“It is not important to predict the future, but it is important to be prepared for it”
– Pericles, Athenian orator, statesman and general (c. 495 – 429 BC)
“It is not important to know the future, but to shape it”
– Antoine de Saint Exupéry, French writer and aviator (1900 – 1944)
which I can see can be valid in many areas of life such as sport, warfare, economics, and politics. However, it is invalid in solar-terrestrial physics. What undoubtedly does apply is:
“Prediction is very hard, especially when it is about the future”
– Niels Bohr, Danish Physicist (1885 – 1962)
But perhaps the wisest of all is a variant on Bohr’s quote:
“Never make predictions, especially about the future”
– Lawrence (‘Yogi’) Berra, American Baseball Player, coach and author, (1925 –)
Ignoring the obvious wisdom of Berra’s advice, this last section uses the knowledge outlined in the previous sections to look into the probable future of solar activity.
A great many papers have looked at predicting sunspot numbers, particularly those expected at the start of a new cycle, and the methods employed have been presented in the Living Review by Petrovay (2010). Because of the difficulty in making such sunspot number predictions for just the cycle ahead, the degree to which there is some predictability in several solar activity indices on longer timescales has not been exploited. Lockwood et al. (2011b) have used the predictability measure based on autocorrelation functions devised by Hong and Billings (1999) to show that although the predictability of sunspot numbers is indeed relatively low, it is greater over longer lags for the open solar flux and the solar modulation potential . Lockwood et al. (2011b) find that this predictability is great enough over sufficiently long lags to allow forecasting of the onset of a grand solar minimum such as the Maunder minimum.
The SEA10 reconstruction of near-Earth heliospheric field discussed in Section 10 was derived from the homogenised composite of the heliospheric modulation parameter from 10Be abundance sequences in various ice cores compiled by Steinhilber et al. (2008). Figure 36 shows the full composite in 25-year means , which covers 9300 years.
The present value of is near 600 MV, which Figure 36 reveals to be high compared to the average value for this interval. The level is shown by the horizontal orange line and intervals when exceeded this are shaded red. Lockwood (2010) and Barnard et al. (2011) use this as a threshold value to define a “Grand Solar Maxima” (GSM) as this definition means the GSM that has persisted through the space age has recently come to an end. It can be seen that such GSMs are relatively rare, indeed there are just 24 of these prior to the recent one if we adopt this definition (an average repeat period of about 390 years, but there is a large spread about this mean value as their occurrence is far from regular and these GSMs are notably more common in the second half of this composite). The times when they end (when falls back below the 600 MV level) are shown by the vertical lines. The Maunder minimum (MM) is also marked and the lowest within it is marked by the horizontal green line. It can be seen that the Maunder minimum is not the lowest in the sequence, and although they are more evenly spread than the GSMs, the minima are also more common in the second half of the interval. There are 12 grand minima that are at least as deep (in terms of the minimum within them) as the Maunder minimum (average repeat period 780 years) and 30 that are at least as deep as the Dalton Minimum (average repeat period 310 years). Abreu et al. (2008) noted that at the end of the data composite of 25-year averages (the last data point being in 1994), the Sun was still within the recent GSM but that this maximum had lasted longer than other in the past 9300 years and was currently declining, consistent with the decline commencing in 1985 noted by Lockwood (2003) and discussed in the context of global climate change by Lockwood and Fröhlich (2007). Abreu et al. (2008) concluded the GSM was likely to come to an end in the near future, a conclusion supported from the reconstructed and directly-observed open solar flux and IMF by Lockwood et al. (2009d). The discussion below shows that recent neutron monitor data reveal the recent GSM actually did end in 2001 in the 25-year means for the adopted definition.
As yet we have no predictive models of the solar dynamo that can model this time series (see the Living Review by Charbonneau, 2010) and so the only ways to use these data to predict the future remain almost exclusively empirical. Two methods have been deployed. Steinhilber and Beer (2013) have recently used two types of spectral techniques whereas Lockwood (2010) and Barnard et al. (2011) have made “analogue forecasts”. The results of these three methods are remarkably similar and lead to the same general conclusions. This section exemplifies those conclusions using analogue forecasts, which are based on studying how has behaved in the past following a situation analogous to the present day. The situation is defined to be analogous if falls to 600 MV having previously exceeded this value: further restrictions could be applied but because the recent have been so high, even this only gives 24 previous analogues in 9300 years. The times when falls back down to 600 MV (the vertical lines in Figure 36) have been “composited” (also called a “superposed-epoch” or “Chree” analysis) such that they are all at time zero in Figure 37, and the black lines show the variations around this time for the 24 previous GSMs.
