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Predicting the Solar Cycle

Leif Svalgaard

Stanford University

SORCE 2010

Keystone, CO, May 20, 2010

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State of the Art: Predicting Cycle 24What the Sun seems to be doing

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Near Normal Distribution = No Skill?Some preference for Climatological Mean

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0 25 50 75 100 125 150 175 200 225

Distribution of Predicted Solar Cycle 24 Size

Climatological Mean

Rmax

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Flux Transport Dynamo Models

• Dikpati, M., de Toma, G., Gilman, P.A.: Predicting the strength of solar cycle 24 using a flux-transport dynamo-based tool, Geophys. Res. Lett., 33, L05102, 2006.

Rmax24 = 160-185• Choudhuri, A.R., Chatterjee, P., Jiang, J.: Predicting

Solar Cycle 24 with a solar dynamo model, Phys. Rev. Lett., 98, 131103, 2007.

Rmax24 = 75

• Difference is primarily due to different assumptions about the diffusivity of magnetic flux into the Sun [high = weak cycle]

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High Diffusivity: LeftLow Diffusivity (Advection): Right

Conveyor BeltP is a proxy for T

One year between dots

Dikpati et al.Choudhuri et al.

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Grow-N-Crash ‘Model’Easy to get a high correlation

Dikpati et al. 2006

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Supply a Scaled Standard Cycle Body to get ‘Stunning’ Correlation

Crash-N-GrowDikpati et al.

Dikpati et al. assumed constant Meridional Circulation, except for cycle 24

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Meridional Circulation

Both (Dikpati, Choudhuri) of these Flux Transport Dynamo Models produce strong polar fields and short cycles when the meridional flow is fast. However: “Measurements of the meridional flow over Cycle 23 now show that on the approach to Cycle 24 minimum in 2008 to speeds significantly higher than were seen at the previous minimum (David Hathaway, SOHO-23)”

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Meridional Circulation

Lisa Rightmire, David Hathaway (2009): Cross-correlating full-disk magnetograms

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‘Flux Transport Models Not Ready Yet’

• “In these models this higher meridional flow speed should produce strong polar fields and a short solar cycle contrary to the observed behavior.

• “These observations, along with others, suggest that Flux Transport Dynamo Models do not properly capture solar cycle behavior and are not yet ready to provide predictions of solar cycle behavior.

Hathaway, 2009

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Is This Too Harsh?

• The polar fields were built several years ago before the increase in the Meridional circulation [the polar fields were essentially established by mid-2003]

22 23

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And Have Not Increased Since Then, rather Beginning to Show the expected

Decrease due to New Cycle Activity

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-100

-50

0

50

100

150

2003.0 2004.0 2005.0 2006.0 2007.0 2008.0 2009.0 2010.0 2011.0

S

N

N+S

WSO Polar Fields

Year

uT

N-S

model WF

Bad Filter

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Issues with Meridional Circulation

• The question is not whether the M.C. is there or not (multiple cells?), but rather what role it plays in the solar cycle, probably hinging on the value of the turbulent diffusivity.

• An unknown is the degree to which M.C. is affected by back-reaction from the Lorentz force associated with the dynamo-generated magnetic field (chicken and egg).

• The form and speed of the equatorward return flow in the lower convective zone is at present unknown (possibly SDO/HMI will tell us).

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Perhaps a Shallow Dynamo?

Ken Schatten [Solar Physics, 255, 3-38, 2009] explores the possibility of sunspots being a surface phenomenon [being the coalescence of smaller magnetic features as observations seem to indicate] and that the solar dynamo is shallow rather than operating at the tachocline, based on his Cellular Automata model of solar activity.

See poster

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In his Model, the Polar Flux also Predicts the Sunspot Flux

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Other Dynamo Models

Kitiashvili, 2009

The Ensemble Kalman Filter (EnKF) method has been used to assimilate the sunspot number data into a non-linear α-Ω mean-field dynamo model, which takes into account the dynamics of turbulent magnetic helicity.

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Back to Empirical Predictions?

With predictions based on Flux Transport Dynamos in doubt or less enthusiastically embraced (and the Shallow Dynamo and the EnKF approach not generally pursued) we may be forced back to Precursor Techniques where some observed features are thought to presage future activity.

