PREDICTING CYCLE 24 USING VARIOUS DYNAMO-BASED TOOLS

High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)

The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder 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

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)

First attempt by Schatten in

1970’s

Postulated a “magnetic persistence” between previous cycle’s polar field (after reversal) and next cycle’s peak

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

Prediction of cycle 24 using Schatten’s technique

(Schatten, 2005, GRL)

(Svalgaard, Cliver & Kamide, 2005, GRL)

Geomagnetic activity and solar cycle prediction

aaT

aaP

aaT

Geomagnetic activity can be split into two components:

, in-phase with solar cycle; can be related to toroidal fields

aaP , out-of-phase with solar

cycle; can be related to poloidal field

(Feynman, 1982)

Cycle 24 prediction using geomagnetic indices

(Hathaway & Wilson, 2006, GRL)

(a) There is a baseline level of geomagnetic activity proportional to sunspot number,

R

aa I aaR(b) Relationship among aa, and

aaR

(c) Forecast comes from near solar minima aa I

(a) (b)

(c)

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)

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

<

Mathematical FormulationUnder 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 rotationand meridional circulation

from helioseismic data

Poloidal field source from active region

decay

Turbulent magnetic diffusivity

(1)

(2)

. BBUB

ηt

, BBBUB

ηαt

Toroidal field Poloidal field Meridionalcirculation

Differentialrotation

, ˆ ,, ˆ ,, φφφ tθrAtθrB eeB ,ˆ ,Ωsin, φθrθrθr euU

Assume axisymmetry, decompose into toroidal and poloidal components:

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)

Results: Timing prediction for cycle 24 onset

Dikpati, 2004, ESA-SP, 559, 233

Evidence of end of cycle 23 in butterfly diagramPred.

cycle 24 onset

Cycle 23 onset

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

Amplitude prediction: construction of surface poloidal source

Period adjusted to average cycle

Original data (from Hathaway)

Assumed pattern extending

beyond present

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)

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

Results from seperating North & South hemispheres

Model reproduces relative sequence of peaks in N & S separately, but smoothes short-time scale solar cycle features

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

Hathaway & Wilson correlation results

The sunspot cycle period is antiThe sunspot cycle period is anti--correlated with the drift velocity correlated with the drift velocity at cycle maximum. The faster the drift rate the shorter the periat cycle maximum. The faster the drift rate the shorter the period. od. This is also expected from dynamo models with deep meridional This is also expected from dynamo models with deep meridional flow.flow.

R=-0.595% Significant

Drift Rate Drift Rate –– Period AntiPeriod Anti--correlationcorrelationThe drift velocity at cycle maximum is correlated to the amplituThe drift velocity at cycle maximum is correlated to the amplitude de of the second following (N+2) cycle. This is also predicted by of the second following (N+2) cycle. This is also predicted by dynamo models with deep meridional flow. It also provides a dynamo models with deep meridional flow. It also provides a prediction for the amplitudes of future cycles.prediction for the amplitudes of future cycles.

R=0.7R=0.799% Significant99% Significant

Drift Rate Drift Rate –– Amplitude CorrelationsAmplitude Correlations

Cycle 24 Amplitude PredictionCycle 24 Amplitude Prediction

The fast drift rates at the maximum of the last (22The fast drift rates at the maximum of the last (22ndnd) cycle (red oval ) cycle (red oval ––northern hemisphere, yellow oval northern hemisphere, yellow oval –– southern hemisphere) indicate a southern hemisphere) indicate a larger than average amplitude for the next cycle (24larger than average amplitude for the next cycle (24thth).).

H&W cycle 24 and 25 predictions

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.

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

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

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.

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

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)