A Model-Derived Empirical Formulation for Wave Run-Up on Naturally Sloping Beaches

Maarten Van Ormondt,Ap Van Dongeren,Dano Roelvink

doi:10.3390/jmse9111185

Maarten Van Ormondt, Ap Van Dongeren + Show 1 more

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https://doi.org/10.3390/jmse9111185

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Abstract

A new set of empirical formulations has been derived to predict wave run-up at naturally sloping sandy beaches. They are obtained by fitting the results of hundreds of XBeach-NH+ model simulations. The simulations are carried out over a wide range of offshore wave conditions (wave heights ranging from 1 to 12 m and periods from 6 to 16 s), and surf zone (Dean parameters aD ranging from 0.05 to 0.30) and beach geometries (slopes ranging from 1:100 to 1:5). The empirical formulations provide estimates of wave set-up, incident and infragravity wave run-up, and total run-up R2%. Reduction coefficients are included to account for the effects of incident wave angle and directional spreading. The formulations have been validated against the Stockdon dataset and show better skill at predicting R2% run-up than the widely used Stockdon relationships. Unlike most existing run-up predictors, the relations presented here include the effect of the surf zone slope, which is shown to be an important parameter for predicting wave run-up. Additionally, this study shows a clear relationship between infragravity run-up and beach slope, unlike most existing predictors.

Highlights

Coastal zones are subject to wave and wind-induced hazards such as wave attack, flooding, and erosion
The model results indicate that the location of this tipping point is not fixed but depends on the surf zone conditions
When combined with the reduction factors for incident wave angle (Section 3.5) and directional spreading (Section 3.6), the use of these new relations results in improved error statistics compared to the S06 relations, using the same dataset

Summary

Introduction

Coastal zones are subject to wave and wind-induced hazards such as wave attack, flooding, and erosion. Wind fields associated with storms exert a shear stress on the water surface which causes a water level gradient towards the coast called storm surge. This is exacerbated by the inverse barometer effect which causes an uplift of the water surface by the low-pressure fields near the eye of the storm. These wind-induced processes have been incorporated into hydrodynamic forecast and planning models such as Delft3D [1], ADCIRC [2], and SLOSH [3], which are routinely used. A very thorough overview of existing run-up predictors and their performance is provided by Gomes da Silva [13]

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