Discussion on Solar Variability and Sunspot Indices

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Received on Sep 27, 2018
in VarSITI Newsletter #19

on "Solar Variability and Sunspot Indices"
Katya Georgieva

The number of sunspots is the solar activity proxy with the longest record, and widely used to evaluate both solar variability and its terrestrial impacts.

Two sunspot indices were used until recently:

The RZ series provides yearly/monthly/daily sunspot index values from 1700/1749/1818, respectively, to May 2015, and the RG series – from 1610 to 1995. To quantify the long-term solar variability, some researchers have used RZ, others RG, and still others a combination of the two because RZ is not available before 1700, and RG – after 1995.

RZ and RG are closely correlated, however their longterm trends differ (Fig.1), and so do estimates of solar variability and its terrestrial impacts based on the one or the other. In particular, using RG leads to higher estimated past solar forcing on the Earth’s climate than using RZ.

Figure 1. Trends in RZ (upper panel) and RG (lower panel).

In 2011, a group of scientists united around the idea that, “given the importance of the sunspot time series, the coexistence of two conflicting series is a highly unsatisfactory situation that should now be actively addressed” (Clette et al., 2014). To address the situation, a series of Sunspot Number Workshops was held with the goal “to rectify the discrepancies” between RZ and RG, and “to publish a single consensus sunspot data series” (Cliver et al., 2013).

Recalibrations of both indices were accordingly undertaken, and as a result, two new indices were constructed to replace RZ and RG. The goal “to rectify the discrepancies” between them was achieved, and the new sunspot and group sunspot numbers (SN and GN ) match very well (Clette et al., 2014) – Fig.2. However, the goal to come to “a single consensus sunspot data series” totally failed, as the publication of SN and GN triggered a number of other alternative new sunspot and group sunspot series (Cliver, 2016). Nevertheless, since July 2015, RZ was terminated and replaced by SN

Figure 2. Original and recalibrated sunspot and group sunspot numbers, from Clette et al. (2014)

Thousands of studies are based on RZ and RG. Their termination affects a number of topics like constraining dynamo models, solar cycle predictions, reconstructions of solar irradiance, ionospheric models, calibration of long-term proxies like cosmogenic isotope abundances, etc. Their replacement by a number of new indices makes past results incomparable to recent ones, and recent results using alternative indices incomparable to each other.

As the research in the framework of the VarSITI program critically depends on the quantification of the solar variability, VarSITI’s Steering Committee decided to start a discussion on the "Solar variability and sunspot indices". The questions to be discussed include, but are not limited to:


Clette F., Svalgaard L., Vaquero J., Cliver E., Space Sci. Rev. 186 (1-4), 35, 2014.

Cliver E.D., Solar Phys. 291, 2891-2916, 2016.

Cliver E.W., Clette F., Svalgaard L., Central Europ. Astrophys.Bull. 37, 401, 2013.

Hoyt D.V., Schatten K.H., Solar Phys. 181 (2), 491, 1998.

Wolf R., Mitteilungen der Naturforschenden Gesellschaft in Bern, 207, 89, 1851.

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Received on Oct 09, 2018
from Frédéric Clette

Reply to on "Solar Variability and Sunspot Indices"
Katya Georgieva

Following the publication in the VarSITI Newsletter of a communication by K. Georgieva about the new revised sunspot number, I need to correct several incorrect or inaccurate statements that give a wrong picture of the recent and present status of the sunspot (Sn) and group (Gn) number revisions.

In the Newsletter, I read:
"The goal to come to “a single consensus sunspot data series” totally failed, as the publication of SN and GN triggered a number of other alternative new sunspot and group sunspot series (Cliver, 2016)."

