Dune erosion

Definition of Dune erosion:

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.

This is the common definition for Dune erosion, other definitions can be discussed in the article

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.

Dunes as sea defense

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.

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 defense

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.

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.

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.

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.

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.

Figure 2 Rate of erosion as a function of frequency of exceedance

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.

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. 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. 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.

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.

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 erosion is not accepted, proper protection measures must be applied.

Quantification of rate of dune erosion

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.]

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.

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).

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.

DUROSTA 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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