Difference between revisions of "Dune erosion"

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|name=Job Dronkers
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{{Definition|title=Dune erosion
 
{{Definition|title=Dune erosion
|definition= [[Dune]] erosion involves that, during a severe [[storm surge]], sediments from the mainland and upper parts of the [[beach]] are eroded and settled at deeper water within a short time period; this is a typical cross-shore sediment transport process.}}
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|definition= Sand loss from a dune under wave attack, mainly by avalanching and slumping processes.}}
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==Introduction==
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[[Image:DuneScarpEgmond.jpg|400px|thumbnail|right|Fig. 1. Post-storm eroded dune, Egmond aan Zee.]]
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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]]. 
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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. 
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[[Image:imageDu002.JPG|350px|thumbnail|left|Fig. 2. Storm-induced dune foot retreat as a function of frequency of exceedance]]
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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.
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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.
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==Impact of dune erosion==
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[[Image:BadhotelSchiermonnikoog_1924.jpg|350px|thumbnail|right|Fig. 3. Badhotel at Schiermonnikoog after the 1924 storm.]]
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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.  
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The basis of this article is especially written for the Coastal Wiki by the main author referred to at the bottom of this page.
 
  
This article is under construction; not yet finished.
 
  
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==Brief explanation of dune erosion processes==
  
==Dunes as sea defence==
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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.  
River and sea dikes are good examples of structures to protect low-lying areas from flooding. Also a dune area (dune row) serves that aim in some cases. E.g. the safety of large parts of The Netherlands, often with ground levels even below Mean Sea Level (MSL), relies on dikes, but also on dunes for their protection against flooding.
 
  
Visiting the beach and the coastal zone in e.g. The Netherlands under normal weather conditions would easily give the impression that the dunes are certainly strong enough to properly protect the hinterland. However, during a severe storm surge, with under design conditions water levels at sea which are approximately 5 - 6 m above MSL and together with the much more severe wave conditions than normal (cf. wave heights Hs ≈ 7 - 9 m and peak periods Tp ≈ 12 -18 s), the dunes will be eroded in a very short period of time.
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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 <ref> 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.</ref>, see Fig. 4 and Fig. 5.  
  
Existing design rules in The Netherlands yield erosion rates of 80 - 100 m of the dunes during design storm conditions. (The rates of 80 - 100 m are given as an order of magnitude value only to facilitate the further discussion; the actual erosion rates under design conditions depend on the specific local conditions; e.g. shape of initial cross-shore profile and particle size of the dune material.) It must be realized that because of the specific Dutch conditions, the design conditions in The Netherlands are very strict.
 
  
===Rather wide dune area is sea defence===
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[[Image:DuneFailureMechanisms.jpg|450px|thumbnail|left|Fig. 4. Dune failure mechanisms.]]
Often the dune areas in The Netherlands are wide enough to accommodate 80 - 100 m of dune erosion during a single severe storm surge. In some cases, however, the row of dunes is rather slender; a careful judgement has to be passed whether the dunes provide the required rate of protection. Is a break-through expected under design conditions?, and if yes: what reinforcement is necessary to fulfil the requirements?
 
  
So far in the discussion the safety problem of people living behind the dunes was raised as the main issue. In the Sections 'Large scale safety problem' and 'Small scale safety problem' of this article it will be shown that more issues related to dune erosion are relevant to a coastal zone manager. Aspects like the safety of single houses and hotels in the erosion zone are dealt with.
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[[Image:DuneErosionEgmond.jpg|450px|thumbnail|right|Fig. 5. Dune scarp after collapse. The people standing on the dune scarp have not read this article.]]
  
Also topics like how to deal with structural erosion and global sea level rise are relevant topics for a coastal zone manager. They are briefly discussed in this article with the present Dutch policy and insights as starting points.
 
  
From the discussions it will become clear that for many reasons a proper insight in the rates of dune erosion as a function of the boundary conditions is necessary. Section 'Quantification of rate of dune erosion' will deal with the dune erosion process and the methods to quantify the rates of erosion during a severe storm surge.
 
  
===Brief explanation of dune erosion process===
 
Figure 1 shows schematically what happens with a (in this case: wide enough) dune during a severe storm surge.
 
[[Image:imageDu001.JPG|350px|thumbnail|right|Figure 1 Dune erosion due to storm surge]]
 
The initial cross-shore profile, which might be considered to be in a more or less dynamic equilibrium condition with the normal occurring boundary conditions, will be reshaped during the severe storm surge. The  much higher water levels and the 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 sediments from the dunes. Sand is eroded from the dunes and is settled at the foreshore again. During these reshaping processes the slopes of the cross-shore profile gradually decrease, and consequently it can be understood that the rate of dune erosion will decrease with time during the storm surge. It is, however, not expected that a real equilibrium profile will develop during the storm surge. The time available during the storm is too short to achieve such a real equilibrium profile, but the developments are in the direction of achieving equilibrium. The shape of a cross-shore profile as encountered after the storm surge is often called 'erosion profile'.
 