Not at all. On the contrary, we are instead overwhelmed by the success of this enterprise undertaken in 2011, when we considered just making a one-shot improvement with a modest team of a few researchers. The success is twofold:

In spite of the initial lack of coordination between publications, the present proliferation of publications about the group and sunspot number series actually initiates a continuous upgrade process. Such an iterative revision process is equivalent to what is done for most other solar measurements series. As better knowledge is acquired about the calibration of the source instruments, and as new measurements become available, those series are reconsidered and new corrections are introduced and finally included in new releases, after comparative studies. For what regards the sunspot and group numbers, for historical reasons, this is indeed a rather new evolution, while it is standard and fully adopted for e.g. spectral or total solar irradiance series. Users expect and even call for new improved versions of such data sets.

The text also speaks about the "termination" of the SN and GN series:

In this respect, contrary to what is said in the Newsletter, there is no "termination" of the series, but simply upgrades to new versions, like for most standard modern data series (irradiance, radio flux, etc.). The community must only be ready to adapt to those upgrades. Until the release of Version 2 in 2015, this was not common practice because the past sunspot number remained static (by then, surprisingly, nobody questioned the anomaly of an immutable scientific data series!).

In the same vein, I read: "The past results are not comparable anymore"

This is incorrect, as for the first time, the new series are fully documented and have associated publications. Moreover,the past sunspot number series (Version 1) and the original Hoyt & Schatten group number series remain accessible in the SILSO archive Web pages. Therefore, past analyses can be repeated with the same data, but now can also be compared with an identical analysis by just replacing the old SN series by the new one. It is thus perfectly possible to determine rigorously how results of a certain study are affected solely by the change in the version of SN data.

Then coming to the questions:
"Is it justified to try to rectify the discrepancies (between SN and GN)?"

We draw the attention on the fact that corrections brought to the SN and GN series were never based on attempts to erase differences between the two series.

Each series was recalibrated separately, simply because:

  • the method originally used to built the two series are completely different (single pilot station for SN, daisy-chaining of multiple observers for the GN)
  • consequently, the nature of the inhomogeities affecting either series is completely different and requires different approaches and methods
  • The problems appear at different epochs for each series. They don't span the same time interval and they are not based on the same set of observers (there is a large common base, but the input data are not overlapping).

Moreover, it is a misconception to believe that the ultimate goal is to achieve a total equivalence of the SN and GN, allowing to merge them, or e.g. abandon part of either series in favour of the other. Early on, during the past SN workshops, several analyses showed that although there is a common base to the SN and GN (sunspots as tracers of emerging toroidal flux ropes), they contain a significantly different information, as found e.g. by Dudok de Wit (Presentation from SN Workshop 1, 2011; http://www.leif.org/research/SSN/DudokdeWit.pdf). This can be understood as the GN counts each group as 1, regardless of its actual size, while the SN also includes the count of sunspots inside groups, which is a measure of group size. An apparently stable but non-linear relation on long-timescales between the SN and GN was also found by Clette et al. 2016 (Sol. Phys, 291, p. 2750, fig. 16).

Instead, the actual goal is to RECONCILE the series, i.e. demonstrating that some prominant differences are non-solar, but clearly due to imperfections in their construction.

This includes artificial secular trends: as the average number of spots per group is a rather stable property, there is no physical explanation that could account for a factor 3 difference between the trends found in the original H&S GN and and the original Zürich SN. This must be artificial, and past work indeed revealed changes in the underlying methods and data that can precisely lead to the identified trends.

This also includes sharp jumps occurring only in one of the series: as both the SN and GN probe the same underlying quantity, there is no physical explanation that can produce such unlateral effects or their abruptness. The jumps occur at random times relative to the evolution of the solar cycle. Onthe other hand, most of them could be traced to historical transitions in the data production: start of Wolf's own observations (1849), recruiting of the first assistants in Zürich (1864), departure of W.Brunner and full renewal of the Zürich team (1947), switch to a new reference series (Greenwich photographic catalogue, 1875), etc.

The hope is that when the residual homogeneities will become smaller than the actual solar-based differences between the SN and GN series, we can learn about the solar cycle from the long-term evolution of those subtle differences. This is why the SN and GN series continue to be produced and distributed as separate series.

