Synoptic Maps of Magnetic Field from MDI Magnetograms: polar field interpolation.

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Synoptic Maps of Magnetic Field from MDI
Magnetograms polar field interpolation.

• Y. Liu, J. T. Hoeksema, X. P. Zhao, R. M. Larson
  Stanford University
• yliu_at_solar.stanford.edu

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Abstract

• In this poster, we compare various methods for
  interpolation of polar field for the MDI synoptic
  charts of magnetic field. By examining the
  coronal and heliospheric magnetic field computed
  from the synoptic charts based on a Potential
  Field Source Surface model (PFSS), and by
  comparing the heliospheric current sheets and
  footpoints of open fields with the observations,
  we conclude that the coronal and heliospheric
  fields calculated from the synoptic charts are
  sensitive to the polar field interpolation, and a
  time-dependent interpolation method (Method 5)
  using the observed polar fields is the best among
  the seven methods investigated.

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Question
4
(No Transcript)
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Polar field interpolation

1. 1D cubic spline interpolation method
2. Potential field method
3. Modified 1D cubic spline interpolation method
   (smoothed)
4. Polar field model method (BBpcos(colatitude)8)
   (e.g. Svalgaard et al 1978)
5. 2D temporal interpolation method
6. 2D spatial interpolation method
7. flux transportation model based method (data from
   Schrijver and DeRosa, 2002).

Method 1
Method 5
Method 6
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Description of Method 5

• Using observed polar field data.

Observational polar field data
After doing surface fitting
2D fitting
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Description of Method 5 (cont.)
Polar field measurement in southern pole from
1996 to 2004.
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Interpolated polar field for CR1914
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Data for test

• Rising phase of cycle 23 (1996-1997)
• CR1914 ( Sep 1996 Oct 1996)
• CR1917 (Dec 1996 Jan 1997)
• CR1920 (Mar 1997 Mar 1997)
• Maximum phase of cycle 23 (2000-2001)
• CR1967 (Sep 2000 Sep 2000)
• CR1971 (Dec 2000 Jan 2001)
• CR1974 (Mar 2001 Apr 2001)
• Declining phase of cycle 23 (2004-2005)
• CR2021 (Sep 2004 Oct 2004)
• CR2024 (Dec 2004 Dec 2004)
• CR2027 (Feb 2005 Mar 2005)

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Comparison
Method
1 2 3 4 5 6 7
CR1914 CR1917 CR1920
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Comparison
Method
Detail here
1 2 3 4 5 6 7
CR1967 CR1971 CR1974
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Comparison
Method
1 2 3 4 5 6 7
CR2021 CR2024 CR2027
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Polar field reversal
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Polar field reversal (?)
CR1972 CR1983
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Heliospheric field
CR1960 (02/2000-03/2000)
CR1975 (04/2001-05/2001)
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Discussions and conclusion

• Method 1 This method is bad because closed
  fields are computed in polar regions in solar
  minimum
• Method 2 This method is based on Method 1 (bad)
• Method 3 Improved but questionable during polar
  field reversal. When trailing field reaches high
  latitude but the polar field is not reversed, the
  interpolated polar field might already give a
  reversed polar field because this method uses low
  latitude data to interpolate polar field (see
  CR1967)
• Method 4 generally is good, but might be
  questionable in solar maximum because no evidence
  has been presented to show this model is still a
  good approximation in solar maximum
• Method 5 might be the best
• Method 6 also uses the low latitude data to fill
  in the polar regions. It may be questionable
  during polar field reversal (see CR1967)
• Method 7 strongly depends on flux transportation
  model that would be very complicated. Also show
  earlier polar field reversal (CR1967).