This study aims to advance the current understanding of the role that the berm plays in modulating wave run-up dynamics for elevation control purposes. Accurate prediction of wave run-up is essential for coastal hazard assessment and management, yet existing empirical models often fail to account for the dynamic influence of berm morphology. This study introduces a new empirical formula for wave run-up that solves the current wave run-up empirical formula can not adequately consider the instantaneous changes in the berm (including width, elevation, and onshore slope). Using field measurements from sandy beaches in Haikou, China, combined with numerical simulations (XBeach) and video-derived run-up data from a Coastal Shore-based Video Imagery Monitoring System (COSVIMS), we analyze run-up behavior on composite-profile beaches featuring a gentle berm and steep dune. Results demonstrate that berm geometry significantly attenuates run-up: a higher and wider berm reduces both vertical elevation and horizontal extent of run-up. The proposed model which including berm height (hB), berm platform length (LB), and the onshore slope of the berm ridge (βSon) outperforms established formulations across multiple international beach datasets, showing higher correlation and lower root-mean-square error (RMSE = 0.046) than old models. By capturing real-time feedback between berm evolution and run-up, this improved formula resolves the issue of asynchrony between hydrodynamics and run-up, thereby providing a robust basis for real-time calculations of wave-topography interactions.
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