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Procedure

Shepherd et al., [2002] identified quasi-stable periods of $E_\mathsf{KL}$, the Kan-Lee electric field [Kan and Lee, 1979], as measured by the Advanced Composition Explorer (ACE) between February 1998 and December 2000. These periods also satisfy the criteria that $\Phi_\mathsf{PC}^\mathsf{SD}$, determined using the Johns Hopkins University Applied Physics Laboratory Fitting technique or APL Fit [Ruohoniemi and Baker, 1998; Shepherd and Ruohoniemi, 2000], were suitably well-defined by the SuperDARN LOS Doppler velocity data.

Figure 1. Global convection map and $\Phi_\mathsf{PC}^\mathsf{SD}$ derived from SuperDARN velocity data for an example 10-min period during this study. The dots indicate anchor points of the velocity data and contours represent constant potential curves.
\begin{figure}\figbox*{\hsize}{}{\epsfig{file=figs/map.ps}} %% PREPRINT
\end{figure}

Figure 1 shows an example of a global convection map for a 10-min period from the Shepherd et al., [2002] study. For this period SuperDARN LOS velocity data were obtained over large portions of the dawn and dayside sectors. The coveraged was sufficient to fix the values of the potential extrema and hence to determine $\Phi_\mathsf{PC}$.

We use a subset of 1317 10-min periods from the Shepherd et al., [2002]Shepherd:00 dataset for this study. Because the statistics are greatest in the range $E_\mathsf{KL}$ $\le$ 30 kV/R$_\mathsf{E}$, we use only the periods which fall in this range. Appropriately time-lagged 10-min averages of the ACE/SWEPAM solar wind speed ($V$) and mass density ($\rho$), and the ACE/MAG IMF ($\vec{B}$) are used to derive $\Phi_\mathsf{PC}^\mathsf{Hill}$. $\Phi_\mathsf{PC}$ is also computed for the Boyle model [Boyle et al., 1997] for comparison. $\Phi_\mathsf{PC}$ for these models are then directly compared to the SuperDARN-derived transpolar potential ( $\Phi_\mathsf{PC}^\mathsf{SD}$).

The formulation of the Hill model we use in this study is given by [Siscoe et al., 2002]

\begin{displaymath}
\Phi_\mathsf{PC}^\mathsf{Hill} = \frac{57.6 E_\mathsf{sw} p^...
...)} {p^\frac{1}{2} + 0.0125 \xi \Sigma E_\mathsf{sw} F(\theta)}
\end{displaymath} (1)

where $E_\mathsf{sw} = V B_\mathsf{T}$ is the solar wind electric field with $V$ being the solar wind speed and $B_\mathsf{T} = ({B_\mathsf{y}^2 +
B_\mathsf{z}^2})^\frac{1}{2}$. $p$ is the solar wind ram pressure. $F(\theta)$ is the IMF clock angle dependence of reconnection at the magnetopause, taken to be $\sin^2(\theta/2)$. A relation for $\xi$, a factor that depends on the geometry of the currents flowing into the ionosphere, is given as $4.45 - 1.08
\log \Sigma$, where $\Sigma$ is the ionospheric conductance and is assumed to be uniform. We note that the choice of $F(\theta)$ allows us to rewrite (1) as
\begin{displaymath}
\Phi_\mathsf{PC}^\mathsf{Hill}(\Sigma) =
\frac{57.6 E_\math...
...frac{1}{3}}
{p^\frac{1}{2} + 0.0125 \xi \Sigma E_\mathsf{KL}}
\end{displaymath} (2)

where $E_\mathsf{KL}$ is identified as the Kan-Lee reconnection electric field [Kan and Lee, 1979] corresponding to the fastest merging rate at the subsolar magnetopause [Sonnerup, 1974].


next up previous
Next: Data and Discussion Up: Testing the Hill model Previous: Introduction


Simon Shepherd 2002-06-04