There is a focus on two different effects that occur due to the presence of buildings: (1) the erosion that occurs during a storm is altered and (2) the aeolian transport on the beach and in the dunes is altered. It must be noted that the research into these types of effects are very separated. However, striving for dune resilience means that the dunes should be able to recover after dune erosion has occurred. This means that the exchange of sediment from the beach towards the dunes through aeolian transport should be sufficient to cause dune growth after a storm surge. Therefore, it is important to consider both the dune erosion and the aeolian processes. This research is working towards integrating both processes into the same tool to give an indication of dune resilience.

Tool Setup

Following the explanation of the parameterization of the effect of buildings on dunes, an consideration was made which parameterizations should be included in the preliminary setup of the tool. This also involved weighing to which end the tool can be a quantification tool, depending on the available parameterizations. The complete
consideration is explained and the setup of the model is presented. The preliminary
setup was developed in the form of several flowcharts. These flowcharts display the
processes that should be included in the tool, but allow (some) flexibility in the way in
which the tool is further developed.

Theoretical effects
Coastal dunes are very dynamic morphological features that are subject to periods of
erosion and periods of accretion. Dune erosion occurs due to marine processes such as
wave action and currents that occur during a storm surge. The accretion of the dunes
mainly occurs due to aeolian processes.

The quantification of dune accretion is less established and predictive tools
are not available. The balance between the dune accretion and erosion determines the
resilience of the coastal dunes, because accretion can cause the recovery of the dunes
after a period of dune erosion. The processes in the coastal zone are important to
testing the strength of the dunes. The presence of buildings can both influence the dune erosion and the dune accretion processes. The research into these effects still is very separated, so dune resilience is an underexposed subject.

The effects of buildings on dune erosion

To determine the (theoretical) effects of buildings on dunes, it is important to identify
which buildings are considered. Only the hard structures that do not have a function in the flood defence are considered. Thus, a possible increase in the strength of the flood defence is not considered (Boers & Steetzel, 2012). The effect of these Non-Water retaining Objects (NWO’s) is largely determined by their characteristics. The dimensions, construction and position of the objects determine the way they
influence the processes that occur on the beach and in the dunes. For instance, the
influence of an object is much different when it disintegrates during a storm, it remains
in one piece and is displaced or when it remains in one piece but does not move (Boers & Steetzel, 2012). Note that the terms NWO and building are used interchangeably in this website. For an elaborate discussion of all the different characteristics of NWO’s refer to Steetzel (1993).

Dune erosion

Dune erosion occurs during storm surges when the water level rises and the waves can
reach the dune face. The wave-induced mass flux of water that is directed towards the
shore during a storm is compensated by a strong undertow. The erosion of the dune
face causes a high concentration of sediment. Combined with the undertow this results
in a large offshore directed sediment transport. More seaward, the flow speed and thus
the transport capacity decreases, resulting in settling of the sediment. This sediment
forms a coastal profile that is in better equilibrium with the storm conditions that are
occurring at that moment (Van Thiel de Vries, 2009; Nederhoff et al., 2015) (Figure 2). The material that is deposited on the shore face results in an increase of wave dissipation. Therefore, the dune erosion rates will decrease as the storm progresses (Ministerie van Verkeer en Waterstaat, 2007).

Non-Water retaining Objects (NWO’s) that are present influence the way in which waves and currents erode the dunes. In short, the NWO’s can cause the erosion point to retreat landwards towards the maximum erosion point. This reduces the resistance of the dunes, causing the safety margin present to reduce or even cause the flood defence to fail during norm conditions (Boers et al., 2014). The effects of the NWO’s can be summarized in two tracks: (1) the cross-shore effects and (2) the longshore effects (Boers & Steetzel, 2012).