Also shown in Figure 37 are 22-year running means of the annual heliospheric modulation potential reconstruction for the past century, compiled by Usoskin et al. (2002) from modern neutron monitor data, ionisation chamber records and cosmogenic isotope records (red line) and of the modulation potential from the Oulu neutron monitor counts, from a third-order polynomial fit to the red line for the interval when they overlap. The horizontal dashed line is the value of shown in Figure 36. The blue line confirms that has recently dropped below the 600 MV level and so, by this definition, the recent GSM has come to an end. In addition Figure 37 also implies that the recent decrease in solar activity (meaning the long, low minimum between cycles 23 and 24 and the weak cycle 24 thus far) has given a decline more rapid to exit a GSM than any seen in the past 9300 years.
Lockwood (2010) noted that in two cases of the 24, fell below within 40 years () and so concluded there was a chance of a Maunder-like minimum in the next 40 years. We can make estimates of the probability of any level being exceeded () into the future by counting the fraction of the composited values that exceed a certain value at each epoch time . By interpolation this can be used to predict the evolution of at a given level of probability. Lockwood et al. (2011a) and Barnard et al. (2011) used empirical regressions and theoretical relations between and 25-year means of other parameters (either observed such as and or reconstructed such as ) and then, for each, evaluated the fractional deviation of annual mean values from the 25-year means as a function of the solar cycle phase, . Hence, for a given and solar cycle phase , an annual value could be computed. Using the at a certain probability and assuming all future cycles are 11 years in duration (to prescribe ), annual values of at a given probability level could be predicted into the future. The same procedure was applied to the predicted 25-year means of other parameters. The results for the various probability levels are shown by the coloured lines in Figure 38 which also gives the past variations which are either observed (in black) or reconstructed (in mauve).
The plot shows that there is only a 5% probability that solar activity cycles will remain as large as or exceed recent cycles but that, at the other extreme, there is a 5% probability that they will fall to Maunder minimum levels within just under 40 years. The most likely scenario is between the yellow and green lines which places the next grand minimum some time after 2060. An interesting question becomes how is cycle 24 evolving in relation to these predictions? To answer that question, one first has to establish where in the cycle 24 we currently are.
This is here done using the method described by Owens et al. (2011b) who noted from the Greenwich/USAF sunspot data (Hathaway, 2010) that the variation of sunspot latitude with solar cycle phase was very similar, independent of the amplitude of the cycle. For most past cycles the mean latitude of the spots has been roughly equal in the northern and southern solar hemispheres, but a complication is that cycle 24 is proving exceptional in that the southern hemisphere is lagging considerably behind the northern (Lockwood et al., 2012). As a result, the conclusion from the northern hemisphere mean sunspot latitude is that cycle 24 has passed its peak but for the southern hemisphere is that it is imminent (as of 20 April 2013).
Figure 39 takes an independent look at the evolution of cycle 24 by analysing the solar polar magnetic fields. The timing of the polar field reversal, relative to sunspot maximum, was first observed during solar cycle 19 (SC19) by Babcock (1959) using data from the Hale Solar Laboratory (HSL) magnetograph. He noted that the average field emerging from the south solar pole reversed polarity between March and July 1957 and that in the north pole reversed in November 1958. The 12-month running mean of monthly sunspot number peaked in March 1958, midway between these two reversals. Figure 39 employs the continuous data on the solar polar field available from the Wilcox Solar Observatory (WSO). As noted by Babcock during SC19, the two poles do not reverse at exactly the same date, and the raw data are also complicated by a strong annual periodicity introduced by the annual variation in Earth’s heliographic latitude. Because of these two effects, the average polar field reversals are most readily seen by taking the difference between the north and south fields, . In order to give the variations of this difference the same appearance in each cycle, thereby allowing easy comparisons, the upper panel of Figure 39 shows multiplied by , where for odd-numbered cycles and for even ones: the variation of with solar cycle phase, (determined using the average of the absolute values of the northern and southern mean sunspot latitudes), is plotted in the top panel for the WSO measurements, which are made every 10 days. The area shaded gray is between the earliest (lowest ) reversal which was seen during cycle 23 (green line) and the latest possible reversal date which was the brief return to during cycle 22 (blue line). (However, notice that the best estimate of the reversal for cycle 22 was at considerably lower ). The lower panel shows and where and are the northern and southern polar field variations after they have been passed through a 20 nHz low-pass filter to smooth them and remove the annual variation. The vertical lines give the phases of the corresponding cycle peaks in 12-point running means of monthly sunspot numbers. Red, blue, and green are used to denote cycles SC21, SC22, and SC23 and black is for SC24. The Figure shows that the polar fields during SC24 thus far have been weaker than they were in the corresponding phase of the previous three cycles. It is noticeable that for the odd-numbered cycles the reversal of the poles is within roughly a month of the smoothed sunspot number peak. However, for the even-numbered cycles the polarity reversal took place considerably after the cycle peak.
