The role of frequency spread on swash dynamics


The swash zone is the most dynamic part of the upper beach. Here breaking waves interact with sediments, leading to beach morphodynamics, and eventually to coastal erosion and flooding. An understanding of swash characteristics such as the vertical excursion and mean swash period is of vital importance to identify and predict the possible impact of storms in coastal areas. The prediction of these swash parameters is commonly based on bulk offshore spectral wave parameters and the beach slope, the latter being expensive to monitor. In this study, a dataset from an intermediate beach on the south-west coast of Sylt, Germany was derived to analyze swash characteristics. Field observations show high variability in swash excursion even for similar incident wave conditions if expressed by bulk parameters. Here, the role of frequency spread was further investigated. An inverse relationship between swash frequency spread and swash characteristics (excursion and mean period) was identified. A parameterization for the swash frequency spread based on incident wave parameters is proposed, and a new approach to obtain total swash excursion and mean swash period is developed. The parameterization is validated using two independent swash datasets (Duck 1982 and Duck 1994) and compared to the predictive ability of other parameterizations. It is highlighted that common parameterizations based on peak period do not perform well in characterizing incident conditions when bi-modal spectra are present. The choice of the right descriptor for wave periods may have a more pronounced influence on the predictive skill than the inclusion of the beach slope.

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The authors thank Helmholtz Zentrum Geesthacht (HZG) for hosting the camera system in the COSYNA framework and for the wave data which was obtained from Bathymetric data was provided by Landesbetrieb für Küstenschutz, Nationalpark und Meeresschutz Schleswig-Holstein. Jennifer Montaño acknowledges the Uni-Bremen bridge scholarship for prospective PhD students. We thank Alec Torres-Freyermuth and the anonymous reviewers for valuable suggestions to improve the manuscript.


This study has been supported by the DFG-Research Center/Cluster of Excellence “The Ocean in the Earth System.”

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Correspondence to Jennifer Montaño.

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Previous run-up parameterizations used in this study

Stockdon et al., (2006)

$$ S=\sqrt{S_{\mathrm{in}}^2+{S}_{\mathrm{ig}}^2} $$

Incident swash excursion is calculated as \( {S}_{\mathrm{in}}=0.75\beta \sqrt{H_0{L}_0} \) and swash excursion at the infragravity band is calculated as \( {S}_{\mathrm{ig}}=0.06\sqrt{H_0{L}_0} \).

Passarella et al. (2018)

The two equations proposed by Passarella et al. 2018 were applied in this study. However, only those obtained with P18-[1] are shown in the figures. The results obtained with P18-[2] were similar to those obtained with P18-[1].

Passarella 18-[1]:

$$ S=12.314\beta +0.087{T}_p-0.047\frac{T_p}{H_0} $$

Passarella 18-[2]:

$$ S=146.737{\beta}^2+\frac{T_p{H}_0^3}{5.8+10.595{H}_0^3}-4397.838{\beta}^4 $$

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Montaño, J., Blossier, B., Osorio, A.F. et al. The role of frequency spread on swash dynamics. Geo-Mar Lett 40, 243–254 (2020).

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