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Astron. Astrophys. 345, 1006-1010 (1999)

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3. Forcasting potential

The analysis in Sect. 2 implies that the temporal behavior of a sunspot cycle is governed by two parameters, amplitude and the starting time of the cycle. These parameters would be useful in forecasting future activity if they could be determined early in the cycle or found to vary predictably from one cycle to the next. Given a series of different values of the starting time [FORMULA] (about 300 values around the observational minimum time of a cycle) and a series of different values of the amplitude parameter a (about 3000 values around the observational maximum amplitude), for each cycle we calculate the errors of the sunspot area data and the two-parameter function values. Each set of parametric values, consisting of one value of [FORMULA] and one value of a, gives one error value, and about 900000 error values are obtained for each cycle. Then we chose the parametric values corresponding to the minimum error as the best-fit result. Fig. 3 shows determinations of the amplitude parameter a at 3-month time intervals into each cycle. The ratio of the estimated values a to its final value determined at the end of the cycle is plotted in the figure for each cycle. The value for parameter a can, in fact, be quite accurately determined with the first 4-5 years following the start of the cycle, (as the sunspot cycle progresses, the amplitude can be determined to within 10% at 4.3 years into its cycle). Fig. 4 shows determinations of the starting time parameter [FORMULA] at 3-month intervals into each cycle. The difference between the estimated values [FORMULA] and its final value determined at the end of the cycle is plotted in the figure for each cycle. The value for the starting time [FORMULA] can be well determined with the first 5-6 years following the start of the cycle, about one year longer than for the amplitude parameter, and can be determined to within [FORMULA]0.3 year at the first 4.5 years into the cycle. This suggests that fitting the behavior of the solar cycle by means of the two-parameter function during the rising phase gives a prediction of the behavior of solar activity over the remaining 5 to 10 years of the cycle. What needs emphasis is that the two parameters a and [FORMULA] are determined at the same times.

[FIGURE] Fig. 3. Determinations of the amplitude parameter a at 3-month intervals into each cycle. The ratio of the estimated values of a to its final value determined at the end of the cycle is plotted for each cycle.

[FIGURE] Fig. 4. Determinations of the starting time parameter [FORMULA] at 3-month intervals into each cycle. The difference of the estimated values of [FORMULA] and its final value determined at the end of the cycle is plotted for each cycle.

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© European Southern Observatory (ESO) 1999

Online publication: April 28, 1999
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