An Automatic Procedure for Dune Foot Position Detection: Application to the Dutch Coast
ABSTRACT
Diamantidou, E.; Santinelli, G.; Giardino, A.; Stronkhorst, J., and de Vries, S., 2020. An automatic procedure for dune foot position detection: Application to the Dutch coast. Journal of Coastal Research, 36(3), 668–675. Coconut Creek (Florida), ISSN 0749-0208.
Coastal indicators are a useful proxy in coastal zone management to describe the status of a physical system and to assess the effectiveness of possible interventions. They can be used as a basis to implement and evaluate coastal erosion policies, as it is done, for example, in The Netherlands. One often used coastal indicator is the position of the dune foot. In the current definition used in The Netherlands to describe the dune foot position, the actual geometry of the profile is, however, not accounted for, but this is simply based on one reference value for the entire coastline. In the present study, an automatic procedure for the detection of the dune foot position is proposed based on the actual shape of the cross-shore profile and on the evaluation of the first and second derivatives of the cross-shore topography. The methodology is compared to visual observations as well as satellite images for case studies in The Netherlands and Portugal, hence showing that the methodology is generally applicable. The algorithm to derive the dune foot position in a cross-shore profile and the database derived from this study are publicly available.
INTRODUCTION
Coastal dunes are defined as a ridge, or a series of ridges, of sediment that form at the rear of a beach. They differ from most other coastal landforms in that they form because of the sediment movement by air (aeolian transport) rather than by tidal, wave, or current action (Sloss, Hesp, and Shepherd, 2012a). A large variety of specific dune morphologies can be distinguished, but a general classification into primary and secondary dunes also can be made (Davis, 1980). Primary dunes are dunes with a sand supply derived primarily from the beach, whereas secondary dunes develop following the subsequent modification of primary dunes (Sloss, Shepherd, and Hesp, 2012b). Primary dunes are the main focus of this paper.
The morphological development of primary dunes is mainly the result of both accretive processes (aeolian transport) and erosive processes (dune erosion by wave attack) (Keijsers et al., 2015). Accretion is generally a slow process that can occur over a period of months to years, whereas dune erosion takes place during storm events. Accretion is mainly influenced by wind conditions (wind speed, angle, fetch), beach geometry, sediment availability, and characteristics (Bagnold, 1954; Bauer and Davidson-Arnott, 2002); erosion is mainly dependent on sea level, wave conditions, sediment characteristics, and availability (Vellinga, 1982). Sediment availability is in turn influenced by additional variables such as the moisture content and the presence of vegetation or hard structures (de Vries et al., 2014).
At many sandy coasts around the world, coastal dunes represent the main natural coastal defence against flooding. Moreover, coastal dunes have a number of additional functions. They are extremely valuable from an ecological point of view, for the development of the touristic sector, and for the provision of a substantial drinking water supply. One of the best examples of the important role fulfilled by sandy dunes is in The Netherlands, where coastal dunes represent the primary defence against flooding for a large part of the country. In 1990, the Dutch government introduced the Dynamic Preservation policy (MinV&W, 1990). This policy has shown that the hold-the-line approach, which imposes the maintenance of the coastline position to that of 1990, would provide the best balance between the cost of maintenance and the benefits derived by maintaining the coastline. The Dynamic Preservation policy implies a soft engineering approach that tackles the net sediment deficit and is based on the use of sand nourishments into the coastal zone. To assess the effectiveness of sand nourishments the Momentary Coastline (MCL) was introduced as a coastal indicator that represents the coastline location based on an active volume of sediment in the coastal zone, which is between the assumed dune foot position at NAP +3m and the NAP –5m depth contour, where NAP is the Dutch reference system. More specifically, as shown in Figure 1, the calculation of MCL for a given profile is based on an area A (or volume per linear m) of sand between two horizontal planes. The two planes are located at a vertical distance H from the mean low water (MLW) level, where H denotes the distance between the dune foot and the MLW. The momentary coastline is denoted in Figure 1 by the relative distance between A/2H with respect to a reference line. New MCL positions are computed on a yearly basis. Linear trends are derived by interpolating MCL values over 10 years and compared to a preset baseline position. Whenever the coastline retreats more than a preset baseline position, sand nourishments are applied (Giardino et al., 2011, 2019; van Koningsveld and Mulder, 2004). Starting in 1990, a yearly nourishment volume equal to 6 × 106 m3 of sand was applied along the entire coast. This volume was increased to 12 × 106 m3 in 2001 to account for the morphological development at a larger scale, induced by sand losses at larger water depths and attributable to sea-level rise.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
One of the most important indicators for the monitoring and implementation of this policy is the position of the dune foot assumed at the NAP +3m level. This assumed dune foot is used for defining the landward boundary for the computation of the MCL indicator. The dune foot position can also be used as a proxy to define the safety levels against flooding, as the position of the dune foot is related to the volumes of sand present in the dunes (Giardino, Santinelli, and Vuik, 2014). Moreover, this indicator is used to describe the beach width, defined as the horizontal distance between the dune foot and the water level at high or low tide (de Vries et al., 2012). Changes in beach width between different years can also be associated to differing potentials for the development of the tourism sector.
