The anticipation of sea-level rise and increases in extreme weather conditions has led to the
initiation of an innovative coastal management project called the Sand Engine.
In this pilot project a large volume of sand (21.5 million m
Global sea-level rise poses a risk for coastal areas, especially when combined with an increase in the frequency and intensity of storm surges (Michael et al., 2013; Nicholls et al., 2010; Wong et al., 2014). Particularly small islands (Chui and Terry, 2013; Holding and Allen, 2015; Mahmoodzadeh et al., 2014) and low-lying deltas (Giosan et al., 2014; McGranahan et al., 2007; Oude Essink et al., 2010) are vulnerable to rising sea-levels. Many low-lying deltas, such as the Mekong Delta (Vietnam) and the Ganges–Brahmaputra delta (Bangladesh), are already frequently subjected to extensive floods, leading to considerable economic losses, property damage, and in severe cases loss of life (Few and Matthies, 2006; de Sherbinin et al., 2011; UNDP, 2004). In addition, many ecosystems and inhabitants of deltas are threatened as a result of high subsidence rates, over-exploitation of fresh groundwater resources, and contamination of coastal aquifers (Crain et al., 2009; de Sherbinin et al., 2011; Syvitski et al., 2009; UNDP, 2004). Sea-level rise and storm surges will enhance the pressure on these coastal regions (Kooi et al., 2000; Yang et al., 2013, 2015), and will likely exacerbate the loss of agricultural land, damage of ecosystems and the salinization of fresh groundwater resources (Hoggart et al., 2014; Nicholls, 2010; Oude Essink et al., 2010; Wong et al., 2014).
Situation of the Sand Engine and morphological development in 2011–2014.
In order to protect the livelihood of densely populated coastal areas against climate-related impacts, a growing number of studies recognizes the need for the adoption of coastal defence strategies (Giosan et al., 2014; Nicholls et al., 2010; Temmerman et al., 2013; Wong et al., 2014). Fortunately, the awareness of the threats posed by climate change is growing, and coastal defence in a number of countries – especially developed countries – have been intensified, specifically at vulnerable locations (Goodhew, 2014; Kabat et al., 2009; Sterr, 2008). One example is the Netherlands – a vulnerable low-lying country – where coastal defence systems have been reinforced on several occasions, in accordance with its long history of intensive coastal protection (Charlier et al., 2005). Centuries of continuing erosion, flooding, and subsidence led first to the implementation of hard engineering methods (e.g. groynes and sea walls), and later soft engineering methods (e.g. sand replenishment or nourishment; van Koningsveld et al., 2008). Since 1990 the application of sand nourishments, particularly beach and shoreface nourishments, has become the dominant coastal defence strategy. Sand nourishments are applied on an annual basis – where necessary – to maintain the position of the coastline (Keijsers et al., 2015; de Ruig and Hillen, 1997).
Since 2001, the position of the entire Dutch coastline has been successfully
maintained with 12 million m
The effectiveness, benefits and drawbacks of concentrated (mega) nourishments
are currently being investigated with a pilot project named the Sand Engine
(also called Sand Motor) (Mulder and Tonnon, 2011; Stive et al., 2013). In
this project a mega-nourishment of 21.5 million m
The primary objective of this study is to quantify the potential effect of the Sand Engine on the regional groundwater system, particularly on fresh groundwater. During the lifespan of the Sand Engine, the (direct) influence of the North Sea is diminished, because of the seaward displacement of the shoreline – and possibly growth of adjacent dunes. The extension of the beach–dune system and the reduction in seawater intrusion may lead to a growth of fresh groundwater resources. In combination with an increase of groundwater levels, the construction of the Sand Engine may also lead to a decline in the upwelling of saline groundwater and a decreased salt load in adjacent low-lying areas.
The long-term morphological evolution of the Sand Engine – powered by coastal and aeolian sediment transport – will also affect to local groundwater system with time. Erosion and deposition of sand will alter the position of the shoreline and the surface elevation with time, which simultaneously gives rise to dynamic changes in seawater intrusion and submarine groundwater discharge. The morphological evolution of the Sand Engine and the dynamic nature of this coastal system will probably lead to considerable changes in groundwater head and divide, the direction and velocity of groundwater flow, and the stored volume of fresh groundwater.
