How come there are data with values between 0 and 11?

  • Posted on: 18 June 2018
  • By: Admin

Since July 2015, there are sunspot number values between 0 and 11, although by definition the minimum non-null Wolf number is 11 ( 1 group = 10 + 1 spot = 1 , making a grand total of 11). How come there are data with values between 0 and 11? 

While the Wolf number is defined for a single observer, the actual calculation of the sunspot number involves a mean over many observers. By low activity, this thus often produces values between 0 and 11. By tradition during many decades, in order to simulate a single observer, such values were simply set to either 0 or 11 in a very last step, after the calculation. This final manipulation is rather artificial, and brings several adverse consequences:
- Part of the information is lost: the fact that the solitary spot was so marginally small that it does not qualify statistically as a 100% spot, or that the spot was so short-lived that it did not appear during the full 24H UT time bin over which the daily sunspot number is calculated.
- this lack of proportionality in the low end leads to a non-linear relation between the sunspot number and other modern solar indices (sunspot area, total magnetic flux, F10.7cm radio flux, etc.) in the low range, while it is highly linear for larger values.
- When using the series as input data other scientific analyses, the number includes a big jump just above 0 instead of a continuous range of values. So, this leads to weird non-standard statistical artifacts, making the use of the sunspot number mathematically difficult.
- On average in the past, it led to a systematic overestimate of solar activity near solar cycle minima. (In most cases, when the mean result was non-null, it was mapped to 11, the first possible positive value obeying the rule, thus producing an inflation.)

Since the re-calibration of the sunspot number in 2015, we decided to get rid of this rule. You should also note that this was never considered as an absolute rule, as R.Wolf himself produced average numbers between 0 and 11 in the last part of his career, between 1878 and 1893 (you can observe it already in the original Version 1 of the daily series). It was thus just adopted as a practice in the Zürich time (1893-1980), when >80% of daily values were simple taken as the Wolf number of the Zürich observer alone.

So, you should get used to see such intermediate 0-11 values in the future. Simply take them as an indication that over a 24h time period, a sunspot definitely existed but was not equivalent to a 100% effective/observable sunspot, thus only giving a fraction of 11.