We have carefully selected a set of 10-min-averaged periods between February 1998 through December 2000 to study the relationship between the solar wind and IMF conditions and . The periods were chosen such that (1) the solar wind and IMF conditions at the ACE spacecraft were quasi-stable for 40 min and (2) the coverage of SuperDARN backscatter was adequate to determine . To satisfy the stability criteria it was decided that the effective interplanetary electric field could not vary by more than 7% for the 40 min period, making the calculation of the transit time from ACE to the ionosphere less critical. Suitable ionospheric coverage is defined as those times when >200 SuperDARN data points exist in the dayside sector (0600-1800 MLT) or >400 data points exist anywhere in the high-latitude region. A total of 9464 10-minute-averaged periods were found to satisfy the first criteria, and a subset of 2721 10-minute periods satisfied both criteria. By dropping the first and last 10-minute period of each event, 1638 high-confidence periods remain.
The resulting solutions of obtained by applying the APL FIT technique to the set of 10-minute-averaged periods show that for quasi-steady solar wind and IMF, (1) is nonlinear in , (2) saturates at high values of , and (3) is extremely variable for all values of . These results indicate that simple formulations involving the upstream solar wind and IMF conditions are inadequate to describe the instantaneous in anything but a statistical sense. A model that includes internal processes, such as that developed by Hill et al.,  and Siscoe et al., , is necessary to describe the relationship between the solar wind parameters, , and possibly other geomagnetic parameters. Further study is necessary to confirm the fit of these models with the data in our study.
This work was supported by NSF grant ATM- and NASA grant NAG5-. Operation of the Northern Hemisphere SuperDARN radars is supported by the national funding agencies of the U.S., Canada, the U.K., and France. We gratefully acknowledge the ACE/MAG instrument team, the ACE/SWEPAM instrument team, and the ACE Science Center for providing the ACE level 2 data.