One of the innovative aspects of this study is to incorporate detailed predictions of the long-term morphological evolution of the Sand Engine in a 3-D numerical model, which simulates variable-density groundwater flow. At the moment no studies have investigated the influence of local mega-nourishments on groundwater systems, and only a few groundwater modelling studies have incorporated a changing morphology in their calculations (Delsman et al., 2014). We also assess the effect of climate change (e.g. sea-level rise) on fresh groundwater resources in the study area, in combination with the morphological evolution of the Sand Engine. To our knowledge, no other studies have integrated the effect of the morphological evolution of coastal areas and climate change on fresh groundwater resources, and the number of quantitative studies that investigate the possibility to combine coastal defence with the protection of fresh groundwater resources are scarce (Oude Essink and Waterman, 2016; Oude Essink, 2001). However, studies on small islands have shown that great losses in the volume of fresh groundwater can occur as a result of decreases in groundwater recharge and sea-level rise, and especially small and thin lenses seem vulnerable to salinization (Chui and Terry, 2013; Holding and Allen, 2015; Mahmoodzadeh et al., 2014). In relation to the morphological dynamics of coastal regions, studies have shown that the erosion and accretion of sand can lead to substantial changes within the beach–foredune area (Bakker et al., 2012; Keijsers et al., 2014), and that climate change might exacerbate coastal erosion (FitzGerald et al., 2008; Zhang et al., 2004). Morphological developments in coastal areas can therefore have a substantial effect on fresh groundwater resources, and coastal management strategies that compensate, limit, or counteract coastal erosion, or seawater intrusion may help to protect fresh groundwater resources.
The paper first describes the construction of the Sand Engine and the characteristics of the study area. It then reviews the methodology for the development of the regional groundwater model, and the model scenarios. Next, the model calibration and model results are described and examined as well as the impact of different climate scenarios on simulated fresh groundwater resources. Finally, the methodology and results are discussed, emphasizing the limitations and implications for fresh groundwater resources.
The construction of the Sand Engine was commissioned and designed by the
executive branch of the Ministry of Infrastructure and the Environment
(Rijkswaterstaat) and the provincial authority of South Holland (Provincie
Zuid-Holland) (Mulder and Tonnon, 2011). Large trailing suction hopper
dredgers were used to extract sand from several sand pits in the North Sea
and to transport this sand to the project site. The dredged material was
stored in the hopper and deposited on the project site with three different
techniques: by opening the bottom valves of the vessel on-site
(depositing), by pumping a mixture of sand and water to the site through
a pipeline (pumping), and by spraying a mixture of sand and water from
the vessel's bow to the site (rainbowing). When the construction of the
Sand Engine was completed (in July 2011), the area above mean sea level
(a.m.s.l.) was 1.3 km
Map of the dune area Solleveld with multi-level monitoring wells and pumping wells, including transects A and B (geological profiles in Fig. 3).
The Sand Engine peninsula is connected to the mainland by a sandy beach, and
is bounded by a coastal dune area called Solleveld. Solleveld is relatively
small dune area (circa 2 km
Beyond the dunes the area gradually transforms into urban area and low-lying
agricultural areas (polders). The low-lying polders have surface elevations
of
The subsoil consists of unconsolidated sediment of predominantly fluviatile
and marine origin, as illustrated by two geological profiles in Fig. 3. The
upper part of the subsoil (10 to 30 m) consists of sand, clay, and peat,
which were deposited during the Holocene: primarily fine- to medium-grained
sand in the higher situated dunes and urban areas, and primarily sand and
clay in the low-lying areas. However, the lower section of the Holocene
deposits (between
Geological profiles (based on the databases of the Geological Survey of the Netherlands) across the model domain with conceptual fresh–salt water distribution (locations are shown in Fig. 2).
