Post on 30-Dec-2015
description
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.
SIMULATING AND PREDICTING SOLAR CYCLES USING A FLUX-TRANSPORT DYNAMO
Mausumi DikpatiHigh Altitude Observatory, NCAR
Principal collaborator:
Other collaborators:
Peter Gilman (HAO/NCAR)
C.N. Arge (AFGL), P. Charbonneau (Montreal), G. de Toma (HAO/NCAR), D.H. Hathaway (NASA/MSFC), K.B. MacGregor (HAO/NCAR), M. Rempel
(HAO/NCAR), O.R.White (HAO/NCAR)
Random vs. persistent, cyclic features
butterfly diagram, polar reversal
mixed-polarity turbulent fields
Courtesy: D.H. Hathaway
Courtesy:
T. Berger
Courtesy: G. de Toma
active longitudes
What is a dynamo?
A dynamo is a process by which the magnetic field in an electrically conducting fluid is maintained
against Ohmic dissipation
In astrophysical object, there can always be a dynamo whenever the plasma consists of
seed magnetic fields and flow fields
Observational signature forrandom evolution of magnetic fields
Courtesy: P. Sutterlin,
Dutch Open Telescope Team, SUI
Observational signature for systematic, cyclic evolution of solar magnetic fields
Courtesy:
D.H. Hathaway
Many evidences for coexistence of small-scale and large-scale dynamos
Large-scale dynamo processes
(i) Generation of toroidal (azimuthal) field by
shearing a pre-existing poloidal field
(component in meridional plane) by
differential rotation (Ω-effect )
(ii) Re-generation of poloidal field by lifting and twisting a toroidal flux tube
by helical turbulence (α-effect)
(iii) Flux transport by meridional circulation
= FLUX-TRANSPORT DYNAMO
<
A possible α-effect arising from decay of tilted bipolar active regions
Babcock 1961, ApJ, 133, 572
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 rotationand meridional circulation
Displacing andtwisting effect
by kinetic helicity
Diffusion(turbulent + molecular)
(1)
(2)
. BBUB
ηt
, BBBUB
ηαt
Evolution of Magnetic FieldsIn a Babcock-Leighton Flux-Transport Dynamo
Dikpati & Charbonneau 1999, ApJ, 518, 508 Dynamo cycle period ( T ) primarily governed by meridional flow speed
Analogy with ocean conveyor belt
Broecker 1991
Calibrated Flux-transport Dynamo Model
Near-surface diffusivity same as used by Wang, Shelley & Lean, 2002; Schrijver 2002
in their surface flux-transport models.
N-Po
leS-
Pole
Red: α -effect locationGreen: rotation contoursBlue: meridional flow
Magnetic diffusivity used Flows derived from observations
Contours: toroidal fields at CZ base Gray-shades: surface radial fields
Observed NSO map of longitude-averaged photospheric fields
Validity test of calibration
(Dikpati, de Toma, Gilman, Arge & White, 2004, ApJ, 601, 1136)
Why is solar cycle prediction important?
Precursor methods
Schatten 2005, GRL
We postulate that “magnetic persistence”,
or the duration of the Sun’s “memory” of its own magnetic field, is
controlled by meridional circulation.
Flux-transport Dynamo-based Prediction Scheme
<
Correlation between spot area and surface magnetic flux
Construction of surface poloidal source from observations
Construction of surface poloidal source from observations (contd.)
Period adjusted to average cycleOriginal data (from Hathaway)
Assumed pattern extending beyond present
Three techniques for treating surface poloidal source in simulating and forecasting cycles
1) Continuously update of observed surface source including cycle predicted (a form of 2D data assimilation)
2) Switch off observed surface source for cycle to be predicted
3) Substitute theoretical surface source, derived from dynamo-generated toroidal field at the bottom, for observed surface source
Forecasted quantity : integrated toroidal magnetic flux at the bottom in latitude range of 0 to 45 degree (which is the
sunspot-producing field)
We use these three techniques in succession to simulate and forecast
Simulating relative peaks of cycles 12 through 24 (model fed by surface poloidal source continuously)
Observed cycles
We reproduce the sequence of peaks of cycles 16 through 23
We predict cycle 24 will be 30-50% bigger than cycle 23
We obtain similar results for diffusivities between and
(Dikpati, de Toma & Gilman, 2006, GRL, in press)
Skill test for different magnetic diffusivities
How does the model work?
Red and blue contours are poloidal field lines in the plane of the board; red (blue) denotes
clockwise (counterclockwise) field directions
Color shades denote toroidal field strengths; orange/red denotes positive (into board)
fields, green/blue negative
Latitudinal component of poloidal fields near the bottom is primary source of new toroidal
fields
How does the model work? (Contd.)
Latitudinal B Toroidal B
Latitudinal fields in the conveyor belt from past 3 cycles combine near the bottom to form the
source of new cycle toroidal field.
Mechanism is shearing by latitudinal
differential rotation.
(Dikpati & Gilman, 2006, ApJ, in preparation)
Comparison of effects of zero and continuously updated surface sources on predicted cycles
Continuous poloidal source updating Zero poloidal source
Can we forecast beyond one cycle ahead?
C
Peak of cycle 20 is the same as when continually update surface poloidal source; but cycle 21 is nearly zero. This is true for diffusivities up to about Above that, dynamo is increasingly diffusion-dominated, and loses
memory of past cycles
Surface poloidal source
constructed from the predicted
bottom toroidal field; BL flux-
transport dynamo in self-excited mode
Skill tests
Zero poloidal source for predicted cycles
Babcock-Leighton poloidal source (from bottom toroidal field) for predicted cycles
Summary and future directions
Flux-transport dynamo with input of observed surface magnetic flux displays high skill in forecasting peak of the next solar cycle, as well as significant skill for
2 cycles ahead
We will do specific forecast for cycle 25 in the near future
Test forecast-model back to cycle 1
Simulate and forecast differences between N and S hemispheres
Go beyond longitude-averaged solar cycle features, e.g., simulate and predict ‘active longitudes’ (in progress – supported by opportunity fund)