Solar activity prediction: Timing predictors and cycle 24

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A11, 1377, doi: /2002ja009404, 2002 Correction published 7 March 2003 Solar activity prediction: Timing predictors and cycle 24 Kenneth Schatten a.i. solutions, Inc., Lanham, Maryland, USA Received 22 March 2002; revised 22 May 2002; accepted 31 May 2002; published 16 November [1] Solar activity forecasting uses numerous methods. Some methods employed are purely numerological, whereas others utilize readily available, well-established mathematical techniques. There often is, however, no physical basis for some of these methods. Within this arena, however, there is a small subset, called precursors, which does have a physical basis. We briefly describe the physical basis of these methods and relate them to solar dynamo physics. Further, we develop techniques to reduce one major source of uncertainty or error in these solar activity predictions. This uncertainty is in the timing of the solar cycle. The importance of solar activity timing is apparent when one considers that past solar cycles have periods varying from 8 to 17 years. This makes the timing of the solar cycle only second in importance in solar activity prediction to obtaining the amplitude of any cycle. Two solar phenomena are utilized to obtain a time mark for each solar cycle. These are the polar field reversal and the march of activity centers towards the equator. This latter phenomenon is often referred to as the butterfly diagram. These timings essentially provide a phasing of the cycle. With this, we provide a preliminary prospective on solar cycle 24. INDEX TERMS: 7536 Solar Physics, Astrophysics, and Astronomy: Solar activity cycle (2162); 7524 Solar Physics, Astrophysics, and Astronomy: Magnetic fields; 7534 Solar Physics, Astrophysics, and Astronomy: Radio emissions; 2162 Interplanetary Physics: Solar cycle variations (7536); KEYWORDS: solar activity, solar forecasting, solar cycle, sunspot number, geomagnetic activity, solar radio flux Citation: Schatten, K., Solar activity prediction: Timing predictors and cycle 24, J. Geophys. Res., 107(A11), 1377, doi: / 2002JA009404, Introduction [2] Solar activity forecasting began with purely numerical methods. These methods have some value for short time periods. As an example, one of the better-known techniques is the Lincoln-McNish method. Basically, the method uses a form of curve fitting to existing data and then the prediction provides a regression towards the mean. This works reasonably well for short periods (1 year), which their inventors prescribed for its use. Other numerical schemes, such as Fourier analysis, sound solid, because the technique does have a sound mathematical basis. Nevertheless, having a sound mathematical basis does not imply any scientific or physical basis exists for its use in forecasting in a particular physical regime. [3] Continuing our example, Fourier analysis is not used in conventional weather forecasting on short timescales, since the coefficients of a Fourier analysis are as dependent upon the input data that occurred in the distant past as on the data which occurred more recently. With weather processes, however, as with many other phenomena, where a degree of persistence occurs, distant past data become less important than recent data. [4] Considering then the Fourier series, although it is mathematically sound, to analyze or decompose any numerical series as a Fourier sum, there is no particular Copyright 2002 by the American Geophysical Union /02/2002JA reason why any physical data set needs to be continued with the same (or a similar) Fourier series or with any other mathematical data decomposition. The Fourier series might be applicable if one showed that for example, one were analyzing the air pressure in a musical instrument, which would allow particular modes to be excited. Nevertheless, the systems we are considering are more complex than a musical instrument. In these systems, a strict Fourier analysis has the obvious flaw that the coefficients are as dependent upon the data in the distant past (say 1000 years ago, if the data were available) as on recent data. In solar phenomena, where the convection zone is deep, however, the distant