The last [SESC,NOAA] sunspot number reported was on July 20th.

REPLY: I’m going to make a separate post to clear up this confusion. – Anthony

When Schwabe discovered the sunspot cycle [and it was brought to a wider attention in von Humboldt's wildly popular 'Cosmos'] there was immense interest in this phenomenon. Rudolf Wolf in Switzerland began his own careful count in 1849 and continued until his death in 1893. He had also wrote to astronomers around the world to assist him in getting an unbroken record. He had first thought of measuring the area of all the spots, but discovered that this was impractical and too much work [especially to impose on his collaborators abroad] so settled for a simpler method. He had determined that on average a sunspot ‘group’ of related spots [born and decay as an ensemble] had about 10 spots and thought [correctly] that the group was an important physical aspect of sunspots. To reflect that he devised his famous formula: W = 10 * G + S, where G is the number of groups and S is the number of spots, giving group ten times as much weight as a spot [that is where the '10' comes from]. He also discovered that S was very sensitive to what astronomers call ‘seeing’, the constant ‘jitter’ of the image caused by movement of the heated air through which we observe the Sun. This was especially a problem for the smallest spots [the pores], that simply disappeared if the seeing was bad. His solution to this problem was to not count the smallest spots [and even count the biggest spots twice or more - getting the 'area' in through the back door, so to speak]. Hoyt and Schatten about a decade ago went so far as to suggest not counting any spots at all, and only count the groups – their famous Group sunspot number. Wolf found that his scheme worked well and that his collaborators could produce reasonable [as judged by Wolf, of course] results, and so was born the Sunspot Number – or as he wanted it called, the Wolf Number. Because it is not a ‘real’ count of spots, but a sort of index, he called it the “Relative sunspot number” [hence its designation by the letter R].

Wolf also scoured the astronomical literature and dug up all the observations that he could find and tried to re-construct the sunspot number from these old observations. This turned out to be a lot harder than he had thought because the observations were done by different people with different telescopes at sites with different seeing [Sunny Italy vs. foggy England]. Wolf worried a lot about the ‘calibration’ of his reconstructed counts. His partial solution to this problem was to introduce a ‘constant’ k [from the German word Konstant] to compensate for the differences: R = k * W. He discovered on several occasions that the numbers he had already published were incorrectly calibrated [this means that he had assigned the wrong 'k' to an observer], so the sunspot record kept changing [in 1861 where the numbers were adjusted upwards by 25%, in 1872 when the numbers before 1800 were simply doubled, in the 1880s, ...]. Wolf was well aware of the implications of just changing a series that people were already using for correlations of all sorts: the weather, the price of grain, you name it…] so these ‘adjustments’ were not much publicized; he simply publish an adjusted series without too many comments – perhaps hoping that people wouldn’t notice too much.

The reason that Wolf was confident that his adjusted and corrected ['monkeyed' with some would say] sunspot number series was an improvement over the raw counts from disparate sources, was that several people around 1845-1855 had discovered that the ‘magnetic needle’ was sensitive to variations in the sunspot number: many spots and the needle’s variations were greater. The Sun’s Far Ultraviolet radiations creates and maintains the ionosphere in which currents flow that create a magnetic field
at the surface of the Earth, adding to the Earth’s own field and changing the direction of a compass needle slightly. They did not know [yet] about the ionosphere and FUV, but the variation of the needle was discovered a long time ago by Graham in London in 1722 and was easy to measure, even with 18th [and 19th] century instruments. wolf devised another famous formula: r = a + b * W, where r was the ‘range’ of the needle’s variation during a day [typically 5-10 arc minutes], W is his Wolf number, and a and b two constants that seemed to vary a bit from station to station. Wolf also asked the observatories to keep track of ‘r’. At the end of each year when Wolf had worked up his Wolf number for the year, he would calculate [a true prediction] the value of ‘r’ for the different observatories well ahead of getting ‘r’ in the mail [no internet then!] from far-away places. He never failed to marvel at [and forcefully point out] how well his prediction worked, because it did. He was almost always right on. This gave him confidence in his adjustments.

Meanwhile, in 1875 Wolf hired an assistant, Alfred Wolfer. Wolfer disagreed with Wolf about counting of small spots and argued that all spots should be counted [no matter how small, even pores]. As long as Wolf was alive, Wolfer did not prevail [although I think he stopped counting big spots twice] and Wolf’s method carried the day. Wolfer had in secret kept two counts: using Wolf’s method and using his ‘all-spot-counted’ method, and had determined that if the all-spot number was multiplied by k = 0.6 they would fir Wolf’s number reasonably well. So, when Wolf died, Wolfer switched to the all-spot method [which is used to this day], but all counts are scaled down by the factor 0.6, in addition to whatever other factor is determined by the size of the telescope, the observer, the location, etc.

Wolfer also calculated the range of the needle [the so-called 'Declination'] using Wolf’s formula and set of constants a and b, and noted that although it had worked well for Wolf back in the 1860s, the calculated values of r began to drift and the disagreement with the observed values grew [systematically] with time. In addition, the famous and influential geophysicist Sidney Chapman did not care for ‘empirical’ adjustments and pooh-poohed the method, pointing out that the variation of a and b with location was not understood and so there were no rigorous theoretical justification for the relationship, and use of the formula was eventually abandoned by the 1920s. This means that we lost the valuable cross-check on the sunspot number that the formula had provided.

So, what was wrong with the formula? It turns out to be two things: First, the magnetic force resulting from the ionospheric current controlled by the Sun is constant [over a large range of latitudes, 15-65 degrees] at any given time [although varies width]. But he deflection of the needle from true North is the resultant of two forces: the constant solar-induced force and the Earth’s own magnetic force, and that latter varies from place to place, from a maximum at the equator to zero at the poles. so, that was one source of variation of a and b. And second, the Earth’s magnetic field is itself slowly decreasing [10% since the time of Wolf], altering one of the two forces in the vector addition that gives us the final deflection. These reason were not known [although they could have been] when the formula was abandoned. If we take these two factors into account, Wolf’s formula works again [he would have been delighted] and we can now see that Wolfer’s 0.6 adjustment was not quite right and that Max Waldmeier who took over the production of the sunspot number in Zurich in 1945 introduced a 20% error in the calibration [due to his inexperience - there is a wonderful anecdote about that his predecessor, Brunner, would not help Waldmeier to get started because as Brunner said "I'm retired and cannot be expected to work anymore"].

When Zurich stopped the sunspot number production in 1980, Brussels took over, with the usual problems of getting the calibration correct – splicing two series with no overlap. Use of the rediscovery that Wolf’s formula works again is being resisted by entrenched institutions and individuals that find it easier to adopt a ‘do nothing’ posture. We can see this in small things as well: the plot at NOAA of the predicted and observed cycle 24 values for the f10.7 flux is wrong, but ‘cannot be changed’. The adopting of 0.5 as August’s official sunspot number is still not changed even after SIDC has admitted that it may be [slightly] in error. The cycle 24 prediction panel has not updated their prediction taking into account the drawn-out minimum of SC23, and on and on.

I hope you find this story of interest. It has many human element, good and sad, as life in general. Science is also a social process.