A Closed-Form Analytical Solution for HFSWR Wind Direction Inversion Using the von Mises Model

Wind direction inversion in high-frequency surface wave radar (HFSWR) relies heavily on the directional distribution model (DDM). The classical Longuet-Higgins (L-H) model causes non-physical spatial discontinuities due to energy truncation in the upwind direction. While the Donelan model corrects this defect and achieves higher accuracy, its inversion still relies on non-linear optimization or numerical discretization, resulting in low computational efficiency. The Apel model, though simple in form, also lacks a unified analytical inversion formula. To address these issues, this letter introduces the von Mises (VM) model—a natural circular distribution ensuring physical continuity—into HFSWR wind direction inversion. We derive an explicit closed-form analytical solution for dual-station inversion by exploiting the VM model’s exponential properties, transforming complex numerical searches into efficient algebraic calculations. Field experiments in the Taiwan Strait demonstrate that the VM model achieves accuracy slightly superior to the Donelan model (with an overall RMSE of 9.49° and MAE of 7.28° across cross-wind and onshore scenarios), while ensuring spatial smoothness and accelerating the computation by over three orders of magnitude.