Perspective https://doi.org/10.1038/s41550-018-0638-2

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

Andrés Muñoz-Jaramillo 1,2,3* and José M. Vaquero 4,5

The periodically reshapes the magnetic structure and radiative output of the and determines its impact on the roughly every 11 years. Besides this main periodicity, it shows century-long variations (including periods of abnormally low solar activity called grand minima). The (1645–1715) has generated significant interest as the archetype of a grand minimum in magnetic activity for the Sun and other , 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.

he solar cycle was first hypothesized by Christian Horrebow (1) using the sunspot number series to reconstruct total and spec- in the 1770s and later rediscovered by Heinrich Schwabe in tral solar irradiance2, and other related indices; 1844, as a clear, roughly decadal modulation of the number (2) understanding the connection between solar activity and ter- T 3 of visible on the solar disk (see Fig. 1). Schwabe’s results, restrial climate change ; publicized by Alexander von Humboldt, motivated Rudolf Wolf, at (3) using the Sun as a reference measuring stick to characterize the Zurich Observatory, to collect all prior available sunspot obser- stellar magnetic cycles4; vations and use them to make the first determination of the Wolf (4) using the Maunder Minimum as an illustrative scenario of sunspot number (WSN) series — a weighted average of the amount what may happen in the future5. of sunspots and sunspot groups — in 18481. From the beginning, piecing together sunspot observations of different observers has In particular, we would like to warn users of sunspot data to be proved to be a challenging endeavour — an active field of research wary of building highly speculative scenarios — as these scenarios even today. However, most users of sunspot series data are unaware amplify the challenges and uncertainties of contextualizing the of the nuances and challenges of piecing together a homogeneous Sun as a , and the role that solar variability plays in terrestrial series out of a heterogeneous set of observers and thus take the sun- climate change. spot series for granted. The goal of this Perspective is not to endorse a particular view of the secular evolution of solar activity over the The challenges of assembling a sunspot number series past 400 years, but to provide a clear visual guide that users of his- The study of the secular evolution of solar activity during the past toric sunspot data, as well as their derivate data products, can use 400 years largely focuses on underpinning the transition between to understand the limitations of historic sunspot observations. This two extrema: on the one hand, we have the Maunder Minimum — a Perspective is part of a concerted community-wide effort to raise period where solar activity was abnormally low during the second awareness of these issues and provide users with a new, live, sunspot part of the seventeenth century;6 on the other hand, we have the series that is more transparent and open to further improvement in modern maximum (including the strongest cycles for which we have the future. As such, we represent here a snapshot assessment current direct observations) taking place during the second half of the 1900s7. to 2018, which will be revised in the future as more historic data is We can confidently determine solar activity levels since the unearthed and our methods improve, leading to better reconstruc- beginning of the twentieth century, and the majority of current stud- tions of long-term solar activity. ies that use information from documentary sources suggest very low levels solar activity during the Maunder Minimum8–11, which What studies need to be careful with long-term solar data? is confirmed by cosmogenic isotopes12. However, it is difficult to There is a wide variety of studies that hinge on an accurate assess- ascertain activity levels in between. The main challenge arises from ment of the evolution of solar activity. Without attempting to per- having to piece together heterogeneous observers with: form a comprehensive review of all of them, it is important for users of the sunspot number series, as well as users of secondary products (1) diferences in the telescope aperture and its optical quality, and derived from their analysis, to be aware of the limitations of work- the observational method used by diferent observers; ing with historical sunspot records. These studies include, but are (2) diferences in each observer’s visual acuity (as well as possible not limited to: degradation with age);

1SouthWest Research Institute, Boulder, CO, USA. 2High Altitude Observatory, Boulder, CO, USA. 3National , Boulder, CO, USA. 4Departamento de Física, Universidad de Extremadura, Mérida, Spain. 5Instituto Universitario de Investigación del Agua, Cambio Climático y Sostenibilidad (IACYS), Universidad de Extremadura, Mérida, Spain. *e-mail: [email protected]

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Hevelius 3–16 May 1644 SDO/HMI 7 January 2014

