1. High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. PREDICTING CYCLE 24 USING VARIOUS DYNAMO-BASED TOOLS Mausumi Dikpati High Altitude Observatory, NCAR

2. Attempts to build a dynamo-based predictive tool Magnetic persistence between the current sunspot cycle’s amplitude and previous cycle’s polar fields (Schatten, late 1970’s; Svalgaard et al. 2006) Correlation between geomagnetic indices and the Sun’s magnetic field components (Feynman, 1980’s; Hathaway & Wilson 2006) Flux-transport dynamo-based tool, driven by surface magnetic field data from past cycles; latitudinal fields from past 3 cycles combine to form “seed” for next cycle (DGdT, 2004, 2006) Surface flux-transport model; amount of low-latitude, cross-equatorial flux determines amplitude of next cycle (Cameron & Schussler, 2006) Qualitative Quantitative Latitudinal drift speed of centroid of sunspot-zone is positively correlated with the strength of second following cycle (Hathaway & Wilson, 2004)

3. First attempt by Schatten in 1970’s Postulated a “magnetic persistence” between previous cycle’s polar field (after reversal) and next cycle’s peak

4. Some questions about polar field precursor approach Q1. How are polar fields transported down to shear layer in 5.5 years? Q2. Do they remain radial down to shear layer? Q3. Are stronger radial fields associated with stronger or weaker latitudinal fields? < < < 1. Weak radial; strong latitudinal 2. Strong radial; weak latitudinal 3. Weak radial; weak latitudinal It depends on the field geometry inside the convection zone: see 3 possible cases

5. Prediction of cycle 24 using Schatten’s technique (Schatten, 2005, GRL) (Svalgaard, Cliver & Kamide, 2005, GRL)

6. Geomagnetic activity and solar cycle prediction aa T P T Geomagnetic activity can be split into two components:, in-phase with solar cycle; can be related to toroidal fields aa P, out-of-phase with solar cycle; can be related to poloidal field (Feynman, 1982)

7. Cycle 24 prediction using geomagnetic indices (Hathaway & Wilson, 2006, GRL) (a) There is a baseline level of geomagnetic activity proportional to sunspot number, aa I R (b) Relationship among aa, and aa R (c) Forecast comes from near solar minima aa I (a) (b) (c)

8. Schematic diagram for flux-transport dynamo mechanism Shearing of poloidal fields by differential rotation to produce new toroidal fields, followed by eruption of sunspots. Spot-decay and spreading to produce new surface global poloidal fields. Transport of poloidal fields by meridional circulation (conveyor belt) toward the pole and down to the bottom, followed by regeneration of new toroidal fields of opposite sign. (Dikpati & Gilman, 2006, ApJ, 649, 498)

9. Physical foundation of “magnetic persistence” In flux-transport dynamos, “magnetic persistence”, or the duration of the Sun’s “memory” of its own magnetic field, is controlled by meridional circulation. The time the poloidal flux takes to go from sunspot latitudes to mid- latitude at the bottom is ~20 years,rather than 5.5 years as in polar field precursor approach <

10. Mathematical Formulation Under MHD approximation (i.e. electromagnetic variations are nonrelativistic), Maxwell’s equations + generalized Ohm’s law lead to induction equation : Applying mean-field theory to (1), we obtain the dynamo equation as, Differential rotation and meridional circulation from helioseismic data Poloidal field source from active region decay Turbulent magnetic diffusivity (1) (2) Toroidal fieldPoloidal field Meridional circulation Differential rotation Assume axisymmetry, decompose into toroidal and poloidal components:

11. Calibrated Model Solution Contours: toroidal fields at CZ base Gray-shades: surface radial fields Observed NSO map of longitude-averaged photospheric fields (Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)

12. Results: Timing prediction for cycle 24 onset Dikpati, 2004, ESA-SP, 559, 233

13. Evidence of end of cycle 23 in butterfly diagram Pred. cycle 24 onset Cycle 23 onset

14. End of cycle 23 in white light corona Mar. 29, 2006 Early 1996 Nov. 1994 Current coronal structure not yet close to minimum; more like 12-18 months before minimum Corona at last solar minimum looked like this

