The icing disaster of overhead lines seriously threatens the safe operation of power grids. Overhead ground wires are more susceptible to icing due to the absence of current flow and their relatively higher suspension height compared to conductors. To investigate the relationship between high-frequency ice-melting current and environmental conditions, this study proposes a mathematical dependency model based on discrete data fitting. Using the overhead ground wire of a DC transmission project as the research subject, an electromagnetic-thermal bidirectional coupling model was developed to quantitatively study the relationship between ice-melting current and environmental conditions. Based on extensive data, a mathematical model relating high-frequency ice-melting current to wind speed was developed, revealing a cubic polynomial relationship between them. Both the mean error and root mean squared error of the fitting curve are relatively small. This study provides valuable guidance for calculating the required ice-melting current under specific environmental conditions, based on comprehensive research into high-frequency ice-melting of ground wires.