past may be very long indeed, making older events still significant but ever more subtle to detect [see Kurths and Ruzmaikin, 1990]. [5] In weather forecasting what must be done to predict a data series is to obtain the physical basis for the phenomenon and determine what leads to future information about changes in the phenomenon. For weather forecasting this would require, for a particular region, examining the motion of high and low pressure regions to see how the meteorological conditions change. Considering solar activity forecasting, one needs to understand what leads to the eruption of future active regions and to predict the extent that their eruption will be more or less active. [6] The precursor techniques of Ohl [1966], Ohl and Ohl [1979], and Brown and Williams [1969] found correlations of geophysical phenomena with levels of future solar activity. As far as geomagnetic precursors, one of the first to SSH 15-1

2 SSH 15-2 SCHATTEN: SOLAR ACTIVITY PREDICTION Figure 1. (a) The start of a solar cycle begins with a polar field; (b and c) the field is stretched into a toroidal field by differential rotation; (d) the stretched subsurface toroidal field erupts owing to buoyancy; (e) it forms a bipolar active region in the photosphere, and the tilt of the regions reverses the polar field; (f ) the cycle starts with a reversed sign. Now, implicit in this mechanism is that the amplification of future field (the solar cycle) depends upon the amplification of existing field (the polar field). point out the significance of the Aa index in tracking longterm solar activity was Feynman [e.g., see Feynman and Gu, 1986]. Feynman separated the geomagnetic Aa index into two components: one in phase with sunspot number and one out of phase. This effectively led to active and quiet components. She found that the quiet signal tracked the sunspot numbers several years in advance, similar to Ohl s [1966] and Ohl and Ohl s [1979] results. The maximum in the quiet geomagnetic signal occurred at sunspot minimum and is proportional to the sunspot number during the following maximum. Many others further improved upon the geomagnetic precursor methods; one of the most successful has been Thompson [1993], however, how this terrestrial signal propagated from the Earth back to the Sun or why the Sun s future activity should be present in the geomagnetic indices was not clear. [7] The physical explanation for how these methods worked was suggested by Schatten et al. [1978]. To test the methods, Schatten et al. developed the solar precursor technique, which used information about the Sun s polar field as a precursor to future levels of solar activity. This view also helped explain how precursors worked, in general. The success of these methods was supported by NASA s use [see Joselyn et al., 1997] of precursor techniques to provide information on solar predictions for the last three cycles. A more recent reference reviewing much of the prediction field is by Hathaway et al. [1999]. [8] IntheSchatten et al. [1978] view the Sun s polar field served as a predictor of solar activity on the basis of dynamo physics. They utilized the Babcock view for understanding. This view is somewhat simplified since the Sun does not have its poloidal field directly aligned with its rotation axis [see Stix, 1976; Ruzmaikin and Feynman, 2001]. Figure 1, showing the Babcock solar dynamo, may be used to illustrate the precursor method. In Figure 1a the start of a solar cycle begins with a polar field; in Figures 1b and 1c the field is stretched into a toroidal geometry by differential rotation; in Figure 1d the stretched subsurface toroidal field erupts owing to magnetic buoyancy; in Figure 1e the magnetic field forms a bipolar active region in the photosphere. In Figure 1e the tilt of the regions and diffusion of the field to the poles reverses the polar field; in Figure 1f the cycle starts again but now with a reversed sign. Now, implicit in this mechanism is that the amplification of future magnetic field (future solar cycles) depends upon the amplification of existing field (the Sun s polar field), thus B / B i or R Z = CB p, showing that the activity level, R Z, of a future cycle depends on the polar field, B p,at the start of that solar cycle.

