Parameterization of the Subsolar Standoff Distance of Earth's Magnetopause based on Results from Machine Learning

Abstract. The subsolar standoff distance r₀ of Earth's magnetopause is a key parameter in understanding the interaction between the solar wind and the magnetosphere. Despite decades of modeling efforts, significant uncertainties persist between model predictions and satellite observation of the magnetopause location. This study introduces a new data-driven parameterization of r₀, based on a dataset containing over 220,000 dayside magnetopause crossings obtained by the THEMIS (2007–2022) and Cluster (2001–2020) missions. Each crossing is paired with high-resolution upstream solar wind parameters from the OMNI database. Four established empirical models are benchmarked against this dataset, yielding root-mean-square errors (RMSE) of ≳ 1 R_E globally and ≳ 0.8 R_E in the subsolar region. To determine the primary physical factors of r₀, an XGBoost regression model is trained and interpreted using SHapley Additive exPlanation (SHAP) values. The solar wind dynamic pressure is found to be the dominant contributor, followed by geomagnetic indices (AE, SYMH), interplanetary magnetic field (IMF) magnitude, dipole tilt angle, and IMF cone angle. The IMF B_z component contributes only marginally when geomagnetic indices are included. A support vector regression (SVR) model using the six most influential parameters achieves a RMSE of 0.68 R_E, improving on the best analytic model by approximately 17 %. A second-order polynomial expression with 14 terms is derived, providing a compact, interpretable, and accurate representation of r_0. The SVR model and the polynomial representation is not able to predict r₀ for extreme input conditions, e.g., during the passage of interplanetary coronal mass ejections. Accordingly, the parameter ranges that define the validity domain of the models are specified. The presented results offer improved predictive accuracy of the subsolar standoff distance and highlight the role of so far unconsidered parameters in modeling Earth's magnetopause.