Fig. 1 | Historical (left) versus modern (right) observations of sunspot groups. Historical observers often used the same disk to draw the time evolution of sunspot groups as can be seen in the left close-up panel where Hevelius recorded the evolution of three different sunspot groups (a, b and c) on the 6, 7 and 8 May 1644 (faint lines indicate when a day ends and the next begins). Even with measurements of the magnetic field, shown in the right close-up panels using green–blue (red–yellow) to indicate positive (negative) magnetic fields, it is challenging to tell different sunspot groups apart when they are close to each other. Both close-up panels share the same scale so visible structures across this figure are directly comparable. Credit: left panels, courtesy of the Library of the Astronomical Observatory of the Spanish Navy; right panels, courtesy of NASA’s Solar Dynamics Observatory

(3) diferences in each observer’s defnition of a sunspot group and used them to define a new sunspot-based series: the group and how they should be counted; sunspot number (GSN). As opposed to Wolf’s number, which uses (4) lack of uniform observational coverage and consistency; a weighted average of the amount of visible sunspots and sunspot (5) determining which observer should be used as the groups (10 ×​ number of groups +​ number of sunspots), the GSN is standard against which all other observers are calibrated based exclusively on the number of groups. (absolute calibration). The GSN painted a different picture of the secular evolution of solar activity during the past 400 years than the WSN (see solid These challenges are compounded when working with early his- pink and black dashed lines in Fig. 2a): one in which the 1800s and torical data before the mid-nineteenth century (see Fig. 1), due to 1700s display levels of activity that are nearly half of those dur- the need for dealing with: ing the 1900s; leading to the idea of the modern period being as unusual in its strength as the Maunder Minimum was in its weak- (1) signifcant observational gaps; 7 14 (2) Latin originals; ness . However, recent work has called into question the methods (3) observers that did not have a common vocabulary to describe used to calculate both the WSN and the GSN. One of the important the same phenomena; results of the subsequent conversation is that we are no longer cer- (4) surveys with scientifc objectives unrelated to measuring solar tain that the modern period is truly extraordinary (that is, activity activity; levels after the Maunder Minimum may have been comparable to (5) drawings that combine multiple days of observation on the those of the twentieth century), so care must be taken when using same solar disk and/or arbitrarily scale objects to make ‘better’ the old GSN as basis for modern exceptionalism. use of the empty space of the quiet Sun. From the Maunder Minimum to the present While both the GSN and WSN are important for our understand- Wolf sunspot number versus group sunspot number ing of long-term solar variability, in this Perspective we focus exclu- Our understanding of long-term variability for more than 100 years sively on GSN reconstructions. The reason is that, at the moment, has been based on the WSN. This changed in 1998 when Hoyt and the GSN series is the only one for which we have the original raw Schatten13 revisited and collected all available historic data in 1998 data, making it the only series that can potentially be extended all

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Hoyt and Schatten (1998)13 Zolotova and Ponyavin (2015)21 Ivanov and Miletsky (2017)23 Chatzistergos et al. (2017)18 Lockwood et al. (2014)25 Svalgaard and Schatten (2016)16 Vaquero et al. (2015)10 Wolf sunspot number/20 Cliver and Ling (2016)17 Willamo et al. (2017)20 Clette and Lefèvre (2016)15

1600 1650 1700 1750 1800 1850 1900 1950 2000 a

15

10

Group number 5

b 0 Networks of overlaping observers

c 15

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5 Current-series blended group number 60 d Galileo Staudacher Spörer Debrecen 40 Scheiner Spoerer and observers Hevelius from the Paris Observatory 20

0

−20 Latitude (°)

−40 Malapert, Gassendi and Marcgraf Schwabe RGO KMAS −60 1600 1650 1700 1750 1800 1850 1900 1950 2000 Year

