Rudolf Wolf, one of the first observers of sunspots, noticed that different people saw different numbers of sunspots on the same day. He realized that the different counts came from using different equipment. If you look at the Sun through properly filtered low-power binoculars you might see a few large sunspots while if you looked at the same Sun with a high-power telescope you might see many more. If you look at the Sun with young eyes you might see smaller sunspots than someone with older eyes. To deal with these differences, in 1848 Rudolf Wolf developed the Wolf Sunspot Number by combining the number of individual sunspots with the number of groups of sunspots seen on the sun through a telescope with an 80 mm aperture and a magnification of 64x. He defined the Wolf Sunspot Number as RZ = k(10g + s). To generate the Wolf Sunspot Number you had to measure
- s = the number of individual sunspots
- g = the number of sunspot groups (either a set of counted spots or a fuzzy blob that may contain more than one sunspot)
- k = the observer factor (explained below)
The observer factor (k) is a number that normalizes the sunspot number observed by any person to that of Rudolf Wolf. Each observer has their own value of k, which is usually between 0.4 and 1.7. Wolf included k so that he could combine observations from observers with eyes, telescopes, and cloudiness that were not the same as his. Assigning k’s to each observer allows us to average values of RZ from several observers to get the official sunspot number. You can also use k to account for how an observer's eyes change with time.
As a rule of thumb, if you divide the Wolf number by 15, you’ll get about number of individual sunspots visible on the solar disk. (This works better at large sunspot number and does not work today.)
I see two groups on the HMI image, the group on the left is a single spot while the group on the right has maybe three. That means my estimate of the Sunspot Number is RZ = k(10 x 2 + 1 + 3) = 24 if I set k to 1. The HMI telescope has a 140 mm aperture, which is larger than Wolf's telescope, so it sees more detail or smaller spots and gives a larger Sunspot Number.
That's why we study the magnetic field!