The conceptual fresh–brackish–saline groundwater distribution (blue striped
lines; Fig. 3) are based on chloride measurements, performed at multi-level
monitoring wells. Chloride measurements in Solleveld indicate that the
boundary between fresh and brackish groundwater (1 TDS g L
In order to timely observe changes in groundwater level, flow and quality an extensive monitoring network was implemented in Solleveld. After the construction of the Sand Engine this monitoring system was expanded and intensified in the western part of the dune area. The aim of the expansion of the monitoring system was to observe long-term changes in groundwater level, flow, and quality and to observe hydrogeological effects caused by the Sand Engine and previous small-scale nourishments (Buma, 2013). The current monitoring system consists of more than 300 observation wells, where the groundwater level is measured with varying frequency (ranging from wells with hourly frequency to wells that are only read off every 3 months). The groundwater salinity is measured twice every year in at least 50 monitoring wells, with various methods: groundwater data loggers with measurement of electrical conductivity, electro-magnetic measurements, and analyses for chloride (Buma, 2013). Apart from measurements within the monitoring system, groundwater level measurements of 61 additional (onshore) monitoring wells were available in the national database of the Geological Survey of the Netherlands.
In addition to the expansion of the monitoring system, additional measures were taken to prevent salinization of fresh groundwater in the dunes. On the western base of the dunes a line of 28 interceptor (pumping) wells was installed in 2012 to maintain the groundwater level, and prevent any (negative) impact of the Sand Engine and previous nourishments on the extracted fresh groundwater in the dunes. These interceptor wells were not included in our study, because of a lack of information on the pumping rates and the expectation that the effects on the regional scale are small to negligible.
In order to gain specific information on the geohydrological dynamics within the Sand Engine, eight additional monitoring wells were installed with shallow filters (2 to 10 m below surface) and four monitoring wells with deep filters (16 to 20 m below surface). Since May 2014 the groundwater levels in the monitoring wells have been continuously monitored with groundwater data loggers. The salinity of the groundwater is monitored with electro-magnetic measurement within all eight monitoring wells.
For the quantification of fresh groundwater resources in the study area, we constructed a regional 3-D groundwater model, in which variable-density groundwater flow was simulated with the computer code SEAWAT (Langevin et al., 2008). SEAWAT has been developed by the United States Geological Survey (USGS), and numerous studies have used the code to simulate variably-density, transient groundwater flow (Heiss and Michael, 2014; Herckenrath et al., 2011; Rasmussen et al., 2013). In SEAWAT the governing flow and solute transport equations are coupled and solved with a cell-centred finite difference approximation. The model domain was discretized in 234 rows, 234 columns, and 50 layers, with a uniform horizontal cell size of 50 m and a varying layer thickness of 1 to 10 m (smallest thickness in upper layers, increasing in underlying layers; Fig. 4). The discretization and extent of the model were based on three criteria: minimize the effect on simulated groundwater heads and salinities in the study area, limit computation time, and optimize the calculation of the fresh groundwater volume. For the justification of the temporal and spatial discretization, we have performed a grid convergence test (Appendix A).
Conceptual representation of a slice of the model with layer thicknesses and boundary conditions.
The model boundaries, as visualized in Fig. 1, were defined either
perpendicular to the coastline (the south-west and north-east sides of the model), or
parallel to the coastline (the north-west and south-east side of the model). Model boundaries
that were defined perpendicular to the coastline, lie parallel to the
dominant groundwater flow direction in the coastal area, and were therefore
defined as no-flow boundaries. The other model boundaries were defined as
illustrated in Fig. 4: “specified-head” and “head-dependent
flux”
boundary conditions (taking into account density differences), which
represent the North Sea and local groundwater system, respectively. The
specified-head boundary conditions equalled the average level of the North
Sea, and were applied to the seafloor. Local groundwater conditions were
defined by a previous model simulation of the south-west of the Netherlands
(Oude Essink et al., 2010). The base of the model was defined equal to the
hydrogeological base of the model domain, which is approximately
Hydrogeologic parameters used in the simulations, where the upper part of
the phreatic aquifer (1a: above
Simulation of historical coastal erosion (based on palaeogeographic maps of Vos and de Vries, 2013), sea-level rise (black line) and groundwater extraction (blue) in the period 1810–2010; dashed lines indicate estimates, and vertical grey lines refer to stress periods (CBS et al., 2013).
