Introduction

Climate change is expected to have a significant impact on groundwater in large parts of the world (Richard et al. 2013). While precipitation and hence groundwater recharge are projected to decrease in many regions, the seasonal distribution of rainfall in northern Europe is expected to change towards more winter precipitation and less summer precipitation. Several studies on the impact of climate change on water resources in Denmark (e.g. van Roosmalen 2007; Karlsson et al. 2015; Seidenfaden et al. 2022) have shown the same tendency. Most climate models project a significant increase in winter precipitation, resulting in more groundwater recharge (Han et al. 2017) and higher water tables, especially during winter and spring (van Roosmalen et al. 2009). Already today, the water table, generally in Denmark during winter and spring, is relatively high and located within the first couple of meters below the soil surface. In rural areas dominated by agriculture, groundwater levels close to the surface pose problems for crop growth and activities in the field (ploughing, sowing, etc.); therefore, in more than 50% of the agricultural fields in Denmark, tile drains are installed at a depth of approximately 0.5 m to remove the excess water (Møller et al. 2018). In many urban areas, the groundwater level may also increase, often resulting in problems with moist basements and stability problems of infrastructure like roads and railway tracks resulting in undermining. Unwanted infiltration of groundwater into the sewer system (Karpf and Krebs 2013) is another severe problem that results in increased wastewater discharge and higher costs for wastewater treatment.

In the review by Fletcher et al. (2013), several examples of the impact of rising water tables reaching the sewer networks are described. If the sewer pipes are non-watertight, groundwater may infiltrate into the sewers in quantities that exceed the volume of runoff as a result of rain events. According to the findings of Karpf and Krebs (2013), the most sensitive parameter for infiltration of groundwater into the sewer pipes is the infiltration factor which is a function of the backfill hydraulic conductivity and the trench dimensions. If the sewer pipes are in good condition and therefore close to watertight, groundwater levels located above the sewer level will not cause leakage into the sewer system. However, if the system is non-watertight, it is expected to function as a groundwater drain in situations where the water table reaches the sewer pipe elevation resulting in significant groundwater inflow to the sewers. Hence, leaky sewers may mediate the situation where increasing groundwater recharge results in rising groundwater levels; however, this effect is obtained at the expense of high groundwater inflow rates to the sewer system and elevated rates of wastewater with low sewage concentration to be treated at a high cost. The situation may worsen if forced infiltration (Jeppesen and Christensen 2015) of rainwater is implemented, where water from roofs and other paved areas is diverted to infiltration beds to decrease rainwater inflow to a sewer system with limited capacity (Kidmose et al. 2015); however, forced infiltration unintentionally results in rising groundwater levels that make the situation worse. Renovation of the sewer system to reduce groundwater inflow also results in increasing groundwater levels; hence, as the discharge in the sewer system is reduced and the cost of wastewater treatment is reduced, but the problems related to high water tables are increased, this may outweigh the savings obtained from less sewer water to clean.

Different types of adaptation measures to lower the shallow groundwater level are available (Mourot et al. 2022). One solution is to increase evapotranspiration and hereby reduce groundwater recharge. This may be attained by increasing the area planted with trees. Both interception and transpiration losses from forests are higher than from agricultural areas (Ladekarl et al. 2005; van der Salm et al. 2006; Verstraeten et al. 2005; Sonnenborg et al. 2017) and from urban areas dominated by paved surfaces. Hence, afforestation of areas neighbouring the districts with too-high groundwater levels may be effective. Additionally, there may be numerous places where trees can be planted, e.g., along roads, in parking lots, or in parks dominated by grass. This measure also has the potential to increase biodiversity and recreational quality in the urban area; however, the effectiveness of this method to reduce the water table is unknown.

Paved impermeable surfaces will most often also result in less infiltration and more inflow to the sewer system compared to more natural surfaces (Salvadore et al. 2015). However, increasing the fraction of paved area will decrease the fraction of green areas in the urban area and has negative impacts on, e.g., evapotranspiration during summer, resulting in higher temperatures and fewer shady areas in the town; hence, this approach is not considered a viable solution.

