1}$], the group sunspot number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new "backbone" group sunspot number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the "corrected" sunspot number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each sunspot number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linear…
We discuss recent papers very critical of our Group Sunspot Number Series (Svalgaard & Schatten [2016]). Unfortunately, we cannot support any of the concerns they raise. We first show that almost always there is simple proportionality between the group counts by different observers and that taking the small, occasional, non-linearities into account makes very little difference. Among other examples: we verify that the RGO group count was drifting the first twenty years of observations. We then show that our group count matches the diurnal variation of the geomagnetic field with high fidelity, …
We investigate the phase difference of the sunspot cycles in the two hemispheres and compare it with the latitudinal sunspot distribution. If the north-south phase difference exhibits a long-term tendency, it should not be regarded as a stochastic phenomenon. We use datasets of historical sunspot records and drawings made by Staudacher, Hamilton, Gimingham, Carrington, Spouml;rer, and Greenwich observers, as well as the sunspot activity during the Maunder minimum reconstructed by Ribes and Nesme-Ribes. We employ cross-recurrence plots to analyse north-south phase differences. We show that duri…
We report progress on the ongoing recalibration of the Wolf sunspot number (SN) and Group sunspot number (GN) following the release of version 2.0 of SN in 2015. This report constitutes both an update of the efforts reported in the 2016 Topical Issue of Solar Physics and a summary of work by the International Space Science Institute (ISSI) International Team formed in 2017 to develop optimal SN and GN re-construction methods while continuing to expand the historical sunspot number database. Significant progress has been made on the database side while more work is needed to bring the various p…
The Astronomical Observatory of the University of Coimbra has a huge collection of solar images, acquired daily since 1926. From the beginning, only spectroheliograms in the CaiiK line has been recorded, and since 1989 in the H_alpha line also. Such dataset requires efficient tools to detect and analyze solar activity features. The objective of this work is to create a tool that allows to automatic detect sunspots, umbra, and penumbra, that can be applied to the entire dataset. To achieve this, two different approaches have been developed, one based on mathematical morphology and another based…
The long-standing disparity between the sunspot number record and the Hoyt and Schatten (1998, H&S) Group Sunspot Number series was initially resolved by the Clette et al. (2014) revision of the sunspot number and the group number series. The revisions resulted in a flurry of dissenting group number series while the revised sunspot number series was generally accepted. Thus, the disparity persisted and confusion reigned, with the choice of solar activity dataset continuing to be a free parameter. A number of workshops and follow-up collaborative efforts by the community have not yet brought cl…
Photographic images are valuable data resources for studying long term changes in the solar magnetic field and its influence on the Earth's climate and weather. We digitized more than 100 years of white light images stored in photographic plates and films that are available at Kodaikanal observatory starting from 1904. The digitized images were calibrated for relative plate density and aligned in such a way that the solar north is in upward direction. A semi-automated sunspot detection technique was used to identify the sunspots on the digitized images. In addition to describing the calibratio…
Context. The presence of the moat flow around sunspots is intimately linked to the mere existence of sunspots. Aims. We characterize the moat flow (MF) and Evershed flow (EF) in sunspots to enhance our knowledge of sunspot structures and photospheric flow properties. Methods. We calibrated HMI synoptic Doppler maps and used them to analyze 3h time averages of 31 circular, stable, and fully developed sunspots at heliocentric angles of some 50$^{\circ}$. Assuming axially symmetrical flow fields, we infer the azimuthally averaged horizontal velocity component of the MF and EF from 51 velocity map…
Observing and counting sunspots constitutes one of the longest-running scientific experiment, with first observations dating back to Galileo and the invention of the telescope around 1610. Today the sunspot number (SN) time series acts as a benchmark of solar activity in a large range of physical models. An appropriate statistical modelling, adapted to the time series' complex nature, is however still lacking. In this work, we provide the first comprehensive uncertainty quantification analysis of sunspot counts. Our interest lies in the following three components: the number of spots ($N_s$), …
Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (1998a,b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in c…
The Sunspot Number, created by R.Wolf in 1849, provides a direct long-term record of solar activity from 1700 to the present. In spite of its central role in multiple studies of the solar dynamo and of the past Sun-Earth relations, it was never submitted to a global critical revision. However, various discrepancies with other solar indices recently motivated a full re-calibration of this series. Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described in Clette et al. 2014, we assembled all corrections in order to produce a new…
