The polar cap index (PCI) has been shown to be quite useful as an index of the electrodynamic processes within the high-latitude ionosphere. Here we use between 150 and 180 magnetometers to model the high-latitude electrodynamics with the assimilative mapping of ionospheric electrodynamics (AMIE) technique for all of 1997--2001. We compare AMIE calculations of the cross polar cap potential (CPCP), polar cap electric field, and polar cap area to the Northern PCI and the existing PCI-based relationships for these quantities. We find that the existing PCI estimates underestimate all of the AMIE derived quantities. The PCI is best correlated with the CPCP, while it correlates least with the polar cap electric field. In addition, there is a seasonal effect in the relationship between all AMIE quantities and the PCI. It is most pronounced in the electric field. The polar cap area is shown to have a linear fit in the summer and an asymptotic fit in the winter. These differences indicate that there may be a conductance difference in the techniques. We derive new relationships between the Northern PCI and the AMIE derived polar cap area, CPCP, and polar cap electric field which include the seasonal dependence.