Introduction

Climate change impacts have been observed over the last few decades. The CO2 concentration in the atmosphere, the global surface temperature as well as global mean sea level have increased (IPCC 2014, 2021). Representative concentration pathways (RCP) describe several climate change scenarios depending on greenhouse gas emissions, atmospheric concentrations, air pollutant emissions, and land use until the year 2100 (IPCC 2014). The stringent mitigation scenario RCP2.6 represents a scenario that aims to restrict global warming compared to preindustrial temperatures likely below \(2^\circ{\rm C}\) , whereas the very high greenhouse gas emission scenario RCP8.5 assumes no additional efforts to reduce emissions (IPCC 2014). Global mean sea-level rise (SLR) is projected to reach 0.26–0.55 m for scenario RCP2.6 and 0.45–0.82 m for RCP8.5 until 2100 compared to the 1986–2005 period, whereby local sea-level projections will deviate (IPCC 2014).

In addition to sea-level rise, changes in storm-surge activity could contribute to future changes in extreme water levels (Muis et al. 2023). Increased storm-surge activity and an increase in storm-surge levels are projected for the North Sea (Vousdoukas et al. 2016; Muis et al. 2023). Furthermore, regions not only on the north coast of Australia, Alaska, but also parts of the coasts of China, northern Caribbean, or eastern Africa, may experience higher storm-surge levels in the future as well (Colberg et al. 2019; Muis et al. 2023).

Climate change impacts on precipitation patterns will depend on climate and region. The annual mean precipitation in high latitudes and the equatorial Pacific will likely increase until the end of this century under scenario RCP8.5. Whereas many mid-latitude and subtropical dry regions will likely experience a mean precipitation decrease, mean precipitation in many mid-latitude wet regions will likely increase in the RCP8.5 scenario (IPCC 2014). Evapotranspiration is likely to increase as a result of temperature increase, and thus impact groundwater recharge (IPCC 2014).

Climate change effects on freshwater lenses (FWLs) and coastal aquifers are well studied. Several studies examined the effect of SLR (e.g. Masterson and Garabedian 2007; Masterson et al. 2014; Gulley et al. 2016), the effect of changes in groundwater recharge (e.g. Mollema and Antonellini 2013), or both (e.g. Werner and Simmons 2009; Rozell and Wong 2010; Sulzbacher et al. 2012; Unsal et al. 2014; Ketabchi et al. 2014, 2016; Mahmoodzadeh et al. 2014; Holding and Allen 2015; Babu et al. 2020). However, some studies modelled SLR as one or few instantaneous shifts (Rozell and Wong 2010; Ketabchi et al. 2014, 2016; Mahmoodzadeh et al. 2014; Holding and Allen 2015; Babu et al. 2020) instead of a continuous process.

Under unconfined aquifer conditions, the impact of SLR on freshwater resources varies according to the hydrogeological setting, specifically, topography-limited and recharge-limited aquifers (Werner and Simmons 2009; Michael et al. 2013). In topography-limited cases, the vadose zone above the water table is thin; thus, SLR, which causes the FWL to ascend within the aquifer, accompanied by a rise in the water table, can result in surface inundation by fresh groundwater. Consequently, the freshwater volume decreases (Rotzoll and Fletcher 2013; Masterson et al. 2014; Manda et al. 2015; Gulley et al. 2016). In recharge-limited cases, the FWL rises within the aquifer without inundating the surface as the vadose zone is sufficiently thick (Michael et al. 2013; Morgan and Werner 2014; Holding and Allen 2015). Some studies modelled the change of annual recharge rate as a certain percentage change (Rozell and Wong 2010; Sulzbacher et al. 2012; Unsal et al. 2014; Mahmoodzadeh et al. 2014) instead of using temporally variable recharge projections.

Many of the aforementioned studies are case studies of islands with FWLs (Rozell and Wong 2010; Sulzbacher et al. 2012; Holding and Allen 2015; Babu et al. 2020), others are generic analyses. Ketabchi et al. (2014) simulated a generic circular island with a two-layer aquifer based on characteristics of atoll islands. They investigated the effect of SLR with and without land surface inundation on the FWL volume for several ratios of hydraulic conductivity of the upper and lower aquifer layers. Furthermore, a sensitivity analysis examined the impact of additional parameters such as recharge in combination with SLR on the FWL volume. Unsal et al. (2014) investigated the effect of different pumping rates in combination with SLR and/or decreased recharge on the FWL volume and the freshwater–seawater interface position of a circular island. They also examined the impact of different hydraulic conductivity and porosity values. Gulley et al. (2016) modelled a cross-section of a generic topography-limited strip island on which SLR led to the creation of a lake in the island centre. They analysed the effect of this lake on the FWL volume of the island. Strip islands feature a length significantly greater than their width, and they have parallel boundaries (Vacher 1988; Chesnaux et al. 2021). Therefore, strip islands can be represented by a cross-sectional model as the three-dimensional (3D) affects can be disregarded.

In general, the size of a FWL depends on several island characteristics including island size (Fetter 1972; Vacher 1988) and shape (Thissen et al. 2024). Additionally, FWLs grow with increasing groundwater recharge and shrink with greater hydraulic conductivity (Fetter 1972; Vacher 1988; Bailey et al. 2009).