15. Amplitude prediction: construction of surface poloidal source Period adjusted to average cycle Original data (from Hathaway) Assumed pattern extending beyond present

16. Results: simulations of relative peaks of cycle 12 through 24  We reproduce the sequence of peaks of cycles 16 through 23  We predict cycle 24 will be 30-50% bigger than cycle 23 (Dikpati, de Toma & Gilman, 2006, GRL)

17. Evolution of a predictive solution Color shades denote latitudinal (left) and toroidal (right) field strengths; orange/red denotes positive fields, green/blue negative Latitudinal fields from past 3 cycles are lined-up in high-latitude part of conveyor belt These combine to form the poloidal seed for the new cycle toroidal field at the bottom (Dikpati & Gilman, 2006, ApJ, 649, 498) Latitudinal field Toroidal field

18. Results from seperating North & South hemispheres Model reproduces relative sequence of peaks in N & S separately, but smoothes short-time scale solar cycle features

19. Skill tests for North and South Significant degradation of skill happens when model-output is compared with input data averaged over less than 13 rotations

20. Hathaway & Wilson correlation results H&W cycle 24 and 25 predictions

21. Unifying methods for predicting cycle period, timing and amplitude  So far, amplitude and timing have been predicted in two different calculations. But we know they are linked.  In order to be able to simultaneously predict them, we must drop the compression and stretching, and incorporate information on cycle length and timing from previous cycles.  Data assimilation techniques developed for meteorological forecasting problems may be useful for doing this.

22. Surface flux-transport model (Cameron & Schussler, 2006, ApJ, in press) Correlation between peaks of cycles n and n-1 Correlation between maximum of unsigned polar field resulting from surface flux-transport model and next cycle’s peak amplitude Correlation between magnetic flux diffusing across the equator per unit time resulting from flux- transport model, and next cycle’s peak amplitude Correlation between dipole component of surface fields resulting from flux-transport model and next cycle’s peak amplitude r=0.47 r=0.35 r=0.90 r=0.83

23. Cross-equatorial flux and next cycle using surface flux-transport model (contd.)  Correlation between flux crossing equator, calculated from the average sunspot activity 3 years before the minima, and next cycle’s peak is r= 0.84. This method predicts a strong cycle 24.  r goes down to 0.45 when actual emergence latitudes of sunspot are used to compute flux crossing equator

24. Concluding remarks  All dynamo-based tools including geomagnetic precursors (H&W), cross- equatorial flux precursor (C&S), sunspot drift-speed and second following cycle correlation (H&W), and combination of latitudinal fields from past 3 cycles (DGdT) predict high cycle 24, but polar field precursor method (S and SCK) gives a low cycle 24  In future relationship between solar precursors and solar dynamo-based predictions needs to be investigated  Data assimilation techniques, developed in meteorology in previous decades, are just starting to be applied to dynamo-based prediction models. Using such techniques, it may be possible to unify methods for predicting timing, length and amplitude of solar cycles.

25. Answering mean-field dynamo skeptics  Predicting solar cycle peaks using mean-field dynamo is impossible Our results speak for themselves; skeptics have used no model that contains either meridional circulation or Babcock-Leighton type surface poloidal source. Can’t use the output from (their) model “B” to disprove the skill of (our) model “A”  Too many assumed inputs Most inputs constrained by observations; model calibrated to observations to set diffusivity  Meridional circulation is unimportant, so can be ignored Meridional circulation is crucial for getting the correct phase between the poloidal and toroidal fields, and for transporting poloidal fields of previous cycles to high-latitudes at depth where ‘seed’ for new cycle is created

26. Answering mean-field dynamo skeptics (contd.)  Babcock-Leighton poloidal source “old-fashioned” It is observed, so can’t be ignored  Solar dynamo is in deterministic chaos, and heavily nonlinear, therefore unpredictable We have demonstrated predictive skill by reducing the dynamo to a linear system forced at the upper boundary by the observed poloidal fields of previous cycles. Atmospheric models achieve predictive skill beyond “chaotic” limits if they involve known boundary forcing (El Nino forecasts and annual cycles). Nonlinear feedbacks of induced magnetic fields on inducing solar motions (e.g. differential rotation) are small (torsional oscillations)