Predicting future cycle amplitudes based on geomagnetic precursors

7.3 Predicting future cycle amplitudes based on geomagnetic precursors

One class of precursors for future cycle amplitudes that has worked well in the past uses geomagnetic activity during the preceding cycle or near the time of minimum as an indicator of the amplitude for the next cycle. These “Geomagnetic Precursors” use indices for geomagnetic activity (see Section 3.7) that extend back to 1844. Ohl (1966 ) found that the minimum level of geomagnetic activity seen in the aa index near the time of sunspot cycle minimum was a good predictor for the amplitude of the next cycle. This is illustrated in Figure 39

. The minima in aa are well defined and are well correlated with the following sunspot number maxima (r = 0.93). The ratio of max(R) to min(aa) gives

This standard deviation from the relationship is significantly smaller than that associated with the average cycle prediction. The current (declining) level of the smoothed aa index indicates a small cycle 24 – R_max(24) = 78 ± 18. One problem with this method concerns the timing of the aa index minima – they often occur well after sunspot cycle minimum and therefore do not give a much advanced prediction.

Figure 39: Ohl’s method for predicting cycle amplitudes using the minima in the smoothed aa index (panel a) as precursors for the maximum sunspot numbers of the following sunspot number maxima (panel b).

Two variations on this method circumvent the timing problem. Feynman (1982 ) noted that geomagnetic activity has two different sources – one due to solar activity (flares, CMEs, and filament eruptions) that follows the sunspot cycle and another due to recurrent high speed solar wind streams that peaks during the decline of each cycle (see Section 3.7 and Figures 18 and 19 ). She separated the two by finding the sunspot number dependence of the base level of geomagnetic activity and removing it to reveal the “interplanetary” component of geomagnetic activity. The peaks in the interplanetary component prior to sunspot cycle minimum are very good indicators for the amplitude of the following sunspot cycle as shown in Figure 40 .

Figure 40: A modification of Feynman’s method for separating geomagnetic activity into a sunspot number related component and an “Interplanetary” component (panels a and b). The maxima in aa_I prior to minimum are well correlated with the following sunspot number maxima (panel c).

Hathaway and Wilson (2006 ) used a modification of this method to predict cycle 24. At the time of that writing there was a distinct peak in aa_I in late 2003. This large peak led to a prediction of R_max(24) = 160 ± 25. While this method does give predictions prior to sunspot number minimum it is not without its problems. Different smoothings of the data give very different maxima and different methods are used to extract the sunspot number component for the data shown in Figure 39 a. Feynman (1982 ) and others chose to pass a sloping line through the two lowest points. Hathaway and Wilson (2006 ) fit a line through the 20 lowest points from 20 bins in sunspot number. These variations introduce significant uncertainty in the actual predictions.

Thompson (1993 ) also noted that some geomagnetic activity during the previous cycle served as a predictor for the amplitude of the following cycle but, instead of trying to separate the two, he simply related the geomagnetic activity (as represented by the number of days with the geomagnetic Ap index ≥ 25) during one cycle to the sum of the amplitudes of that cycle and the following cycle (Figure 41 ). Predictions for the amplitude of a sunspot cycle are available well before minimum with this method. The number of geomagnetically disturbed days during cycle 23 gives a prediction of R_max(24) = 131 ± 28. Disadvantages with this method include the fact that two cycle amplitudes are involved, the fact that longer cycle will have more disturbed days simply due to their length, and the standard errors are larger.

Figure 41: Thompson method for predicting sunspot number maxima. The number of geomagnetically disturbed days in a cycle is proportional to the sum of the maxima of that cycle and the next.

Hathaway et al. (1999 ) tested these precursor methods by backing-up in time to 1950, calibrating each precursor method using only data prior to the time, and then using each method to predict cycles 19 – 22, updating the data and recalibrating each method for each remaining cycle. The results of this test were examined for both accuracy and stability (i.e. did the relationships used in the method vary significantly from one cycle to the next). An updated (including cycle 23 and corrections to the data) version of their Table 3 is given here as Table 6. The RMS errors in the predictions show that the geomagnetic precursor methods (Ohl’s method, Feynman’s method, and Thompson’s method) consistently outperform the other tested methods. Furthermore, these geomagnetic precursor methods are also more stable. For example, as time progressed from cycle 19 to cycle 23 the Gleissberg cycle period changed from 7.5-cycles to 8.5-cycles and the mean cycle amplitude changed from 103.9 to 114.1 while the relationships between geomagnetic indicators and sunspot cycle amplitude were relatively unchanged.

Table 6: Prediction method errors for cycle 19 – 23. The three geomagnetic precursor methods (Ohl’s, Feynman’s, and Thompson’s) give the smallest errors.

Prediction Method	cycle 19	cycle 20	cycle 21	cycle 22	cycle 23	RMS
Mean Cycle	–97.4	–1.6	–55.4	–46.7	–6.9	54.4
Even–Odd	–60.1	?	–26.7	?	61.4	52.0
Maximum–Minimum	–109.7	24.9	–18.6	–8.1	5.2	51.2
Amplitude–Period	–75.3	18.4	–73.5	–25.6	15.0	49.6
Secular Trend	–96.4	14.6	–40.6	–25.4	18.9	49.3
Three Cycle Sawtooth	–96.5	14.6	–38.5	–25.4	18.8	49.0
Gleissberg Cycle	–64.8	48.0	–36.9	–31.8	–0.9	42.1
Ohl’s Method	–55.4	–5.9	2.3	–9.1	10.5	28.7
Feynman’s Method	–43.3	–22.4	–1.0	–14.8	25.9	28.6
Thompson’s Method	–17.8	8.7	–26.5	–13.6	40.5	27.0

The physics behind the geomagnetic precursors is uncertain. The geomagnetic disturbances that produce the precursor signal are primarily due to high speed solar wind streams from low latitude coronal holes late in a cycle. Schatten and Sofia (1987 ) suggested that this geomagnetic activity near the time of sunspot cycle minimum is related to the strength of the Sun’s polar magnetic field which is, in turn, related to the strength of the following maximum (see next Section 7.4 on dynamo based predictions). Cameron and Schüssler (2007 ) suggest that it is simply the overlap of the sunspot cycles and the Waldmeier Effect that leads to these precursor relationships with the next cycle’s amplitude. Wang and Sheeley Jr (2009 ) argue that Ohl’s method has closer connections to the Sun’s magnetic dipole strength and should therefore provide better predictions.