In The Netherlands, it is widely assumed that the dune foot is located at the most seaward crossing between the cross-shore profile and the NAP +3m, which roughly corresponds to mean sea level. Many studies performed in The Netherlands have adopted this assumption (De Jong et al., 2014; Quartel, Kroon, and Ruessink, 2008; Ruessink and Jeuken, 2002; Southgate, 2011; Bochev-van der Burgh, Wijnberg, and Huslscher, 2011). However, the assumption that the dune foot is located at NAP +3m along the Dutch coast is largely empirical and site specific. As a result, other definitions have been suggested. Hoonhout and de Vries (2017) defined the dune foot at the Sand Motor (a mega-nourishment at the Holland coast) at NAP +5m. Guillen, Stive, and Capobianco (1999) defined the dune foot position of the Holland coast as the intersection of the NAP +1m with the maximum slope of the profile between NAP +1m and NAP +5m. No definitions currently exist to detect a dune foot position in a generic sense and based on the actual profile shape. The lack of a general definition makes it difficult to execute comparative studies that describe the dune development in time.
In the present study, an automatic and simple procedure for the detection of the dune foot position is proposed. This procedure is based on the actual shape of the profile and the evaluation of the first and second derivatives of the cross-shore profile locations. The procedure was developed using a large database of cross-shore profiles of the Dutch coast. The methodology has been compared to visual field observations and satellite images for The Netherlands and a coastal stretch in Portugal. The results show that the methodology is applicable to different coastal areas with different characteristic and subject to diverse hydrometeorological conditions. A more accurate definition of the dune foot position and its morphodynamic evolution could result in a more precise estimation of possible erosive trends, a better definition of measures to counteract these trends (e.g., volumes of sand nourishments required) with consequent money saving and finally in a better assessment of their effectiveness.
METHODS
The study areas, the existing and proposed methodology for the dune foot detection, and the comparison methods are descripted in this section.
Study Areas
The Netherlands is located along the North Sea and has a coastline length of 432 km. Sandy dunes are a typical morphological feature that can be observed along 59% of the entire Dutch coastline (Ruessink and Jeuken, 2002). Only 10% of the Dutch foredunes are formed completely naturally without any human interference; these dunes can be found mostly on the Wadden region (Arens and Wiersma, 1994). The remaining foredunes have been stabilized or remodelled by human interventions through the placement of sand fences, marram grass, or the implementation of nourishment volumes.
The Dutch coast can be divided into three regions with distinct morphological characteristics and different hydrodynamic conditions (Figure 2): (1) the Wadden Coast that comprises five main barrier islands and tidal inlets; (2) the Holland Coast, with long stretches of beaches and aeolian sand dunes; and (3) the Delta Coast formed by islands, tidal inlets, and estuaries. The procedure for the detection of the dune foot position was developed and validated using data on these three coastal regions.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
In addition, the Portuguese coastline near Aveiro (Figure 3) was considered because of data availability and the more extreme hydrodynamic conditions at the Atlantic Ocean. The coastline orientation and severe wind waves and swell at the Aveiro coast result in a large littoral sediment drift. This area is also characterized by a sandy system with beaches backed by dunes with a height of about 10–15 m (e.g.,Stronkhorst et al., 2018).
