4.4 Cycle amplitudes

The amplitude of a cycle is another key characteristic. As we have seen in Tables 3 and 4, the actual value for the amplitude of a cycle depends upon the activity index used and the type of smoothing. These uncertainties can even change the relative amplitudes of the cycles. In Table 3 we see that the second largest cycle is cycle 21 according to the 13-month mean of the International Sunspot Numbers but with the same smoothing the second largest in sunspot area and 10.7 cm flux is cycle 22. Cycles 15 and 16 were very similar according to sunspot area but cycle 15 is significantly larger than cycle 16 according to the International Sunspot Number. The Group Sunspot Numbers do provide information on earlier cycles but show systematic differences when compared to the International Sunspot Numbers. The maxima determined by the 13-month mean with the International Sunspot Numbers and the Group Sunspot Numbers are given in Table 5.


Table 5: Cycle maxima determined by the 13-month mean with the International Sunspot Numbers and the Group Sunspot Numbers. The Group values are systematically lower than the International values prior to cycle 12.
Cycle
International Maximum
Group SSN Maximum
  Date Value Date Value
–4     1705/05 5.5
–3     1719/11 34.2
–2     1730/02 82.6
–1     1739/05 58.3
0     1750/03 70.6
1 1761/06 86.5 1761/05 71.3
2 1769/09 115.8 1769/09 106.5
3 1778/05 158.5 1779/06 79.5
4 1788/02 141.2 1787/10 90.5
5 1805/02 49.2 1805/06 24.8
6 1816/05 48.7 1816/09 31.5
7 1829/11 71.5 1829/12 64.4
8 1837/03 146.9 1837/03 116.8
9 1848/02 131.9 1848/11 93.2
10 1860/02 98.0 1860/10 85.8
11 1870/08 140.3 1870/11 99.9
12 1883/12 74.6 1884/03 68.2
13 1894/01 87.9 1894/01 96.0
14 1906/02 64.2 1906/02 64.6
15 1917/08 105.4 1917/08 111.3
16 1928/04 78.1 1928/07 81.6
17 1937/04 119.2 1937/04 125.1
18 1947/05 151.8 1947/07 145.2
19 1958/03 201.3 1958/03 186.1
20 1968/11 110.6 1970/06 109.3
21 1979/12 164.5 1979/07 154.2
22 1989/07 158.5 1991/02 153.5
23 2000/04 120.7 2001/12 123.6

These cycle maxima and their distributions are shown in Figure 23View Image. The mean amplitude of cycles 1 to 23 from the International Sunspot Numbers is 114 with a standard deviation of 40. The mean amplitude of Cycles –4 to 23 from the Group Sunspot Numbers is 90 with a standard deviation of 41.

View Image

Figure 23: The left panel shows cycle amplitudes as functions of cycle number. The filled circles show the 13-month mean maxima with the Group Sunspot Numbers while the open circles show the maxima with the International Sunspot Numbers. The right panel shows the cycle amplitude distributions (solid lines for the Group values, dotted lines for the International values). The Group amplitudes are systematically lower than the International amplitudes for cycles prior to cycle 12 and have a nearly normal distribution. The amplitudes for the International Sunspot Number are skewed toward higher values.

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