One problem with the modified McNish–Lincoln technique is that it does not account for systematic changes in the shape of the cycle with cycle amplitude (i.e. the Waldmeier Effect, Section 4.6). Another problem with the McNish–Lincoln method is its sensitivity to choices for the date of cycle minimum. Both the systematic changes in shape and the sensitivity to cycle minimum choice can be accounted for with techniques that fit the monthly data to parametric curves (e.g. Stewart and Panofsky, 1938; Elling and Schwentek, 1992; Hathaway et al., 1994). The two-parameter function of Hathaway et al. (1994) (Equation (6)) closely mimics the changing shape of the sunspot cycle. Prediction requires fitting the data to the function with a best fit for an initial starting time, t0, and amplitude, A.
Both the Modified McNish–Lincoln and the curve-fitting techniques work nicely once a sunspot cycle is well under way. The critical point seems to be 2 – 3 years after minimum near the time of the inflection point on the rise to maximum. Predictions for cycles 22 and 23 using the Modified McNish–Lincoln and the Hathaway, Wilson, and Reichmann curve-fitting techniques 24 months after minimum are shown in Figure 38. Since cycle 23 had an amplitude very close to the average of cycles 10 – 22, both of these predictions are very similar. Distinct differences are seen for larger or smaller cycles and when different dates are taken for minimum with the McNish–Lincoln method.
Predicting the size and timing of a cycle prior to its start (or even during the first year or two of the cycle) requires methods other than auto-regression or curve-fitting. There is a long, and growing, list of measured quantities that can and have been used to predict future cycle amplitudes. Prediction methods range from simple climatological means to physics-based dynamos with assimilated data.
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