Comparison of the Hill–Siscoe polar cap potential theory with the Weimer and AMIE models

The magnetic storm on November 2004 was characterized by a high solar wind pressure and thus offers a unique opportunity to test the Hill–Siscoe formula (H–S) for the polar cap potential (PCP). To estimate the polar cap potential, we use the Weimer Statistical Convection Model (WCM), and the Assimilative Mapping of Ionospheric Electrodynamics Model (AMIE), based on ingestion of a number of data sets. H–S is in excellent agreement with WCM, and with AMIE during times when DMSP is used in the latter. The implication is that the AMIE conductivity model yields conductivities that are too high by a factor of 2–3. Both H–S and WCM display saturation effects, although WCM is more severe. The two methods track well until an IEF of about 20 mV/m occurs, where H–S continues to increase while WCM levels off. Even at high electric field values, the pressure increases the denominator of the H–S formula by 60%, keeping the potential lower than its saturation value. There are several H–S points above 250 kV, even up to 400 kV, that are not found in WCM and occur right after a rapid transition from Bz north to south. For Bz north, we find evidence for a saturation effect on the PCP at large IEF, little effect as a function of solar wind velocity, and an increase of the PCP with increasing pressure. This seems to rule out viscous interaction but may involve geometric changes in the high-altitude polar cusp that affect recombination there for Bz north.