Observations and predictions of run‐up

<jats:p>For a significant range of offshore wave conditions and foreshore slopes, run‐up observations are compared to semiempirical formulations and predictions of an existing numerical model based on the depth‐averaged one‐dimensional nonlinear shallow water equations with bore‐like breaking wave dissipation and quadratic bottom friction. The numerical model is initialized with time series of sea surface elevation and cross‐shore velocity observed in 80 cm mean water depth (approximately 50 m offshore of the mean shoreline) on a gently sloping beach and in 175 cm water depth (100 m offshore of the shoreline) on a steep concave beach. Run‐up was measured with a stack of resistance wires at elevations 5, 10, 15, 20, and 25 cm above and parallel to the beach face. At sea swell frequencies (nominally 0.05 < <jats:italic>f</jats:italic> ≤ 0.18 Hz), run‐up energy is limited by surf zone dissipation of shoreward propagating waves so that increasing the offshore wave height above a threshold value does not substantially increase the predicted or observed sea swell run‐up excursions (e.g., run‐up is “saturated”). Existing semiempirical saturation formulations are most consistent with the observations and numerical model predictions of run‐up excursions nearest the bed. In contrast, at infragravity frequencies (0.004 < <jats:italic>f</jats:italic> ≤ 0.05 Hz) where surf zone dissipation is relatively weak and reflection from the beach face is strong (e.g., saturation formulas are not applicable), the run‐up excursions increase approximately linearly with increasing offshore wave height. The numerical model also accurately predicts that the tongue‐like shape of the run‐up results in sensitivity of run‐up measurements to wire elevation. For instance, run‐up excursions and mean vertical superelevation (above the offshore still water level) increase with decreasing wire elevation, and continuous thinning of the run‐up tongue during the wave uprush can result in large phase differences between run‐up excursions measured at different wire elevations. Numerical model simulations suggest that run‐up measured more than a few centimeters above the bed cannot be used to infer even the sign of the fluid velocities in the run‐up tongue.</jats:p>