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Precursors

• Coronal Structure [Rush to the Poles]

• Torsional Oscillation [At Depth]

• H-alpha Maps [Magnetic Field Proxy]

• Geomagnetic Activity [Solar Wind Proxies]

• Open Flux at Minimum

And that old stand-by:

• Polar Fields

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Green Corona Brightnessto Determine Time of Maximum

?

?

Altrock, 2009

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Torsional Oscillation Polar BranchWhere is it? (Chicken & Egg)

Howe, 2009

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Large-Scale ‘Magnetic’ Field from Neutral Lines on Hα Maps

Tlatov et al., 2006

Assigning fields of +1 and -1 to areas between neutral lines, calculate the global dipole μ1 and octupole μ3 components. They predict the cycle 69 months aheadMcIntosh

A(t)

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Geomagnetic Activity at MinimumPolar Field Proxy?

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160

180

1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 20200

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14

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Rmax = 22.5 + 13.42 Apmin R2=0.88

Rmax = 24.85 * Apmin0.7956 R2=0.89

Rmax Apminobs

Sunspot Number at Maximum Following Ap at Minimum

Svalgaard, 2009

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AA-index as Proxy for Open Heliospheric Magnetic Flux

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Wang & Sheeley, 2009

Min AA based on last 12 months

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The Size of Recurrent Activity Peaks [Corrected for Sunspot Activity] has

been used as a Precursor of the Next Cycle [Physics is Obscure Though]

Hathaway et al.

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Picking the Wrong Peak [From Filtered Data] Can Lead You Astray

-0.6

-0.4

-0.2

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0.2

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0.8

1

1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Sargent's Recurrence Index

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1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Geomagnetic Activity (aa*)

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“Picking the Peak”• Using the large peak in 2003 predicted a large

cycle [Rmax ~ 160], but perhaps the peak to use [based on the Recurrence Index] is the one in 2008 that predicts a small cycle [Rmax ~ 70]

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1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Geomagnetic Activity

Flares

"Recurrence Peak"

Large Cycle Small

cycle

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Definition of Polar Fields

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Measurements of Polar Fields

1953 1965

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300

400

1970 1975 1980 1985 1990 1995 2000 2005 2010

Mount Wilson Solar Obs. Wilcox Solar Obs.

Solar Polar Magnetic Fields (N-S, microTesla)

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Another Measure of the Polar fields

Nobeyama Radioheliograph, Japan

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1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

K

Year

Polar Field Proxy from Nobeyama 17 GHz Brightness Temperature

North

South

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0

50

100

150

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Data Bad

WSO Polar Fields

North

South

uT

Year

17 GHz Radio Flux

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Polar Field Scaled by Size of Next Cycle is Possibly an Invariant

Rmax24 = 72

Our Prediction-400

-300

-200

-100

0

100

200

300

400

1970 1975 1980 1985 1990 1995 2000 2005 2010

Mount Wilson Solar Obs. Wilcox Solar Obs.

Solar Polar Magnetic Fields (N-S, microTesla)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

45

72

165

Solar Dipole Divided by Sunspot Number for Following Maximum

R24

21 22 23 2420

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Cycle TransitionsThe current minimum is very low [the lowest in a century], and it is clear that Minimum is now behind us.Dashed line: Hathaway New Prediction

2007.0422007.1212007.2032007.2852007.37

2007.4522007.5372007.6222007.7042007.7892007.8712007.9562008.0412008.1232008.2052008.2872008.3722008.4542008.5392008.6242008.7062008.7912008.8732008.9582009.0422009.1212009.203

050

100150200250300350400450500

1980 1985 1990 1995 2000 2005 2010 2015

232221

Active Region Count

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1983 1984 1985 1986 1987 1988 1989

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1993 1994 1995 1996 1997 1998 1999

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2005 2006 2007 2008 2009 2010 2011

23 240

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2007.75 2008.25 2008.75 2009.25 2009.75 2010.25

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Active Region Days (per Month)

3 Ri

23+24

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The Diverse 23-24 Minima:Mean Field, TSI, F10.7, SSN(s)