Another question:
"Which observatory can provide the continuation of the terminated Wolf index?"

As mentioned above, there is no point maintaining an old data series with known defects when there is a new better version available. When reproducing past published analyses is really needed, SN version 1 is thus available. Anyway, in those cases, all data used in the analysis stopped at a past date.

This being said, while the SN series is continuously extended as the main task of the World Data Center SILSO, the GN series was always the output of a one-shot publication. All published GN series thus stop around the date of a past publication, and they are not continued afterwards. Therefore, once a better synthesis of recent results will have been achieved, the WDC-SILSO plans to include the parallel production of the GN, to also extend continuously the GN series in the future, based on the same worldwide observing network as for the SN.

A final question about
alternate indices possibly replacing the sunspot number:

The possibility to build new sunspot-based indices relying on recent techniques like CCD imaging is a very important topic. However, on its own, it can be part of a whole separate discussion. At this point, it is however important to mention the following remarks:

  • imaging techniques, flux measurements, etc. were introduced only recently (2-3 solar cycles). Therefore, they cannot address long-term issues. The only way to put those recent data in a long-term perspective is to continue the base visual sunspot number in parallel, to calibrate any new index to the multi-secular reference. This calibration must encompass the whole range of activity levels, which means producing parallel series during at least one solar cycle, and probably more, as cycles are not equivalent.
  • modern instruments are based on technologies that evolve over short timescales relative to the long time scales that we need to capture (decades to centuries). Images recorded on photographic film and in CCD images have different properties. The pixel count of CCD detectors increased by more than one order of magnitude in just a decade. Consequently, merging and comparing such data on a common base is extremely difficult, over even a single solar cycle. The discrepancies can reach factors 1.2 to 1.5 (e.g. automated sunspot counts from SoHO/MDI, and SDO/HMI; STARA catalogue, F. Watson; http://hmi.stanford.edu/hminuggets/?p=981), and are thus larger than the largest inhomogeneities found in the visual SN and GN series.

Thus, in spite of its limitations, the visual observing technique provided and still provides the inherent stability of a technique and detector (the human vision system) that does not evolve significantly over centuries. Just check the 1610 drawings by Galileo to be fully convinced! Human vision and other factors contributed to limit the range of discrepancies between sunspot counts made by observers of widely different epochs. Still, because of their sparsity and the cruder earlier techniques (telescopes), data from early observers before the 19th century are definitely less accurate. This will be the topic of more attention in coming years, leading to specific improvemements of the early parts in the next versions of the SN and GN series. But just keep in mind that corrections between observers from the 17th and from 21th century will be of the same magnitude as corrections to image-based counts separated only by 10-20 years in the present epoch.

Possible role of VarSITI:

Finally, although VarSITI offers an interesting channel to involve the scientific community around this recalibration effort, it does not provide a permanent framework inside which an official evaluation and endorsement of a new candidate version of the SN/GN series can take place on the long run. Therefore, steps have been taken in the context of the International Astronomical Union to promote the adoption of the sunspot series as an astronomical standard, which would be submitted to regular assesments through the same processes as other existing astrophysical standards. This is now proposed through the Inter-Division Working Group on solar synoptic observations

For now, the joint work towards the next improved SN and GN series is articulated around an ISSI Working Team. For more information see: http://www.issibern.ch/teams/sunspotnoser/

By bringing together all key researchers currently working on this recalibration, this Working Team is prefiguring the kind of expert body that would carry out future evaluations and vetting of the best version given the state of knowledge at the time of each release.

Although ISSI rules limit the number of team members, the work involves the participation of a wider community of "guest" scientists who can bring unique expertise, useful information or an independent viewpoint on specific issues.

Key action items are:

Frédéric Clette (October 2018)

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Received on Jan 23, 2019
from Tamara Gulyaeva


"Comments on re-calibration of sunspot numbers for VarSITI"
Tamara L. Gulyaeva

First of all the SSN re-calibration has been made already so we should accept this action as a fact. I believe that we have to thank Dr Frederick Clette et al [1] for this action which stimulated new efforts of the STP experts and led to new publications [2-11].

