Lag Time Determination

In order to directly compare the solar wind measurements from ACE with the corresponding ionospheric radar measurements, and because the statistical model pattern used in APL FIT is keyed to the IMF, we must determine the amount of time to delay the ACE measurements to allow for propagation to the ionosphere. This time delay, or lag time, between ACE and the ionosphere depends on the solar wind speed and density and can range from ~30 min to longer than 90 min.

The sensitivity to errors in the determination of the lag time is greatly reduced by selecting time periods with quasi-stable solar wind and IMF conditions. A nominal value for the lag time is found by applying a relatively standard technique, whereby the lag time is comprised of three parts: the solar wind advection time $\tau_{sw}$, the magnetosheath transit time $\tau_{ms}$, and the Alfvén transit time along magnetic field lines from the subsolar magnetopause to the ionosphere $\tau_{alf}$.

The three components are given by

$$\tau_{sw} = \left( X_{sc} - X_{bs} \right)/v_{sw},$$ (3)

$$\tau_{ms} = \left( X_{bs} - X_{mp} \right)/v_{sw} \times 8,$$ (4)

$$\tau_{alf} = 2 \, \mathrm{min},$$ (5)

where $X_{sc}$ is the position of ACE projected onto the Sun-Earth line, $X_{bs}$ is the subsolar bow shock location following Peredo et al. [1995], $X_{mp}$ is the subsolar magnetopause location following Sibeck et al. [1991, 1992], and $v_{sw}$ is the antisunward solar wind speed (written as $V$ in equation (1)). The 2-min value chosen for Alfvén transit time is the average of the 1-3 min thought to occur in practice [e.g., Lester et al., 1993; Khan and Cowley, 1999]. The factor of eight in equation (4) is due to the slowing of the plasma in the magnetosheath [Spreiter and Stahara, 1994].