Sunspot area data play an important role in the studies of solar activity and its long-term variations. In order to reveal real long-term solar variations precise homogeneous sunspot area databases should be used. However, the measured areas may be burdened with systematic deviations, which may vary in time. Thus, there is a need to investigate the long-term variation of sunspot area datasets and to determine the time-dependent cross-calibration factors. In this study, we investigate the time-dependent differences between the available long-term sunspot databases. Using the results, we estimat…
The Maunder Minimum was the period between 1645 and 1715 whose main characteristic was abnormally low and prolonged solar activity. However, some authors have doubted this low level of solar activity during that period by questioning the accuracy and objectivity of the observers. This work presents a particular case of a sunspot observed during the Maunder Minimum with an unusual shape of its umbra and penumbra: a hexagon. This sunspot was observed by Cassini in November 1676, just at the core of the Maunder Minimum. This historical observation is compared with a twin case that occurred recent…
Kanzelhöhe Observatory (KSO) was founded during World War II by the "Deutsche Luftwaffe" (German Airforces) as one station of a network of observatories, which should provide information on solar activity in order to better assess the actual conditions of the Earth's ionosphere in terms of radio wave propagation. The solar observations began in 1943 with photographs of the photosphere, drawings of sunspots, plage regions and faculae, as well as patrol observations of the solar corona. At the beginning all data was sent to Freiburg (Germany). After WWII international cooperation was established…
Institute for Space-Earth Environmental Research, Nagoya University（名古屋大学地球-宇宙环境研究所）；Institute for Advanced Research, Nagoya University（名古屋大学高级研究院）；Space Physics and Operations Division, RAL Space, Science and Technology Facilities Council, Rutherford Appleton Laboratory（科学与技术设施委员会拉尔夫空间实验室空间物理与运行部门）；Nishina Centre, Riken（理化学研究所西村中心）
Solar activity is an important driver of long-term climate trends and must be accounted for in climate models. Unfortunately, direct measurements of this quantity over long periods do not exist. The only observation related to solar activity whose records reach back to the seventeenth century are sunspots. Surprisingly, determining the number of sunspots consistently over time has remained until today a challenging statistical problem. It arises from the need of consolidating data from multiple observing stations around the world in a context of low signal-to-noise ratios, non-stationarity, mi…
We present reconstructed sunspot positions based on observations reported in letters between Gottfried Kirch and other contemporary astronomers from AD 1680 to 1709, i.e. in the last decades of the Maunder Minimum. The letters were compiled and edited by Herbst (2006). The letters (and observations) from Kirch are mostly by Gottfried Kirch, but some also by his 2nd wife Maria M. Kirch (married 1692) and their son Christfried Kirch (born 1694). Using excerpts from the letters, some with drawings, we found some 35 sunspot groups (often for several days in a row or with interruptions) by Kirch an…
In this paper, we try to improve the magnetogram calibration method of the Solar Magnetic Field Telescope (SMFT). The improved calibration process fits the observed full Stokes information, using six points on the profile of Fe ı 5324.18 Å line, and the analytical Stokes profiles under the Milne-Eddington atmosphere model, adopting the Levenberg-Marquardt least-square fitting algorithm. In Comparison with the linear calibration methods, which employs one point, there is large difference in the strength of longitudinal field $B_l$ and tranverse field $B_t$, caused by the non-linear relationship…
The weak-field approximation implying linear relationship between Stokes $V/I$ and longitudinal magnetic field, $B_{\Vert}$, often suffers from saturation observed in strong magnetic field regions such as sunspot umbra. In this work, we intend to improve the magnetic field observations carried out by the \textit{Solar Magnetic Field Telescope} (SMFT) at Huairou Solar Observing Station, China. We propose using non-linear relationship between Stokes $V/I$ and $B_{\Vert}$ to derive the magnetic field. To determine the form of the relationship, we perform a cross-calibration of the observed SMFT d…
Solar surface magnetic field seems to be able to explain variations in Total Solar Irradiance on timescales from hours to decades. Using magnetograms from spacecraft (MDI and HMI) and ground-based observatories (MWO and WSO) I build a composite dataset of the Total Line-of-Sight Unsigned Magnetic Flux over the solar disk stretching back to 1976, validated by excellent correlations with the solar microwave flux (F10.7) and the Sunspot Group Number. Direct measurements of TSI by space borne sensors have been carried out since late 1978. The early instruments were plagued by scattered light enter…
The length of the solar activity cycle fluctuates considerably. The temporal evolution of the corresponding cycle phase, that is, the deviation of the epochs of activity minima or maxima from strict periodicity, provides relevant information concerning the physical mechanism underlying the cyclic magnetic activity. An underlying strictly periodic process (akin to a perfect "clock"), with the observer seeing a superposition of the perfect clock and a small random phase perturbation, leads to long-term phase stability in the observations. Such behavior would be expected if cycles were synchroniz…