Fig. 2 | Long-term evolution of solar activity. a, There are currently a wide variety of different reconstructions of solar activity using different techniques. Series whose names are highlighted in black10,16,18,20,23 are considered the best estimates we currently have and they are used in our dispersion analysis. Series whose names are highlighted in red are included for completeness, but are considered to be superseded13, provisional17,25 or refuted21 by more recent work. The international (Wolf) sunspot number divided by 20 (ref. 15), name highlighted in blue, is included for reference. All series (using different colours and line styles) are shown as provided with no effort to scale them to each other. b, The challenge of establishing a connection between historic and modern observers is visualized by constructing a graph network where each node is a unique observer and each edge connects observers with sufficient observational overlap. Only observers within a coloured network have significant overlap with each other. Dots are placed in the centre of each observer's period of observation and randomly scattered vertically to facilitate visualization. c, We propose the combination of current series10,16,18,20,23 into a single heatmap, instead of picking and choosing only one of them, as a more conservative way of assessing long-term solar activity. d, We also include the long- term butterfly diagram, using the latitude and time observed for individually observed groups, as valuable supplemental data to the sunspot series. We include all published modernized latitude–time sunspot group observations (using different colours to indicate different observers and surveys)27,30,33–41, and preliminary data based on original drawings, to provide a complete picture of long-term solar variability. KMAS, Kislovodsk Mountain Astronomical Station. RGO, Royal Greenwich Observatory. the way back to the seventeenth century. However, there is currently Before 1750, things become more complicated due to the nature, a parallel effort to improve the WSN as well15. quality and coverage of historical observations. There are currently Two main approaches have been proposed for piecing together four main proposed approaches (the first of which is only included GSN observations from 1750 to the present. for completeness).

(1) Te use of a carefully selected skeleton of main observers (1) Te construction of highly speculative scenarios based on the that acts as a scafold to combine all available observers into a assumptions that an 11 year solar cycle operated continuously single series16–18. during the Maunder Minimum and that observations during (2) Using the fraction of active (at least one sunspot visible on the Maunder Minimum are fawed because observers were not disk) versus quiet (no sunspots visible) days to determine the aware of the existence of the solar cycle nor interested in its as- visual acuity of historical observers enabling their calibra- sociated phenomena21. Tese speculative scenarios have been tion to a highly detailed ‘objective observer’ such as the Royal since refuted8 and should not be used as estimates of solar Greenwich Observatory photographic series19,20. activity for the Maunder Minimum.

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Svalgaard and Schatten (2016)16 Willamo et al. (2017)20 Ivanov and Miletsky (2017)23 Chatzistergos et al. (2017)18 Vaquero et al. (2015)10 a 15

10 numbe r

roup 5 G

b 30 e v i 25 t c A h 20 t e i mon t

15 u numbe r Q he 10 g Day in t n i s

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usin g 15 100 80 day s 10 60

5 40 observed 20 d 0 Group number ma sk ed 50 <15 25 (° ) <10

ude 0 t i <5

La t −25 0 −50 1600 1650 1700 1750 1800 1850 1900 1950 2000 Observational Year coverage (%)

Fig. 3 | Observational coverage of historical sunspot group data. a, Traditional visualization of sunspot number series use continuous curves and shaded areas to indicate solar activity level and its uncertainty. However, they fail to illustrate how many observations were used to estimate activity level. b, We use a grid of daily observations stacked in 30-day intervals where each grid square is a day coloured to show whether it was active (purple; at least one observer reported a sunspot group), quiet (blue; all observers reported a naked Sun) or missing (white; no observations available) to illustrate the stark difference in coverage between the Maunder Minimum and the modern period. c, We propose to use colour and transparency to mask the proposed series such that highly speculative intervals are no longer visible and thus the user’s perception of the historical period differs significantly from that of the modern period. In this colour-transparency scheme, white (red) represents 100% (0%) observational coverage, while other colours represent intervals of coverage values (that is, orange indicates coverage between 0 and 5%, yellow between 5 and 10%, and so on). Above 15% we use a continuous colour map going from grey to white. d, Observational coverage is particularly poor for the historic butterfly diagram data. Because of this, we plot the colour mask behind the data or nothing would be visible. Comparing historic and modern butterfly diagram data must be done with extreme care.

