5 Summary Evaluation

The performance of various forecast methods in cycles 21 – 23 was discussed by Li et al. (2001) and Kane (2001).

Precursor methods stand out with their internally consistent forecasts for these cycles which for cycles 21 and 22 proved to be correct. For cycle 23 these methods were still internally consistent in their prediction, mostly scattering in a narrow range between 150 and 170; however, the cycle amplitude proved to be considerably lower (Rmax = 121). It should be noted, however, that one precursor based prediction, that of Schatten et al. (1996Jump To The Next Citation Point) was significantly lower than the rest (138 ± 30) and within 0.6 σ of the actual value. Indeed, the method of Schatten and Sofia (1987) and Schatten et al. (1996) has consistently proven its skill in all cycles. As discussed in Section 2.2, this method is essentially based on the polar magnetic field strength as precursor. UpdateJump To The Next Update Information

Extrapolation methods as a whole have shown a much less impressive performance. Overall, the statistical distribution of maximum amplitude values predicted by “real” forecasts made using these methods (i.e., forecasts made at or before the minimum epoch) for any given cycle does not seem to significantly differ from the long term climatological average of the solar cycle quoted in Section 1.3 above (100 ± 35). It would of course be a hasty judgement to dismiss each of the widely differing individual approaches comprised in this class simply due to the poor overall performance of the group. In particular, some novel methods suggested in the last 20 years, such as SSA or neural networks have hardly had a chance to debut, so their further performance will be worth monitoring in upcoming cycles.

One group of extrapolation methods that stands apart from the rest are those based on the even–odd rule. These methods enjoyed a relatively high prestige until cycle 23, when they coherently predicted a peak amplitude around 200, i.e., ∼ 70% higher than the actual peak. This can only be qualified as a miserable failure, independently of the debate as to whether cycle 23 is truly at odds with the even–odd rule or not.

In this context it may be worth noting that the double peaked character and long duration of cycle 23 implies that its integrated amplitude (sum of annual sunspot numbers during the cycle) is much less below that of cycle 22 than the peak amplitude alone would indicate. This suggests that forecasts of the integrated amplitude (rarely attempted) could be more robust than forecasts of the peak. Nevertheless, one has to live with the fact that for most practical applications (space weather) it is the peak amplitude that matters most, so this is where the interest of forecasters is naturally focused.

Finally, model based methods are a new development that have had no occasion yet to prove their skill. As discussed above, current dynamo models do not seem to be at a stage of development where such forecasts could be attempted with any confidence, especially before the time of the minimum. (The method of Choudhuri et al., 2007Jump To The Next Citation Point, using polar fields as input near the minimum, would seem to be akin to a version of the polar field based precursor method with some extra machinery built into it.) The claimed good prediction skills of models based on data assimilation will need to be tested in future cycles and the roots of their apparent success need to be understood.

Table 1 presents a collection of forecasts for the amplitude of cycle 24, without claiming completeness. (See, e.g., Pesnell, 2008, for a more exhaustive list.) The objective was to include one or two representative forecasts from each category. Update


Table 1: A selection of forecasts for cycle 24.
Category Peak amplitude Link Reference
Precursor methods      
     Minimax 80 ± 25 Eq. 10View Equation Brown (1976); Brajša et al. (2009Jump To The Next Citation Point)*
     Minimax3 69 ± 15 Eq. 11View Equation Cameron and Schüssler (2007)*
     Polar field 75 ± 8 Sect. 2.2 Svalgaard et al. (2005)
     Polar field 80 ± 30 Sect. 2.2 Schatten (2005)
     Geomagnetic (Feynman) 150 Sect. 2.3 Hathaway and Wilson (2006)
     Geomagnetic (Ohl) 93 ± 20 Sect. 2.3 Bhatt et al. (2009)
     Geomagnetric (Ohl) 101 ± 5 Sect. 2.3 Ahluwalia and Ygbuhay (2009)
     Geomagnetic (interpl.) 97 ± 25 Sect. 2.3 Wang and Sheeley Jr (2009)
     Field reversal 94 ± 14 Eq. 12View Equation Tlatov (2009)*
Extrapolation methods      
     Linear regression 90 ± 27 Sect. 3.1 Brajša et al. (2009)
     Linear regression 110 ± 10 Sect. 3.1 Hiremath (2008)
     Spectral (MEM) 90 ± 11 Sect. 3.2 Kane (2007)
     Spectral (SSA) 117 Sect. 3.2 Loskutov et al. (2001)
     Spectral (SSA) 106 Sect. 3.2 Kuzanyan et al. (2008)
     Attractor analysis 87 Sect. 3.3.1 Kilcik et al. (2009)
     Attractor analysis 65 ± 16 Sect. 3.3.1 Aguirre et al. (2008)
     Attractor analysis 145 ± 7 Sect. 3.3.1 Crosson and Binder (2009)
     Neural network 145 Sect. 3.3.4 Maris and Oncica (2006)
     Neural network 117.5 ± 8.5 Sect. 3.3.4 Uwamahoro et al. (2009)
Model based methods      
     Explicit models 167 ± 12 Sect. 4.3 Dikpati and Gilman (2006)
     Explicit models ∼ 80 Sect. 4.3 Choudhuri et al. (2007)
     Explicit models ∼ 85 Sect. 4.3 Jiang et al. (2007)
     Truncated models ∼ 80 Sect. 4.4 Kitiashvili and Kosovichev (2008)
References marked with * are to the basic principle used in the given prediction method while the actual numerical evaluation for cycle 24 was done by the author. The application for forecast purposes does not necessarily reflect the original intention of the basic principle, as laid out in the cited publications.

The incipient cycle 24 may be a milestone for solar cycle forecasting. Current evidence indicates that we are at the end of the Modern Maximum when the Sun is about to switch to a state of less intense long term activity. The appearance of a number of novel prediction methods, in particular the model based approach, as well as the unusually large discrepancy between forecasts based on the precursor approach imply that, whichever course solar activity will take in the coming years, we have a lot to learn from the experience.


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