Another solution to the problem of high water tables is to remove water from the shallow aquifer. This may be achieved if a so-called third pipe, a drainage pipe, is installed. In contrast to the sewer pipe and the rainwater pipe, this pipe is designed to allow groundwater inflow and may be installed at the same location and depth as the sewers. The installation costs may be minimized if the drainage pipes are installed in connection with renovation work. An alternative method to remove some of the shallow groundwater is to install a number of pumping wells to withdraw water from the shallow aquifer. It may only be necessary to abstract groundwater during winter and spring when the problems with high groundwater levels are most significant.

The main objective of this study is to test alternative adaptation measures to reduce high groundwater levels in a typical town in the western part of Denmark. Four different adaptation measures are tested: (1) draining the town through a system of groundwater drainage pipes installed along roads, a third pipe, (2) abstracting water from wells installed in the shallow aquifer below the town, (3) afforestation in the vicinity of the town combined with an increased number of trees inside the town (greening of the town), and (4) additional drainage through a ditch running through the central part of the town. A subsequent objective is to test the robustness of the four alternative adaptation measures in a future climate, using results from a climate model that projects a wetter climate. The novelty of the work is found in the procedure proposed for selecting the best adaptation measure from the several alternatives. The method should be considered as the first step toward a procedure that evaluates the robustness to changes in climate, with a focus on precipitation, and groundwater recharge and level.

Study area and data

The study area, Fig. 1, is located in the central part of Jutland on a Weichselian outwash plain slightly sloping towards WNW with elevations varying from 55 m above sea level in the east to 40 m in the western part. The study area is 47 km2 and covers the town of Sunds, Lake Sunds, and surrounding agricultural areas. Several rivers are present in the study area, which are all part of the Storaa River catchment. The Storaa River flows from central Jutland towards the west coast, where it discharges into Nissum Fjord and the North Sea. Lake Sunds is part of the river system and is located to the northeast of the town. Built-up areas with private housing are found along most of the lakeshore.

Fig. 1
figure 1

Data overview and location of study area. The two dotted black lines represent the cross sections shown in the subsequent figure

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Geological setting

The near-surface geology in and around the study area is characterized by sandy outwash plain sediments from the Weichselian glaciation (Würm; Wisconsin) on top of older Quaternary sandy and clayey sediments (e.g. Nielsen 1981). The pre-Quaternary sediments below consist of predominantly marine clay and sand sequences of the Miocene (Rasmussen et al. 2010). The Quaternary sediments vary in thickness from a few meters up to more than 100 m in areas where buried tunnel valleys of Quaternary age are incised into the pre-Quaternary strata (Sandersen and Jørgensen 2016). Beneath the shallow Lake Sunds, boreholes show significant thicknesses of late- to postglacial organic-rich sediments (Jupiter borehole database; GEUS 2022). The uppermost Miocene sediments are predominantly represented by middle to upper Miocene clays of the Maade Group, whereas the lower Miocene deposits are characterized by layers of mica sand and quartz sand of the Bastrup and Odderup formations separated by thick clayey and silty successions of the Klintinghoved and Arnum formations (Rasmussen et al. 2010). Based on investigations within the region, it has been proposed that tectonic events during the Quaternary have disturbed the Miocene deposits (Koch et al. 1989; Lykke-Andersen et al. 1996; Madirazza 2002).

Geological and geophysical data

All boreholes within the study area are visualized as blue points in Fig. 1 (Jupiter database; GEUS 2022). A large number of shallow boreholes were drilled as part of lignite investigations in the 1940s. Ten of these boreholes were drilled in Lake Sunds. Only a few boreholes contain geological information of the sedimentary succession of stratigraphy, deeper than 150 m.

A suite of traditional and new geophysical methods has been applied in the study area including WalkTEM (the Transient ElectroMagnetic method; Danielsen et al. 2003), GCM (Ground Conductivity Meter; Christiansen et al. 2016) and DC-IP data (time-domain spectral induced polarization data; Gazoty et al. 2012). Furthermore, a survey using the tTEM method (towed Transient ElectroMagnetic method; Auken et al. 2019; Sandersen et al. 2021) both on the open fields (tTEM approx. 600 acres) and on Lake Sunds (FloaTEM approx. 90 acres) has been made. The southwestern part of an older vibro-seismic line crosses the area as seen in Fig. 1.

