Adapted empirical modelling of near-Sun solar-wind speeds for use in ensemble forecasts

Empirical relations are used to link modelled coronal magnetic field structure — particularly flux-tube expansion and distance to coronal hole boundary — to solar-wind speed. There is a lot of uncertainty embedded within these relations, particularly when used as an interface for heliospheric models. Hence, augmenting these relations could provide a powerful way to sample model uncertainty using ensemble techniques. We present a simplified empirical solar-wind speed equation that can be readily optimised for different configurations of an open-source Potential Field Source Surface and Schatten Current Sheet (PFSS+SCS) coronal model, in-lieu of the full Wang–Sheeley–Arge (WSA) equation. Optimisation is performed using a 10-year reanalysis dataset of in-situ solar-wind speed observations, reconstructed at 21.5 rS across longitudes at the sub-Earth point via a combined corotation and backmapping technique. We trial several functional forms for the simplified equation and explore three linear-regression techniques, highlighting the challenges of fitting empirical relations to noisy data. To minimise overfitting, we select a regression approach that fits directly to the distribution of reconstructed observations. We find an equation candidate that successfully reproduces the distribution of observed solar-wind speeds and performs comparably to WSA when coupled with the Heliospheric Upwind eXtrapolation with Time-dependence (HUXt) model to generate hindcasts at 1 AU. The new equation is not intended to replace WSA; the internal complexity remains a key element for WSA. Due to its simplicity, our equation produces less variability than WSA on average. The trade-off in complexity is balanced by usability within ensemble/multi-model frameworks. The equation can be easily perturbed to quantify uncertainty in windspeed magnitude and easily re-optimised for PFSS+SCS models with different source-surface and outer-boundary heights.