8383838383838383

1359.0

1359.5

1360.0

1360.5

1361.0

1361.5

1362.0

2008.00

2008.07

2008.15

2008.22

2008.30

2008.37

2008.45

2008.52

2008.60

2008.67

2008.75

2008.82

2008.90

2008.97

2009.05

2009.12

2009.19

2009.27

2009.34

2009.42

2009.49

2009.57

2009.64

2009.72

2009.79

2009.87

2009.94

2010.02

2010.09

2010.17

2010.24

2010.31

2010.39

2010.46

2010.54

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110

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TSI

F10.7

23SN24

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60

MF

NOAA

SIDC

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Fractional Year

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F10.7 at minimum between two large

cycles 18 & 19 and two smallish cycles

23 & 2460

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2006 2007 2008 2009 2010

F10.7 at Minima 1954 and 2008-2009

A

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What Will Cycle 24 Look Like?• Perhaps like cycle 14, starting 107 years ago• Note the curious oscillations, will we see some this time?• If so, I can just imagine the confusion there will be with

‘verification’ of the prediction

Cycle 14

Alvestad, 2009

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If We Can Just See the Spots…

• Sunspots are getting warmer, thus becoming harder to see. Will they disappear? Or will the Sunspot Number just be biased and too small…

William Livingston, Pers. Comm. 2010

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1990 1995 2000 2005 2010 2015 2020

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1B Gauss Intensity

Year

Livingston & Penn Umbral Data

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F10.7 Flux Relationship with Sunspot Numbers is Changing

Ratio of observed SSN and SSN computed from F10.7 using formula for 1951-1990

Recent SSN already too low ?

Svalgaard & Hudson, 2009

0

1

2

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Observed Rz,i / Calculated Rz,i [for Rz,i >4]

SIDC

mmmmm

Zürich

mm

y = -1.4940E-11x6 + 1.6779E-08x5 - 7.4743E-06x4 + 1.7030E-03x3 - 2.1083E-01x2 + 1.4616E+01x - 4.1029E+02

R2 = 0.9759

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0 50 100 150 200 250 300

F10.7 sfu

R

Sunspot Number vs. F10.7 Flux Monthly Averages

1951-1990

1996-2010

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So What Do We Predict? SSN or F10.7 Flux or Magnetic Regions?

• Since the prediction is based on the magnetic field, we are really predicting a proxy for the field:

• F10.7 120 sfu

• Magnetic Regions 72/12 = 6

• Sunspot Number Who knows?

• Was the Maunder Minimum like this?

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Conclusion"It cannot be said that much progress has been made towards the disclosure of the cause, or causes, of the sun-spot cycle. Most thinkers on this difficult subject provide a quasi-explanation of the periodicity through certain assumed vicissitudes affecting internal processes. In all these theories, however, the course of transition is arbitrarily arranged to suit a period, which imposes itself as a fact peremptorily claiming admittance, while obstinately defying explanation"

Agnes M. Clerke, A Popular History of Astronomy During the Nineteenth Century, page 163, 4th edition, A. & C. Black, London, 1902.

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AbstractWe discuss a number of aspects related to our understanding of the solar dynamo. We begin by illustrating the lack of our understanding. Perhaps as exemplified by SWPC's Solar Cycle 24 Prediction Panel. They received and evaluated ~75 prediction papers with predicted sunspot number maxima ranging from 40 to 200 and with a near normal distribution around the climatological mean indicative of the poor State of the Art. Flux Transport Dynamo Models were recently hyped? or hoped? to promise significant progress, but they give widely differing results and thus seem inadequate in their current form. In these models, higher meridional flow speed should produce strong polar fields and a short solar cycle, contrary to the observed behavior of increased meridional flow speed, low polar fields, and long-duration cycle 23. Poorly understood Precursor-methods again seem to work as they have in previous cycles. I review the current status of these methods. Predictions are usually expressed in terms of maximum Sunspot Number or maximum F10.7 radio flux, with the implicit assumption that there is a fixed [and good] relation between these measures of solar activity. If Livingston & Penn’s observations of a secular change in sunspot contrast hold up, it becomes an issue which of these two measures of solar activity should be predicted and what this all means. The coming cycle 24 may challenge cherished and long-held beliefs and paradigms. .