Hydrological and hydrogeological data

Several sources of hydrological observations are used for setting up and calibrating the hydrological model. The data include observations of groundwater levels, water levels in Lake Sunds and discharge from rivers. Data from a synchronous groundwater measuring campaign in October 2012 includes 68 shallow boreholes and measurements of water levels at 33 locations in the river systems, as well as water levels measured at 107 locations around the rim of Lake Sunds. Time series of groundwater levels from seven shallow boreholes and one deep borehole have been made available for the hydrological model (Fig. 1). The longest time series started in 2012. At the western outlet of Lake Sunds, the water level of the lake is measured continuously. In the Møllebæk Creek, east of Lake Sunds, the river discharge to the lake is measured continuously. Sampling frequency varies from station to station, from 10 min to 1 h. Daily mean values are used in the calibration, as the hydrological model works with daily time steps.

Data on groundwater abstraction is obtained from the national groundwater resources database Jupiter (GEUS 2022) where yearly values are available. Groundwater for drinking water purposes in Sunds is abstracted from quartz sand aquifers of the Bastrup Formation. Groundwater pumping for irrigation is based on a demand-driven estimation method (van Roosmalen 2009; DHI 2022). Data on daily precipitation and temperature are available on a national 10-km2 grid from the Danish Meteorological Institute.

Methods

A three-dimensional (3D) geological voxel model was constructed as subsurface architectural input to the hydrological model. The hydrological model was constructed to (1) describe the spatio-temporal variations of the groundwater levels under present conditions at Sunds, (2) quantify the effect of the ongoing renovation of the sewer system and local infiltration solutions on the depth to the shallow groundwater, (3) evaluate the effects of different adaptation measures for lowering the shallow groundwater level in the town, and (4) to analyse the possible effects of projected climate change on the depth to the shallow groundwater and the robustness of the adaptation measures.

Geological modelling

The 3D geological model was based on an integrated geological interpretation of all acquired and existing data. The model was set up as a combined 3D voxel model with stratigraphic 2D grids related to 19 geological units and using a voxel (XYZ) discretization of 25 m × 25 m × 2 m in the software GeoScene3D (I-GIS 2022; Table 1).

Table 1 The 19 geological units of the voxel model (For formation names see Rasmussen et al. 2010)
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In Fig. 2, two cross-sections oriented west–east (profile A) and south–north (profile B) are shown. In Fig. 2a, c, the geophysical and geological data are shown along with overall geological interpretations, whereas Fig. 2b, d shows the voxel model. For simplification, the voxel panels only show the lithological units above 50 m bsl (meters below sea level; see legend in Table 1).

Fig. 2
figure 2

Two cross-sections oriented west–east (profile A) and south–north (profile B) showing borehole data: a Profile A with the geophysical and geological data along with overall geological interpretations, b Profile A with the voxel model. c Profile B with the geophysical and geological data along with overall geological interpretations, d Profile B with the voxel model. For simplification, the voxel panels show only the lithological units above 50 m bsl (see description in Table 1)

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Numerical hydrological model

The numerical hydrological model is set up with the coupled model codes MIKE SHE and MIKE HYDRO (DHI 2022), where MIKE SHE includes the hydrological processes of evapotranspiration based on land use, overland and unsaturated zone flow, as well as flow in the saturated zone including drainage, irrigation and groundwater pumping or injection. All these processes are coupled to river flow, which is simulated in MIKE HYDRO. MIKE SHE is widely used to simulate detailed dynamic groundwater conditions (level and flow) on both national (e.g. Henriksen et al. 2008; Seidenfaden et al. 2022) and local scales (e.g. van Roosmalen et al. 2007; Kidmose et al. 2013). The integrated estimation of groundwater recharge as a result of calculated evapotranspiration, surface or overland runoff and flow through the unsaturated zone enable a full assessment of the land-based water cycle under the historically observed, or future climatic conditions. In areas with high groundwater levels, the MIKE SHE model is especially suitable for simulating the shallow water table because, besides simulating groundwater flow and discharge to different sinks, it can simulate direct withdrawal by trees or other vegetation from the uppermost shallow groundwater (e.g. Sonnenborg et al. 2017). The dynamic nature of MIKE SHE, e.g. running with daily timesteps, is also important to simulate the high groundwater levels that are threatening the urban area being studied (Kidmose et al. 2015; Randall et al. 2013).

