Solitary wave runup on coastal cliffs with basal notches: High-fidelity simulations and new predictive equations

Wave impact and runup investigations are increasingly important due to intensifying extreme coastal events. While sandy coasts have been widely studied, coastal cliffs remain underexplored despite hosting critical natural, urban, and cultural assets and being exposed to high-energy wave action. Most empirical runup formulations are derived for idealized settings and do not account for geomorphological features such as basal notches, which are widespread along natural cliffs. This study addresses this gap by systematically investigating solitary-wave runup on vertical cliffs with basal notches using 160 high-fidelity two-dimensional computational fluid dynamics simulations, varying relative wave height, notch submergence, and notch width. Results show that relative wave conditions primarily control runup, while deviations are governed by the vertical position of the notch roof, with a clear transition between hydrodynamically inactive submerged notches and emergent notches that amplify runup by up to 42% under energetic waves. For deep emergent cases, notch width introduces secondary modulation. Based on these findings, a hierarchical empirical framework for cliff-stability assessments is developed and validated on unseen wave conditions, improving the accuracy of runup prediction on notched cliffs by ∼55% relative to existing analytical formulations. Incorporating three-dimensional configurations and natural notch profiles would further refine the proposed framework.