*3.2.2 Large-scale calculation of the sediment budget east of Dunkirk*

Four topographic survey campaigns were carried out with an airborne topographic LiDAR in May 2008, March 2011, November 2012, and January 2014 on a 8 km long coastal stretch east of Dunkirk. For each measurement campaign, a DTM with a spatial resolution of 1 m was calculated. In order to understand sediment transfer between beach and dunes, these DTMs were used to calculate sediment volume variations in the mid foreshore, upper beach, and dune (**Figure 11**). The lower foreshore limit corresponds to the minimum elevation at the time of LiDAR measurements and therefore depends on the tidal level. The upper limit of the mid foreshore is the Mean High Water level (MHW, 2.83 m French elevation datum at Dunkirk). The upper beach is the area between the MHW level and the shoreline determined using the gradient method (see Section 3.1). The seaward limit of the dunes is the shoreline, whereas the inner limit is determined by photo-interpretation according to the type of dune vegetation identified in order to exclude areas with high vegetation (e.g., sea buckthorn) where the differences between the DTM and the actual ground topography may exceed 50 cm.

**Figure 11** shows that the shoreline east of Dunkirk experienced a sediment accumulation of approximately 326 × 103 m3 from 2008 to 2014. Almost half of this accumulation is observed in the coastal dunes (154 × 103 m3 ), mainly in the eastern part, next to the Belgian border. The average vertical accretion is 1 m. In the whole study zone where the shoreline has been stable from 2008 to 2014, the sediment budget of the dunes is positive even if dune front erosion occurred in places. Estimates of changes in sediment volume indicate that accumulation in coastal dunes occurred primarily prior to erosive events in the fall and winter of 2013, particularly between 2008 and 2011 when a gain of more than 122 × 103 m3

#### **Figure 11.**

*(A) Map of shore evolution between Dunkirk and the Belgian border from 2008 to 2014 and (B) volumetric evolution of the foreshore, upper beach, and dunes (adapted from Ref. [38]).*

*Spatial Variability in Environmental Science - Patterns, Processes, and Analyses*

calculating a linear regression with the pixel heights at each date.

/m2

The map of the annual rate of change calculated with the four DSMs (**Figure 10c**) confirms the previous observations: erosion of the sand bar, upper beach and dune front, and accumulation in the trough landward of the upper intertidal bar and in the blowouts. The topographic and statistical cross-shore profiles (**Figure 10d**) show that the highest negative evolution rates are corresponding to the foredune front. As indicated in Section 2.2.3 of this chapter, such map must be interpreted with caution. In bare areas, the geomorphological analysis can be validated, but in the vegetated zones, the changes detected may be due to vegetation growth and not to geomorphological changes. The interpretation of these DSMs must therefore always be combined with observation of aerial photographs.

, i.e., −0.15 m3

eroding, although blowouts were filling up.

was eroded (−0.25 m3

negative (−5041 m3

lated, and 6410 m3

*3.2.1 Very high spatial resolution and short-term shoreline analysis at Zuydcoote*

Four photogrammetric survey campaigns were carried out in November 2017, May 2018, September 2018, and February 2019. Very high spatial resolution DSMs were then calculated (5 cm/pixel; **Figure 10a**). The DSMs were compared in pairs (e.g., **Figure 10b**). In order to synthesize the four DSMs, a statistical analysis was also conducted. For example, a map of the annual rate of change was produced by

For example, between November 2017 and May 2018, the sediment budget was

), 1368 m3

/m2

the beach and dune front. The comparison map of the DSMs (**Figure 10b**) shows a flattening of the upper intertidal bar and the upper foreshore, and the disappearance of the aeolian sand accumulation features identified on the DSM of November 2017 (**Figure 10a**). The DSM comparison also shows that the dune front has been

*Examples of (a) DSM computed from photogrammetry data (November 2017), (b) evolution map (November 2017 to May 2018), (c) map of annual rate of evolution, and (d) cross-shore topographical and evolution rate* 

(0.22 m3

/m2

). Erosion was very mainly detected on

) of sediment accumu-

**104**

**Figure 10.**

*profiles.*

of sand was observed. Sediment accumulation was about 69 × 103 m3 in the coastal dunes during the following period (2011–2012), which corresponds to a constant average accumulation rate of about 0.13 m3 /m2 /year in the dunes during both periods. Subsequently, storms in late 2013 [50] resulted in widespread coastal retreat associated with the erosion of coastal dunes west of Bray-Dunes (**Figure 11**). About 36.5 × 103 m3 and 15.7 × 103 m3 were eroded from the Dune Dewulf and the Dune Marchand, respectively, between 2012 and 2014. However, the Perroquet Dune, east of Bray-Dunes, remained fairly stable or even accumulated slightly during this storm period. Although coastal dune erosion was significant during the 2012–2014 period, a comparison of the 2008 and 2014 DTMs shows an accumulation in the dunes almost everywhere along the coast (**Figure 11A**) due to the supply of aeolian sand from the beach. Such vertical accretion is visible even where coastal dune erosion has occurred (e.g., Dune Dewulf), suggesting that wind-blown sand may also have been transported landward as the dune front eroded and retreated.

The upper part of the beach was also characterized by accretion along most of the study site, with a total gain of nearly 90 × 103 m3 between 2008 and 2014, with maximum accumulation (>0.5 m) measured in the eastern part of the study site (**Figure 11B**). As for the dunes, sand accumulation on the upper beach occurred mainly between 2008 and 2012, while slight erosion occurred locally between 2012 and 2014. Comparison of the 2008 and 2014 DTMs shows characteristic patterns of topographic change of intertidal bars and troughs on the foreshore. The corresponding volume changes are very limited: about +83 × 103 m3 over the whole foreshore, corresponding to only 0.04 m3 /m2 .