The interface between the freshwater and the underlying saltwater is characterised by groundwater mixing and the formation of a transition zone of brackish water. This zone is geochemically active and may feature enhanced dissolution of carbonates (Hanshaw and Back 1980; Back et al. 1986; Mylroie and Carew 1990). The transition zone can be very thick, extending almost up to the surface of the water table (Fratesi 2013).

The effect of variable recharge on FWLs and their transition zones has been investigated in several studies using conceptual hydrogeological models. Post et al. (2019) found that applying transient meteoric groundwater recharge caused a wider transition zone to form relative to the use of a constant mean recharge value when comparing several model approaches for the German North Sea island of Langeoog. Mollema and Antonellini (2013) also noted that invoking larger recharge variability results in smaller lenses and thicker transition zones relative to scenarios with lower recharge variability when they compared the influence of several recharge patterns from different climate regions on FWLs. These results agree with Eeman et al. (2012), who demonstrated that larger amplitudes of seasonal recharge variation resulted in a greater transition zone thickness.

Tidal signals are important to consider due to their impact on the transition zone, and the phenomenon of tidal overheight. Tidal overheight is the average tide-induced increase of the near-shore groundwater level above mean sea level (Nielsen 1990). Its magnitude depends on beach slope, tidal amplitude and hydraulic diffusivity (Nielsen 1990; Chang et al. 2010; Haehnel et al. 2023) and effects the thickness of the FWL (Pauw et al. 2014). However, many studies that investigated the effect of climate change on island or coastal freshwater resources neglected the effects of tides (e.g. Werner and Simmons 2009; Rozell and Wong 2010; Sulzbacher et al. 2012; Mollema and Antonellini 2013; Green and MacQuarrie 2014; Mahmoodzadeh et al. 2014; Holding and Allen 2015; Ketabchi et al. 2016; Babu et al. 2020).

To summarise, the majority of climate change studies on FWLs rely on simplified recharge and/or sea-level boundary conditions. Specifically, these studies did not take into account possible changes of variability in boundary conditions by using detailed projections based on climate models.

Therefore, this study aims to analyse in which way (1) future sea-level dynamics without SLR, i.e., only caused by tides and storm surges, (2) future sea-level dynamics with SLR, and (3) future sea-level dynamics with SLR and future recharge will change the state variables (a) FWL volume, (b) FWL depth, and (c) the thickness of the transition zone as compared to the past under several hydrogeological conditions. Approaches (1), (2), and (3) were chosen to distinguish between the effects of projected storm surges, SLR, and future groundwater recharge on FWLs, respectively. Therefore, a semi-generic approach was used that has, at least to the best of the authors’ knowledge, never been used before: a generic strip-island was modelled, employing climate projections of monthly recharge and high temporal resolution sea-level projections which are projected for an existing barrier island. This study aims to examine climate change impacts to FWLs of the East Frisian islands in north-west Germany, and to provide qualitatively transferable information to other regions and islands. Therefore, data on the island Norderney and parameter ranges typical of the East Frisian islands were used in an otherwise generic approach. To assess the results, the relative change of the considered state variables between a reference (1971–2000) and a future period (2071–2100) is shown for several combinations of projections from sea-level and recharge models available to further assess model uncertainties in the results.

Methods

Model

Model setup

The cross-sectional model represented a hypothetic, symmetrical sandy barrier strip island of 500, 1,000, and 2,000 m width with homogeneous geology. These widths are in the range of widths of the East Frisian barrier islands. The model was built using FloPy version 3.3.5 (Bakker et al. 2022) and the software SEAWAT (Langevin et al. 2008). For simplicity, only half of the respective symmetrical island was modelled (Fig. 1) and a flat island topography of 10 m above sea level was assumed; thus, the FWL was recharge-limited. Dunes were represented by a strong gradient of the topography towards the sea with a base at 3.5 m, which is approximate to the dune base on the East Frisian island Spiekeroog as described by Beck et al. (2017) and Seibert et al. (2019a). The beach was represented by a constant sloping morphology and the topography was considered to be temporarily invariant. The model had a horizontal and vertical discretisation of 10 and 1 m, respectively. A preliminary modelling experiment using spatial discretisations of 5 and 0.5 m in the horizontal and vertical directions, respectively, did not lead to significantly different results. Note that the hybrid method of characteristics for solving the advection–dispersion equation was used, which is robust against artificial dispersion and oscillation. It is also essentially independent regarding the grid-peclet number and, therefore, functions well even with coarser grids (Zheng and Bennett 2002). An exception to the general spatial discretisation was the top layer, which had a larger vertical discretisation that included the ground level (10 m) to –1 m. The base of the top model layer was set to –1 m to avoid the SEAWAT-specific numerical difficulties that often arise during drying and re-wetting of model layers in transient, unconfined aquifer simulations. Towards the sea, the upper 10 layers featured a decreasing vertical extent to maintain a constant number of layers in each column with the top layer representing the topography. The base case, shown in Fig. 1, featured a depth of 170 m, thus, 170 layers, one row, and 150 columns in the case of a 1,000-m-wide island. The beach slope was 0.4°. The length of the beach was chosen in order to keep the tidal boundary condition of the tidal phase with the lowest low tide within the model domain. The selected depth of the aquifer allowed the FWL to grow freely. All chosen parameter ranges and fixed parameters (Table 1) were based on those typical for the East Frisian islands—Fig. S1 in the electronic supplementary material (ESM). The East Frisian islands form a barrier island chain in the North Sea in north-west Germany that is exposed to semidiurnal tides with tidal ranges from 2.2 to 2.8 m (Wang et al. 2014). Boundary conditions were based on those of the island Norderney. All software settings that differ from default values and are not mentioned otherwise are provided in Table S1 in the ESM.

