Leif Svalgaard
Stanford University
SORCE 2010
Keystone, CO, May 20, 2010
1

State of the Art: Predicting Cycle 24
What the Sun seems to be doing
2

25
20
15
10
5
0
0
30
Near Normal Distribution = No Skill?
Some preference for Climatological Mean
Distribution of Predicted Solar Cycle 24 Size
25 50 75
Climatological Mean
150 175 200 225 100
Rmax
125
3

• Dikpati, M., de Toma, G., Gilman, P.A.: Predicting the strength of solar cycle 24 using a flux
-transport dynamobased tool, Geophys. Res. Lett., 33, L05102, 2006.
Rmax
24
= 160-185
• Choudhuri, A.R., Chatterjee, P., Jiang, J.: Predicting
Solar Cycle 24 with a solar dynamo model, Phys. Rev.
Lett., 98, 131103, 2007.
Rmax
24
= 75
• Difference is primarily due to different assumptions about the diffusivity of magnetic flux into the Sun [high = weak cycle]
4

High Diffusivity: Left
Low Diffusivity (Advection): Right
P is a proxy for T Conveyor Belt
Choudhuri et al.
One year between dots
Dikpati et al.
5

Easy to get a high correlation
Dikpati et al. 2006
6

Supply a Scaled Standard Cycle
Body to get ‘Stunning’ Correlation
Crash-N-Grow
Dikpati et al.
Dikpati et al. assumed constant Meridional Circulation, except for cycle 24
7

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)”
8

Lisa Rightmire, David Hathaway (2009):
Cross-correlating full-disk magnetograms
9

‘
’
• “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
10

• 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
11

And Have Not Increased Since Then, rather Beginning to Show the expected
Decrease due to New Cycle Activity
150 uT
100
50
0
-50
-100
-150
2003.0
N
2004.0
S
WSO Polar Fields
Bad Filter
2005.0
N-S
2006.0
N+S
2007.0
Year model
WF
2008.0
2009.0
2010.0
2011.0
12

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).
13

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
14

In his Model, the Polar Flux also
Predicts the Sunspot Flux
15

The Ensemble Kalman Filter (EnKF) method has been used to assimilate the sunspot number data into a nonlinear
α
-
Ω mean-field dynamo model, which takes into account the dynamics of turbulent magnetic helicity.
Kitiashvili, 2009
16

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.
17

• 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
18

Green Corona Brightness to Determine Time of Maximum
?
Altrock, 2009
?
19

Torsional Oscillation Polar Branch
Where is it? (Chicken & Egg)
Howe, 2009
20

Large-Scale ‘Magnetic’ Field from
Neutral Lines on H
α
Maps
Assigning fields of +1 and -1 to areas between neutral lines, calculate the global dipole
μ
1 octupole μ
3 components . They and predict the cycle 69 months ahead
McIntosh
Tlatov et al., 2006
A(t)
21

Geomagnetic Activity at Minimum
Polar Field Proxy?
180
Sunspot Number at Maximum Following Ap at Minimum obs
Rmax Apmin 16
160
14
140
12
120
10
100
80
8
60
6
40
4
Rmax = 22.5 + 13.42 Apmin R
2
=0.88
20
Rmax = 24.85 * Apmin
0.7956
R
2
=0.89
2
0
1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
0
Svalgaard, 2009
22

AA-index as Proxy for Open
Heliospheric Magnetic Flux
24
Min AA based on last 12 months
Wang & Sheeley, 2009
23

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.
24

Picking the Wrong Peak [From
Filtered Data] Can Lead You Astray
Geomagnetic Activity (aa*)
70
60
50
40
30
20
10
0
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Sargent's Recurrence Index
1
0.8
0.6
0.4
0.2
0
-0.2
1870
-0.4
-0.6
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
25

70
60
50
40
30
20
10
0
1996
• 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]
Geomagnetic Activity
80
1997 1998 1999 2000 2001 2002
Large
Cycle
Flares
2003 2004 2005 2006
"Recurrence
Peak"
Small cycle
2007 2008 2009 2010
26

27

1953 1965
400
Mount Wilson Solar Obs.
300
200
100
0
1970
-100
-200
-300
-400
1975 1980 1985 1990 1995 2000
Solar Polar Magnetic Fields (N-S, microTesla)
Wilcox Solar Obs .
2005 2010
28

