$\lambda$ should be related by $\tan i=2\tan\lambda$ (see Page 50 of @Fowler:1990 ). From the related two rows in Table \[tab:parameter\] we find that this relation is not well satisfied for each plume and $|\tan i| < 2|\tan \lambda|$ in all cases. Therefore the magnetic field is not well approximated by this dipole field and is more horizontal, as also shown in the middle panel of Figure \[fig:dipole\_tan\]. In the bottom panel we check how much plumes deviate from the dipole field and how this deviation changes with the latitude. We find that at lower latitudes, the plumes are more horizontal than the dipole field. This was already noted by @Saito:1965 who used a bar magnet of finite length to fit the plumes/rays at different distances from the Sun observed during a solar eclipse. @Banaszkiewicz:etal:1998 described a simple analytic model for the magnetic field at solar activity minimum. A dipole and a quadruple field were added to construct the coronal magnetic field in the solar minimum. The reconstructed 3D plumes could be used as a reference in the polar region to test other, more sophisticated magnetic field models [@Neukirch:1995; @Ruan:etal:2008].

### Plume’s width analysis

Besides the orientation, we calculated the 