Fig. 1
figure 1

Grid and boundary conditions of the base case model. Depth of the model is measured relative to the sea level (masl: metres above sea level). R: recharge boundary condition, GHB and DRN: tidal boundary condition (general-head boundary and drainage boundary; 3rd-type boundary conditions)

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Table 1 Overview of parameter values and ranges
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Boundary conditions

For the tidal boundary, water-level projections from 1951 to 2100 with a temporal resolution of 20 min at a position north of Norderney (latitude: 53.731197, longitude: 7.179276) were used. These data were derived from the hydrodynamic TRIM-NP model based on the regional climate projections obtained with the regional climate model REMO from two global climate models: MPI-ESM and HadGEM2 (Gaslikova 2023). For both global climate models, scenarios RCP2.6 and RCP8.5 (IPCC 2014) were available. Due to the large memory and time requirements of tide-resolved simulations, a phase-averaged approach based on Pauw et al. (2014) was applied (Appendix 1). In this tidal boundary condition, a stress period, i.e., a period of time-invariant boundary conditions, has the length of one tidal cycle; thus, models with HadGEM2 and MPI-ESM as sea-level models had 103,646 and 105,862 stress periods, respectively. Land surface inundation was considered implicitly. For simulations including mean SLR, annual SLR values were added (Fig. 2)—for the historical period 1961–1990, the difference between the 30-year moving average from observed annual mean sea level at Norderney (WSV 2021) and the observed mean sea level averaged for the 1961–1990 period was used; for the projection period 2020–2100, the median SLR estimates for RCP2.6 and RCP8.5 scenarios at Delfzijl, The Netherlands, from the FACTS model (Fox-Kemper et al. 2021; Garner et al. 2021) were applied; the data were linearly interpolated between those periods for the intermediate period 1991–2019.

Fig. 2
figure 2

Annual SLR values of climate change scenarios RCP2.6 and RCP8.5 (Fox-Kemper et al. 2021; Garner et al. 2021; WSV 2021). These values were added to the tidal boundary condition for simulations that included SLR

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In the flow model the groundwater recharge was modelled by assigning a second type boundary condition to the cells of the top layer above 0 m. The corresponding salinity was set to zero. Groundwater recharge projections with monthly data from 1970 to 2100 were provided by the regional hydrological model mGROWA22 for the German state of Lower Saxony (Hajati et al. 2022). For both climate change scenarios RCP2.6 and RCP8.5, three models out of eight or eleven, respectively, of the mGROWA ensemble were used (Fig. 3 and Fig. S2 of the ESM ). These models covered the whole range of the climatic water balance of the model ensemble: the model with the largest change in climatic water balance between the reference period 1971–2000 and the future period 2071–2100 on Norderney (“max”), the one with the smallest change (“min”), and the one nearest to the mean change (“mean”). These changes in mean monthly recharge are shown in Fig. 3c. Mean monthly recharge decreases between the reference period 1971–2000 and the future period 2071–2100 for recharge scenarios “min”. There is almost no change between analysed periods for recharge scenarios “mean”, and an increase for recharge scenarios “max”. The names of corresponding climate models are provided in Table S2 of the ESM. The spatial mean over all cells covering Norderney was used per month (Fig. S3 of the ESM ). If a stress period started in 1 month and extended into the following, it was attributed to the month in which it began. To adjust the length of recharge projections to that of sea-level projections, the monthly means of the first 10 years (1970–1979) were assigned to the corresponding months of the years 1951–1969. No-flow boundary conditions were assigned to the bottom and vertical boundaries in both flow and transport models.

Fig. 3
figure 3

Annual groundwater recharge values of all six groundwater models used for this study. Time series of years 1970–2100 are shown for climate change scenarios a RCP2.6 and b RCP8.5 (these time series are shown enlarged in Fig. S2 of the ESM ). Boxplots in c show mean monthly recharge (dotted lines) of reference period 1971–2000 (blue, red) and future period 2071–2100 (purple, dark red) for recharge scenarios “min”, “mean”, and “max”. (Solid line inside boxes: median, dotted line inside boxes: mean, blue colours: RCP2.6, red colours: RCP8.5)

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Initial conditions

To investigate the effect of changes to boundary conditions over the time span of 150 years without including the effects of initial conditions, the model started in a dynamic equilibrium. This was reached by repeatedly running the model over the years 1951–1960. The first run started with initial conditions described in the following, and consecutive runs always started with the final situation of the previous run. These consecutive runs were repeated until the mean of all three investigated quantities over these 10 years visually reached a dynamic equilibrium (Fig. S4 of the ESM). Hydraulic heads and salinity distribution of the final time step of the last of these previous runs were then used as “true” initial conditions for the run over all 150 years.

