7.1 Predicting an ongoing cycle

One popular and often used method for predicting solar activity was first described by McNish and Lincoln (1949). As a cycle progresses the smoothed monthly sunspot numbers are compared to the average cycle for the same number of months since minimum. The difference between the two is used to project future differences between predicted and mean cycle. The McNish–Lincoln regression technique originally used yearly values and only projected one year into the future. Later improvements to the technique use monthly values and use an auto-regression to predict the remainder of the cycle.

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, 1938Elling and Schwentek, 1992Hathaway et al., 1994Jump To The Next Citation Point). The two-parameter function of Hathaway et al. (1994) (Equation (6View Equation)) 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 38View Image. 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.

View Image

Figure 38: Predictions for cycles 22 and 23 using the Modified McNish–Lincoln (M-M-L) auto-regression technique and the Hathaway, Wilson, and Reichmann (H-W-R) curve-fitting technique 24 months after the minima for each cycle.

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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