3 SCHATTEN: SOLAR ACTIVITY PREDICTION SSH 15-3 [9] Why then do the geomagnetic precursors work? This requires us to understand how the Sun broadcasts its future activity level to the Earth. Given that the polar field at solar minimum serves as a precursor for future solar activity, let us see how this field can affect the Earth s environment. If we examine the coronal structure near solar minimum, we see that this polar field sweeps from high latitudes to low in interplanetary space. In sweeping past the Earth the interplanetary field influences geomagnetic activity through the reconnection process. There is a fairly good correlation between geomagnetic activity and the interplanetary magnetic field and hence with the Sun s polar field. Thus the geomagnetic activity indices become a precursor of future solar activity. This provides an explanation of the geomagneticians findings. [10] Before turning to the remainder of the paper in which we discuss solar activity cycle timing, let us examine how this cycle s solar precursor prediction has turned out. 2. Solar Activity Prediction [11] To move the solar activity predictions into a more physical regime, Schatten and Pesnell [1993] attempted to glimpse the amount of buried magnetic flux within the solar interior during any phase of the solar cycle. A Solar Dynamo Amplitude (SODA) index provided a measure of the Sun s buried magnetic flux. Its form was initially written as. ( F10:7ðÞ 60 t 2 SODAðÞ¼60 t þ 146 þ B ) polarðþ t 2 1=2 : Moving more towards physical observables, the amount of buried solar flux may written as SODAðÞ¼F t B toroidal ðþ; t B polar ðþ t ¼ C 1 þ 2þ 2g C 2 B toroidal ðþ t C3 B polar ðþ t 1=2 ; where the two field components of the Sun s field vary roughly sinusoidally but out of phase with the solar cycle. By choosing the constants C 2 and C 3 correctly, it is possible to have the bracketed term resemble the form {sin 2 (t) + cos 2 (t)} 1/2, which by its nature would be constant if these terms were ideal and the Sun s dynamo had no secular changes. Since we are dealing with the solar dynamo and not mathematically ideal sines and cosines, higher-order dynamo harmonics occur, and there would be temporal variations, etc. Ruzmaikin and Feynman [2001] note differences in this ideal sine-cosine explanation provided here. [12] Using the SODA index, Schatten et al. [1996] predicted a smoothed sunspot number of 138 ± 30 and F10.7 values of 182 ± 30. These values, along with past cycles predictions [see Schatten et al., 1978, 1996; Schatten and Orosz, 1990; Sofia et al., 1998], are shown in Figure 2. The detailed values predicted are simply obtained by using the SODA index to directly obtain F10.7 from the latest smoothed values of the SODA index (180 SODA is 180 F10.7), as the SODA index is in radio flux units. The radio flux units are then converted to sunspot numbers using an approximate linear relationship based on correlation, Figure 2. F10.7 Radio Flux for the past 50 years and previously published Schatten et al. [1978, 1996] predictions for the last three cycles are shown. We note that cycle 23, the present cycle, seems to be a better fit to the predicted values both in timing and amplitude than previous cycles. Although this may be fortuitous, it may also be a sign that our skill level is increasing. The recent increase in solar activity illustrates that cycle amplitude has structure on short time scales, making smooth functions a somewhat simplistic description of the real Sun. outlined by Layden et al. [1991]. The observations seem to follow the predictions very well. Additionally, this cycle refutes the Odd/Even hypothesis wherein odd-numbered solar cycles have been historically larger than the preceding even-numbered ones. This SODA prediction is somewhat smaller than the NOAA panel estimate cited by Joselyn et al. [1997]. F10.7 Radio Flux for the past 50 years and previously published Schatten et al. predictions for the last three cycles are shown. We note that cycle 23, the present cycle, seems to be a better fit to the predicted values, both in timing and amplitude, than previous cycles. Although this may be fortuitous, it may also be a sign that our skill level is increasing. 3. Solar Activity Forecast: Timing/Phasing [13] Many solar activity forecasts have phase uncertainties of ±1 year because of the timing uncertainty of solar minima. Namely, even if we could determine the amplitude of the next cycle, we may not be able to tell you precisely when it will occur! If one were to project a typical 11-year solar activity forecast curve and, while keeping its amplitude constant, shift its maximum phase by ±1 year, one would find significant variations in the predicted amplitude during various phases. These changes are largest where the slope is largest, during the rising portion of the cycle, and are of the order of 25%, since the cycle rises in only a few years. Near solar maximum they are nearer 12%, still a considerable value. Thus we seek to determine the timing of future solar cycles more precisely than by using traditional timing markers. Harvey and White [1999] consider how well solar minimum may be determined through a synthesis of time series of the activity indicators. They

