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

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. Four established magnetopause models are benchmarked against this dataset by computing the difference between predicted and observed r₀, yielding root-mean-square errors (RMSE) of > 1 R_E globally and > 0.8 R_E in the subsolar region. Since different models use a variety of input parameters, it remains uncertain which parameters are most suitable to model the subsolar standoff distance of Earth's magnetopause to date. To address this question, a machine learning approach is used: 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 mentioned parameters achieves a RMSE of 0.68 R_E, improving on the best analytic model by approximately 17%.  To allow for straightforward modeling of the subsolar standoff distance, a second-order polynomial expression with 14 terms is derived, providing a compact, interpretable, and accurate representation of r₀. We note that the SVR model and the polynomial representation is not able to predict r₀ for extreme input conditions, e.g., during periods of very high solar wind dynamic pressure that is caused by, e.g., the passage of interplanetary coronal mass ejections. Accordingly, the parameter ranges that define the validity domain of the models are specified. We plan to broaden the range of possible input parameters in future iterations to account for, e.g., storm conditions as well. The presented results offer improved predictive accuracy of the subsolar standoff distance and highlight the potential of so far unconsidered parameters and rarely used techniques in modeling Earth's magnetopause.