The subsoil of the model was schematized to four aquifers and three aquitards
(Fig. 4), based on borehole data, and the national geological databases
REGIS II.1 (Vernes and van Doorn, 2005) and GeoTOP (Stafleu et al., 2013) of
the Geological Survey of the Netherlands. The upper part of the phreatic
aquifer (above
Other model parameters such as recharge, and surface water levels were defined by spatially distributed and time-average values of the current situation. The average monthly precipitation and reference evapotranspiration between 1981 and 2000 (Royal Netherlands Meteorological Institute, KNMI) were used to estimate the average seasonal (DJF, MAM, JJA, and SON) precipitation and evapotranspiration. Crop and interception factors were used to estimate the actual evaporation in different land use classes (e.g. forest, agriculture, urban areas) (Droogers, 2009; Hooghart and Lablans, 1988; Meinardi, 1994; Statistics Netherlands, 2008). Water levels, depths, and widths of canals and ditches were provided by the Delfland Water Authority, and drainage levels were based on local knowledge and estimations from the Netherlands Hydrological Instrument model (de Lange et al., 2014; Massop and van Bakel, 2008). Information on the extraction of groundwater and the infiltration of surface water in the dune area Solleveld was provided by the drinking water company Dunea.
In this paper, we have used TDS, where TDS equals salinity
(g TDS L
The main purpose of the model calibration was to generate a valid
representation of the pre-development conditions of the Sand Engine (prior to
March 2010). In order to exclude anomalous effects of recent sand
nourishments on groundwater heads and concentrations, only observations prior
to 2010 were included in the model calibration. We considered three
calibration criteria: the error between simulated and observed groundwater
head and TDS concentration should be similar or smaller than the observed
variations in groundwater level (the average standard deviation of
observations is 0.4 m) and concentration (the average standard deviation of
observations is 0.7 g TDS L
The calibration comprised sensitivity analyses, (restricted) manual model parameter calibration, and comparisons of simulated groundwater heads and TDS concentrations with averaged observations of recent years. Historical processes that promote or diminish seawater intrusion were included in the calibration, because a salinity distribution often takes decades to hundreds of years to reach an equilibrium (Delsman et al., 2014; Webb and Howard, 2011). Examples of historical processes that have substantially influenced the groundwater salinity in the Dutch coastal area are coastal erosion, sea-level rise, and groundwater extractions (Post et al., 2003). These processes were therefore included in the model simulations to attain a better match between simulations and observations, and the method of incorporation of the processes is briefly described in Table 2 and visualized and in Fig. 5. Other historical changes in, for example groundwater recharge and subsidence, were not included, because measurements and historical data indicate that these processes probably have a negligible impact on the current head and concentration distribution in the study area (CBS et al., 2012; Hoofs and van der Pijl, 2002). The simulation was restricted to the period 1500–2010, because the focus of this study lies on the present conditions, and we assume that the most substantial effects on the present salt distribution will probably occur in this period. Before the simulation of the period 1500–2010, a transient simulation of the approximate conditions in AD 1500 was executed until the model converged to a dynamically stable state in terms of both groundwater heads and salinity.
Simulation of processes and method of incorporation in groundwater model.
Model climate change scenarios for the period 2011–2050, with two rates of SLR, starting at 0.05 m a.m.s.l. and seasonal variation in groundwater recharge (DJF, MAM, JJA, SON).
In order to attain an optimal calibration result with a limited number of model simulations, model parameters were manually adjusted with small increments from an initial best guess. The adjustments were performed on a selection of the model parameters: (horizontal and vertical) hydraulic conductivity, drainage resistance, stream bed resistance of canals and ditches, and (longitudinal and transverse) dispersivity. Other parameters such as groundwater recharge and surface water levels were based on measurements, maps or expert knowledge, and were excluded from the calibration. The optimized model parameters that were implemented for the model scenarios are described in Sect. 3.1.
The effect of the Sand Engine on fresh groundwater resources will primarily depend on the morphological evolution of the coastal area. To assess the potential effect of the mega-nourishment on coastal groundwater, we performed model simulations containing projections of the morphological change of the Sand Engine during the period 2011–2050 (Table 2). The morphological development of the Sand Engine in this period was simulated with the hydrodynamics and morphodynamics model code Delft3D (Lesser et al., 2004). This numerical morphodynamic model was calibrated for the period 2005–2010 and validated for the period 1990–2005, prior to the construction of the Sand Engine (Fiselier, 2010; Tonnon et al., 2009). Based on representative tidal boundaries and wave conditions of the current situation, the morphodynamic model was used to simulate the change in bathymetry from 2011 to 2050 (Fig. 6). These simulated changes in the bathymetry were incorporated in the groundwater model by sequential grid regenerations of the model grid, for every 3 months (viz. season) in the simulation period. Subsequent changes in the area of inundation, groundwater recharge and thickness of the phreatic aquifer were also adapted in the associated model input files. Estimations of the change in the mean water level in the lagoon (at the northern side of the Sand Engine), which result from the morphological changes, were also included in the model scenarios (de Vries et al., 2015). The expected maximum mean water level in the lagoon equalled 0.9 m a.m.s.l. in the simulation period.
