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Waves on the beach: how high is water brought by wave breaking?

The forwards and backwards movement of waves breaking on a beach is one of the processes by which the sea shapes the shoreline and interacts with human constructions. Being able to predict the maximum height reached by water according to local conditions is therefore necessary.


When it comes to the impact of the sea on the shore, and particularly to the risks for society (erosion, submersion, damage to infrastructures), considering the mean sea level is not sufficient as the breaking of waves can bring water at a much higher height. The thorough study of these processes is therefore very important for all those involved in coastal area management.

All the water brought by the waves cannot immediately move back and water accumulates along the beach with a surface ascending towards the beach: this called the setup. But the maximum level reached by water is even higher because each wave projects towards the beach a layer of water called swash. Runup is defined as the difference between discrete water elevation maxima (swash) and still water level (i.e. without agitation),

Many studies dealt with this important parameter, which can be calculated from beach slope, swell wavelength and wave height. Several equations were proposed from field measurements but none was obtained from sites where tide amplitude is high as in Brittany. In this so-called macrotidal context, they cannot be used because the foreshore is wide and its topography is complex, so that it is generally not possible to define and measure an average slope for the beach, the swash zone or the foreshore itself.

The paper uses in situ measurements to estimate the parameters of an equation suitable to this type of beaches. The field work was conducted during 22 trips between April 2008 and June 2010, on a beach of Guissény on the north coast of Finistère (Brittany, France). Owing to the high tidal range (up to 9 m) and the very low average beach slope, the foreshore is wide, about 300 m; its slope is steeper and more variable on the upper part (the active section).


Minimum, maximum and average profile of the Vougot beach (MWL : mean water level ; MHWS et MLWS : mean level of high and low water of spring tides)

The maximum level reached by water during a tidal cycle is shown by the limit between dry and wet sands; its altitude was recorded by GPS with a precision of about 1 cm. This method is much more precise than the video techniques usually employed to observe runup processes. The precise measure of the average high tide level without agitation was done using a pressure sensor fixed on a rock emerging only at the lowest tides: the pression depends on the hight of water above the sensor and the atmospheric pressure (measured by another sensor). The observed runup is the difference between the maximum and the avarage levels.


GPS measurement of the position and altitude of the runup (in the foreground, the limit between dry and wet sand is underlined in black)

On Vougot beach, runup is very variable: during the study period, it varied between a few tens of centimeters to more than three meters.


Height measured during the study period; the runup is shown by the red area (difference between the maximum level –high tide mark- and the average level –observed tide)

In addition, theoretical values of the runup were computed for each date using the published equations, taking as beach slope the slope measured for the whole foreshore and for its active part. This confirms that these equations are not adapted to this macrotidal context, estimated runup is underestimated in one case, closer but overestimated in the other. A new equation was elaborated to better describe the relation between runup and the variable that influence it on the Vougot beach. In the model, beach morphology is no longer represented by an average slope (meaningless for macrotidal beaches) but by the slope of its active part. The latter slope provides the best fit with field measurements, as expected from what is known about the setup, one of the two components of the runup: it was shown that the accumulation of water along the shore is very dependent on the slope of the active part of the beach.

The coefficient used in the equation of the Vougot beach is different from the one found for another macrotidal beach of the Finistère (Porsmilin); this confirms the role of morphological and hydrodynamical characteristics of each beach.

Even if extreme water levels can be reached before or after high tide, this methodology makes it possible to predict, for given beach and sea conditions, the higher limit of hydrodynamism action on natural (dunes, sandspits) or man-built (constructions) structures.


The paper

Cariolet J.-M., Suanez S., 2013. Runup estimations on a macrotidal sandy beach. Coastal Engineering 74 : 11–18.
See the first page


The authors

This work was conducted in the laboratory LETG-Géomer of IUEM


La revue

Coastal Engineering is an international journal for scientists and engineers working in the field of marine and coastal technology. It combines practical application with modern technological and scientific achievements. The papers published deal with waves and currents, coastal morphology, estuary hydraulics, harbour and offshore structures.



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