### 3.1 Sunspot numbers

The International Sunspot Number is the key indicator of solar activity. This is not because everyone
agrees that it is the best indicator but rather because of the length of the available record. Traditionally,
sunspot numbers are given as daily numbers, monthly averages, yearly averages, and smoothed numbers.
The standard smoothing is a 13-month running mean centered on the month in question and using half
weights for the months at the start and end. Solar cycle maxima and minima are usually given in terms of
these smoothed numbers.
Additional sunspot numbers do exist. The Boulder Sunspot Number is derived from the daily Solar
Region Summary produced by the US Air Force and National Oceanic and Atmospheric Administration
(USAF/NOAA) from sunspot drawings obtained from the Solar Optical Observing Network (SOON) sites
since 1977. These summaries identify each sunspot group and list the number of spots in each group. The
Boulder Sunspot Number is then obtained using Equation (1) with k = 1.0. This Boulder Sunspot Number
is typically about 55% larger than the International Sunspot Number (corresponding to a correction factor
k = 0.65) but is available promptly on a daily basis while the International Sunspot Number is posted
monthly. The relationship between the smoothed Boulder and International Sunspot Number is shown in
Figure 3.

A third sunspot number estimate is provided by the American Association of Variable Star Observers
(AAVSO) and is usually referred to as the American Sunspot Number. These numbers are available from
1944 to the present. While the American Number occasionally deviates systematically from the
International Number for years at a time it is usually kept closer to the International Number than the
Boulder Number through its use of correction factors. (The American Number is typically about 3% lower
than the International Number.) The relationship between the American and International Sunspot number
is shown in Figure 4.

A fourth sunspot number is the Group Sunspot Number, R_{G}, devised by Hoyt and Schatten (1998).
This index counts only the number of sunspot groups, averages together the observations from multiple
observers (rather than using the primary/secondary/tertiary observer system) and normalizes the numbers
to the International Sunspot Numbers using

where N is the number of observers, k_{i} is the i-th observer’s correction factor, G_{i} is the number of sunspot
groups observed by observer i, and 12.08 normalizes the number to the International Sunspot Number.
Hathaway et al. (2002) found that the Group Sunspot Number follows the International Number fairly
closely but not to the extent that it should supplant the International Number. In fact, the Group Sunspot
Numbers are not readily available after 1995. The primary utility of the Group Sunspot number is in
extending the sunspot number observations back to the earliest telescopic observations in 1610. The
relationship between the Group and International Sunspot number is shown in Figure 5 for the period 1874
to 1995. For this period the numbers agree quite well with the Group Number being about 1% higher than
the International Number. For earlier dates the Group Number is a significant 24% lower than the
International Number.
These sunspot numbers are available from NOAA. The International Number can be obtained monthly
directly from SIDC.