Indeed, at the level of a single observation by a single observer, there is inevitably a degree of subjectivity. However, as sunspots are simple well-defined features, the range of subjectivity remains limited. The rms dispersion between simultaneous daily observations by many separate observers is about 8%. Part of this dispersion is also due to random variations in local conditions (weather, seeing), indicating that the actual impact of human subjectivity is even lower.

The main source of subjectivity are: 
- the limit for the smallest sunspots: Here the subjectivity range is bounded by the existence of a sharp lower limit for the smallest sunspots, namely 2500km (~2 arcsec) corresponding to the average size of solar photospheric granules. This also limits the effect of different telescope apertures, once the aperture is larger than ~70mm. 
- how groups are split, when they are complex and densely packed on the solar disk: This factor of subjectivity only dominates during periods of high solar activity. However, its impact is limited by the fact that such complex situations involve only a small fraction (< 5 %) of all sunspot groups.

Now, the sunspot number is derived by a global statistics over many observers. The daily random disparity among observers is then behaving like a detector noise, equivalent to the noise in any measuring equipment. It is efficiently reduced by the statistrical averaging over many observers. On the other hand, the systematic bias of an observer (i.e. tendency to over/undercount, or over/under split) is included in his k personal scaling coefficient. This coefficient is determined on a monthly basis for each observer relative to the Locarno pilot station and is used to bring each station to the same scale as the entire network. What is important here is that each observer remains stable in his/her counting practice to keep his/her k coefficient as constant as possible over years.  
This global process thus largely eliminates the subjectivity of each individual observation. This is confirmed by the current comparisons with other indices obtained by modern instruments (flux measurements, automated image-based counts). They give very high linear correlations, typically above 95%.  
 

The yearly average sunspot number is now obtained by taking the average of all daily numbers for the corresponding year. The result can thus be slightly different from a simple average of the 12 monthly mean values. Indeed, the months have different lengths. 
For years before 1849 and in particular before the 19^th century, the yearly mean becomes more approximate. Indeed, when collecting past historical observations, R. Wolf had to derive monthly and yearly averages when sunspot counts were not available every day. For that period, the yearly average was then often obtained by averaging the monthly means.

Our observers, among which very faithfull ones for more than 30 years, would probably tell you that they simply enjoy sunspot observing because: 
- it is one of the best ways to have a front-row view of the changing solar activity 
- it is not highly demanding: a few minutes per day at any time of the day is just what is needed to get this global count. Some of our observers do it even at their workplace, e.g. during the lunch break. Very flexible! 
- it is cheap: no costly camera or optics. Just a small telescope, a paper screen and your eyes are all you need. So, even young beginning observers enter this activity 
- it is comfortable: no need to drag yourself out of your bed in the middle of the night!

Moreover, the main benefit that our observers will mention is to be part of a worldwide scientific data collection effort. For them, knowing that they contribute to scientific research and to our efforts to understand the fundamental mechanisms of solar magnetic activity is both exciting and personally meaningful.

In fact, few pro-am collaborations have been more fruitful than sunspot observing and this is certainly the longest of all. Imagine: walking in the footprints of Galileo, Flamsteed, Herschel, Cassini, Schröter, Schwabe, Carrington. And the story still goes on, as the sunspot number series feeds more research topics than ever (more than 100 science papers per year). Recently, the "Nature" scientific journal identified the sunspot number series as one of the longest scientific experiment ever (actually the longest of all, with more than 400 years). 
So, why not become part of it?

Anyone can become member of our world wide observing network. We have both professional observatories(~30%) and amateur astronomers (~70%), from more than 30 different countries. As our current network is rather concentrated in Europe, we are particularly happy to welcome observers from other continents and latitudes. 
There are only a few base requirements: 
- a telescope equipped for solar observing (eyepiece observations with proper solar filter or prejection on a screen) with an aperture of min. 50 mm. 
- dedication: observers are expected to provide observations on about 10 days per month on average and to be committed to observe for at least several years once they register in the network. 
- good consistency: stable observing practices, good observing skills. 

We don't impose specific technical rules regarding the observing equipment and counting method. In case of doubts, we can of course provide guidance and advices. However, we consider more important to let each observer choosing her/his preferred observing method and then naturally sticking to it (long term stability!) than to impose a common well-coded method requiring a personal adaptation of the observer. Indeed, it introduces a risk that after some time, the observers drift away from this imposed standard, spoiling the long-term stability, or that the observers become discouraged and quit because some rules prove too awkward in their local observing context.