The geological model consists of 103 geological input layers, each of 2 m in thickness corresponding to the voxel geological model with a model grid resolution of 25 m × 25 m. The model extends to a maximum depth of 140 m bsl. In the hydrological model, the geological layers are integrated into nine numerical layers based on the overall modelled geological structural framework (Fig. 2).

In the hydrological model for Sunds, three categories of drainage systems have been implemented. In the rural areas, drains have been implemented at a constant depth of 1 m below land surface and with a constant leakage factor. In the urban areas where the sewer system acts as a drainage system for shallow groundwater, the sewer and drainage areas have been divided into two zones—one is characterized by the newer and less leaky sewers, and the other drainage zone is the centre of the old town where an older and more leaky sewer system is found (Fig. 3c). The latter is subject to an ongoing renovation with the purpose of reducing the inflow of shallow groundwater to the sewer system. In the urban area, drain depths are distributed based on the actual depth of the sewers. An average depth has been calculated for each model grid cell of 25 m × 25 m based on information on the depth of the sewers within the actual grid cell (Fig. 3b).

Fig. 3
figure 3

a Surface elevation in Sunds town, b depth to sewer, c fraction of paved area

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In the town of Sunds, large areas are paved or have impervious cover, e.g., roofs, whereby the precipitation that falls on the impervious areas is directed to the nearest stream. The paved area fraction (PAF) shows the fraction of the surface of a given area and model grid that is covered by impervious materials (Fig. 3c).

The land use distribution in the hydrological model is based on the 500-m resolution from the DK-Model (Højberg et al. 2013). The land use in the urban area of Sunds is adjusted to the 25-m grid to ensure that paved and impervious areas are distributed in accordance with the extent of the urban areas. The northern and southern boundary conditions are no-flow, whereas the eastern and western are gradient-based (from previous regional-scale modelling documented in Stisen et al. 2018).

Model calibration

The hydrological model for Sunds was calibrated against groundwater heads and river runoff using the parameter estimation software PEST (Doherty 2015). The PEST calibration follows the procedures used in the calibration of the national water resources model, the DK-model (Højberg et al. 2013). Parameter values for hydraulic conductivity, storage, and porosity for the different soils, and leakage factors for rivers and drains are estimated. To reduce the number of calibration parameters, a sensitivity analysis was performed before the calibration. A total of 82 parameters were tested for their sensitivity, whereby 76 of these—the vertical and horizontal conductivity of the geological layers, as well as specific yield and specific storage—are connected to the 19 geological units. Three parameters represent the drainage coefficient, one parameter represents the leakage coefficient of Lake Sunds, and one represents the leakage coefficient of the riverbed and downstream of the lake. The model is calibrated in the period from 01-01-2010 to 31-12-2019 preceded by a model warm-up period from 01-01-2008. Time steps of 24 h were used.

Four adaptation measures to high groundwater levels

Four adaptation measures were tested to compare their effectiveness to reduce high groundwater levels. Two grey scenarios were tested: the third pipe (scenario A), and groundwater pumping from shallow wells (scenario B). One green scenario was tested: plantation of new coniferous forest around the town and in the town (scenario C). One blue scenario was tested: establishing a new ditch in a low-lying part of the town (scenario D).