4 SSH 15-4 SCHATTEN: SOLAR ACTIVITY PREDICTION Figure 3. The absolute value of the latitude of active regions for the past two solar activity cycles is shown. This encompasses the Spoerer butterfly diagram. Additionally, the overlying white line provides a 100-point moving average of these sunspot latitudes. This allows the average latitude to be better viewed with decreased scatter. concluded that sunspot number alone was insufficient to determine solar minimum. Additionally, solar minimum was not an exact date. With solar activity levels changing from minimum to maximum phase in 2 3 years a 1-year phase uncertainty can represent a very considerable amplitude uncertainty! Note that the phase uncertainty is much more important than an equal period uncertainty! If solar minimum is off by a year, solar maximum is off by a year. If, however, the phasing is correct but the period is off by a year, then since solar maximum is only 1/3 of the cycle length into the cycle, the time would be off only a third of a year. Let us consider how the general timing uncertainty of the broad solar activity shape may be reduced. [14] We see that the traditional phasing of solar cycles using sunspot minimum may not be good enough for solar activity prediction. Additionally, Harvey and White [1999] find that solar minimum is a broad phase of the solar cycle and not a precise date. This does not directly ease the task of determining a phasing to base future predictions upon, even if the amplitude of future solar activity were known. Considering many of the solar index curves Harvey and White [1999] present as representative of various altitudes within the solar atmosphere, using global measures of coronal and chromospheric observations, determining the minimum of these rather noisy activity curves, they still do not provide a good index for the dynamo minimum. The bottom of these curves have many local minima which do not agree with each other, and any particular one chosen is based upon the vagaries of their fluctuations. We support Harvey and White s conclusion that solar minimum is a rather a broad minimum, from which it is difficult to extract a rather accurate date to time solar activity from. [15] Thus, consistent with Harvey and White [1999], rather than choosing information from the broad minimum values near solar minimum to phase the timing of the solar cycle, we have moved to examine other aspects of the solar cycle which have the hope of being more sharply defined and also are timed to the developmental phase of the solar cycle. Note additionally that we do not wish to develop a timing method based upon Fourier analysis of solar indices, as that would cause a complaint of the type we first versed in the introduction, namely that it was as dependent upon past data as upon recent data. Thus we have examined the following temporal markers for the cycle s timing: (1) the equatorward march of active regions in accord with the butterfly diagram, and (2) the reversal of the Sun s polar fields. We now employ timing aspects related to these two phenomena.

5 SCHATTEN: SOLAR ACTIVITY PREDICTION SSH 15-5 Figure 4. The Solar Dynamo Amplitude (SODA) index is a composite index attempting to combine the changing toroidal and poloidal fields of the Sun. As these fields vary with time, the combined SODA index allows us to monitor the buried magnetic flux present in the Sun s ever-changing dynamo. [16] Figure 3 shows the equatorward march of active regions as the solar cycles progress. Additionally, in white, covering the raw data is a trendline based upon a least squares fit to a moving average. Examining the trendline, we can choose or set a phase based upon this smoothed line. We refer to the time when the smoothed trendline crosses 16 as the Butterfly Maximum of a cycle, since this corresponds to the conventional (Zurich sunspot) maximum. It is, however, based upon the location of active regions, as well as their eruption. Hence it involves more data associated with events caused by cycle phenomena deep within the Sun s interior. Similarly, a Butterfly Minimum can be determined by, for example, the reversal of active regions toward the equator towards new spots appearing at high latitudes. Since the Butterfly Maximum involves data from more regions (although it occurs later), this timing may be more reliable. [17] The trendline in Figure 3 shows the latitudes rising to 27 in 1988 then decreasing rapidly, at a few degrees per year. It crosses the 16 line in mid 1990, then decreases more slowly with slopes near 2 per year towards a minimum in early During this phase, new active regions appear at high latitude. Hence we may call this the start or Butterfly Minimum between cycles 22 and 23. The cycle behavior repeats, and cycle 23 s trendline crosses 16 latitude in mid It now has reached 13 latitude, suggesting we are now just passing maximum phase and entering the declining phase of cycle 23. This data provides a cycle duration of roughly 10 years, significantly shorter than the average 11-year interval over the past 3 centuries. This behavior of large cycles as we have had the last half of the 20th century and short duration cycles goes along with Waldmeier s inverse relation of cycle length versus size [see Waldmeier, 1955, 1968]. Let us now examine the polar field data to ascertain what this data implies about the progress of solar cycle 23. [18] The polar field data has been obtained from the WSO [P. Scherrer, Wilcox Solar Observatory Polar Field strengths, 3 0 aperture, 20 nhz low pass filter, private communication, 2001; Hoeksema et al., 2001]. We have examined the daily data (Big Bear and NSO), as well as the 20 nhz low bandpass filtered data from WSO, used to remove the yearly projection effects. Although a somewhat tighter definition can be obtained by examining the raw data, the low bandpass filtered data shows the same general behavior and provides a single dipole moment value for the Sun, as opposed to two separate values for each hemisphere. This allows us to define a Polar Field Reversal Maximum as the reversal of the low bandpass filtered polar field data. Briefly, although detailed examination shows the polar fields reverse at different times, the polar field reversal maximum occurred for this and the last two cycles near 2/5/ 2000 ±3 months, 1/28/1990 ±3 months, and 1/21/1980 ±3 months.