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
The NAP +3m Method
Starting in 1965, JarKus measurements became available for the entire Dutch coast. The JarKus (“Jaarlijkse Kustmeting,” Annual Coastal Measurement) programme comprises surveys performed annually between April and September. This dataset contains cross-shore transect measurements, which are taken with respect to a series of permanent beach poles along the coast (Bochev-van der Burgh, Wijnberg, and Huslscher, 2011). In the cross-shore direction, elevation samples are collected every 5 m, and the alongshore interval of two consecutive transects is around 250 m, depending on the region. An example of the measurement at a JarKus profile over one decade is given in Figure 4.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
Since JarKus measurements have become available, the dune foot position has been pragmatically defined in The Netherlands as the intersection between the JarKus profile and the NAP +3m. In this paper, this is referred to as the NAP +3m method for dune foot position detection.
The Second Derivative Method
The new methodology is based on the detection of the dune foot by solely using the profile geometry.
The detection of the dune foot position requires the cross-shore profile and the mean high-water level as input data. For the Dutch coast, the cross-shore profile is provided by the JarKus dataset (see details below) and the mean high-water level is derived by water-level time series along the coast.
Two spatial constraints, the seaward and landward constraints, are defined to specify the part of the profile where the dune foot detection takes place. These constraints are defined as follows. (1) Seaward: the position of the most seaward intersection between the mean high-water level and the profile is chosen. (2) Landward: the position of the most seaward dune peak is used. Only peaks with height larger than or equal to 2.4 m are considered to be dune peaks, whilst peaks with heights less than 2.4 m are considered secondary morphological features. This critical value has been derived after a series of tests along the Dutch coast, which were then validated also for the Portuguese case. For cases in which the height of the most seaward dune peak is larger than NAP +6m, the intersection of NAP +6m level with the profile is assumed as the landward constraint for the method.
The profile (testing profile), delimited by the two constraints, is used for the analysis, whereby the first two derivatives of the profile with respect to the cross-shore axis are calculated. The calculation of the first and second derivatives and the dune foot detection for a specific JarKus transect is shown in Figure 5.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
A threshold value (of 0.001) is used to set low absolute values of the first derivative to zero. Long sequences of zeroes correspond to long, flat stretches, and they are removed. Profile positions with a value of a first derivative lower than the threshold are represented with dots at the middle panel of Figure 5, and they are not considered anymore for the calculation of the second derivative. The same steps of thresholding (threshold of 0.01), zero padding, and removal are taken after the calculation of the second derivative. Profile positions with a value of a second derivative lower than the threshold are represented with stars at the lower panel of Figure 5.
The final step of the method is to locate the most seaward position with a value of a second derivative larger than the predefined threshold. The dune foot position corresponds to this location, representing the transition from a constant slope to another one. The red line is used to highlight that the position of the dune foot is detected at the most seaward position with a value of a second derivative larger than a threshold (lower panel, Figure 5). The steps for the second derivative method are summarized in Figure 6.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
The algorithm to derive the dune foot position in a cross-shore profile is available for public use (Diamantidou, 2019).
Visual Method
The results of the second derivative method and the NAP +3m method are compared with visual observations of the dune foot position. Historically, the dune foot position was defined in The Netherlands by yearly visual observations of the break in slope between beach and dune. The cross-shore location of the dune foot was measured yearly from direct in-situ survey, with respect to a fixed reference and compiled by Rijkswaterstaat (Ministry of Transport, Public Works, and Water Management) into a database. This database covers a period spanning from 1843 until 1998 and contains measurements with a spatial resolution of 1 km. In this paper, data during the period 1965–98 will be used and referred to as the visual method of the dune foot position.
Comparison with Visual Method
Root mean square errors (RMSEs) with respect to the visual method are used to compare the second derivative method with the NAP +3m method. They are expressed as:
where, xcomp,i is the cross-shore distance of the computed dune foot position from the beach pole (based on the second derivative method or the NAP +3m method), xvis,i is the cross-shore distance of the dune foot based on the visual method from the beach pole, and N is the sample size, i.e. the number of transects considered in the computation.