Initial conditions of the first run over the years 1951–1960 depended on the sea-level model. Initial heads \({h}_{\text{ini},\text{FWL}}\) between island centre and high tide mark \(\text{HTM}\) of the first high water \(\text{HW}\) were calculated corresponding to Pauw et al. (2014):

$$h\left(x\right)= \delta \sqrt{\frac{-N{x}^{2}-2{C}_{1}x}{K\delta (1+\delta )}}\text{ with }{C}_{1}=\frac{{\left(\frac{{h}_{\text{HTM}}}{\delta }\right)}^{2}\left(\delta K+{\delta }^{2}K\right)+N{\widetilde{L}}^{2}}{-2\widetilde{L}}$$
(1)

where \(x\) is the location of the hydraulic head and \(\delta\) is the relative density difference between saltwater and freshwater \(\left(\frac{{\rho }_{\text{s}}-{\rho }_{\text{f}}}{{\rho }_{\text{f}}}\right)\). \({\rho }_{\text{f}}\) and \({\rho }_{\text{s}}\) are the densities of freshwater and saltwater, respectively. For \(K\) the horizontal hydraulic conductivity was used. \(N\) was originally the precipitation rate; however, the mean recharge rate over the years 1970–1979 was used, and \(\widetilde{L}\) was the theoretical distance from one side of the FWL to the \(\text{HTM}\) on the other side. The corresponding head at \(\text{HTM}\) \({h}_{\text{HTM}}\) was the mean of all \({h}_{\text{HTM}}\) of the years 1951–1960. Seaward of the \(\text{HTM}\), the heads \({h}_{\text{ini},\text{sea}}\) were linearly interpolated between \({h}_{\text{HTM}}\) and 0. The initial FWL depth \(D\) was calculated using the Ghyben-Herzberg relation (Herzberg 1901) and the initial heads \({h}_{\text{ini},\text{FWL}}\) from the island centre to \(\text{HTM}\): \(D= \frac{{\rho }_{\text{f}}}{{\rho }_{\text{s}}-{\rho }_{\text{f}}}\bullet {h}_{\text{ini},\text{FWL}}\). After testing with the base case model, the thickness of the initial transition zone was chosen to depend on the island width as follows: 30 m in the case of \(L=500 \text{m}\), 25 m in the case of \(L=1000 \text{m}\), and 20 m in the case of \(L=2000 \text{m}\). In all cases, the transition zone started 5 m above the calculated initial FWL depth \(D\) and extended down towards the seawater. The salinity was linearly interpolated from 0 to 35 kg/m3. Between \(\text{HTM}\) and the seaward boundary, and below the transition zone, all cells were filled with seawater.

The aim of this study was to investigate the effect of the change of boundary conditions due to climate change on FWLs. Running the model with boundary conditions of the first 10 years until a dynamic equilibrium is reached and using this situation as the initial condition for the run over all 150 years allows for extracting the effect of the change in boundary condition from other influences. It should, however, be mentioned that natural systems often are not in a dynamic equilibrium with their boundary conditions—for example, in the Netherlands, it was found that the density distribution of a groundwater system may need several millennia to reach a dynamic equilibrium (Oude Essink 1996). Similarly, a model of the East Frisian mainland in Germany reached steady-state conditions of salinities after ~3,000 simulated years (Seibert et al. 2023).

Approach

The study was divided into two parts:

  1. Part 1.

    Examination of the influence of several combinations of boundary conditions on different island widths. For the three island widths 500, 1,000, and 2,000 m, the effect of boundary conditions was evaluated in three steps: effects of (1) meteorically driven sea-level dynamics only, disregarding actual SLR, (2) sea-level dynamics with SLR, and (3) sea-level dynamics with SLR and recharge projections. In cases (1) and (2), monthly means of recharge from the reference period 1971–2000 of the models “mean” of the RCP scenario corresponding to the respective sea-level model were applied to account for seasonality but not for changes between past and future.

  2. Part 2.

    Investigation of the effects of sea-level dynamics with SLR and recharge projections (3) for \(L=1000\, \text{m}\) in combination with variations of hydrogeological parameters (Table 1). These parameters were changed separately to smaller and larger values, while unchanged parameters maintained the base case value.

In both parts, the results were examined by calculating the mean of (a) FWL volume, (b) FWL depth, and (c) transition zone thickness over all stress periods in the reference period 1971–2000 as well as in the projection period 2071–2100. (The projection period is 2070–2099 for the HadGEM2 sea-level model, since it ends in 2099. However, for better readability, in the following, the future projection period is referred to as 2071–2100.) The relative difference between these periods was then compared to model runs with similar values of hydrogeological parameters but boundary conditions from different climate models. Thus, per RCP scenario and island width, two (sea level) models were run for approaches (1) and (2) and all possible combinations of two sea-level models and three recharge models; hence, six models for (3). In total, 204 models were run. An overview of both study parts, the approaches with used parameters, investigated boundary conditions, and number of models are given in Table 2.

