1 Interpolation of polar field Y. Liu, J. T. Hoeksema, X. P. Zhao, R. M. Larson – Stanford University

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

4 Comparison CR1914 CR1917 CR Method

5 Comparison CR1967 CR1971 CR Method

6 Comparison CR2021 CR2024 CR Method