In addition to the morphological development of the Sand Engine, climate
change may also have an impact on coastal groundwater. For the assessment of
the potential impact of climate change on fresh groundwater resources, we
have used the KNMI'14 climate change scenarios G
Simulated morphological development of the Sand Engine from 2011 to 2050, illustrated by contour maps with the terrain elevation (m a.m.s.l.).
Comparison of observed and simulated heads
All climate change scenarios were simulated for a reference case without the Sand Engine, and the current situation with the Sand Engine including the projected morphological evolution. The reference case serves primarily as a comparison to the simulations with the morphological evolution of the Sand Engine. The dissimilarity between both situations represents the total impact of the construction of the Sand Engine on local fresh groundwater resources. In turn, the climate change scenarios show the response and sensitivity of local fresh groundwater resources to alterations in sea-level rise, precipitation, and evapotranspiration.
For the calibration of the variable-density groundwater model, we compared
the simulated pre-development groundwater head and TDS concentration with
recent observations of groundwater heads and chloride concentrations
(Fig. 7). The calibration was performed with averaged values of recent
observations, and therefore the transient model was strictly speaking not
calibrated. We think this is acceptable, because of the long-term scope of
this study, the conservative value of 0.15 that was used for the specific
yield in the simulations, and the deficiency in long-term time series of head
and especially salinity. The absolute mean error between observed and
simulated heads was 0.27 m (RMSE of 0.33 m), and between observed and
simulated TDS concentrations was 1.17 g TDS L
The groundwater heads of 137 observation points and the chloride
concentrations of 55 observation points were used to quantify the error and
calibrate the model. Despite this relatively large number of observation
points, it is important to note that all observations of chloride and
72 % of observations of groundwater heads – that were used in the model
calibration – originate from the monitoring system in Solleveld,. The
simulation of the groundwater head and especially the TDS concentration are
therefore most reliable in Solleveld and the immediate surrounding system.
The phreatic groundwater level and depth of the fresh–brackish interface of
the calibrated model are shown in Fig. 8. Phreatic groundwater flows from the
coastal dunes toward the sea, pumping wells, and low-lying drained polders.
The aquitard beneath the phreatic aquifer (between
Phreatic groundwater level (left) and fresh–brackish interface depth (right) after calibration, before the construction of the Sand Engine (2010–2011).
In order to assess the performance of the calibrated groundwater model, we
have compared simulated groundwater heads and TDS concentrations with recent
observations at eight monitoring locations on the Sand Engine (Fig. 9). The
absolute mean error between observed and simulated groundwater heads was
0.36 m, and between observed and simulated TDS concentrations was
6.5 g TDS L
Comparison of
Increase of the volume of fresh groundwater in the situation
without Sand Engine
Transects with the simulated groundwater salinity (in g TDS L
Transects with the simulated groundwater salinity (in g TDS
L
The effect of the construction and long-term morphological evolution of the
Sand Engine on the volume of fresh groundwater is initially small and similar
to the situation without the Sand Engine (Fig. 10). In all model scenarios
the volume of fresh groundwater slightly declines in the first years, because
of the small size of the freshwater lens in the Sand Engine with respect to
the cell resolution and the instability of the initial conditions. However,
the gradual growth of the freshwater lens in the Sand Engine and adjacent
areas eventually leads to an increase of the volume of fresh groundwater in
the model domain of 0.3 to 0.5 million m
The sea-level rise (in total) of 0.15 m in climate scenarios G
In addition to the change in fresh groundwater resources in the beach–dune system, the simulations with the long-term morphological evolution of the Sand Engine show small to negligible increases (smaller than 1 m in 2050) in the freshwater lens thickness in low-lying polders. However, changes in the total salt load in drains, canals, and ditches are small in the situation with and without the Sand Engine. As a result the construction and morphological evolution of the Sand Engine may lead to small decrease of seawater intrusion, but this effect will probably be small to negligible and limited to small low-lying polders in a short distance from the Sand Engine (Fig. 13).