The cross-shore effects

The effect in the cross-shore direction can in turn be divided into two possible scenarios. The first scenario involves the full collapse of the object, so it can be assumed that only the excavation of the building (e.g. the foundation or a cellar) remains. In this case, the presence of the object results in a smaller volume of sediment that is available for erosion during the storm, i.e. the excavation effect. Therefore, the erosion point will move landward compared to the situation where no NWO is present (Figure 3). It is assumed that the change in the volume balance corresponds directly to the displacement of the erosion point, so other processes are not included (Boers et al., 2014).

The second scenario involves a building that stays in place and does not collapse. In
this case, it is assumed that the sediment underneath the object is fixed, so a part of
the sediment supply during erosion is blocked. Therefore, the volume that is available
for the adaptation of the erosion profile is altered (Nederhoff et al., 2015). Normally, the
eroded sediment from the dune face would be deposited on the shore face resulting in
an increase of wave dissipation. The presence of the object blocks the occurrence of this process, so during the storm the waves in front of the object remain relatively energetic. This results in a scour hole in front of the object where the waves bring sediment in suspension, which is transported seawards (Figure 3). Depending on the interaction between the waves and the object and the sediment characteristics the amount and shape of the scour can vary (Steetzel, 1988; Nederhoff et al., 2015).

Longshore effect

The altered (cross-shore) erosion profile as mentioned above results in a larger amount of erosion in front of the NWO (B-profile), i.e. the deprivation effect. This means that a dip in the profile is present compared to the unaltered erosion profiles (A-profile) in longshore direction to both sides of the NWO. A large discontinuity is present between these cross-sections so a transition zone should be present (Figure 3). This discontinuity will result in the occurrence of longshore transport during dune erosion. This transport
will take place by the movement of sediment from the undisturbed profile towards the
profile with the hard structure. Steetzel (1993) described a volume balance that derives
the transition zone, and thus the area of influence of the NWO.
Based on laboratory experiments and numerical simulations using XBeach, (van Geer,
de Vries, van Dongeren & Van Thiel de Vries, 2012) identified a series of processes that
are responsible for the occurrence of the longshore transport:

1. Different bathymetry: The cross-shore effect of the NWO results in a lower bed
   elevation in front of the structure compared to the adjacent (unaltered) dune profile.
2. Difference in wave breaking: The difference in elevation causes waves to break
   earlier on the dune profile than in front of the NWO.
3. Difference in water level setup: The difference in wave breaking causes a difference in water level setup, resulting in a water level gradient from the dune towards the NWO.
4. Alongshore current: The water level gradient results in a mean current.
5. Lateral sediment transport: Sediment is transported towards the NWO by the
   alongshore current.
6. Additional erosion of the dune front: Due to the alongshore sediment transport a bed elevation change occurs in the area adjacent to the NWO. This means that, compared to an undisturbed dune profile, additional erosion of the dune front
   occurs in the transition zone adjacent to the NWO .

Aeolian processes

After dune erosion has occurred due to a storm surge, the width of the beach has increased. The newly formed coastal profile is not in equilibrium with the (more quiet)
post-storm hydrodynamic conditions. In the period after the storm, the waves, tide and
the wind redistribute the sand of the beach and the dunes. Assuming that no alongshore sediment transport gradients are present, the dunes recover to pre-storm volume. This process of dune recovery takes place on much longer time scales than the process of dune erosion (Van Thiel de Vries, 2009; Nederhoff et al., 2015). The aeolian processes that blow sand from the beach into the dunes are the main contributor to this recovery process, so the dunes can only recover if these processes are able to (fully) develop. This shows that the ratio between the aeolian processes and the occurrence of dune erosion determines the resilience of the dunes. Therefore, the most important factor that determines the resilience of the dunes is considered to be the duneward transport.