Table 2 Overview over the study structure
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In the following, FWL depth refers to the depth of freshwater where 2.5% of the salinity of seawater is reached. The value is taken at the island centre, which corresponds to the leftmost column of the model (Fig. 1). The transition zone is defined as the brackish water zone from 2.5 to 95% salinity of seawater, likewise taken at the island centre. The FWL volume is the volume of freshwater (i.e. <2.5% of the salinity of seawater) below the island in all model columns that never get inundated by seawater. Only these columns were considered, since the freshwater volume below the beach is highly dependent on the saltwater fingering which occurred in the intertidal zone. Developing saltwater fingers are highly dynamic on a relatively short time scale and are of variable size (e.g. Greskowiak 2014; Fang et al. 2021) and, hence, strongly affect the freshwater volume within the intertidal zone. Note that salt fingering flow below beaches has so far not been observed in the field, but its occurrence has been described in experimental and modelling studies (e.g. Greskowiak 2014; Röper et al. 2015; Fang et al. 2021). This paper, however, aims to investigate the long-term effects of climate change; furthermore, the freshwater below a beach is usually not considered for use as drinking water because pumping wells are typically installed in more protected areas. Therefore, the beach was disregarded when calculating the freshwater volume (Fig. 1).

Calculation, representation, and interpretation of model results

Results are presented as relative differences between the averages over all time steps in the 30-year future projection period 2071–2100 and in the reference period 1971–2000. Thus, decreases in values of the investigated quantities from the reference to the future period are described with negative values, while positive values indicate an increase from past to future. Using averages over 30-year periods to calculate climate change impacts is typically done and recommended by the World Meteorological Organisation (2017). To the authors’ knowledge, however, this approach has so far never been used in hydrogeology to investigate climate change impacts on coastal aquifers and freshwater lenses.

Furthermore, it is recommended to use a model ensemble instead of one single climate model to account for uncertainties (Benestad et al. 2021). For the sea-level dynamics, the two existing models (Gaslikova 2023) and, thus, the largest possible model ensemble was used. For groundwater recharge those three models per RCP scenario were used as a subsample of the mGROWA22 model ensemble, representing the full range of projected climate change signals (Benestad et al. 2021; Hajati et al. 2022).

To investigate the uncertainties in the model projections the bandwidth of the results of the model ensemble have to be defined by either calculating mean and standard deviation or median and lower and upper percentiles (Benestad et al. 2021). The second possibility is less influenced by outliers. Therefore, results in “Results” section are represented as boxplots.

Sea-level projections and groundwater recharge models were combined in all possible combinations to include uncertainty resulting from using model projections. Due to this approach, however, boundary condition models originating from different climate models driven by different climate forcings were also combined. Therefore, model runs in this study cannot be associated with a single climate model.

Results

Impact of boundary conditions and island width

The positions of the transition zone in the first stress period of the reference period and the last time step of the future period are compared in Fig. 4 for models with sea-level model HadGEM2 RCP8.5 and recharge model “mean” RCP8.5 as boundary conditions and an island width of 1,000 m. With sea-level dynamics only (approach (1)), the transition zone maintains its position and its thickness increases only very little (Fig. 4a). However, when SLR is considered in addition to sea-level dynamics (approach (2)), the transition zone shifts upwards and expands slightly (Fig. 4b). When adding recharge projections to sea-level dynamics and SLR in approach (3), the transition zone shifts upwards and its thickness increases strongly (Fig. 4c). In all cases, an unstable, salt finger forming upper saline plume exists below the sloping beach.

Fig. 4
figure 4

Salinity distribution including the transition zone boundaries at 2.5 and 95% salinity of seawater (white solid lines) of the last time step of the future period (2099), and transition zone boundaries at 2.5 and 95% salinity of seawater at the first time step of the reference period (1971, white-dashed line) for a approach (1), i.e., sea-level dynamics only, b approach (2), i.e. sea-level dynamics + SLR, and c approach (3), i.e., sea-level dynamics + SLR + recharge projections calculated with the sea-level model HadGEM2 RCP8.5 and recharge model “mean” RCP8.5 and \(L=1000\, \text{m}\)

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The time series of the model in Fig. 4c is shown in Fig. 5, together with the time series of models with the same island width and sea-level model but different recharge projections. Results of models with recharge models “mean” and “min” are similar to each other and project a decrease in FWL volume and depth. If the average monthly recharge is projected to increase in the future (recharge model “max”, Fig. 3), FWL volume and depth are projected to increase first and then decrease slightly. The transition zone thickness is projected to increase for all three models. Note that initial conditions are not identical because the models started each with their dynamic equilibrium over the years 1951–1960 (see section “Initial conditions”).

Fig. 5
figure 5

Time series of a FWL volume, b FWL depth, and c transition zone thickness over all 150 modelled years for approach (3), i.e., sea-level dynamics + SLR + recharge projections of models with \(L=1000\, \text{m}\), sea-level model HadGEM2 RCP8.5 and each one of the recharge models “max” RCP8.5, “mean” RCP8.5, or “min” RCP8.5. 30-year reference and future periods are highlighted in grey

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For all models and all island widths for approaches (1), i.e., sea-level dynamics only, and (2), i.e., sea-level dynamics + SLR, relative differences in per cent between 30-year averages of reference and future period are displayed in Fig. 6. Negative values describe a decrease in the variables from past to future, while positive values describe an increase. FWL volume and depth are maintained for all cases in approach (1), while they are projected to decrease slightly for all cases in approach (2). The relative loss of freshwater volume is stronger for smaller islands. The effect on the transition zone thickness likewise depends on the island width. Smaller islands experience an increase in transition zone thickness. The increase is larger but still rather small in cases with SLR, approach (2). For larger islands, the transition zone thickness hardly changes at all—approaches (1) and (2)—or may even slightly decrease, approach (1). There are almost no differences between climate change scenarios RCP2.6 and RCP8.5.