Comparison with Satellite Images
For situations where visual observations of the dune foot position are lacking, the second derivative method can be evaluated by comparison to satellites images. In this study two options were considered: GoogleEarth(™) and SENTINEL-2A (GoogleEarth, 2019; ESA, 2019), the polar-orbiting, multispectral high-resolution imaging mission for land monitoring that is able to provide images of vegetation, soil and water cover, inland waterways and coastal areas with a spatial resolution of 10 meters (ESA, 2015). GoogleEarth images were used for two transects at the Portuguese coast near Aveiro (Figure 3). In the case of SENTINEL-2A, an image made on 12 March 2016 of the island Texel (The Netherlands) was used.
The start of vegetation is used as a qualitative measure and is assumed to approximately indicate the dune foot position. Keijsers, De Groot, and Riksen (2015) argue that the vegetation is one of the factors that determine the sedimentation pattern and thus morphology on the foredune. Moreover, Bauer and Davidson-Arnott (2002) define the landward boundary of the beach, the dune line, as either the limit of dune vegetation or a significant break in slope.
RESULTS
Results are presented in this section by comparing results from the second derivative method with the NAP +3m method as well as satellite images.
Statistical Comparison of Computed and Visually Observed Dune Foot Positions
The scatter plot in Figure 7 shows the relation between the dune foot positions derived from the second derivative method for the entire Dutch coast and the dune foot positions based on the visual method. The reference point (0 m) represents the position of the permanent beach pole for each transect. Positive numbers refer to cross-shore distances (from the beach pole) of points located seaward of the beach pole. Figure 8 shows the distribution of the RMSEs up to 120 m.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
For the entire Dutch coastline, the RMSEs for the second derivative method and the NAP +3m method with respect to visual observations is 33 m and 58 m, respectively (Table 1). This shows that the RMSEs between the visual observations and the second derivative method are smaller than the NAP +3m method. A big difference in the outcome can be seen at subregion #12 Goeree, where the second derivative method results in RMSE of 71 m, whereas the NAP+3m method results in RMSE of 150 m. This also applies to subregion #4 Terschelling with RMSEs for the second derivative method and NAP +3m method of 49 m and 81 m, respectively. For the other subregions, the differences are much smaller and include cases where the NAP +3m method show smaller RMSE than the second derivative method (Table 1).
Comparison of the Second Derivative Method with Satellite Observations
Figure 9 shows the satellite image acquired from SENTINEL-2A on 12 March 2016 at the location of Texel (The Netherlands). The image indicates that the dune foot positions (blue pins) computed with the new method are approximately located at the boundary between sand and vegetation, which can be considered a proxy for the dune foot position.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
Figure 10 depicts the dune foot location derived from the second derivative method (square marks) for the two selected cross-shore profiles along the coast of Aveiro. The parameter values and thresholds used to derive the dune foot position remain the same as for the Dutch coast. The comparison between computed dune foot positions and presence of vegetation from satellite images indicates that, also at this case, the computed dune foot positions correspond. Additionally, one can see that estimating the dune foot position using the +3m NAP reference line (as commonly done in The Netherlands) would result in an estimation of dune foot position, which is located at the backshore zone and to a deceptive assessment of the current state of the coast.
Citation: Journal of Coastal Research 36, 3; 10.2112/JCOASTRES-D-19-00056.1
DISCUSSION
For clarity, discussion topics have been grouped into sections.
Robustness of the Algorithm
The second derivative method was observed to be robust, in particular at subregions Goeree and Terschelling. In a very dynamic environment, such as these particular islands, sandy banks forming on the beach may or may not reach the dunes. If those banks are higher than NAP +3m, with the NAP +3m method the intersection will be taken as a result, which leads to a large horizontal distance from the actual dune foot. The new method aims at removing the influence of those banks and seeks a suitable definition of the dune foot excluding the influence of the sand banks.
A number of assumptions may affect the result of the second derivative method to estimate the dune foot. First, the detection of the dune foot position is possible only for a situation characterized by a clear dune system and transition from the beach to the dune. Second, the robustness of the methodology is dependent on the spatial resolution of the dataset because the calculation of the first and second derivatives is affected by the cross-shore distance between two consecutive points. The spatial resolution of the dataset used in this study (JarKus dataset) is 5 m. In the case of an application to another dune system, with different data availability and characterized by a lower or higher spatial resolution, the robustness of the methodology may be affected. Finally, difficulties in detecting the dune foot position may be encountered in the case of anomalies at the seaward side of the dune foot position, for instance, when sand peaks are present in the cross-shore profile because of temporal accretion.