The third pipe is installed at the same depth and same location as the sewer in the old part of the town (Fig. 4a). It is most cost-effective to install a new drainage pipe during the renovation of the old leaky sewer system; a side effect of installing new non-leaking sewer pipes is that the drainage effect is reduced which may cause an increased risk of a higher water table. Installing new tight sewer pipes does not completely reduce unwanted groundwater in the sewer system, because pipe connections and sewer systems of private landowners may still be leaky. The second pipe is the rainwater pipe discharging rainwater to nearby streams, rivers, or lakes. The water drained to the third pipe will be discharged to nearby streams. Three scenarios were completed to test the effect and sensitivity of the drainage coefficient (conductance; Fig. 5). The calibrated drainage coefficient for the old sewers was assumed to be representative of the leakage coefficient for the third pipe.

Fig. 4
figure 4

Four adaptation scenario setups: a third pipe, b pumping-and-storage, c new forest, and d new ditch

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Fig. 5
figure 5

Modelled adaptation and climate change scenarios

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Installing shallow wells in the uppermost aquifer to lower the water table by pumping during wintertime is another grey measure. Ten shallow wells with depths of 20 m were placed in the model in areas with high groundwater levels (Fig. 4b). Constant pumping during the six months from November to April was used, resulting in a total volume of 1 million m3 per season. During the same period, the same amount of groundwater was injected into a deeper groundwater aquifer. Three scenarios were tested, (1) injection to the upper deeper aquifer, the Odderup Fm. The Odderup aquifer is separated from the shallow aquifer by a clay layer, Maade Group, of thickness from zero and to 15 m, (2) injection to a deeper aquifer, Bastrup Fm., separated from the Odderup quartz sand aquifer by continuous clay layer of 20 to 30 m thickness, the Arnum Fm., and (3) discharge of the extracted groundwater to a nearby stream (Fig. 5). Two injection wells are situated in the town at locations where the Maade clay layer is relatively thick, 10–15 m, the third injection well is located northwest of the town (Fig. 4b).

Planting of new coniferous forests around and in the town is implemented in the hydrological model by adapting land use parameters accordingly. Coniferous forest is chosen over deciduous forest because of the higher water consumption via evapotranspiration, at least for mature trees where the interception loss is significantly higher in the evergreen coniferous forest than in the deciduous forest. Areas for the new forest are agricultural areas, primarily on the border of the town (395 ha). To see the effect of the greening of the town, forests are implemented in parts of the old town, an area of 43 ha (Fig. 4c). The forest is implemented in the hydrological model as areas where the paved area coefficient on average is below around 50%. The effective forest area in the town corresponds to the percentage of the nonpaved area.

The new ditch was implemented in the hydrological model as a depression in the surface elevation (Figs. 3a and 4d) and connected to a smaller stream further downstream in the western part of the model area. The new ditch has a simple V-shaped profile to a depth of 1.5 m, comparable to other minor streams in the area. Two leakage coefficients (conductance) of the riverbed are tested, (1) one equal to the calibrated leakage coefficients for other streams in the model area, and (2) the other being a factor of 100 higher, assuming that a new ditch can be constructed with a high-permeability bottom material meaning that it will mainly be the hydraulic properties of the aquifer material that control the inflow rates to the ditch (Fig. 5).

The scenarios were designed based on input from stakeholders, including local water utility and municipality authorities, and the regional planning authority. Both the types of measures and the design of measures, for instance, the depths of ditches, the depths of the third pipe, and the location of the “new” forest, were discussed with the mentioned local stakeholders. The local water utility company has estimated the amount of unwanted groundwater entering the sewer system to be around 1 million m3/year, which has been the guiding amount of groundwater to be removed when designing all of the adaptation measures (the third pipe, the pumping and the ditch scenarios). For each of the adaptation scenarios, the hydrological model simulated a 15-year period (2005–2019) including a 5-year warm period with a subsequent 10-year simulation period (2010–2019) used for data analysis.