Interested to join? In order to get your station number, be registered in our network and have access to your personal data input Web page, just send us an e-mail. We will provide you the instructions to get you started.

Other sunspot numbers, like the Boulder sunspot number or Wolf numbers provided by individual stations, are often 20 to 50% higher than the International Sunspot Number. You may thus wonder if anything is wrong with either data set. In fact, this difference is easy to understand and find its roots in the past origins of the sunpot number. 
Back in 1849, when he started producing the sunspot from his own sunspot counts, Rudolph Wolf considered essential to keep his spot counts on the same scale as all ancient telescopic observations made before him. Knowing that the crude early telescopes could only show rather large sunspots, he thus decided to deliberately ignore the smallest short-lived spots and also the internal spot structure (multiple umbrae in a large common penumbra), although he could perfectly see them with own 80mm Fraunhofer doublet-lens refractor.  
At the end of Wolf's carreer, his assistant and successor, Alfred Wolfer, considered that this elimination introduced unnecessary personal subjectivity in the resulting counts and that it was dropping very useful information. He thus started counting all sunspots that he could actually detect. Of course, his counts were systematically higher than Wolf's counts. However, he consistenly made his counts in parallel with Wolf during 17 years (1875 - 1892) until Wolf's death. 
Based on this long simulataneous series spanning more than one full solar cycle, he derived an stable average ratio between the new counts and the original Wolf counts. In order to bring the new higher counts to the Wolf scale, they had to be multiplied by a factor 0.6. 
Since that time, all modern raw sunspot counts used to produce the sunspot number have been multiplied by this constant 0.6 factor to reduce them to the scale of the original series established by Wolf before 1892. 
Therefore, before other sunspot numbers can be compared to the international sunspot number, they should be multiplied by this 0.6 factor.

The smoothed monthly number results from an averaging of monthly mean values over the 13 months, from 6 months before to 6 months after a base month. All months are weighted equal except for the extreme ones, which are weighted by 1/2. This is expressed by the formula: 
 Rs= (0.5 R_m-6 + R_m-5 + R_m-4 + R_m-3 + R_m-2 + R_m-1 + Rm + R_m+1 + R_m+2 + R_m+3 + R_m+4 + R_m+5 + 0.5 R_m+6 ) / 12 
In signal processing jargon, this would be called a "tapered box-car" smoothing function. 

This smoothing formula was introduced in the early 20^th century by the Zürich observatory, then in charge of the sunspot number production. It was probably chosen for its simplicity for manual calculations. Today, we know many other smoothing functions, often with better low-pass filtering charactristics. However, as it was used as a standard for so many decades, it remains the base reference allowing an easy comparison of various scientific analyses based on the sunspot number. 
Indeed, the smoothed series is meant for two main purposes: 
 - generating a series that reflects only the overal evolution of each solar cycle, by filtering out the fast variations (random surges and 27-day rotational modulation) 
 - defining the times of maximum and minimum for each cycle, thus providing the consistent timebase on which other series can be linked to the solar semi-regular periodicity. 
  
NB: as the symmetrical smoothing process requires 6 monthly means around each base month, the smoothed values cannot be calculated for the first and last 6 months of the series. The last smoothed number thus always lags by 6 month behind the latest monthly mean sunspot number.

Indeed, nowadays, we can observe the Sun in many different and sophisticated ways: CCD imaging, spectrocopy, space probes, radioastronomy. These techniques allow to probe our star in various quantitative ways. However, they were created only over the past few decades. Many modern instruments are also unique and have a limited lifetime (spacecrafts). Therefore, the associated data sets are limited to just one or a few solar activity cycles, i.e. a duration that is too short to study the secular variability of this cycle. 

By contrast, telescopic visual observations exist since the epoch of Galileo, more than 400 years ago. Therefore, sunspot counts and the resulting sunspot number offer the only direct record of solar activity spanning tens of 11-year solar cycles. The sunspot number series thus remains the prime reference to connect our modern observations to the distant past. As in any experiment, in order to keep results from different epochs strictly comparable, the observing technique and processing methods should not be changed. This is why this essential long-term census of sunspots is still continued visually.

By their simplicity, visual observations also bring key advantages that remain valid today and probably for some time in the future: 
- simple low-cost obsevations can always be done by many observers. This allows to obtain a robust time series, with very low chances of interruption due to e.g. the local political situation or the availability of funding. 
- moreover, the multiplicity of stations allows extensive cross-validation and calibration between many simultaneous observations, thus preventing unrecognized biases that may affect isolated observatories, whatever their level of sophistication. 
Thus, the sunspot number also brings the power of a collective endeavour !