6 SSH 15-6 SCHATTEN: SOLAR ACTIVITY PREDICTION [22] Figure 4 displays the toroidal and poloidal field proxy data. On the basis of the current data we obtain a value for the next cycle s peak coronal activity index (a proxy for F10.7) to be near 175 ± 50. This corresponds to a smoothed sunspot number near 120 ± 40. With the new timing of roughly a decade ±3 months, rather than 11 years, we expect cycle 24 to peak in April 2011, rather than Figure 5 provides a graph of the future levels of activity (for F10.7) based upon these results. Figure 5. Predicted coronal activity levels (F10.7 proxy, preliminary) for solar cycle 24. [19] Although we state the exact dates, this is just as the date as tabulated. We recognize that the actual reversal, even if it could be globally defined, would have a timing uncertainty on the order of months, since the data cannot be measured over the Sun from the same angle but once a year! Thus we have provided uncertainties of ±3 months. These cycle reversals have occurred about a decade apart. Additionally, since the polar field is an integral part of the solar dynamo, with the fields originating deep within the Sun, it seems to be a more deeply seated part of the cycle as opposed to the equatorward march of the active regions. Comparisons with sunspot minimum allow us to choose a Polar Field Reversal Minimum as the maximum time minus 4 years, with the rise time then being 4 years. This minimum time is somewhat earlier than the standard minimum time; however, in our phasing we start the cycle when the first, early harbingers of new cycle activity begin, as opposed to a few months later when the new cycle activity surpasses the remnants of the old activity. [20] Both new cycle timing methods give similar results, just a few months apart, and since the 16 latitude is only a marker, its precise timing is somewhat arbitrary, making only relative timings particularly useful. To summarize, we have found two new methods for timing the phase of the solar cycle. They both yield phasing results with modern periods of roughly a decade (±3 months), which seems consistent with Waldmeier s observations of larger cycles having shorter durations. Let us now examine the SODA (Solar Dynamo Amplitude) index [Schatten et al., 1996] to obtain a measure of how active the next cycle s activity is expected to be. 4. An Early Prospective on Cycle 24 [21] Let us consider the amplitude of the next solar cycle. The SODA index [Schatten et al., 1996, 1993] provides a measure of the strength of the magnetic fields within the Sun. It uses field data and proxies to ascertain the poloidal and toroidal field strength. Since the magnetic field oscillates between these two components as the cycle progresses, one must combine the two sets to obtain a measure of the cycle s strength independent of the normal field oscillations occurring. 5. Conclusions [23] Currently, solar cycle 23 seems to have reversed the trend this past century of odd-numbered cycles having larger amounts of solar activity than previous even-numbered cycles. At present the peak smoothed sunspot number for this cycle 23 is near 125 ± 15 and F10.7 Radio Flux near 180 ± 15, on the basis of the observed behavior. [24] A physical explanation for the use of geomagnetic and solar precursors lies in dynamo physics. Namely, the question of how the Sun broadcasts its future behavior to the Earth is found by an examination of solar dynamo physics. Although more advanced dynamo models may be used, even the simple Babcock dynamo model has the property that future (toroidal) magnetic fields are generated through the amplification of existing (polar) fields at the start