  
Right after a severe storm surge, when the boundary conditions are normal again, the shape of the (erosion) profile does not fit with these normal conditions. Onshore directed sediment transports will occur; wind will blow sand from the beach to the dunes; the 'old' situation will gradually be restored. Dune erosion because of severe storm surges is thus a temporary and a reversible process.
 
  
===Large scale safety problem===
 
If, like in some cases, the dunes are really slender and landward of the row of dunes the ground levels are even below MSL (like in some places in The Netherlands) a large scale safety problem might occur. A break-through of the dunes causes flooding and will cause loss of lives and results in a lot of damage in the densely populated low-lying areas of The Netherlands.
 
Given the dimensions of a row of dunes and the specific design conditions, the Coastal Zone Manager has to judge whether the dunes are 'safe' or not. 'Safe' is in this respect in fact a relative notion. 'Safe' means that the strength (width, height) of the dunes fulfils the requirements. Absolute safety does not exist in many cases; often a set of even more extreme boundary conditions is conceivable which will result in a break-through of a row of dunes which was judged just 'safe' enough. The chance that such a set of boundary conditions will occur, is then, however, apparently smaller than has been agreed for the design conditions.
 
For the judgement of the safety of a row of dunes, a proper computation model is necessary and (a set of) design conditions. Section 'Quantification of rate of dune erosion' deals with these computation models.
 
  
For the further discussion in the present section it is good to realize that because of the many (stochastic) parameters which ultimately determine the rate of dune erosion, a probabilistic approach seems to be appropriate (see e.g. Van de Graaff, 1986). Stochastic parameters like: maximum storm surge level, wave height, wave period, storm duration, accuracy of computation model, particle size of dune sand and shape of initial cross-shore profile, all do play a role in a probabilistic approach.
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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'.
  
In a probabilistic approach an acceptable chance of failure must be the starting point instead of a single set of design conditions. Because of the high importance of the low-lying hinterland, a probability of failure for dunes of 10-5 per year (return period 100,000 years) has been agreed in The Netherlands for the most important parts of the country. This chance seems rather small, but compared to other threats (e.g. accidents with nuclear power plants, air planes or large industrial plants) the probability of failure is not that small taking into account the number of human lives and the high investments that are at stake.
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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.  
  
The probability of failure of 10-5 per year holds for the most important parts of The Netherlands; in some more rural areas larger probabilities of failure are the (legal) norm.
 
  
Figure 2 shows a schematic plot of the relationship between the rate of erosion RD (the distance RD is in Figure 1 the distance between the initial edge of the dune and the edge of the dune after the storm surge) and the frequency of exceedance. According to Figure 2 there is a chance of 10-5 per year that a rate of erosion of 85 m is reached or will be surpassed.[[Image:imageDu002.JPG|350px|thumbnail|right|Figure 2 Rate of erosion as a function of frequency of exceedance]]
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==Quantification of dune erosion==
  
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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.
  
The safety problem of large parts of The Netherlands (as far as the problem depends on the protection by dunes (large scale problem)), seems thus solvable if a proper insight is available in the possible occurring conditions in the (very) small chances range. However, this also introduces many uncertainties. E.g. reliable measurements of (maximum) water levels of the sea in measuring stations near the coast (cf. in ports) are available since approximately 1850. So for only 150 years. With such an in fact restricted data set, it is hard to estimate water levels which are associated with frequencies of exceedance in the range of 10-3 to 10-5 per year.
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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.]
  
Data sets of reliable measurements of wave characteristics cover even shorter periods of time. Nevertheless, these kinds of uncertainties have been taken into account to arrive at figures like Figure 2.
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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.
Based on a legal norm, with the help of a proper computation method, and for a given situation (cross-section of cross-shore profile and dune area) one is next able to judge whether the cross-section meets the requirements; i.e. whether the cross-section is safe enough or not. If not: iteratively an improvement scheme for the dune area can be developed; e.g. a strengthening of the dunes at the landward side.
 
  
===Small scale safety problem===
 
If the width of the row of dunes is rather large (or at least large enough to meet the legal safety standard), the safety problem for the hinterland is not a real issue (any more). That holds for many stretches of the Dutch and other coasts bordering, sometimes, hostile seas.
 