In our papers [6÷11] it is explained why this modification has aroused problems for the ionospheric models such as IRI, IRI-Plas, SMI, NeQuick, which have been built with the former SSN1 data set. As a way out we have introduced extended set of solar and ionospheric indices into the IRI-Plas model system [7]. At the same time D. Bilitza [12] has foreseen for the IRI system to enter 12-monthly smoothed SSN1 time series before December, 2014, and SSN2 afterwards applying conversion of 12-monthly smoothed SSN2 to SSN1 according to [6]:

SSN1 = 0.7xSSN2(1)

Concerning the daily estimates of SSN1 index we introduced its model regression with daily value of SSN2 [9]:

SSN1 = ⟨0.6925× SSN2 – 0.2462 ⟩(2)
Response to suggested questions:

1) We should accept new SSN2 as the only data set available now. Those who need SSN1 values could apply Eqn.1 for 12-monthly smoothed SSN1-proxy indices and Eqn.2 for SSN1-daily proxy values.

2) More solar activity indices and their ionospheric proxies are discussed in our papers [7÷9]


[1] Clette, F., Svalgaard, L., Vaquero, J.M., Cliver, E.W. (2014) Re-visiting the sunspot number: a 400-year perspective on the solar cycle. Space Sci. Rev., 186, No. 1, 35–103.

[2] Georgieva, K., Kilcik, A., Nagovitsyn, Yu., Kirov, B. (2016) About the recalibration of the sunspot record. Proc. “Solar and Solar-Terrestrial Physic – 2016”, 61-66, GAO, Pulkovo, S-Petersburg, Russia, arXiv:1701.06165 [astro-ph.SR]

[3] Georgieva, K., Kilcik, A., Nagovitsyn, Yu., Kirov, B. (2017) The ratio between the number of sunspot and the number of sunspot groups. Geomagn. Aeronomy, 57, Is. 7, 776-782, DOI:10.1134/S001679321707009X.

[4] Nagovitsyn, Yu.A., Georgieva, K. (2017) Versions of time series for classic solar indices and an adequate description of solar activity. Geomagn. Aeronomy, 57, Is. 7, 783-787, DOI:10.1134/S0016793217070131.

[5] Perna, L., Pezzopane, M. (2016) foF2 vs solar Indices for the Rome station: looking for the best general relation which is able to describe the anomalous minimum between cycles 23 and 24. J. Atmosph. Solar- Terr. Phys., 148, 13-21, DOI:10.1016/j.jastp.2016.08.003.

[6] Gulyaeva, T.L. (2016) Modification of the solar activity indices in the International Reference Ionosphere IRI and IRI-Plas models due to recent revision of sunspot number time series. Solar-Terrestrial Physics (Solnechno-Zemnaya Fizika), 2, Is. 3, 87–98, DOI:10.12737/20872; http://ru.iszf.irk.ru/Journal_Solar-Terrestrial_Physics._Vol._2 Iss._3 2016.

[7] Gulyaeva, T.L., Arikan, F., Sezen, U., Poustovalova, L.V. (2018) Eight proxy indices of solar activity for the International Reference Ionosphere and Plasmasphere model. J. Atmos. Solar-Terr. Phys., 172, 122-128, DOI:10.1016/j.jastp.2018.03.025.

[8] Gulyaeva, T.L., Gulyaev, R.A. (2018) Coherent changes of solar and ionospheric activity during long-lived coronal mega-hole from Carrington rotation CR2165 to CR2188. J. Atmos. Solar-Terr. Phys., 179, 165-173, DOI:10.1016/j.jastp.2018.07.007.

[9] Gulyaeva, T.L. (2018) Predicting indices of the ionosphere response to solar activity for the ascending phase of the 25th solar cycle. Adv. Space Res., doi:10.1016/j.asr.2018.11.002.