Thickness of fresh groundwater [m] in reference scenario near the Sand Engine from 2011 to 2050.
The model simulations show that the construction of the Sand Engine may
result in the growth of the volume of fresh groundwater by several
million m
Comparisons of observed and simulated groundwater heads and salinities show a good correspondence before and after the construction of the Sand Engine, despite large variations between observed and simulated groundwater salinities at individual locations. To some extent these discrepancies can be accounted for by the relatively sharp transition between fresh and salt groundwater, through which small variations in depth can result in large differences in groundwater salinities. Other factors that were not included in the simulations and that probably led to discrepancies in observed and simulated groundwater heads and salinities are historical events (e.g. changes in groundwater level and salinity during the construction of the Sand Engine), large inundations of the Sand Engine due to storm-surges (e.g. two major storms in 2011–2016 inundated approximately 56 % of the Sand Engine), variations in extraction rates of pumping wells, fluctuations in sea salinity, and unaccounted vertical layering of the Sand Engine deposits. These factors were not included in the model simulations because of the absence or shortage of data, and the long-term scope of this study. However, the overall similarity between observations and simulations, in combination with the absence of systematic errors in the model calibration, confirms the reliability of the model. Most of the observations – in particular groundwater salinity – emanate from the monitoring system in the adjacent dune area Solleveld and to a lesser extent the Sand Engine. The simulated groundwater heads and salinities are therefore most reliable in our area of interest, and the reliability is less in other areas in the model domain. However, the most substantial changes in groundwater salinity will take place in the area close to the Sand Engine, and variations in groundwater head and salinity in other areas will probably have a small to negligible impact on the potential effects of the Sand Engine.
Considering the scale and nature of our research objective, we neglected small and local variations in hydraulic parameters (e.g. hydraulic conductivity, layer thickness, porosity, and storage coefficient) in the model simulations. Supported by geological data and models, each aquifer and aquitard was defined homogenous and anisotropic, with the exception of the phreatic aquifer. This reduction of the model complexity enhances the ability to differentiate and to understand the simulated processes, and leads to a smaller computation time of the model. However, small or local variations in groundwater head or salinity that are caused by heterogeneity will not be accurately reproduced in the model simulations.
One of the largest uncertainties in the study is the long-term morphological evolution of the Sand Engine, despite extensive calibration and validation and the large number of processes that are included in Delft3D (e.g. wind shear, wave forces, tidal forces, density-driven flows). The highly dynamic nature of the coastal zone, the absence of aeolian transport in the Delft3D simulations, and the lack of understanding of some processes, can lead to incremental differences with reality. Even though measurements of the last 4 years show a reasonable fit with the projections of the sediment volume changes and erosion patterns (de Schipper et al., 2014), future morphological change can turn out to be significantly different from the morphological model. For example, the growth of dune grasses and the exposure of shell deposits may prove to reduce erosion and decelerate the morphological evolution of the Sand Engine, or an accumulation of sand in the lagoon might lead to earlier silt up, and therefore a reduction of seawater intrusion in comparison with the projections. The implementation of one simulation of morphological change in the model calculations is therefore a significant limitation in the estimation of the potential fresh groundwater resources. For a more extensive analysis of the uncertainties in the prediction of the effects on fresh groundwater resources, it is recommended to simulate more morphological scenarios in future studies.
In addition to the long-term morphological evolution of the Sand Engine, large uncertainties also exist in the climatological predictions of sea-level rise, precipitation, and evaporation in future decades. Predictions of sea-level rise for the North Sea in 2050 range between 15 to 40 cm a.m.s.l., and model simulations have shown that substantial changes in the growth or volume of fresh groundwater resources can occur within this range. Changes in sea-level rise and the intensity or frequency of storm surges will not only significantly influence fresh groundwater, but will also contribute to coastal erosion and alter the morphological development of the Sand Engine.
