Shape of the open–closed boundary of the polar cap as determined from observations of precipitating particles by up to four DMSP satellites

The shape of the open–closed boundary is studied using auroral oval crossings from up to four DMSP satellites, providing a maximum eight‐point determination per hemisphere. The spectra of both precipitating ions and electrons are examined, and boundary crossings are determined by visual inspection. A subset of crossings with between six‐ and eight‐point determinations observed during intervals spanning 15 to 58 min are used to form a cubic spline approximation to the open–closed boundary for each interval. The variability in the size, shape, and location of the boundary is characterized. Approximately half the time the points can be well fit by a circle, but for the remaining intervals the shape is more complex. The speed at which the boundary moves is estimated, and the accuracy of determining the amount of open flux from n observed boundary crossings is tested. When only one point is used to determine the open flux (by assuming an offset circle), the standard deviation of the relative error is 33%, dropping to 16% for a four‐point measurement. The variation of the open flux with measures of solar wind coupling is tested and found to be roughly proportional. These findings have implications for space weather applications which require the construction of a data set of open flux.