(2) Te estimation of activity based on the fraction of active derived studies) is largely perceived as a consistent, complete and versus quiet days by using direct comparison with the relation- accurate record. This perception is so commonplace that the sun- ship between the active day fraction and activity of the period spot record is currently listed by the Guinness World Records as the between 1850 and 199510,22. “longest continuous observational science data”26. (3) Te use of the highest daily count of sunspot groups for each Figure 2b clearly illustrates the challenge of trying to estimate the year by any observer during the Maunder Minimum (‘the relative amplitude of historic versus modern solar activity. It shows a brightest star’) under the assumption that such occurrences of network graph of all the 715 observers (from Galileo until the pres- spottedness represented relatively rare episodes of activity that ent) for which we currently have sunspot number observations11. were more likely to be noticed and reported16. Each node in the network denotes a unique observer temporally (4) Te estimation of activity level based on the width of active centred at the middle of its observational period. Two observers are latitudes (that is, butterfy wings)23. connected if they:

15,24 (1) have at least 60 diferent overlapping days of All of these proposed series, along with the WSN , the (now) observations (each unique pair of days within 2 days superseded series of Hoyt and Schatten13, and the provisional series 25 17 of each other); of Lockwood et al. and Cliver & Ling , are illustrated in Fig. 2a. (2) each observer reported at least 4 diferent values of group They form part of an ongoing community effort to identify the numbers during their observational survey (a bare minimum best methods to ascertain the level of solar activity during the past to enable cross-calibration). four centuries. The main clusters of connected observers are highlighted using Users take the sunspot series for granted different colours, demonstrating the difficulty of establishing a One of the biggest problems leading to unsubstantiated claims direct observational connection between the present and years and conclusions is that the sunspot series (and automatically any before 1850.

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1600 1625 1650 1675 1700 1725 1750 1775 1800 a 15.0 100 usin g 12.5 ed 80

day s 10.0 60 7.5

observed 5.0 40

2.5

Group number mas k 20 b 0.0 <15 40

20

(° ) <10

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−40 0

1600 1625 1650 1675 1700 1725 1750 1775 1800 Observational Year coverage (%)

1825 1850 1875 1900 1925 1950 1975 2000 c 15.0 100 in g s u 12.5 80 ked

day s 10.0 60 7.5

observed 5.0 40

2.5 20 Group number ma s d 0.0 <15 40

20 <10 (° ) 0 ude t i <5 La t −20

−40 0

1825 1850 1875 1900 1925 1950 1975 2000 Observational Year coverage (%)

Fig. 4 | New way of visualizing observational gaps in historical solar data. a–d, Instead of the traditional way of looking at the sunspot number series (Figs. 2a and 3a), we propose a new way of visualizing historic data that simultaneously captures current understanding of long-term variability, our disagreements regarding the level of solar activity observed during the past 400 years and information on the quality of observational coverage for different historical periods. Coverage and confidence on the sunspot number (a,c) and butterfly diagram (b,d) is markedly different prior to (a,b) and after the discovery of the sunspot cycle (c,d).

Use series disagreement as empirical evidence of uncertainty. (3) Evaluate the combined/added PDFs using a range of group Instead of picking and choosing a particular series for their research, number values (0–20) and append the resulting array into a we suggest that users see the existing proposed series as a map of the two-dimensional array that is used for visualization. In this inherent empirical uncertainty of such reconstruction. We illustrate array, each row denotes a group number, each column a year this idea in Fig. 2c by combining, year by year, all available current and each cell contains the combined/added PDF values. series10,16,18,20,23 using the reported activity level and uncertainty of each series. For each year between 1610 and 2017, we: The resulting array can be used to visualize a ‘heatmap’ that darkens where the series agree and lightens where they disagree. (1) Defne a normalized Gaussian probability density function Normalized PDFs naturally highlight regions where there is more (PDF) separately for each series with valid data for that year. than one proposed series, and dim regions that have not been ana- Tese PDFs are centred on each series’ reported activity level, lysed by multiple groups. Figure 2c provides a more conservative and have a standard deviation equal to each series’ reported overview of the possible ranges of solar activity over the past 400 uncertainty. Tis procedure converts the reported activity level years (as well as its uncertainty) than any single one of the proposed for each year and each series into a continuum of possibilities series shown in Fig. 2a. It is important, however, to stress that this that can be added. proposed approach is only temporary and will be superseded by the (2) Superimpose the PDFs of all series with valid data in that year revised framework and protocols that the solar community is cur- using simple addition. rently working on.