Another Measure of the Polar fields
17 GHz Radio Flux
Nobeyama Radioheliograph, Japan
1500
K
North
1000
500
0
-500
-1000
-1500
1993
South
1994 1995
Polar Field Proxy from Nobeyama 17 GHz Brightness Temperature
1996 1997 1998 1999
Year
2000 2001 2002 2003 2004 2005 2006 2007 uT
150
100
50
0
-50
-100
-150
-200
1993
North
South
1994 1995 1996 1997 1998
WSO Polar Fields
Data Bad
1999
Year
2000 2001 2002 2003 2004 2005 2006 2007
29

3.0
2.5
2.0
1.5
1.0
0.5
0.0
1965
Polar Field Scaled by Size of Next
-200
-300
-400
Cycle is Possibly an Invariant
400
Mount Wilson Solar Obs.
300
200
100
0
1975 1980 1985 1990 1995 2000
Wilcox Solar Obs .
2005 2010
R max24
= 72
Our Prediction
Solar Polar Magnetic Fields (N-S, microTesla)
Solar Dipole Divided by Sunspot Number for Following Maximum
4.0
3.5
20
1970 1975
21
1980 1985
22
1990 1995
23
2000 2005 2010
R
24
45
72
24
165
2015
30

140
120
100
80
60
40
20
0
2005
140
120
100
80
60
40
20
0
1983
140
120
100
80
60
40
20
0
1993
500
450
400
350
300
250
200
150
100
50
0
21
1980
Active Region Count
Cycle Transitions
1985
21
1984
1994
2006
23
22
1990
22
1985
1995
2007
1995
1986
1996
2008
2000
23
1987
1997
2009
2005
22
1988
23
1998
2010
24
2015
The current minimum is very low [the lowest in a century], and it is clear that Minimum is now behind us.
1989
24
1999
100
90
80
70
60
50
40
23
30
20
10
24
0
2007.75
Dashed line: Hathaway New Prediction
(matches ours now )
Active Region Days (per Month)
2008.25
2008.75
23+24
2009.25
3 Ri
2009.75
2010.25
2010 2011 31

1362.0
1361.5
1361.0
1360.5
1360.0
1359.5
1359.0
TSI
The Diverse 23-24 Minima:
Mean Field, TSI, F10.7, SSN(s)
MF
0
F10.7
90
80
70
60
60
NOAA
23
SN
24
SIDC
0
50
40
30
Fractional
Year
160
150
140
130
120
110
100
32

200
180
160
140
120
100
80
60
2006
F10.7 at Minima 1954 and 2008-2009
A
2007 2008 2009 2010
F10.7 at minimum between two large cycles
18 & 19 and two smallish cycles
23 & 24
33

• 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 34

• Sunspots are getting warmer, thus becoming harder to see. Will they disappear? Or will the
Sunspot Number just be biased and too small…
Livingston & Penn Umbral Data
4000
B Gauss
3500
3000
Intensity
1
0.8
0.6
2500
2000
1500
1990 2015 Year
0
2020
0.4
0.2
1995 2000 2005 2010
William Livingston, Pers. Comm. 2010
35

2
50
150
100
F10.7 Flux Relationship with
Sunspot Numbers is Changing
250
R
Sunspot Number vs. F10.7 Flux Monthly Averages y = -1.4940E-11x 6 + 1.6779E-08x 5 - 7.4743E-06x 4 + 1.7030E-03x 3 - 2.1083E-01x 2 + 1.4616E+01x - 4.1029E+02
R
2
= 0.9759
200
1951-1990
Ratio of observed SSN and SSN computed from F10.7 using formula for 1951-1990
1996-2010
0
0 50 100 150 200 250
F10.7 sfu
300
Recent SSN already too low ?
Observed Rz,i / Calculated Rz,i [for Rz,i >4]
Zürich SIDC
1 m
0
1950 m
1955 1960 m
1965 1975 m
1980 m
1985 1990 1970
Svalgaard & Hudson, 2009
1995 m
2000 2005 m
2010
36

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
• Magnetic Regions
• Sunspot Number
120 sfu
72/12 = 6
Who knows?
• Was the Maunder Minimum like this?
37

"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, 4 th edition, A. & C.
Black, London, 1902.
38

We 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.
.
39