Fig. 6
figure 6

Relative differences between 30-year averages of FWL volume, depth, and transition zone thickness for all 12 models each of a approach (1), i.e., sea-level dynamics only, and b approach (2), i.e., sea-level dynamics + SLR of reference period 1971–2000 and future period 2071–2100 for both climate change scenarios RCP2.6 (blue) and RCP8.5 (red). Negative values describe a decrease in the variables from past to future, while positive values describe an increase. Note that each RCP scenario consists of two sea-level projections from climate models, i.e., HadGEM2 and MPI-ESM

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Relative differences between averages of reference and future period of all model combinations of sea-level and recharge boundary conditions of approach (3), i.e., sea-level dynamics + SLR + recharge projections, are plotted in Fig. 7. FWL volume and depth are projected to decrease in most cases. Their mean and median decrease is projected to be only slightly larger in the case of the high emission scenario (RCP8.5) compared to the stringent mitigation scenario (RCP2.6). For islands with \(L=2000\, \text{m},\) mean and median of FWL volumes and depths show a decrease for the RCP8.5 scenario, while they predict no or only minor changes for scenario RCP2.6. In almost all model runs for approach (3), the transition zone increases. However, boxplot sizes are large; thus, model predictions differ strongly. Means and medians of changes in transition zone thickness are greater for scenario RCP8.5 than for scenario RCP2.6.

Fig. 7
figure 7

Relative differences between 30-year averages of FWL volume, depth, and transition zone thickness for approach (3), i.e., sea-level dynamics + SLR + recharge projections of reference period 1971–2000 and future period 2071–2100 for both climate change scenarios RCP2.6 (blue) and RCP8.5 (red). Each boxplot consists of values of all six models per RCP scenario and island width. Negative values describe a decrease in the variables from past to future, while positive values describe an increase. (Solid line inside boxes: median, dotted line inside boxes: mean)

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Impact of hydrogeological parameters and model setup

Results of model runs with varied hydrogeological parameters for an island with a width of 1,000 m are shown in Fig. 8. Corresponding values of mean, median, minimum, and maximum are listed in Table S3 of the ESM for each parameter setting. For comparison, boxplots in the centre of each pair of three, thus in dark blue and light red, show results with base case parameters equivalent to those in Fig. 7. For all model runs, mean and median show a decrease in FWL volume and depth from reference to future period, while mean and median of the transition zone thickness show an increase in almost all cases. Predicted decreases and increases are more pronounced for the high-emission climate change scenario RCP8.5 when considering means and medians. Also, the sizes of boxplots are usually larger for climate change scenario RCP8.5 than for scenario RCP2.6.

Fig. 8
figure 8

Relative differences between 30-year averages of FWL volume, depth, and transition zone thickness of approach (3), i.e., sea-level dynamics + SLR + recharge projections with variations in hydrogeological parameters of reference period 1971–2000 and future period 2071–2100 for both climate change scenarios RCP2.6 (blue colours) and RCP8.5 (red colours). Each boxplot consists of values of all six models per RCP scenario and island width. Negative values describe a decrease in the variables from past to future, while positive values describe an increase. Boxplots in the centre of each pair of three, thus, in dark blue and light red, represent the base case and are equivalent to results for \(L=1000\text{ m}\) in Fig. 7. Base case parameter values are marked bold within the legends (compare Table 1). (Solid line inside boxes: median, dotted line inside boxes: mean)

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The strongest observed decreases from the reference period to the future period in FWL volume and depth, when looking at means and medians, are projected for larger hydraulic conductivity values (Fig. 8, top rows). If either \({K}_{\text{x}}\) is set to a greater value (\({K}_{\text{x}}=5\bullet {10}^{-4} \text{m}/\text{s}\)) or if \({K}_{\text{z}}\) is changed to result in isotropy (\({K}_{\text{x}}/{K}_{\text{z}} =1\)), mean and median of the relative change of FWL volume and depth become smallest. However, boxplot sizes in both cases, especially for a greater \({K}_{\text{x}}\), are large. Note that if \({K}_{\text{x}}\) is enlarged, also \({K}_{\text{z}}\) has a greater value, since the anisotropy remains constant. For the larger \({K}_{\text{x}}\) the projected mean relative increase in transition zone thickness has a smaller absolute value than the projected mean relative decreases of FWL volume and depth, but there is again a wide boxplot for the climate change scenario RCP8.5. A greater \({K}_{\text{x}}\) combined with scenario RCP2.6 is the only parameter combination for which mean and median are negative and, thus, project a maintenance or even a slight decrease of transition zone thickness. Both model cases with greater hydraulic conductivities than the base case, thus, \({K}_{\text{x}}=5\bullet {10}^{-4} \text{m}/\text{s}\) and \({K}_{\text{x}}/{K}_{\text{z}} =1\), have huge transition zones (Fig. S5 of the ESM). This explains the large absolute change in transition zone thickness and very large boxplots in Fig. S6 of the ESM. If \({K}_{\text{x}}\), however, is smaller than in the base case (\({K}_{\text{x}}=5\bullet {10}^{-5} \text{m}/\text{s}\)) or the anisotropy is greater (\({K}_{\text{x}}/{K}_{\text{z}} =20\)), relative and absolute changes are similar to those of the base case for all three investigated state variables. However, boxplots of FWL volume and depth of absolute values are a bit larger if \({K}_{\text{x}}\) is set to a smaller value.

