lrsp-2010-6
by: Kristóf Petrovay
A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle.
Prediction methods form three main groups. 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. Their implicit assumption is that 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. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time and, therefore, it lends itself to analysis and forecasting by time series methods. Finally, instead of an analysis of observational data alone, model based predictions use physically (more or less) consistent dynamo models in their attempts to predict solar activity.
In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. Nevertheless, most precursor methods overpredicted cycle 23, while some extrapolation methods may still be worth further study. Model based forecasts have not yet had a chance to prove their skills. One method that has yielded predictions consistently in the right range during the past few solar cycles is that of K. Schatten et al., whose approach is mainly based on the polar field precursor.
The incipient cycle 24 will probably mark the end of the Modern Maximum, with the Sun switching to a state of less strong activity. It will therefore be an important testbed for cycle prediction methods and, by inference, for our understanding of the solar dynamo.
Tags: Solar cycle, Solar dynamo
January 5th, 2011 at 8:51 pm
My comment is to section 1.1 of lrsp-2010-6 which reads:
“The counting system employed was changed by Wolf’s successors to count even the smallest spots, attributing a higher weight (i.e., f > 1) to spots with a penumbra, depending on their size and umbral structure.”
The counting method with the higher weight was introduced by Waldmeier in 1945 [not by Wolf's successor, Wolfer]. The change introduces an artificial jump of ~20% in 1945. The argument for this is here:
http://www.leif.org/research/AGU%20Fall%202010%20SH53B-03.pdf
January 6th, 2011 at 5:08 pm
Thank you for this most interesting link, especially for calling attention to the magnetic declination as a good proxy.
Concerning the higher weight given to certain spots, in the Introduction of his book, Waldmeier (1961) states that this has been used since 1882 and that he had not changed anything… He also says that he started his observations in 1936. However, Kopecký (1980), based on an obscure reference to Zelenka (1979), claims that some further modifications (”4th system”) were in fact introduced by Waldmeier.
While the fact that the changes in principal observer approximately coincided with the beginning and end of the “Gleissberg minimum” is certainly suspicious, perhaps one should also be open to the possibility that ratios like relative no./group no. may have changed over time due to physical reasons -e.g. spot groups being more complex and fragmented at times of higher activity.
February 9th, 2011 at 11:45 pm
I appreciate the generous review by Kristóf Petrovay towards my colleagues’ and my work on “polar field precursors” for activity predictions. I add some personal perspectives and at the end acknowledge my good luck with having generous and wise colleagues.
As far as the “polar precursor” method discussed in Section 2.2, we were not so prescient as the author attributes to us, saying: “Even before a significant amount of data had been available for statistical analysis, solely on the basis of the Babcock–Leighton scenario of the origin of the solar cycle, Schatten et al. (1978) suggested that the polar field measurements may be used to predict the amplitude of the next solar cycle.” This was not, unfortunately as completely true as I might dream. Due to Leif Svalgaard’s effervescent personality, Phil Scherrer, John Wilcox and I first learned from Leif of the remarkable work of the Ohls particularly, and then Brown and Williams who used geomagnetic precursors near solar minimum to predict the size of the next cycle. The statistics were extremely good, with correlation coefficients for many cycles near ~0.9.
This presented to us a dilemma, like a “who-done-it” in a detective story. The Earth’s geomagnetic influence was preceding the Sun’s activity, whereas we knew that energy and causality flowed outwards from the Sun. For example, geomagnetic storms follow CMEs, not the other way around. So, we deduced that the Sun’s polar fields might be the causal agent via the solar wind, which allows the Earth to generally be embedded in the Sun’s polar fields near solar minimum, and because of a direct relationship between the interplanetary field (IMF) and geomagnetic fluctuations, is highly correlated with geomagnetic activity at this time and also serves to act as a “precursor” for the upcoming solar cycle in accord with the Babcock-Leighton mechanism. This causal agent fools us into thinking that geomagnetism somehow causes the next cycle’s activity, just as the rooster crows and thinks he has made the Sun rise.
Although it has been reported that we based our predictions only on the 3 subsequent solar cycles, we did not totally trust the geomagnetician’s work because the correlations was so exceptionally high, so we developed some “solar field proxies” which we correlated with each cycle’s subsequent activity. The results from 8 solar cycles were encouraging, and we then felt comfortable making our predictions based on the Sun’s polar field.
Despite the high correlation of geomagnetic precursors we have, ever since, relied on direct solar field measurements for predictions, since geomagnetic activity is not the cause of the Sun’s future activity. Indeed, because of this I personally was not enthused when the solar prediction panel lumped geomagnetic and solar precursors together. My GSFC colleague, Dean Pesnell, pointed out that this grouping leads to a wide diversity of predictions based predominantly on geomagnetic precursors.