of any sunspot cycle. Using this, the Sun s polar and toroidal fields may be used, as has been done with the SODA (Solar Dynamo Amplitude) index. Thus as far as the field of solar activity predictions is concerned, the field is making reasonable gains both in understanding and in forecasting skill. These skills rely on indices, such as sunspot number and F10.7 radio flux; however, rather than using these, Tobiska et al. [2000] have progressed in quantifying solar influences through use of direct solar inputs involving spectral irradiance fluxes. The current level of the SODA index suggests an early prediction for the next cycle s peak coronal activity index (a proxy for F10.7) to be near 175 ± 150, peaking in April 2011 ±3 months. [25] Acknowledgments. This work was supported by NSF grant ATM We appreciate the WSO, Big Bear, and NSO for use of their observatory magnetic field data, in particular Scherrer, Hoeksema, Marquette, and Harvey. We also appreciate the comments and suggestions of our referees. [26] Shadia Rifai Habbal thanks Joan Feynman and two other referees for their assistance in evaluating this paper. References Brown, G. M., and W. R. Williams, Some properties of the day-to-day variability of Sq(H), Planet. Space Sci., 17, , Feynman, J., and X. Y. Gu, Prediction of geomagnetic activity on time scales of one to ten years, Rev. Geophys., 24, 650, Harvey, K. L., and O. R. White, What is solar minimum?, J. Geophys. Res., 104, 19,759, Hathaway, D. H., R. M. Wilson, and E. J. Reichman, A synthesis of solar cycle prediction techniques, J. Geophys. Res., 104, 22,375, Joselyn, J. A., et al., Panel achieves consensus prediction of Solar Cycle 23, Eos Trans. AGU, 78, 205, , Kurths, J., and A. Ruzmaikin, On forecasting sunspots numbers, Solar Phys., 126, , Layden, A., P. Fox, J. Howard, A. Sarajedini, K. Schatten, and S. Sofia, Dynamo-based scheme for forecasting the magnitude of solar activity cycles, Solar Phys., 132, 1, Ohl, A. I., Forecast of sunspot maximum number of cycle 20, Soln. Dann., 12, 84, Ohl, A. I., and G. I. Ohl, A new method of very long-term prediction of solar

7 SCHATTEN: SOLAR ACTIVITY PREDICTION SSH 15-7 activity, in Solar-Terrestrial Predictions Proceedings, vol. 2, edited by R. Donnelly, p , NOAA/Space Environ. Lab., Boulder, Colo., Ruzmaikin, A., and J. Feynman, Strength and phase of the solar dynamo during the last 12 cycles, J. Geophys. Res., 106, 15,783 15,789, Schatten, K. H., and J. A. Orosz, A solar cycle timing predictor The latitude of active regions, Solar Phys., 125, , Schatten, K. H., and W. D. Pesnell, An early solar dynamo prediction: Cycle 23 Cycle 22, Geophys. Res. Lett, 20, , Schatten, K. H., P. H. Scherrer, L. Svalgaard, and J. M. Wilcox, Using dynamo theory to predict the sunspot number during solar cycle 21 00, Geophys. Res. Lett., 5, 411, Schatten, K. H., D. J. Myers, and S. Sofia, Solar activity forecast for solar cycle 23, Geophys. Res. Lett., 23, , Sofia, S., P. Fox, and K. Schatten, Forecast update for activity cycle 23 from a dynamo-based method, Geophys. Res. Lett., 25, , Stix, M., On the origin of stellar magnetism, Astron. Astrophys., 47, , Thompson, R. J., A technique for predicting the amplitude of the solar cycle, Solar Phys., 148, 383, Tobiska, K. W., et al., The SOLAR2000 empirical solar irradiance model and forecast tool, J. Atmos. Solar Terr. Phys., 62, , Waldmeier, M., Astron. Ergenbnisse nd Probleme der Sonnenforschung, 2nd ed., Geest and Porttig, Leipzig, Waldmeier, M., the sunspot activity in the years , Astron. Mitt. Eidg. Sternw., 285, 286, K. Schatten, a.i. solutions, Inc., Derekwood Lane, Suite 215, Lanham, MD 20706, USA. (schatten@ai-solutions.com)