  
If these stretches concern bare dunes, loss of dune area will occur during a severe storm surge and some damage to e.g. nature will occur. Sooner or later the dunes will naturally repaired.
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===Erosion profile method===
However, along the Dutch coast (like along many coasts elsewhere) at some places coastal villages and holiday resorts do exist with roads, houses and hotels built very close to the seaward brink of the dunes. And even if the dunes are safe enough to protect the hinterland, the (required or wanted) safety of single houses and hotels built in the zone prone to erosion during a severe storm surge, might be an issue. This safety problem might be classified as a small scale safety problem.
 
  
It is to the direct interest of a large part of the Dutch population that the large scale  safety problem is properly dealt with. Legal norms are available. The responsibilities of the various parties (Water Boards, Provinces, Central Government) have been legally embodied.
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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 <ref>ENW 2007. Technisch rapport duinafslag. Expertise Netwerk Waterveiligheid, The Netherlands</ref>. 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:
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# the storm duration is sufficient for establishment of a post-storm equilibrium profile <math>y(x)</math>;
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# the post-storm equilibrium profile does not (strongly) depend on the initial coastal profile <math>y_0(x)</math>;
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# eroded dune sediment is deposited within a zone delimited by a storm closure depth <math>y_{max}</math>;
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# 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).  
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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.
  
The small scale safety problem directly regards usually only a rather restricted part of the population. E.g. owners of houses and hotels built (or to be built in future) in the zone prone to erosion during a severe storm surge, but also governmental agencies are directly involved as owners of infrastructure like roads, promenades and car parks.
 
  
The government must also formulate and maintain a set of rules to avoid unbridled developments in the zone prone to erosion during a severe storm surge.
 
It must be realized, however, that within the zone which is 'necessary' during the design conditions for the safety of the hinterland, a distinction can be made in chances that a property will be lost. Close to the seaward brink of the dunes (say RD = 20 m according to Figure 2) the chance of loss of property is larger than at the landward side of the potential erosion zone (say RD = 60 m).
 
  
The coastal zone very close to the brink of the dunes has high socio-economic potentials; many people would like to build houses and hotels with 'sea view' in this zone or would buy existing buildings. Owners of such properties are primarily responsible for possible damage to their properties by a severe storm surge. From this point of view the role of a Coastal Zone Manager would be a limited one in this respect. It is conceivable, however, that 'society' calls for some regulation. Too often (say: on an average of  every 10 years) loss of many properties in the coastal zone might be unwanted. A lot of commotion has to be expected; owners of properties who at once lost 'everything' might be considered as 'poor and innocent' fellow-citizens. At the other hand there seems to be no reason to avoid damage in the zone prone to erosion during a severe storm surge to chances comparable with the chance of failure of the dunes as sea defence. To find an acceptable compromise between these limits is a very difficult task for the responsible Coastal Zone Manager. Many Managers 'struggle' with this issue. E.g. financial, legal and insurance aspects might be helpful to be considered while developing a proper policy.
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[[Image:DUROSmodel.jpg|700px|thumbnail|center|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. ]]
  
So far the discussion referred to the erosion of the dunes due to a single storm surge (episodic effect). However, seen over a long period of time, the position of sandy coasts often show some distinct tendencies. It refers to either accreting, or eroding coasts ([[structural erosion]]), although also a more or less stable position with time of a coast might occur. Especially structural eroding coasts seriously complicate the coastal zone management task in dune areas where coastal villages or holiday resorts do exist. If the structural erosion is 'accepted', the zone prone to erosion during design conditions during severe storm surges is then continuously shifting in landward direction. It is good to realize that the effect of structural erosion (e.g. a few m per year), is quite different from the effect of a really serious storm surge: up to tens of meters per (really severe) event.
 
  
If [[structural coastal erosion]] is not accepted, proper protection measures must be applied.
 
  
===Quantification of rate of dune erosion===
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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.
Both for the ''small scale'' safety problem, but especially for the ''large scale'' safety problem a reliable quantification method for the rate of dune retreat during severe storm surge conditions is necessary. Rather much effort has spent on this specific quantification topic in research programs.
 
  
Although 3D effects are undoubtedly important in the dune erosion process, for the time being often a 2D approach is adopted. In that case the dune erosion process can be considered as a typical offshore directed cross-shore sediment transport problem. Sand from the dunes is transported to deeper water and settles there.
 
  
To a first approach a closed sediment balance in cross-shore direction can be assumed. The same volume of sand which is eroded from the dunes and the very upper part of a cross-shore profile (in m3/m) is accumulated elsewhere in the cross-shore profile. [Because of differences in porosity of the eroded dune material (often relatively loose packed) and of the settled material (often slightly denser packed), the sediment balance is not always strictly closed.]
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===DUROSTA===
  
During really severe storm surges, with a serious increase of the water level (a few meters increase of the water level is possible) 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.
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Based on theoretical work and laboratory experiments, Steetzel (1993) <ref>Steetzel, H.J. 1993. Cross-shore transport during storm surges. Thesis Tech. Univ. Delft, Delft Hydraulics Communications 476.</ref> 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.
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===XBeach===
  
''Erosion profile''
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XBeach <ref>https://xbeach.readthedocs.io/en/latest/user_manual.html</ref> 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.
  
