# Difference between revisions of "Dune erosion"

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 Definition of Dune erosion: Sand loss from a dune under wave attack, mainly by avalanching and slumping processes. This is the common definition for Dune erosion, other definitions can be discussed in the article

## Introduction

Fig. 1. Post-storm eroded dune, Egmond aan Zee.

This article focuses on dune erosion that can occur in a short time during severe storm conditions. Such erosion events may lead to a long-term trend of dune retreat, but this is not always the case. The eroded dune can be restored after the storm under 'normal' hydrodynamic conditions by natural processes, if the pre-storm beach profile was in morphodynamic equilibrium, i.e. not experiencing any erosion trend. Here, 'beach profile' has to be understood as the cross-shore profile of the entire active coastal zone.

A coastal dune can suffer large losses when attacked by storm waves. The front dune can be taken away over several tens of meters, leaving a steep dune scarp, see Fig. 1. For the Dutch coast it has been estimated that the dune foot can recede as much as 80-100 m under exceptional circumstances (extreme storms of very long duration, which may occur with a yearly probability of 1/100,000). The actual dune loss depends on local conditions such as beach width, beach height and dune height.

Fig. 2. Storm-induced dune foot retreat as a function of frequency of exceedance

As an example, Fig. 2 shows a model result of the relationship between dune retreat [math]RD[/math] (expressed as the distance between the initial dune foot location and the dune foot location after the storm surge) and exceedance frequency (the probability that in a particular year a storm occurs that produces greater erosion) for a location along the Dutch coast. According to this figure there is a 1/100,000 probability per year that dune erosion will exceed 85 m. To establish such a plot, a proper insight is needed in the possibly occurring extreme storm conditions in the (very) small probability range. However, such insight is subject to great uncertainty, as reliable measurements of extreme water levels and wave conditions are available only over relatively short periods of the order of 100 years. With such a restricted data set, it is hard to make estimates of storm conditions with a yearly exceedance probability less than about 1/1000.

## Impact of dune erosion

Fig. 3. Badhotel at Schiermonnikoog after the 1924 storm.

Buildings on the front dune situated close to the dune foot are clearly at risk under severe storms, see Fig. 3. A sound estimate of potential dune erosion is required when issuing building permits. At some places, The Netherlands for example, the hinterland is situated below sea level. In this case the dune belt serves as sea defence. Breach of the dune belt may have catastrophic consequences. Dune and beach monitoring and dune management are of crucial importance. In some cases, where the dune belt consists of a single dune row, dune reinforcement or shore nourishment may be needed. To ensure safety, several methods have been developed for estimating dune loss during exceptional storm conditions.

## Brief explanation of dune erosion processes

The initial cross-shore beach profile, which might be considered to be in a more or less dynamic equilibrium condition with normally occurring hydrodynamic conditions, will be reshaped during a severe storm surge. The much higher water levels and much higher wave heights and peak periods call for a quite different shape of an equilibrium profile than the shape of the initial profile. Offshore directed sediment transports will occur, especially with sand eroded from the dunes.

Wave attack at the dune foot steepens the dune profile which may collapse by avalanching. Wave attack may also create a notch at the dune foot leading to mass failure: collapse of a dune slab, initiated by tensile cracking at the top surface of the dune followed by shear failure along an internal failure plane or overturning due to the weight of the overhang [1], see Fig. 4 and Fig. 5.

Fig. 4. Dune failure mechanisms.
Fig. 5. Dune scarp after collapse. The people standing on the dune scarp have not read this article.

The sand deposited at the dune foot is removed by the seaward undercurrent ('undertow') under the breaking waves and deposited on the shoreface. The slope of the cross-shore profile gradually decreases, and consequently the rate of dune erosion will decrease with time during the storm surge. It is, however, not expected that a new equilibrium profile will develop because of the limited storm surge duration. The shape of the cross-shore profile after the storm surge, which is a transient state between the initial profile and the storm equilibrium profile, is often called 'storm erosion profile'.

Right after a severe storm surge, when the hydrodynamic conditions are normal again, the shape of the storm erosion profile does not match these normal conditions. Onshore directed sediment transport will occur; wind will blow sand from the beach to the dunes; the pre-storm situation will gradually be restored. For a coast suffering ongoing erosion (i.e. not in equilibrium in the pre-storm situation) the post-storm restoration will only be partial.

## Quantification of dune erosion

Although 3D effects are undoubtedly important in the dune erosion process, often a 2D approach is adopted. In this case the dune erosion process is considered as a typically offshore directed cross-shore sediment transport problem. Sand from the dunes is transported to deeper water and settles there.

A first approach consists of assuming a closed sediment balance in cross-shore direction. The same volume of sand which is eroded from the dunes and the very upper part of a cross-shore profile is accumulated lower in the cross-shore profile. [Because of differences in porosity of the eroded dune material (often loosely packed) and the settled material (often a bit more densely packed), the sediment balance is not always strictly closed.]

During severe storm surges, with a great water level increase (a water level increase of a few metres is possible along the Dutch coast) huge volumes of sand from the dunes are transported in offshore direction. And because dune erosion is a rather short lasting process, some computation methods take only offshore directed transports into account.