[10] Sezen, U., Gulyaeva, T., Arikan, F. (2018) Performance of solar proxy options of IRI-Plas model for equinox seasons. J. Geophys.Res. Space Phys. 123(2), 1441-1456, DOI:10.1002/2017JA024994.

[11] Sezen, U., Gulyaeva, T., Arikan, F. (2018) Online Computation of International Reference Ionosphere Extended to Plasmasphere (IRI-Plas) Model for Space Weather. Geodesy and Geodynamics, DOI:10.1016/j.geog.2018.06.004.

[12] D. Bilitza, private communication, 2016.

Tamara L. Gulyaeva (January 23, 2019)

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Received on Jan 24, 2019
from Ilya Usoskin


Reply to
"Comments on re-calibration of sunspot numbers for VarSITI"
Tamara L. Gulyaeva

I have red the recent comment by L. Gulyaeva, and I disagree with one point. She writes 1) We should accept new SSN2 as the only data set available now. Those who need SSN1 values could apply Eqn.1 for 12-monthly smoothed SSN1-proxy indices and Eqn.2 for SSN1-daily proxy values. look above

I believe this statement is no good. We should not consider the SSN2 as "the only dataset available now", as there are other datasets, and an international team works at their intercomparison. The SSN2 is not "the only" set but one of several datasets, whose accuracy and methodology needs verification. I would agree that SSN2 supersedes the old WSN series, but it should not supersede other series of GSN. As we discussed, the SSN2 is based essentially on the same methodology and indirect dataset as the WSN only correcting some found/claimed errors. A full revision of the methodology is needed, which requires that all the raw data are available, and this work is in progress now. On the other and, new GSN series use different methodologies applied to raw data and are thus much more transparent.

Best regards, Ilya Usoskin (January 24, 2019)

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Received on Feb 15, 2019
from Frédéric Clette


Reply to Ilya Usoskin

I agree with I.Usoskin that the sunspot number and group number series and issues should be considered separately. There are two main reasons:

1) those two quantities are different and reflect slightly different properties of magnetic flux emergence at the solar surface. So, you can expect different proxy relations. More specifically, as the group number counts all groups as 1, regardless of the size of the group, it misses a measure of the magnitude of the emerging flux, while the sunspot number will be proportional to this magnitude, as it includes the count of individual sunspots. This proportionality may prove important for ionospheric processes as the solar forcing is proportional to the UV flux, which itself depends on the size of the source (chromospheric plages). The specific strength of the group number is that it can be extended back to the 18th and 17th century, when the available historical information is often limited to the number of groups, without detailed counts of individual spots.

2) As stressed by I. Usoskin, the sunspot and group number series are built in a different way on the base of a partly different base of raw data. This brings the advantage that biases and anomalies in each series can be more easily identified. Indeed, both series should show a similar evolution of solar activity, as they are both based on sunspots. Of course, slight differences will appear given the different nature of the indices (cf. above). However, strong differences of relative amplitudes between different cycles, or jumps or local trends appearing only in one of the two series give a clear indication that something is wrong in one of the two series.

Still, I must correct a statement by I.Usoskin saying that the group number calibration rests on raw data while the sunspot number does not and is less "transparent" ("indirect" determination). The sunspot number is actually based on the raw Wolf numbers from the Zürich station, and the main corrections were based entirely on an extended set of raw data series (adding some stations to the ones originally used by the Zürich observatory). So, the sunspot number is no less transparent: most of the series ( up to 1945) is simply the number from the Zürich observatory as fully tabulated in the Zürich Mittheilungen. The recent part after 1945, which is affected by a change in methodology, was entirely recalculated from raw data gathered in the SILSO database (NB: those same SILSO data were added to the new version of the Group number database, limited to the group counts. cf. Vaquero et al. Sol Phys 291, 2016).