A rather straightforward computation procedure uses the concept of a so-called ''erosion profile''. The upper part of the shape of a cross-shore profile right after a (rather severe) storm surge is thought to be known in such a method. In such a procedure, still in use in The Netherlands, the shape of an erosion profile with the maximum storm surge level as reference, depends on the occurring wave height and the particle size of the dune/beach material. Once the characteristics of the erosion profile are known, the relevant dune retreat is easily to be determined with a closed sediment balance method.
 
  
This concept forms the heart in a further probabilistic method taking into account the stochastic character of several dune erosion determining parameters. In TAW (1984) / CUR (1989) the approach followed in The Netherlands is described. The method has recently been adapted in order to take the effect op the (peak) wave period into account. See van Gent ''et al.'' (2008).
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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 <ref>De Winter, R.C,. Gongriep, F. and Ruessink, B.G. 2014. Observations and modeling of alongshore variability in dune erosion at Egmond aan Zee, the Netherlands. Coastal Engineering 99: 167-175.</ref>.  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.  
  
A serious drawback of such a straightforward computation method with a 'known' profile is that hardly any physics is involved. E.g. only the 'end' profile after the storm surge is thought to be known; the development with time is unknown. Effects of varying water levels and varying wave characteristics during the storm surge cannot be accounted for.
 
  
But also dune erosion during a severe storm surge is in reality of course a trypical cross-shore sediment transport process.
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==Impact of sea-level rise on dune erosion==
  
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The XBeach model predicts a linear relationship between dune erosion volume and sea level rise <ref>De Winter, R,C. and Ruessink, B.G. 2017. Sensitivity analysis of climate change impacts on dune erosion: case study for the Dutch Holland coast. Climatic Change (2017) 141:685–701 DOI 10.1007/s10584-017-1922-3</ref>. 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.
  
''DUROSTA''
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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.
  
Based on theoretical and a lot of experimental work, Steetzel has developed the so-called DUROSTA computation model in which at many positions in a cross-shore profile actual sediment transports are calculated with a S = v.c concept.  [Steetzel (1993)]. Although in the mathematical descriptions of the cross-shore sediment transport the so-called wave related transport is neglected, only the current related transport is taken into account, the results of the model compared with e.g. the 'reality' of large scale model tests in the Delta Flume of Delft Hydraulics are rather good.
 
  
During storm surge conditions the rather high breaking waves cause a considerable return flow (v in S = v.c) in the lower part of a water column in the surf zone. The fierce wave conditions result also in high sediment concentrations within the water column (c in S = v.c). Gradients in calculated sediment transport rates allow next for a bottom up-date. And so on. With the DUROSTA model the development with time of a bottom profile during a storm surge can be calculated and studied.
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==Related articles==
  
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* [[Natural causes of coastal erosion]]
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* [[Types and background of coastal erosion]]
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* [[Risk and coastal zone policy: example from the Netherlands]]
  
''XBeach''
 
  
''Not yet finished.''
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==References==
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<references/>
  
==See also==
 
* [[Types and background of coastal erosion]]: article on the background of erosion, dune erosion and [[structural erosion]] (''Jan van de Graaff is also planning to write a separate article on dune erosion'').
 
* [[Natural causes of coastal erosion]]: Effects of e.g. transport gradient, loss of sand, protruding areas, marine deposit shorelines, down stream erosion, sea level rise, subsidence and natural variation on coastal erosion.
 
*[[Policy in the Netherlands]]
 
  
 
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Revision as of 14:43, 27 April 2018



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.


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.


Related articles


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.
  4. https://xbeach.readthedocs.io/en/latest/user_manual.html
  5. De Winter, R.C,. Gongriep, F. and Ruessink, B.G. 2014. Observations and modeling of alongshore variability in dune erosion at Egmond aan Zee, the Netherlands. Coastal Engineering 99: 167-175.
  6. De Winter, R,C. and Ruessink, B.G. 2017. Sensitivity analysis of climate change impacts on dune erosion: case study for the Dutch Holland coast. Climatic Change (2017) 141:685–701 DOI 10.1007/s10584-017-1922-3


The main author of this article is Jan van de Graaff
Please note that others may also have edited the contents of this article.

Citation: Jan van de Graaff (2018): Dune erosion. Available from http://www.coastalwiki.org/wiki/Dune_erosion [accessed on 12-07-2020]