This current cycle, geomagnetic precursors fared particularly badly. In my opinion, this is because of the following. This cycle, the Sun’s polar fields have been so weak, that they were unable to force the polar field down towards the solar equatorial plane (close to the ecliptic plane) and so the Earth was embedded in low latitude, late #23 cycle, equatorial coronal hole fields, left-over from the last cycle’s activity rather than the weak polar fields of the upcoming cycle as usually occurs. Thus the geomagnetic precursors failed to measure the weak polar fields of the Sun adequately this last solar minimum. This has resulted in some soul searching in this arena.
Petrovay’s article also considers the value of the SODA index. This relates to the extension of the method that Dean Pesnell and I developed (using a global “SODA” index – SOlar Dynamo Amplitude index – essentially just like a can of SODA measuring the amount of “fizzy field” inside the Sun). It relates to how early one might be able to predict the next cycle. We cannot answer this question generally, however, for cycle #24, we were able to do so early. As early as 2003 (roughly 5 years before solar minimum), I gave a talk at a AAS SPD meeting asking whether “Solar Activity (is) Heading for a Maunder Minimum?” (see http://adsabs.harvard.edu/abs/2003SPD….34.0603S), and two years later, in 2005, both Leif Svalgaard and I published papers stating that solar cycle #24 would be weak. Yes, as Petrovay states, the polar field near minimum is generally flat; to me this suggests its value is not insignificant and is available before solar minimum. In any case, Dean and I tried to develop an index that would keep track of the internal solar flux leading to future activity. It is my belief that the overall method works predominantly because of “magnetic persistence,” but one needs to consider the dynamo oscillations. The general use of precursors for long-range activity forecasting, as Petrovay points out, makes this not just theoretically interesting, but useful to space agencies in the planning of space missions.
Acknowledgements: I have been fortunate to have worked with NASA GSFC, Flight Dynamics Branch with the steadfast support and leadership of Tom Stengle, throughout many cycles of solar activity predictions, in conjunction with ai-solutions, and the excellent people who have facilitated this work, Bob Sperling, Daryl Carrington, and others. As mentioned I was fortunate to work with Leif Svalgaard, with his great insights in the use of geomagnetism towards understanding solar behavior. In addition, Phil Scherrer and John Wilcox, my Berkeley thesis advisor, have both been devoted solar physicists throughout their careers. We thank Phil Scherrer, J. Todd Hoeksema and staff of WSO and Roger Ulrich, John Boyden and staff of MWO for their tireless efforts to bring us the solar field observations. Leif asked me to mention his inspiration from geomagnetic records is rooted in Julius Bartels’ work and insights. Working with Mayaud was also an important element of his outlook.
Next, many colleagues improved the work, particularly W. Dean Pesnell and Sabatino Sofia. Sabatino and I forecasted #22, as an “exceptionally large even numbered solar cycle.” This aspect went against folklore, which said that even numbered cycles were almost always lower than the preceding odd numbered cycle. Hence most predictions for cycle #22 were lower than the cycle #21 value. Our prediction of a large cycle led NASA to place the Hubble Space Telescope into an orbit as high as possible, with a greater ellipticity, to minimize drag, until it could be re-boosted. This helped save HST from an early demise, and led to starting the Withbroe, NASA supported, NOAA solar activity predictions panel, which has continued to provide an objective approach to forecast solar activity in an impartial manner with experts from the solar community working together.
My colleagues Douglas Hoyt, Guillermo Gonzalez and Jerry Orosz, helped me examine a number of aspects related to the solar activity predictions. Doug helped with understanding long term changes in solar activity and helped develop the group sunspot number. Jerry helped with the timing of the cycle, an underappreciated, and often ignored, but important aspect of solar cycle prediction. For example, we predicted this cycle, #24, would be long, and arrive late, because of Max Waldmeier’s solar cycle length- amplitude size, negative correlation. Max was an inspiring and valued colleague in my early career. I should also mention my excellent colleague, Gerard Thullier, who has used our predictions for ESA’s PICARD mission, and has been a delightful, supportive colleague. Hans Mayr greatly aided my understanding of the fluid dynamics involved in active region energetics.
I have also been privileged to work with Robert Leighton and Bob Howard, both of whom are deserving of more praise than I can say; their intelligence and generosity knew no bounds. Additionally, my career really began with the invaluable help of Norman Ness, who served as a mentor, invaluable colleague, and of course a great magnetometer experimenter measuring magnetic fields at every planet from Mercury to Neptune, plus throughout interplanetary space. Lastly I should like to thank, my wife, Sharon, who supports me as I struggle, even today, to improve my understanding of the Sun’s mysterious workings.