Still, the sunspot number, even in its new version (V2), is still based only on Zürich data over the whole period before 1945. This dependency on a single "pilot" station is actually the main difference with the group number (a difference already present in the original Version 1!). This will change for the next version, as we are currently building a database collecting all raw data from auxiliary stations collected by the Zürich observatory and from individual Zürich observers separately. While the Zürich primary observer only used a small part of those collected data to fill the missing days at Zürich, we will now use those entire raw auxiliary series for the sunspot number determination over the whole length of the sunspot number series, just like the WDC-SILSO does routinely since 1980. Additional data series recovered recently, which were unknown to the past Zürich observers, will also be included.

This database extension is thus still in construction (manual encoding) and verification. A first step has been reached recently: all data published in printed form have been encoded. This will be the occasion of a first official release after quality control. Other sourcebooks containing a large amount of unpublished numbers were found over the past months and weeks: they will also need to be digitized and will lead to future releases and updates over the coming few years (NB: this will be presented at the next VARSITI meeting!). So, we are still in the middle of a transition that will probably take a few more years, following decades of inaction in this field: deep changes are still in preparation in terms of data and methods (but probably with smaller and/or localized changes in the future series compared with Version 2).

So, the base message for users of the sunspot (or group) number remains: the sunspot time series is no more static, but will evolve and be improved regularly in the future. Therefore, when building model and proxies, provision should be taken to update regularly the proxies to include the latest "best" version of the input sunspot series.

Best regards, Frédéric Clette (February 15, 2019)

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Received on Feb 21, 2019
from Jean Pierre Rozelot


Comments on "Solar Variability and Sunspot Indices"
Jean Pierre Rozelot

 Is it necessary to continue the production of the Wolf sunspot number, even if new indices are being created?

Yes, at least for some years more, the time to see how the new indices evolved with time in respect to the ancient ones, and to see if the discrepencies are due to construction errors or took roots elsewhere, such as in magnetic unknown (or poorly known) stratification.

  Is it justified to try to rectify the discrepancies between different indices and to develop a single time series of sunspot numbers, or do these discrepancies have physical reasons?

By looking on a sufficient time ranging (I think we need a solar cycle overlap), we will be able to disentangle the defects. Clette said that jumps are identified; I agree. But not too much with the trends, as said; solar cycles are treacherous... So i agree with the statement "the base is there and new proposed corrections try to refine further". Identyfying those corrections needed could be a subjet of discussion within the group.

 While the number of sunspots constitutes the longest solar activity record, it is not the most informative index. What additional indices can and should be maintained to estimate the variations of different solar activity manifestations (sunspot areas, sunspot group areas, others)?

From our own works (see for instance Eren et al. (2017, MNRAS), Kilcik et al. (2018, MRAS, 2018, Sol. Phys.), it is absolutely necessary to maintain indices concerning sunspot areas, sunspot group areas and their classes (A, B, ....E, F) according to the Zurich classification. Some observatories are working on that, they must be encouraged.

Sunspot number and group number series should be considered separately.

 Which observatories can and are ready to provide the continuation of the terminated Wolf number, and which observatories can and are ready to provide the maintenance of other indices? What are the requirements that such observatories must answer (long-term records, few gaps, possibility to reproduce and verify the data, others)?

That is a true question. Depending on the staff and budget in each observatories. But if WDC-SILSO plans to include the production, let's go !

I do not fully agree with Clette's answer to the statement on "the past results are not comparable anymore". I think so. In most of the cases, when taking results from the literrature, it is not possible to repeat the analysis with the new series '"by just replacing the old one by the new one". This can be done only with the data one has in hand, i.e. the work one has on his table. But cannot be done with the work from other people, unless to repeat the whole analysis made this people... Moreover, if the data used in the paper is correctly quoted (old series or new series), on can judge; but if not quoted, what can be done?

  What can VarSITI do to have the contributing observatories authorized to maintain these indices, and how to ensure the continuity of long-term time series in the current funding "climate"?

Not only for climate, but for other purposes as well. I agree with the possible role of VarSITI as mentionned by Clette in the first (october, 2018) and second points (February 2019). Thanks!

With my best regards, Jean Pierre Rozelot (February 21, 2019)

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