### Erosion profile method

A quick first order estimate of storm dune erosion can be obtained by assuming that the storm erosion profile is close to the storm equilibrium profile. This assumption is unrealistic for storms of short duration and strongly overestimates storm dune erosion in this case. However, for storms of very long duration, which produce great dune losses with low exceedance probability, the assumption of a post-storm equilibrium profile is not unreasonable. The method is still used in the Netherlands, besides other more advanced methods, to provide an upper bound of possible storm dune erosion. It is based on empirical post-storm equilibrium profiles established by laboratory experiments and validated by field data of the Dutch coast [2]. The post-storm equilibrium profile was established for different values of the significant wave height [math]H[/math], peak wave period [math]T[/math] and mean fall velocity of dune sand [math]w[/math]. Major assumption are:

1. the storm duration is sufficient for establishment of a post-storm equilibrium profile [math]y(x)[/math];
2. the post-storm equilibrium profile does not (strongly) depend on the initial coastal profile [math]y_0(x)[/math];
3. eroded dune sediment is deposited within a zone delimited by a storm closure depth [math]y_{max}[/math];
4. the eroded dune scarp has a slope 1:1 and the slope at the toe of the sand deposit is 1:12 (these are less crucial assumptions).

With these assumptions the eroded dune volume is given by the beach volume between [math]y(x)[/math] and [math]y_0(x)[/math], such that the total sand volume landward of the closure depth [math]y_{max}[/math] is preserved. The procedure is explained in Fig. 6, where the parameterized functions for the post-storm equilibrium profile [math]y(x)[/math] and the storm closure depth [math]y_{max}[/math] are also indicated.

File:DUROSmodel.jpg
Fig. 6. Erosion profile method for estimating dune erosion as given by the beach volume between [math]y(x)[/math] and [math]y_0(x)[/math]. Underlying assumptions are explained in the text.

A serious drawback of this straightforward method is that hardly any physics is involved. The development with time of the storm profile is unknown. Effects of varying water levels and varying wave characteristics during the storm surge cannot be accounted for.

### DUROSTA

Based on theoretical work and laboratory experiments, Steetzel (1993) [3] has developed the 2-dimensional DUROSTA computation model, in which actual sediment transports are calculated based on wave-integrated velocity and sand concentration profiles. Although in the mathematical description of the cross-shore sediment transport the intra-wave component is neglected, the results of the model compared well with large scale model tests in the Delta Flume of Delft Hydraulics. During storm surge conditions, breaking waves in the surf zone cause a strong return flow in the lower part of the water column and high sediment concentrations throughout the water column. The cross-shore profile is updated at each time step, based on gradients in the computed sediment fluxes. The DUROSTA model therefore provides estimates of the time evolution of the dune and beach profiles during a storm surge.

### XBeach

XBeach [4] is an open-source process-based numerical model which was originally developed to simulate hydrodynamic and morphodynamic processes and impacts on sandy coasts with a domain size of kilometers and on the time scale of storms. Since then, the model has been applied to other types of coasts and purposes. The model includes the hydrodynamic processes of short wave transformation (refraction, shoaling and breaking), long wave (infragravity wave) transformation (generation, propagation and dissipation), wave-induced setup and unsteady currents, as well as overwash and inundation. The morphodynamic processes include bed load and suspended sediment transport, bed update and breaching. Effects of vegetation and hard structures have been included. The model has been validated with a series of analytical, laboratory and field test cases using a standard set of parameter settings. The avalanching of sandy material from the dune face to the foreshore during storm conditions is taken into account when updating the bed levels. This is modeled through introduction of a critical bed slope (default critical slope of 1 for dry zones and 0.3 for wet zones). When the critical slope is exceeded, material is exchanged between adjacent cells to the amount needed to bring the slope back to the critical slope.

Comparison with observed dune erosion events at the Dutch coast show that XBeach estimates the magnitude and pattern of alongshore variations in erosion volume reasonably well. The 2014-version of XBeach overpredicted the erosion volume in the region where a dune scarp developed and underestimated the erosion volume where the whole dune face collapsed in a series of slumps [5]. XBeach simulations further illustrated that the observed alongshore variation in dune erosion was steered primarily by the pre-storm dune topography i.e., the presence of embryonic dune fields and the steepness of the dune face. The importance of alongshore variability in intertidal beach topography was found to be secondary, but not negligible during the initial stage of the storm, when the surge level was still low.

## Impact of sea-level rise on dune erosion

The XBeach model predicts a linear relationship between dune erosion volume and sea level rise [6]. This is primarily due to the larger water level in front of the dune and not to changes in the significant short-wave or infragravity wave height. Changes in the offshore angle of wave incidence also affect the dune erosion volume. A 30° shift from shore-normal influences the dune erosion volume to the same extent as a 0.4 m sea-level rise. This increase in dune erosion volume is related to strong alongshore currents, generated as a result of the obliquity of the waves, that enhance stirring and hence offshore transport.

The model simulations further show that the effectiveness of coastal sand nourishment to mitigate the impact of sea-level rise, strongly depends on the location in the profile where this sand is added. However, the ratio of the reduction in dune erosion volume to the total added volume remains low (<0.3) for all mitigation options. This suggests that directly increasing the volume of sand in the dunes may be more efficient from a morphological perspective.

## References

1. Erikson, Li, H., Larson, M. and Hanson, H. 2007. Laboratory investigation of beach scarp and dune recession due to notching and subsequent failure. Marine Geology 245 (2007) 1–19.
2. ENW 2007. Technisch rapport duinafslag. Expertise Netwerk Waterveiligheid, The Netherlands
3. Steetzel, H.J. 1993. Cross-shore transport during storm surges. Thesis Tech. Univ. Delft, Delft Hydraulics Communications 476.