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1
Predicting the Solar Cycle
Leif Svalgaard
Stanford University
Solar Analogs II
Flagstaff, AZ, Sept. 22, 2009
2
State of the Art: Predicting Cycle 24Predictions sent to the Prediction Panel
3
State of the Art: Predicting Cycle 24What the Sun seems to be doing
4
Near Normal Distribution = No SkillSome preference for Climatological Mean
0
5
10
15
20
25
30
0 25 50 75 100 125 150 175 200 225
Distribution of Predicted Solar Cycle 24 Size
Climatological Mean
Rmax
5
Early Optimism and PR Effort
• “The next sunspot cycle will be 30-50% stronger than the last one and begin as much as a year late, according to a breakthrough forecast using a computer model of solar dynamics developed by scientists at the National Center for Atmospheric Research (NCAR).”
2004-2006
6
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]
7
High Diffusivity: LeftLow Diffusivity (Advection): Right
Conveyor BeltP is a proxy for T
One year between dots
Dikpati et al.Choudhuri et al.
8
Grow-N-Crash ‘Model’Easy to get a high correlation
Dikpati et al. 2006
Intermittency from threshold effects
9
Grow-N-Crash ‘Model’Easy to get a high correlation
Dikpati et al. 2006
10
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
11
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)”
12
Meridional Circulation
Lisa Rightmire, David Hathaway (2009): Cross-correlating full-disk magnetograms
13
‘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
14
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
15
And Have Not Increased Since Then, rather Beginning to Show a Decrease
-150
-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
16
Latitudes of Active Regions During Cycle 23 were not Unusual
1874-2005
17
Issues with Meridional Circulation
• The question is not whether the M.C. is there or not, 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.
18
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.
19
Schatten’s Cellular Automata Model
20
In the CA Model, the Polar Flux also Predicts the Sunspot Flux
21
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.
22
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.
23
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
24
Green Corona Brightnessto Determine Time of Maximum
?
?
Altrock, 2009
25
Torsional Oscillation Polar BranchWhere is it? (Chicken & Egg)
Howe, 2009
26
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)
27
Geomagnetic Activity During Descending Phase of Cycle
Bhatt et al., 2009
28
Or Just at Minimum
0
20
40
60
80
100
120
140
160
180
1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 20200
2
4
6
8
10
12
14
16
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
29
AA-index as Proxy for Open Heliospheric Magnetic Flux
24
Wang & Sheeley, 2009
Min AA based on last 12 months
30
Recurrent High-Speed Streams Nearing Solar Minimum Create High Geomagnetic Activity
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Sargent's Recurrence Index
0
10
20
30
40
50
60
70
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Geomagnetic Activity (aa*)
31
The Size of these Activity Peaks [Corrected for Sunspot Activity] has
been used as a Precursor of the Next Cycle [Physics is Obscure Though]
Hathaway et al.
32
Picking the Wrong Peak [From Filtered Data] Can Lead You Astray
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Sargent's Recurrence Index
0
10
20
30
40
50
60
70
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Geomagnetic Activity (aa*)
33
“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 ~ 80]
0
10
20
30
40
50
60
70
80
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Geomagnetic Activity
Flares
"Recurrence Peak"
Large Cycle Small
cycle
34
Definition of Polar Fields
35
Measurements of Polar Fields
-400
-300
-200
-100
0
100
200
300
400
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
MSO* WSO
North - South Solar Polar fields [microTesla]
1953 1965
36
Another Measure of the Polar fields
Nobeyama Radioheliograph, Japan
-1500
-1000
-500
0
500
1000
1500
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
-200
-150
-100
-50
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
37
Polar Field Scaled by Size of Next Cycle is Possibly an Invariant
-400
-300
-200
-100
0
100
200
300
400
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
MSO* WSO
North - South Solar Polar fields [microTesla]
Rmax24 = 75
Our Prediction
38
Cycle Transitions2007.2852007.37
2007.4522007.5372007.6222007.7042007.7892007.8712007.9562008.0412008.1232008.2052008.2872008.3722008.4542008.5392008.6242008.7062008.7912008.8732008.9582009.0422009.1212009.2032009.2852009.3662009.4482009.5292009.6112009.692
050
100150200250300350400450500
1980 1985 1990 1995 2000 2005 2010 2015
232221
Active Region Count
24
0102030405060708090
100
1983 1984 1985 1986 1987 1988 1989
21 22
0102030405060708090
100
1993 1994 1995 1996 1997 1998 1999
22 23
0102030405060708090
100
2005 2006 2007 2008 2009 2010 2011
23 240
5
10
15
20
25
30
2007.75 2008 2008.25 2008.5 2008.75 2009 2009.25 2009.5 2009.75 2010
23
24
Region Days (per Month)
Ri/0.323+24
The current minimum is very low [the lowest in a century], and it looks like Minimum is now behind us
39
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
40
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
dy = -54 dx
dy = 0.0186 dx
1500
2000
2500
3000
3500
4000
1990 1995 2000 2005 2010 2015 2020
0
0.2
0.4
0.6
0.8
1B Gauss Intensity
Year
Livingston & Penn Umbral Data
41
F10.7 Flux Relationship with Sunspot Numbers is Changing
y = -9.167E-12x6 + 1.194E-08x5 - 5.900E-06x4 + 1.451E-03x3 - 1.900E-01x2 + 1.378E+01x - 3.978E+02R2 = 9.770E-01
0
50
100
150
200
250
0 50 100 150 200 250 300
F10.7 sfu
R
Sunspot Number vs. F10.7 Flux Monthly Averages
1951-1988
1996-2009
Ratio of observed SSN and SSN computed from F10.7 using formula for 1951-1988
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
m
42
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 6
• Sunspot Number Who knows?
• Was the Maunder Minimum like this?
43
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.
44
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. .