Local mega-nourishments such as the Sand Engine might become an effective
solution for the threats that many low-lying coastal regions face, and with
this study we have shown that fresh groundwater resources can substantially
grow within the lifespan of the nourishment. The results in this study show
that for the Sand Engine, the construction of a mega-nourishment can lead to
increase of fresh groundwater of approximately 0.3 to
0.5 million m
The underlying data of this research can be divided into three categories: data that are collected within the Sand Engine monitoring program, data that were provided by third parties, and publicly available data sets. All data related to the Sand Engine are part of the Sand Engine monitoring program and will become available via the portal Zandmotordata.nl. However, during the course of the program the data access is restricted. For data that are related to the other two categories, we refer to the description of the methodology. For each underlying data set we have provided either a reference to the third party that provided the data, or a reference to a document or website that describes or contains the data set.
In order to justify that the chosen spatial discretization was adequate for
reliable numerical quantifications of the potential effect of the Sand Engine
on fresh groundwater resources, we have executed a grid convergence test for
the period 2011 to 2050 (with and without Sand Engine). The numerical
simulations that are described in this paper were performed with a horizontal
grid size of 50 m, and 50 layers with a variable thickness from 1 (upper
layers) to 10 m (lower layers). This spatial discretization was tested with
three additional simulations with higher and lower spatial resolutions
(Table A1): one with a finer horizontal grid size of 25 m (model
simulation S1), one with a coarser
horizontal grid size of 100 m (S2), and one with an equal horizontal grid
size of 50 m and an increased vertical resolution of the upper layers (S3).
In the upper part of the model, up to a depth of
Stability constraints and accuracy requirements were used for the temporal
discretization of the simulations, and therefore the convergence of the
solutions with regard to the temporal discretization was not tested.
However, we have performed an additional test with respect to the coupling
of the flow and solute-transport equations. The simulations were conducted
with the “explicit coupling” approach. In order to test this coupling
approach, an additional simulation was conducted with the “implicit
coupling” approach (density criterion of 0.2 kg m
All the additional numerical simulations include no climate change scenario, and were compared to the current numerical simulations that contained a horizontal resolution of 50 m and 50 layers. The initial conditions of all additional numerical simulations were equal to the calibrated pre-development groundwater heads and TDS concentrations.
The comparison of the numerical simulations with varying spatial resolutions
(Fig. A1) shows a similar increase of the volume of fresh groundwater during
the simulation period of 2011 to 2050. In the situation with the Sand Engine
(Fig. A1b), a coarser spatial resolution lowered the projected volume of
fresh groundwater (
In order to provide a uniform measure and error analysis of the spatial grid convergence, the Grid Convergence Index (GCI) was applied to the simulated increase of the volume of fresh groundwater in the model domain in 2050. The GCI indicates to what extent the simulated increase in the volume of fresh groundwater differs from the asymptotic volume, which would be reached with further spatial refinements of the model grid. For more information on the GCI we refer to Roache (1994). The GCI of the additional model simulations S1 to S3 (Table A1) was calculated with a safety factor of 1.25. The ratio in the GCI of simulation S1 and S2 showed that the simulation was within the asymptotic range of convergence (ratio approaches 1), which suggests that the grid was sufficiently refined. The GCI of model simulations S1 to S3 confirms that a horizontal refinement leads to small reductions in the numerical error in the volume of fresh groundwater, and that an increase in the vertical resolution could lead to a larger reduction of the numerical error. However, the refined model simulations (Figs. A1 and A3) suggest that the increase in the volume of fresh groundwater would increase with a higher spatial resolution. Therefore, we think that the chosen spatial discretization was adequate for reliable numerical estimations of the effect of the Sand Engine on the volume of fresh groundwater.
Increase of the volume of fresh groundwater in the situation
without Sand Engine
Increase of the volume of fresh groundwater in the situation
without Sand Engine
Grid convergence index (GCI) of the simulated increase in the volume of fresh groundwater in 2050 (situation with Sand Engine), for three simulations that contain different spatial grid refinements (S1 to S3).
We thank Arjen Luijendijk and Pieter Koen Tonnon for providing Delft3D data, and performing additional Delft3D simulations. This research is supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs. This work was carried out within the Nature-driven nourishment of coastal systems (NatureCoast) program.Edited by: I. Neuweiler Reviewed by: G. Houben and two anonymous referees