Note that the predictions made by Steinhilber and Beer (2013), Lockwood (2010) and Barnard et al. (2011) are probabilistic rather than deterministic (or categorical) in nature. Many areas of geophysics, including weather and flood forecasting (Krzysztofowicz, 1998; Bartholmes et al., 2009), have concluded that probabilistic forecasting is more powerful in decision-making, that they are usually scientifically more honest, and that for applications they enable risk-based assessments. Tests of forecast skill have been developed but probabilistic forecasts are not yet in widespread use in solar, heliospheric, and solar-terrestrial science which has remained more deterministic in approach. Their increasing use would be a natural part of the development of solar-terrestrial physics into applications-based “space weather”.
Figure 40, like Figure 39, will be updated as the cycle progresses. Panels (a), (c), and (d) show monthly means (in grey) and 12-month running means (in black) of the international sunspot number , the Oulu neutron monitor cosmic ray counts , and the observed IMF , respectively. These are compared to the predictions shown in Figure 38, presented using the same colour scheme to give the probability of the parameter being lower than the value shown. Panel (b) shows the evolution of the mean sunspot latitude in the northern (in blue) and southern (in red) hemispheres. The current date is shown by the vertical black dashed line (after which the dashed lines show linear extrapolations based on the prior data for cycle 24). The circles on each line mark the latitudes when peak sunspot area in that hemisphere was observed during previous cycles.
At present, all the data shown in Figure 40 (sunspot number, , Oulu neutron monitor cosmic ray flux, , and near-Earth IMF are following the predicted blue lines. These are for low (5 – 10%) , , and values. Thus, the decline in solar activity is very much at the more rapid end of the range predicted from the analogue forecasts, which is consistent with an earlier onset of the next grand minimum. However, it must be stressed there is no dynamo science in these analogue forecasts and without a full understanding of the physics of the long-term changes described in this review, we can have no confidence that an observed trend will continue.
All the indicators are that cycle 24 is close to, or has past, its peak. The northern polar field has flipped and the northern hemisphere spots have migrated equatorward to a latitude below that for sunspot maximum in all but 3 of the 12 cycles for which we have data on spot latitudes. In the southern hemisphere the polar field flip appears imminent, but has yet to occur and the spots have migrated equatorward to a latitude below that for sunspot maximum in 6 of the 12 cycles. Thus, from average sunspot latitudes, the northern solar hemisphere indicates a probability of 75% that the sunspot maximum of cycle 24 has already occurred at this date and the southern hemisphere gives a probability of 50%.
Figure 41 is an updated version of Figure 39 and the upper panel shows a significant development in that the polarity the difference between the northern and southern solar polar fields has reversed. If this is the final reversal (it did flip briefly earlier in the cycle) it means that is at a slightly greater phase of the cycle than we have seen before, but is only slightly later than during cycle 22. The filtered data in the bottom panel (that are effectively extrapolations for the most recent data) indicate that although the northern polar field has flipped, the southern has still yet to do so.
The corresponding update to Figure 40 is shown in Figure 42. Part (a) shows that in the period since the previous update, the monthly sunspot number has shown an increase but the 12-month running means are still considerably below the 95-percentile prediction (blue line). Similarly, part (d) shows that the IMF also remains well below this line in 12-month running means. Part (c) shows that there have been some Forbush decreases that have lowered the monthly mean cosmic ray count (mirroring the rise in ) but the 12-month running mean remains between the 90 and 95 percentiles. The average sunspot latitudes have decreased such that for the northern hemisphere only 1 of the 12 previous cycles has a lower average latitude at cycle maximum and the corresponding number for the southern hemisphere has fallen to 5. Thus, the average sunspot latitudes in the northern and southern hemispheres give probabilities of 92% and 58% that solar maximum has already been reached by this date.