There is a great deal of variability in (particularly in ) for nearly all ranges of . We, therefore, show the mean and standard deviation of the windowed, linear fits to () in Figure 3a.

The two Hill models ( = 0 and = 2 S and 44 S) are the minimum
and maximum values of used by
*Siscoe et al.*, [2002]
and illustrate the
extremes of this model. The other
shown in Figures 2a
and 3 corresponds to the best-fit solution of
()
+ to
. One expects a non-zero minimum potential ()
due to viscous magnetospheric convection or other such processes so we have
added a constant to
which we attribute to the effects of
these processes.

In order to determine the best-fit () + to , total root-mean-square (RMS) differences between the two datasets were calculated in two ways.

The value of = 17 kV is reasonable for the minimum potential. The
lowest value of
for the Boyle model is 20 kV for this dataset
and the lowest
is 18 kV. Some studies report =
22-39 kV
[e.g., *Reiff et al.*, 1981]
but these values were obtained by linear
fitting of data and lower values were clearly present.

While is in good agreement with other studies, the value of
ionospheric conductance, = 23 S, is quite high. A typical
value of uniform ionospheric conductance used in MHD models is 5 S, and a
few S is not unusual
[e.g., *Ridley*, 2001].
Even if one considers the range of for the family of solutions
in Figure 4, the minimum for these solutions is 10 S,
which is still quite high.

The ram pressure dependence of can also be compared to that of . Figure 5

A final observation is the large amount of variability present in (), seen in Figure 2a. Although the events were selected to minimize uncertainties in determining , some part of this variability may be due to variation in the data coverage or variability in the solar wind. However, it is also possible that variability of this magnitude can only be explained by internal effects and that a model of the ionospheric potential requires detailed knowledge of the coupling between the magnetosphere and ionosphere and its time history.

The Hill model is certainly an advance in the sophistication of representing
in terms of measurable quantities. Saturation of the transpolar
potential is a salient feature of this model missing in many others. It
appears, however, that the Hill model, as formulated by
*Siscoe et al.* [2002],
needs some modification to be more consistent with the SuperDARN results.
One would expect a lower uniform ionospheric conductance than
the 23 S of the best-fit solution. The dependence of the data also suggest
a lower but there remain some inconsistencies with the SuperDARN
results.