Greater decreases in FWL volume and depth as well as greater increases in the transition zone thickness than in the base case are also predicted for larger dispersivities (\({\alpha }_{L}=5 \text{m}\)). Smaller dispersivities (\({\alpha }_{L}=0.5 \text{m}\)) result in smaller changes. If the beach slope is smaller (\(\beta =0.1^\circ\)), projected relative mean and median changes and their boxplots are small for FWL volumes and depths. For the transition zones, however, relative changes are projected to be smaller as well, but the boxplots are as large as in the base case scenario. In the case of a steeper beach \((\beta =0.8^\circ\)), relative changes are similar to those of the base case. The same accounts for different aquifer depths (\(B\)) or values of specific yield (\({s}_{\text{y}}\)). For these, all results are similar to those of the base case, only the boxplot sizes of relative differences of the transition zone thickness differ slightly.

Discussion

Climate change impact of boundary conditions and island width

The results describing the impact of boundary conditions and island width illustrate the importance of including both SLR and projections of groundwater recharge simultaneously in calculations of future FWL size. Almost no changes in average FWL volume, depth, and transition zone thickness are projected from reference to future period for approach (1), i.e., sea-level dynamics only. In contrast, changes are projected for approaches (2), i.e., sea-level dynamics + SLR, and (3), i.e., sea-level dynamics + SLR + recharge projections, whereas they are greater for the latter. Uncertainties of changes, represented by the difference between the largest and the smallest projected relative difference and, thus, the size of boxplots, are greatest for approach (3). Changes in the transition zone thickness in approach (1) for islands of width 500 or 1,000 m are mostly less than 1 m, which is the vertical resolution of the model. Thus, these changes are not significant and the effect of the changing dynamics is thus only minor as compared to the effect of SLR. Note that approach (A) was realised to differentiate the effect of mean SLR from the effect of potentially changing water-level variability. Clearly, approach (1) is not a realistic scenario. In approach (2), however, the largest absolute decrease of FWL depth is more than 3 m in scenarios RCP2.6 and RCP8.5 for \(L=500\text{ m}\). The projected increase of the transition zone is close to 2 m in three of four models with \(L=500\text{ m}\). These changes are not negligible as they clearly exceed the vertical model resolution. A slight increase in transition zone thickness by SLR was also observed by Mahmoodzadeh et al. (2014). They modelled the long-term response of an island cross-section based on Kish Island in the Persian Gulf, following an instantaneous SLR until the FWL reached steady-state conditions again. Figures 6 and 7 show that the impact of the boundary conditions is more pronounced for smaller islands than for larger ones. Decreases in volume and depth of the FWL and increases in the transition zone thickness are in most cases predicted to be largest for islands with \(L = 500\) m. For transition zones in approach (3), the impact of the island width is unclear and results show a large uncertainty. Transferred to the East Frisian islands, these results indicate that narrower islands like Juist, with a width of maximum 900 m, are more vulnerable to climate change impacts than wider islands like Norderney or Borkum.

Comparing aproaches (2) and (3) clearly shows the importance of including groundwater recharge projections into models. Groundwater recharge seasonality was already included in approach (2), but it is projected to become more pronounced in the future in all recharge models (Fig. S7 of the ESM). Such changes enhance the increase of transition zone thickness in approach (3) compared to approach (2) (Fig. 4). These results also underline the importance of modelling groundwater recharge as a transient process as stated by Post et al. (2019). This is in agreement with Mollema and Antonellini (2013) who compared FWL size and transition zone thickness of modelled FWLs using potential recharge values of several climatic regions from all around the world. Mahmoodzadeh et al. (2014) stated that under recharge-limited conditions, a change in recharge rate greatly affects FWLs. Depending on whether groundwater recharge increases or decreases, it may both mitigate or increase saltwater intrusion impacts due to SLR. SLR itself, however, has a smaller impact in recharge-limited aquifers since it simply results in a rise of the FWL within the aquifer, whereas the hydraulic gradient between sea and land does not change (Michael et al. 2013). This study shows that changes in groundwater recharge have a greater influence on FWLs than SLR under the given conditions, which was also reported by Holding and Allen (2015) and Ketabchi et al. (2014). Moreover, adding recharge projections in approach (3) results in differences between climate change scenarios RCP2.6 and RCP8.5 that were not observed in approaches (1) and (2). Recharge projections also increase uncertainties of changes between past and future periods (Figs. 6 and 7). Furthermore, a comparison of approaches (1), (2), and (3) shows that projected groundwater recharge has a larger impact on the transition zone thickness than sea-level dynamics. Projected increase of transition zone thickness underlines the importance of including mixing processes into models instead of using sharp-interface models as, for example, done by Babu et al. (2018; 2020) for the island of Tongatapu in the Kingdom of Tonga. Results in Figs. 6 and 7 show that neglecting the transition zone may lead to an underestimation of climate change impacts on FWL volumes and depths.

