Leif Svalgaard: The Sunspot Counting Methods

Posted: August 30, 2012 by tallbloke in Astronomy, Astrophysics, Measurement, methodology, Solar physics, solar system dynamics

Reposted from a WUWT discussion as a reference:

The Sunspot Counting Methods

1) Wolf learned that Schwabe did not count ‘small spots and grey pores’. In order to be compatible with Schwabe [so Wolf could use Schwabe’s counts on days when Wolf did not make an observation], Wolf decided also not to count small spots and grey pores. This was before Wolf realized that a k-factor on the formula R = k (10G+S) was needed, and was the way to ensure compatibility.
2) Wolf did not ‘design’ a threshold in his method. He knew quite well that it was silly to throw away spots just because they were small, especially if they defined a group. But he became victim of the desire to be compatible, and when he realized a threshold was dumb it was too late.
3) Around 1875 Wolf found [from the geomagnetic data supplied by Sciaparelli] that Schwabe after all [even after that Wolf had unfortunately adopted Schwabe’s method] was counting about 25% too, and summarily increased all 1849 values [which he had published in 1861] by those 25%.

4) From the mid 1860s Wolf was traveling so much [he was by then director of the Swiss Geodetic Survey] that he stopped using the 80mm X64 telescope altogether and switched to a much smaller 37mm X20 hand-held telescope that he could take with him on travel. With this small telescope there was no longer any need to omit small spots and grey pores, because they could simply not be seen anyway, so the question of a threshold is now moot. Wolf decided by comparison with his larger [standard] telescope that he got a compatible yearly average relative number by multiplying the one derived from the small telescope by a factor of 1.5. This did not carry over to daily of monthly means, because zero times 1.5 is still zero.
5) Wolfer correctly surmised that valuable information was thrown away by omitting spots, so decided to count everything he could see. Every serious observer since then has accepted the wisdom in this. This, of course, means that a k-factor less than 1 must be applied to be compatible with Wolf’s values [after 1976]. Over a 17-yr period of both low and high solar activity Wolfer [or rather Wolf] adopted a k-factor of 0.6.
6) Later observers have simply adopted that same k-factor [as it can never be measured again].
7) Waldmeier introduced a new classification of groups, using letters A, B, …, J, which was an evolutionary sequence from A, an emerging group of small spots without penumbra and without the typical bi-polar structure, e.g. a single small spot, through B, small spots still without penumbra but with a clear bi-polar structure, to C, etc where the spots grow larger and have penumbra. A and B groups make up almost half of all groups and could not be seen with Wolf’s 37mm telescope [as we can verify today as the telescope still exists] and were presumable the ones he did not count with the 80mm [although we don’t really know what he counted]
8) Wolfer’s k-factor of 0.6 was not made by comparison with Wolf’s count on the 80mm [as it should have been], but by comparing in this way: if Wolf had a sunspot number [using the 37mm] of 100, then that was first multiplied by 1.5, yielding 150 which was then divided by Wolfer’s count of 250 to result in 150/250 = 0.6. If we break it down into groups and spots, then Wolf’s R=100 comes from typically G=8 and S=20, while Wolfer’s R=250 comes from G=15 and S=100. The difference, 7, between 8 and 15 reflects nicely that A and B groups almost half of all groups [seen by Wolfer]. The real difference between Wolf and Wolfer is that Wolfer sees 5 times as many spots as Wolf, commensurate with the fact that the modern sunspot number is made up mostly of small spots.
9) The Waldmeier weighting increases on average the number of spots, S, by 44%.
10) The Waldmeier classification increases on average the number of groups, G, by perhaps 10% [this requires a full and careful – but difficult – analysis].

  1. Hans Jelbring says:

    To me the issue of compatibility between new and old sunspot numbers is an act of nitpicking.
    Below are some viewpoints that might be of interest and a try to explain my opinion.

    What has been done is very good as a measurement of a phenomenon which causes are unknown.
    Today it has been shown that sunspot area numbers are compatible with standard sunspot numbers these are measured at a regular basis.
    The existing data sets have to be seen in relation to what problems there are to be solved and the quality of the amplitude of sunspot numbers is just a relatively minor piece of information and in my opinion it is good enough
    Some questions about the sunspot number quality are:

    – Are the causes to sunspot generation found inside the sun or outside?
    – Is the data set good enough for advanced signal processing techniques to be applicable?
    – Is the time spacing small enough for reaching getting good frequency resolution?
    – Is the data set long enough to detect long term variations?
    – Is the data set good enough to decide the structure of both amplitude and phase variations?

    The first question is what originally caught my interest and it took 15 years for me to reach a valid conclusion and answer. The answer to the second question is yes. Daily measurements are good enough seen in perspective to the normal life time of spots which normally are just a few days. It is seldom a sunspot group survives a solar rotation.
    Solar observations have not been going on long enough for making it possible to resolve relevant long term variations in sunspot activity. To solve this problem Justin Schove gathered historical records of Aurora Borealis since 600 BC in a fantastic project. Auroras are most developed before and after a sunspot maximum.
    The phase information is just as important as the amplitude information and shows the need for investigating cycles at least up to periods about 2000 years long.

  2. Doug Proctor says:

    Sunspots … the connection with the Jovian orbits. Are the processes seen as sunspots a surface expression of an internal event close to the surface that is brought to the surface by gravitational displacement of the solar-planetary centre of mass? Does the centre of mass shift cause a disruption in otherwise almost stable conditions?

    The Maunder minimum: does the cumulative energy release of sunspots and CMBs equal some consistent number that reflects a gravitationally restricted release of routine energy that must build up again to the threshold point at which sunspots start to appear?

    Is there evidence of solar expansion and contraction consistent with sunspot creation and quiescence?

  3. Gerry says:

    There have apparently been four workshops on this sofar. Number five is coming up early next month…

    Click to access Reconciliation%20of%20Group%20&%20International%20SSNs%20-%20Croatia.pdf

  4. tallbloke says:

    Hans, do you have a link for Schove’s data?

    Doug, there are several things going on with effects due to the relative motion of the Sun and the centre of mass of the solar system.

    For some unexplained reason, solar activity drops when the COM is closely incident with the solar surface for several years or more.

    The rate of change of acceleration correlates well with ups and downs in activity on the shorter timecale.

    The up/down motion in the ‘z’ axis correlates with cycle amplitudes, and also with distribution of northern and southern hemisphere spot production.

    We will start another round of posts on this stuff soon. Bart Leplae has sent us an interesting piece to kick it off with.

    Gerry: I fear the outcome of that series of meetings will have more to do with arm twisting than scientific objectivity.