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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@solar.stanford.edu

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Interpolation of the polar regions

1. 1D cubic spline interpolation (Xuepu’s method)

2. Potential field method (Xuepu’s method)

3. Modified 1D cubic spline interpolation (smooth)

4. Polar field model method: B=Bp*cos(colatitude)^8 (suggested by many others)

5. Using observed polar field data.a. Select the synoptic charts when the polar regions are well observed (generally one synoptic

chart per year for one pole region);

b. Transform the data into the polarview plane;

c. Use a least-square-based algorithm to do a surface fitting (algorithm and code are from Rasmus);

d. Transform the fitting data into the Carrington coordinate;

e. Thus we have one modeled polar field distribution per year;

f. Using 1D cubic spline interpolation to fill in the missing-data areas of the synoptic maps based on the modeled polar field data.

6. 2D interpolation (least-square-based algorithm from Rasmus)

7. Flux transport equation based method.

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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 (B=Bp*cos(colatitude)^8);

5. 2D temporal interpolation method;

6. 2D spatial interpolation method;

7. flux transportation model based method.

Method 1

Method 5

Method 6

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• 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)

Data for test

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Comparison

CR1914 CR1917 CR1920

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Method

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Comparison

CR1967 CR1971 CR1974

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Method Detail here

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Comparison

CR2021 CR2024 CR2027

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Method

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Non-uniformed Noise Distribution in Synoptic Frame

Noise added in B_los

Original Charts

With 10 Gauss Noise

With 20 Gauss Noise

With 40 Gauss Noise

With 80 Gauss Noise

With 320 Gauss NoiseCR1917 CR1971 CR2024

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Test for Rescaling Scheme

Modeled IMF from PFSS model:

Blue line: modeled IMF from original MDI synoptic charts;

Green line: modeled IMF from rescaled MDI synoptic charts based on Ulrich et al (2002) & Berger & Lites (2002) [delta^-1 = 0.611*(2.61-0.64Sin^2(rho))];

Red line: modeled IMF from rescaled synoptic charts based on Tran et al (2005);

Black line: Observation.

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Test of rescaling scheme

Comparison of MDI synoptic chart (after rescaled based on Tran et al) and SOLIS synoptic chart for CR2039 (from Zoran Mikic):

Red: average of magnetic field along longitude from MDI chart;

Green: average of magnetic field along longitude from SOLIS chart;

Blue: average of unsigned field along longitude from MDI chart;

Black: average of unsigned field along longitude from SOLIS chart.