Climate change impact of hydrogeological parameters

The second part of this study investigated the impact of several hydrogeological parameters on changes in FWL size and transition zone thickness. Performing a sensitivity analysis for a two-layered circular island model, Ketabchi et al. (2014) discovered that FWL volume is more sensitive to groundwater recharge than to beach slope or hydraulic conductivity across the tested parameter range. Results given in Fig. 8 likewise show that future relative changes of FWL volumes and depths are more sensitive to external factors such as, e.g., groundwater recharge than to hydrogeological conditions or beach slope. The study by Ketabchi et al. (2014) is based on atoll islands but results are nevertheless similar to those of this study. Thus, it is likely that the findings of the present study are transferable from the North Sea region to other parts of the world.

The hydrogeological factor with the largest impact but also highest uncertainty is the hydraulic conductivity. A larger \(K\) increases the transmissivity of the aquifer and, thus, decreases the damping of the tidal amplitude during its motion within the aquifer (Ferris 1952). A larger vertical hydraulic conductivity affects the vertical flow and allows for stronger changes of the vertical extend of FWLs. The recharge model “max”, therefore, leads to a stronger relative increase, while “min” results in a stronger relative decrease of FWL volume and depth, if \({K}_{\text{z}}\) is greater than in the base case. Therefore, uncertainties of the changes of FWL volume and depth are largest if both, \({K}_{\text{x}}\) and \({K}_{\text{z}}\), have greater values or if the aquifer is isotropic with the same \({K}_{\text{x}}\) as in the base case. Another relevant parameter is the dispersivity. When FWLs expand or contract, longitudinal dispersivity dominates the mixing process (Eeman et al. 2011). Therefore, because the vertical transverse dispersivity is increased correspondingly due to a constant \({\alpha }_{\text{VT}}/{\alpha }_{\text{L}}\)-ratio, a larger \({\alpha }_{\text{L}}\) results in a stronger increase in transition zone thickness and a decrease of FWL volume and depth than smaller dispersivities.

It should be noted that changes in Figs. 6, 7 and 8 are those which occur during the simulation time. However, since climate change impacts FWLs slowly, the system is likely not in equilibrium with the new boundary conditions after 150 model years. This could be the reason why there are almost no differences between the RCP2.6 and RCP8.5 scenarios in approach (B), although SLR between both scenarios differs strongly. It should further be considered that the tidal boundary condition in this study includes land surface inundation. However, the effect of land surface inundation is not reflected in the results in Figs. 6, 7 and 8 and Table S3 of the ESM , because only the volume below the island and not below the beach was considered. Neglect of land surface inundation due to SLR would lead to an underestimation of climate change impacts on FWL volumes and depths (Ataie-Ashtiani et al. 2013; Ketabchi et al. 2014; Mahmoodzadeh et al. 2014).

Conclusions

A cross-sectional model of a hypothetical island was modelled with boundary conditions representative of the German North Sea barrier island Norderney. High-resolution sea-level projections, annual SLR data, and monthly groundwater recharge values of several climate models were used to evaluate climate change impacts on freshwater lens volume, depth, and transition zone thickness. Differences between the reference period 1971–2000 and the future period 2071–2100 were quantified. In the first part, the impact of boundary conditions on islands of 500, 1,000, and 2,000 m width was analysed. The effects of the three external factors—sea-level dynamics, SLR, and groundwater recharge variations—were assessed. A multi-parameter study additionally evaluated the impacts of the hydrogeological factors of aquifer depth, hydraulic conductivity, anisotropy of hydraulic conductivity, specific yield, beach slope, and dispersivity on 1,000-m-wide islands.

Key conclusions of this study are:

  • It is very likely that FWL volume and depth on islands will decrease, while transition zone thickness will increase in the future as a consequence of climate change.

  • The smaller the island, the greater the effect of the boundary conditions.

  • The external factors groundwater recharge and SLR have a larger influence on FWLs and their transition zones than most hydrogeological parameters within parameter ranges realistic for the East Frisian islands.

  • From the hydrogeological parameters investigated, hydraulic conductivity has the greatest effect but also the largest uncertainty associated with it. Its anisotropy and dispersivity have a moderate and beach slope a minor influence. Specific yield and aquifer depth have a negligible effect.

  • Recharge projections have a larger effect on the transition zone thickness relative to sea-level dynamics.

  • With respect to the employed recharge and sea-level projection models, recharge projections lead to greater uncertainties regarding the projected changes in the considered state variables.

  • Observed differences between climate change scenarios RCP2.6 and RCP8.5 within the 150 model years largely result from groundwater recharge projections.

In summary, this paper shows that under all (geological) conditions tested, climate change will very likely lead to smaller freshwater lenses in the future, consequently affecting the amount of freshwater available for drinking-water production on sandy barrier islands. This study confirms results of previous studies that predict a decrease in the amount of freshwater due to climate change, but in addition it also illustrates the importance of including variability and uncertainties of projections resulting from climate models.