On the role played by magnetic expansion factor in the prediction of solar wind speed

Over the last two decades, the Wang-Sheeley-Arge (WSA) model has evolved significantly. Beginning as a simple observed correlation between the expansion factor of coronal magnetic field lines and the measured speed of the solar wind at 1 AU (the Wang-Sheeley (WS) model), the WSA model now drives NOAA's first operational space weather model, providing real-time predictions of solar wind parameters in the vicinity of Earth. Here we demonstrate that the WSA model has evolved so much that the role played by the expansion factor term is now largely minimal, being supplanted by the distance from the coronal hole boundary (DCHB). We illustrate why and to what extent the three models (WS, DCHB, and WSA) differ. Under some conditions, all approaches are able to reproduce the grossest features of the observed quiet time solar wind. However, we show that, in general, the DCHB- and WSA-driven models tend to produce better estimates of solar parameters at 1 AU than the WS model, particularly when pseudostreamers are present. Additionally, we highlight that these empirical models are sensitive to the type and implementation of the magnetic field model used: In particular, the WS model can only reproduce in situ measurements when coupled with the potential field source surface model. While this clarification is important both in its own right and from an operational/predictive standpoint, because of the underlying physical ideas upon which the WS and DCHB models rest, these results provide support, albeit tentatively, for boundary layer theories for the origin of the slow solar wind.