Climate scenarios and climate models

From each of the four groups of adaptation measures, the most effective is selected for testing the robustness to climate change. A climate model has been selected from an ensemble of 16 climate models (Pasten-Zapata et al. 2019). All climate models project higher winter precipitation for the Danish area. For summer precipitation, the projections are more diverse with both increasing, decreasing and on average no change for the Danish area (Seidenfaden et al. 2022). The selected climate model, IPSL-IPSL-CM5A-MR_rcp85_r1i1p1_SMHI-RCA4, predicts a more wet winter, and a slight increase in summer precipitation. The average 6 months of winter precipitation increases from 465 mm in the reference period 1990–2019 to 640 mm for the future period 2071–2100 for the IPSL climate model, compared to an average increase for 16 RCP8.5 climate models from 458 to 569 mm (Pasten-Zapata et al. 2019).

The wettest climate model was chosen to test the robustness of the different adaptation measures for the worst possible future for this area already facing a high risk of groundwater flooding. The objective of this study has not been to analyse and compare the robustness of the different adaptation measures against the uncertainty that could be derived by an approach using the full ensemble of climate models available. Rather, this study used data from a specific climate model, which has the advantage that one can include the dynamic changes of precipitation, temperature and potential evapotranspiration on a daily basis over a future 30-year period, instead of, for example, multiplying climatic model inputs with factors for a change. For each of the adaptation scenarios analyzed using the climate change model, the hydrological model was run for a 25-year period (2076–2100) including a 5-year warm period, where the 20-year simulation period (2081–2100) is used for the data analysis (Fig. 5).

Statistical analysis of modelling results

The 95th percentile of the depth to phreatic surface (dtps) is calculated for each model grid for each adaptation scenario as an indicator for high groundwater levels. The 95th percentile is calculated for the historical period 2010–2019, and for the climate model scenarios for the far future period 2081–2100.

Standard statistics of the 95th percentile for each model grid were calculated for each adaptation scenario and each of the two periods; other statistical parameters include minimum, maximum, mean, and standard deviation. The exceedance probability for each model grid, that the water table will be less than 1.5 m below ground surface, is calculated for the two modelling periods. For statistical comparison of the different adaptation scenarios and the climate change scenario, the standard statistical calculations used are the estimated 95th percentile values and the exceedance percentages for the area within the old town.

For a visual comparison of the effect of the different measures, the depth to the phreatic surface (95th percentile) for the base scenario without any adaptation measure implemented is subtracted from the depth to the phreatic surface (95th percentile) for the measure.

To test the robustness of the four adaptation measures when forcing the hydrological model with results from the climate model, the change in depth to the phreatic surface (95th percentile) for 2081–2100 (far future) subtracted from the historic data without any measures implemented is calculated for each of the four most effective versions of the adaptation measures. Water balances have been extracted for all scenarios and compared with the baseline model (B0).

Results

Three-dimensional geological model

The modelling is aimed at describing the upper hydrogeological regime containing late- to postglacial organic-rich sediments below the lake, Quaternary sediments consisting of primarily outwash plain sands, incised buried valleys with infill of mainly Quaternary sand, and a thick sequence of Miocene clay and sand.

Figure 2a,c shows the two cross sections with the conceptual geological interpretations that have been the basis for the three-dimensional (3D) voxel model. The near-surface part is dominated by sand and gravel of the Weichselian outwash plain covering the study area. However, below Lake Sunds, an important element of the geological model is the up to 24-m late- to postglacial, organic-rich lake sediments. The deeper parts of the Quaternary sediments consist of mainly sand deposited as tunnel-valley infill. Beneath the Quaternary sediments, the interpreted and modelled distribution of the clays of the Miocene Maade Group reveals a disturbed and rather complex pre-Quaternary succession probably tectonically disturbed. The Maade clay has a thickness ranging from 0 to 25 m showing undulating trends and large variations. The deepest lithological unit shown in Fig. 2 is the clay of the Miocene Arnum Formation. The bottom of the model, however, is the base of the sandy Miocene Bastrup Formation from where the local waterworks extract groundwater. Based on stratigraphic correlations of the Miocene deposits in the region (Rasmussen et al. 2010), the Maade Group clay is likely to have been preserved in the area due to regional subsidence.

