A significantly better correlation exists between the minimum activity level and the amplitude of the next maximum (Figure 6). The relation is linear (Brown, 1976), with a correlation coefficient of 0.72 (if the anomalous cycle 19 is ignored – Brajša et al., 2009; see also Pishkalo, 2008). The best fit is± 25.
Cameron and Schüssler (2007) point out that the activity level three years before the minimum is an even better predictor of the next maximum. Indeed, playing with the value of time shift we find that the best correlation coefficient corresponds to a time shift of 2.5 years, as shown in the right hand panel of Figure 6 (but this may depend on the particular time period considered, so we will refer to this method in Table 1 as “minimax3” for brevity). The linear regression is
As the epoch of the minimum of R cannot be known with certainty until about a year after the minimum, the practical use of these methods is rather limited: a prediction will only become available 2 – 3 years before the maximum, and even then with the rather low reliability reflected in the correlation coefficients quoted above. In addition, as convincingly demonstrated by Cameron and Schüssler (2007) in a Monte Carlo simulation, these methods do not constitute real cycle-to-cycle prediction in the physical sense: instead, they are due to a combination of the overlap of solar cycles with the Waldmeier effect. As stronger cycles are characterized by a steeper rise phase, the minimum before such cycles will take place earlier, when the activity from the previous cycle has not yet reached very low levels.
The same overlap readily explains the correlations discussed in Section 1.3.3. These relationships may also be used for solar cycle prediction purposes (e.g., Kane, 2008) but they lack robustness. For cycle 24 the correlation, as formulated by Hathaway (2010b) predicts while the methods used by Solanki et al. (2002) yield values ranging from 86 to about 110, depending on the relative weights of and . The forecast is not only sensitive to the value of n used but also to the data set (relative or group sunspot numbers) (Vaquero and Trigo, 2008).
Living Rev. Solar Phys. 7, (2010), 6
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