Comparative Analysis of Various Machine-Learning Models for Solar-Wind Propagation-Delay Estimation

Geomagnetic storms resulting from solar disturbances impact telecommunication and satellite systems. Satellites are positioned at Lagrange point L1 to monitor these disturbances and give warning 30 min to 1 h ahead. As propagation delay from L1 to Earth depends on various factors, estimating the delay using the assumption of ballistic propagation can result in greater uncertainty. In this study, we aim to reduce the uncertainty in the propagation delay by using machine-learning (ML) models. Solar-wind velocity components (\(V_{ \mathrm{x}}\), \(V_{\mathrm{y}}\), \(V_{\mathrm{z}}\)), the position of Advanced Composition Explorer (ACE) at all three coordinates (\(r_{\mathrm{x}}\), \(r_{\mathrm{y}}\), \(r_{\mathrm{z}}\)), and the Earth’s dipole tilt angle at the time of the disturbances are taken as input parameters. The target is the time taken by the disturbances to reach from L1 to the magnetosphere. The study involves a comparison of eight ML models that are trained across three different speed ranges of solar-wind disturbances. For low and very high-speed solar wind, the vector-delay method fares better than the flat-plane propagation method and ML models. Ridge regression performs consistently better at all three speed ranges in ML models. For high-speed solar wind, boosting models perform well with an error of around 3.8 min better than the vector-delay model. Studying the best-performing models through variable-importance measures, the velocity component \(V_{\mathrm{x}}\) is identified as the most important feature for the estimation and aligns well with the flat-plane propagation method. Additionally, for slow solar-wind disturbances, the position of ACE is seen as the second most important feature in ridge regression, while high-speed disturbances emphasize the importance of other vector components of solar-wind speed over the ACE position. This work improves our understanding of the propagation delay of different solar-wind speed and showcases the potential of ML in space weather prediction.