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Users are unaware of the prevalence of observational gaps drawings30 and further comparison to other proxies of solar activ- The traditional way of visualizing solar long-term variability data ity12,31 to maximize informational synergy. There is currently an (see Figs. 2a and 3a) is failing users by not making a strong dis- ongoing concerted effort to combine the strengths of all proposed tinction between the quality and abundance of observations in the methods to address their weaknesses. The end goal is a community- modern versus historical periods. This absence is particularly severe vetted and accepted version, with provision made for further updates and lacking in conventional butterfly diagrams (see Fig. 2d), which as more data are unearthed and our understanding increases. We use the latitude and time of observed sunspot groups to illustrate expect that a new, better, open-source, official sunspot number the equatorward migration of active latitudes with the progression series will be released in early 2020 by the Sunspot Index and Long- of the cycle. term Solar Observations (SILSO) World Data Center. The marked difference in abundance of observations between We are optimistic that the coming decade will see significant modern and historical periods is visible in Fig. 3b, showing a grid improvements in our assessment of long-term solar variability and of daily observations stacked in 30 day intervals. Each grid square its associated uncertainty. However, no amount of sophisticated corresponds to a unique day and is coloured to show whether it was algorithms will be a substitute for the identification and proper active (purple; at least one observer reported a sunspot group), quiet translation of historical documents, as well as for interdisciplin- (blue; all observers reported a naked Sun) or missing (white; no ary teams involving astrophysicists, historians of science and phi- observations available). A quick comparison between the current lologists to revisit historical observations of sunspots9,29,32. New data available GSN series during the Maunder Minimum10,16,23 and our and deeper knowledge of the way historical observers worked are of observational coverage (Fig. 3c) highlights the speculative nature critical importance for improving our understanding of the earlier of our understanding of historic solar activity (especially during the period of solar observations including the Maunder Minimum. first half of the Maunder Minimum). Data availability Mask solar variability data according to their observational cov- A Python Jupyter notebook, along with the necessary data to reproduce all erage. To address this deficiency, we propose to mask the sunspot plots presented here can be found at https://github.com/amunozj/NatAs_SN_ Perspective. We request that you use data in this repository only to reproduce series (and butterfly diagram) encoding observational coverage our analysis, but get them from the original sources if you intend to use them for using colour and transparency (the more sparse the observational research purposes. coverage the more opaque the mask). The calculation and over- plotting of a biennial mask of observational coverage (Fig. 3c) shows Received: 31 May 2018; Accepted: 12 October 2018; how different coverage is during the modern versus historic periods: Published: xx xx xxxx the modern period is nice and white, fully covered and clearly dis- tinct (as it has been shown traditionally), while the historic period References has many intervals that are highly opaque and coloured, masking 1. Vaquero, J. M. & Vázquez, M. 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19. Usoskin, I. G. et al. A new calibrated sunspot group series since 1749: 38. Arlt, R., Senthamizh Pavai, V., Schmiel, C. & Spada, F. Sunspot positions, statistics of active day fractions. Sol. Phys. 291, 2685–2708 (2016). areas, and group tilt angles for 1611–1631 from observations by Christoph 20. Willamo, T., Usoskin, I. G. & Kovaltsov, G. A. Updated sunspot group Scheiner. Astron. Astrophys. 595, A104 (2016). number reconstruction for 1749–1996 using the active day fraction method. 39. Györi, L., Ludmány, A. & Baranyi, T. Comparative analysis of Astron. Astrophys. 601, A109 (2017). Debrecen sunspot catalogues. Mon. Not. R. Astron. Soc. 465, 21. Zolotova, N. V. & Ponyavin, D. I. Te Maunder Minimum is not as grand as 1259–1273 (2017). it seemed to be. Astrophys. J. 800, 42 (2015). 40. Tlatov, A. G., Makarova, V. V., Skorbezh, N. N. & Muñoz Jaramillo, A. 22. Kovaltsov, G. A., Usoskin, I. G. & Mursula, K. 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