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 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.

3. 3 Question

4. 4

5. 5 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) (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

6. 6 Description of Method 5  Using observed polar field data. Observational polar field data After doing surface fitting 2D fitting

7. 7 Description of Method 5 (cont.) Polar field measurement in southern pole from 1996 to 2004.

8. 8 Interpolated polar field for CR1914

9. 9 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

10. 10 Comparison CR1914 CR1917 CR1920 12345671234567 Method

11. 11 Comparison CR1967 CR1971 CR1974 12345671234567 Method Detail here

12. 12 Comparison CR2021 CR2024 CR2027 12345671234567 Method

13. 13 Polar field reversal

14. 14 Polar field reversal (?) CR1972 CR1983

15. 15 Heliospheric field CR1960 (02/2000-03/2000) CR1975 (04/2001- 05/2001)

16. 16 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).