Adapted Empirical Modeling of Near‐Sun Solar‐Wind Speeds for Use in Ensemble Forecasts

Solar wind science and forecasting relies on empirical relations between modeled coronal magnetic‐field structure—particularly flux‐tube expansion and distance to coronal hole boundary—and solar‐wind speed. There is lots of uncertainty in these relations, creating large uncertainties in the inner‐boundary conditions to heliospheric models. This uncertainty could potentially be sampled using ensemble techniques, but current functional forms and numbers of free parameters in empirical relations make this difficult. We present a simplified empirical solar‐wind speed equation that can be readily optimized for different configurations of a Potential Field Source Surface and Schatten Current Sheet (PFSS + SCS) coronal model, in‐lieu of the full Wang–Sheeley–Arge (WSA) equation. Optimization is performed using an 11‐year data set of in situ solar‐wind speed observations, reconstructed at 21.5 rS. We trial several functional forms and explore three linear‐regression techniques, highlighting challenges of fitting empirical relations to noisy data with large class imbalances. To minimize overfitting, we select a regression approach that fits directly to the distributions, rather than time series. Using k‐fold cross validation 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 1AU. The new relation is not intended to replace WSA; the internal complexity remains a key element for WSA. Indeed, the simplified equation produces less variability on average. But this trade‐off is balanced by usability within ensemble frameworks, where now the equation can be easily perturbed to quantify uncertainty in solar‐wind speed.