Comparison with Satellite Images
Satellite images were used as a supplementary method to determine the dune foot position and comparison of the proposed methodology. The start of vegetation is assumed to approximately indicate the dune foot position; however, seasonal variations of the vegetation cover can possibly lead to misleading results. The interesting aspect is that the increasing availability and accuracy of remote sensed techniques could provide useful information to improve the dune foot detection.
The calibration factors used in the second derivative method (e.g., to define a threshold height to detect peaks corresponding to actual primary dune) were derived from the Dutch sandy dune system. The comparison of the Portuguese dune system using a Google Earth image showed a good correspondence regarding the dune foot position, using the same calibration parameters. Additional case studies may be useful to show the genericity of the proposed methodology.
Application in Coastal Management
The second derivative method (described in this paper) is based on a large database of coastal historical profiles and comprises a simple straight-forward algorithm. Both features guarantee good reproducibility and temporal stability of dune foot as a coastal indicator. For coastal management in The Netherlands, the second derivative method provides a way to determine the MCL more accurately.
CONCLUSIONS
A new method for dune foot detection has been developed based on the analysis of the actual geometry of the cross-shore profiles along the Dutch coast. The application of the proposed methodology to the Dutch coast has provided a robust estimation of the spatial position of the dune foot position when compared to the assumption of a dune foot position located at a constant height (i.e. NAP +3m) as it is currently done in The Netherlands. The RMSE between computed and measured dune foot position for the entire Dutch coast is about 40% smaller using the new method. A considerable improvement in dune foot detection was in particular seen at the regions of Terschelling and Goeree. The dataset was also compared to remote sensed images for different sandy dune system along the Dutch and Portuguese coasts, showing promising results.
The new indicator can be used to better describe the coastal area, and it can serve as a tool for coastal management purposes. Given that The Netherlands's nourishment policy and definition of safety levels against flooding are also determined by the dune foot position, the improvement of this indicator represents an important contribution. In addition, the newly derived method relies exclusively on the geometrical characteristics of the transects and is independent of the local water conditions, allowing it to be applied to other dune systems. The derived dataset and algorithm are freely available for future studies.
Computation of the momentary coastline (MCL) volume for a given JarKus transect. A is the area used to compute the MCL position. A is delimited by an upper boundary, corresponding to the dune foot position, and a lower boundary, at a distance equal to 2 × H from the dune foot position. H is defined as the distance between the dune foot position and the mean low water line. RSP is the beach pole reference point from which distances are computed (“rijksstrandpalen”). Therefore, the MCL position can be estimated as MCL = (A/2H) + x, with x being the distance between the RSP line and the dune foot position (Source: Giardino et al., 2019).
Regions and subregions of the coast of The Netherlands considered in this study: Wadden (2–6), Holland (7–9), and Delta (11–16).
Location of the cross-shore profiles along the Portuguese coastline of Aveiro.
Temporal morphological development of one cross-shore JarKus profile.
Dune foot detection steps. On top, JarKus cross-shore profile (dashed line) with dune peak (circle). Detected dune foot (square) is based on the first and second derivatives of the testing profile marked with solid line (between mean high water position and NAP +6m). Centre panel shows the derivative points above and below the first threshold (point, star, respectively). Bottom panel shows the derivative of the profile marked with stars in central panel. Once thresholded, the most seaward of the resulting points is taken as dune foot; Area: Voorne (11), JarKus id: 800, Year: 1981.
Steps undertaken to define the dune foot detection.
Scatter plot of the relative position between dune foot position computed following the new methodology as presented in the paper (x axis) and visual observations collected from 1965 and 1998 (y axis). Dune foot positions are defined with respect to the beach poles for the entire Dutch coast.
Distribution of RMSEs between the new methodology and the visual method for the entire Dutch coast.
Dune foot detections based on the second derivative method (blue spots) are super-imposed on a SENTINEL-2A image made on 12 March 2016 of the island Texel (The Netherlands).
Dune foot detections based on the second derivative method for two transects of the Portuguese coastline (Aveiro). The computed dune foot position is shown as a black square (a) and (c) and as a square mark on (b) and (d), after superimposing on GoogleEarth images.
Contributor Notes
