### 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, 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, t_{0}, 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.