1. 1 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

2. 2 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.

3. 3 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

4. 4 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

5. 5 Comparison CR1914 CR1917 CR1920 12345671234567 Method

6. 6 Comparison CR1967 CR1971 CR1974 12345671234567 Method Detail here

7. 7 Comparison CR2021 CR2024 CR2027 12345671234567 Method

8. 8 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 Noise CR1917 CR1971 CR2024

9. 9 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.

10. 10 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.