The occurrence of aeolian sediment transport in the coastal system can be summarized as the uptake of sand by the wind and subsequently the deposit elsewhere. However, there are many factors that influence this process. Firstly, the wind and sediment characteristics are important because they determine the critical fetch length. The critical fetch length (Fc) is the distance over which the wind must blow to achieve fully developed sediment transport (Bauer et al., 2009). This length is determined by the size and density of the sediment and by the strength of the wind. Smaller and lighter grains are more easy to take up, so the critical fetch length is shorter. Additionally, stronger winds can take up sediment more easily, so this also decreases the critical fetch length. The geometry of the beach and the wind direction determine what fetch length is available. For instance, directly onshore wind will cause a shorter fetch length than wind that blows with an angle to the beach. The aeolian transport is fetch-limited when the fetch distance is too short to allow fully-developed transport (F < Fc) (Bauer et al., 2009; Delgado-Fernandez, 2011).

Buildings influence the aeolian processes in several ways. Firstly, a building fixes the sediment it is placed on, so the sediment availability is reduced. Secondly, buildings cause the air flow to bend around the building causing flow alteration and turbulence, as shown in Figure 4. Lastly, the presence of a building blocks the air flow, so the fetch length is reduced, which reduces the occurrence of sediment transport.

Parameterization (Excavation and Deprivation effect)

The parameterization of the effects of buildings on dune erosion and aeolian processes. The explanation of the parameterization of the cross-shore and longshore effects.

Excavation effect

The way in which the effect of NWO’s can be included is described by Boers et al. (2014).
The parameterization is split up in cross-shore and longshore effect.
For the inclusion of the cross-shore effect it firstly has to be determined whether the
building does or does not collapse during a storm. In the case that the building does
collapse the excavation effect is considered. For the quantification of the excavation
effect the relative position of the building and the size of the excavation are needed.

The relation between these parameters and the shift in the erosion point can be quantified based on the assumption that there is a closed sand balance.

The basic relation between the excavation (Aexc) and the shift in the erosion point (d2) is calculated as follows:

The calculation of the shift in the erosion point is complicated by the fact that the location of the NWO determines the effect of the excavation. The excavation
does not have any influence when it is located far landward of the original erosion point
The basic relation in formula 1 is only valid in the case that the excavation is located entirely within the erosion zone for other situations where the excavation is on the border of the erosion zone or only partly within the erosion zone, the shift of the erosion point is less. In this case, the depth of the bottom of the excavation should also be considered. When the bottom of the excavation is located above the water level, the shift in the erosion point decreases if the excavation is moved landwards.

Deprivation effect

If a building does not collapse during a storm surge, the deprivation effect should be
considered. Both its cross-shore and longshore effect. In Boers et al. (2014), it is assumed that a large part of the scour hole in front of the building is filled in with sand from neighbouring cross-sections. Thus, the largest volume change occurs in the longshore direction and only this effect is considered. The fixed volume of sand (below the building) can be related to the amount of extra erosion based on the volumetric sand balance and several continuity- and slope-related assumptions.

The theoretical quantification results in a relation where the extra erosion (d2) is still dependent on the relatively hard to quantify parameters her and ho (Figure 6). Therefore, a more pragmatic formulation was proposed which directly relates the extra erosion (d2) to the location of the front of the building (d1) (Figure 7). This means that the pursued relation in Boers et al. (2014) is the expression of d2 as a fraction of d1 (d2 = αd1). The development of this simplified expression and the quantification of α are further elaborated in Chapter 4 of Boers et al. (2014). It is assumed that the fixed erosion volume can be approximated based on the height of the dune above the storm surge level (norm condition) hd and the d1 value (Figure 7):

Furthermore, it is assumed that the height of the storm surge level (ho) and the intersection of the front of the building with the erosion profile are located around the same level, so the following is valid:

The relation for the calculation of the extra erosion was determined to be (Boers et al., 2014):

The alongshore influence zone is expressed with the following equation:

This is a general approach to calculate the effect of buildings on dunes, the extra erosion is depending on de position of het building in relation to the calculated erosion. The erosion profile depends on which storm surge is used. So with these symplyfied formula it is possible to calculate the extra erosion.