In the most general sense, precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. The precursor may be any proxy of solar activity or other indicator of solar and interplanetary magnetism. Specifically, the precursor may also be the value of the sunspot number at a given time.
In principle, precursors might also herald the activity level at other phases of the sunspot cycle, in particular the minimum. Yet the fact that practically all the good precursors found need to be evaluated at around the time of the minimum and refer to the next maximum is not simply due to the obvious greater interest in predicting maxima than predicting minima. Correlations between minimum parameters and previous values of solar indices have been looked for, but the results were overwhelmingly negative (e.g., Tlatov, 2009). This indicates that the sunspot number series is not homogeneous and Rudolf Wolf’s instinctive choice to start new cycles with the minimum rather than the maximum in his numbering system is not arbitrary – for which even more obvious evidence is provided by the butterfly diagram. Each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles, as suggested by Wolfgang Gleissberg in the motto of this section.
In Section 1.3.2 we have seen that there is significant evidence for a long-term memory underlying solar activity. In addition to the evidence reviewed there, systematic long-term statistical trends and periods of solar activity, such as the secular and supersecular cycles (to be discussed in Section 3.2), also attest to a secular mechanism underlying solar activity variations and ensuring some degree of long-term coherence in activity indicators. However, as we noted, this long-term memory is of limited importance for cycle prediction due to the large, apparently haphazard decadal variations superimposed on it. What the precursor methods promise is just to find a system in those haphazard decadal variations – which clearly implies a different type of memory. As we already mentioned in Section 1.3.2, there is obvious evidence for an intracycle memory operating within a single cycle, so that forecasting of activity in an ongoing cycle is currently a much more successful enterprise than cycle-to-cycle forecasting. As we will see, this intracycle memory is one candidate mechanism upon which precursor techniques may be founded, via the Waldmeier effect.
The controversial issue is whether, in addition to the intracycle memory, there is also an intercycle memory at work, i.e., whether behind the apparent stochasticity of the cycle-to-cycle variations there is some predictable pattern, whether some imprint of these variations is somehow inherited from one cycle to the next, or individual cycles are essentially independent. The latter is known as the “outburst hypothesis”: consecutive cycles would then represent a series of “outbursts” of activity with stochastically fluctuating amplitudes (Halm, 1901; Waldmeier, 1935; Vitinsky, 1973; see also de Meyer, 1981 who calls this “impulse model”). Note that cycle-to-cycle predictions in the strict temporal sense may be possible even in the outburst case, as solar cycles are known to overlap. Active regions belonging to the old and new cycles may coexist for up to three years or so around sunspot minima; and high latitude ephemeral active regions oriented according to the next cycle appear as early as 2 – 3 years after the maximum (Tlatov et al., 2010 – the so-called extended solar cycle).
In any case, it is undeniable that for cycle-to-cycle predictions, which are our main concern here, the precursor approach seems to have been the relatively most successful, so its inherent basic assumption must contain an element of truth – whether its predictive skill is due to a “real” cycle-to-cycle memory (intercycle memory) or just to the overlap effect (intracycle memory).
The two precursor types that have received most attention are polar field precursors and geomagnetic precursors. A link between these two categories is forged by a third group, characterizing the interplanetary magnetic field strength or “open flux”. But before considering these approaches, we start by discussing the most obvious precursor type: the level of solar activity at some epoch before the next maximum.
Living Rev. Solar Phys. 7, (2010), 6
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