Model calibration

The results of the model calibration are illustrated in Fig. 6a where the spatial distribution of the mean error (ME) is shown. Generally, the errors (observed minus simulated hydraulic head) are located in the interval from –0.6 to 0.6 m and there is no obvious tendency for greater errors in some places than in others. On average, an ME of 0.16 m and a RMSE of 0.28 m are found, which is excellent considering the uncertainties associated with observations and simulations of hydraulic head (Sonnenborg et al. 2003), reflecting that the observations are collected recently, during the last 10–20 years, using high precision equipment. In Fig. 6b, timeseries from two shallow wells in the town are shown. In both cases, the seasonal dynamics with amplitudes in the order of 0.5–1.0 m are well reproduced. Table 2 shows the calibrated model parameters for geological units.

Fig. 6
figure 6

Calibration results: a spatial distribution of the mean error (ME) in the town of Sunds, b water-table elevation from well S ‘Strandvejen’, and water-table elevation from well T ‘Tranevej’, see map for location (a); observations are indicated dots while simulated values are given by the solid line

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Table 2 Model parameters for geological units. Kx,y horizontal hydraulic conductivity, Kz vertical hydraulic conductivity, Sy specific yield, Ss specific storage
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The model is based on a large number of parameters and is possibly overparametrized; however, the risk of overparameterization has been minimized by a number of actions. First, intensive and high-quality observation data have been collected in recent years, including time series of the hydraulic head from both the deep and shallow aquifers and synchronous measurements of hydraulic head in a large number of wells (~65). Additionally, discharge data were available from the streams running through the area. Secondly, a sensitivity analysis was carried out before parameter estimation was begun to secure the requirement that only parameters with a relatively high impact on the model results at the measurement locations were included in the optimization. Based on this analysis, 13 parameters were selected for calibration, mainly hydraulic conductivities of the different geological units. Thirdly, an uncertainty assessment of the calibration parameters revealed that the parameter estimates were associated with relatively small uncertainties. The 95% confidence intervals of most parameters were less than one order of magnitude. In combination with estimated correlation coefficients far below one, the reliability of the model parameters is believed to be relatively high and the risk of overparameterization is therefore expected to be low.

Effectiveness of four different adaptation measures

In Fig. 7 the impact of implementing the four adaptation measures on the 95th percentile is illustrated. All maps show the difference in depth to the water table, where a negative value indicates that the water table fell as a function of the adaptation measure. Figure 7a (scenario A1) shows the results when the third pipe is installed in the old town (red polygon) and the drainage coefficient is equal to the values obtained during calibration. The water table is lowered by 10 cm to 30 cm, compared to the base scenario where no adaptation has been implemented. The 10-cm contour line matches the border of the old town reasonably.

Fig. 7
figure 7

The left panel shows the impact of the third pipe on the change in depth to phreatic surface (dtps; 95th percentile): a old sewer, low drainage coefficient, b medium drainage coefficient, and c high drainage coefficient. The right panel shows the impact of pumping and storage on the change in dtps (95th percentile): d injection to upper aquifer, e injection to lower aquifer, and f no injection

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In Fig. 7b (scenario A2) the drainage coefficient is increased by a factor of 5, representing a more permeable third pipe. As a result, the area delineated by the 10-cm contour line is significantly larger and the hydraulic heads are reduced by up to 60 cm in the northern part of the old town. An even larger effect is found in Fig. 7c (scenario A3), where the drainage coefficient is increased by a factor of 100. Here, most of the areas where sewers are installed are affected by the measure and an increase of the water-table depth by up to 1 m is observed.

In the right panel of Fig. 7, the results from simulations with the 10 pumping wells are shown. In Fig. 7d, results from scenario (B1) where water is injected into the Odderup Fm are presented. The location of both pumping and injection wells is illustrated in Fig. 4b. The impact of groundwater pumping is limited to the location of the shallow wells. When the abstracted water is injected into the deep aquifer, the Bastrup Fm. (Fig. 7e, scenario B2), a slightly different result is found. In Fig. 7f (scenario B3), the result when no water is injected is shown. The results are almost identical to those presented in Fig. 7e (scenario B2), indicating that the Bastrup Fm. is isolated from the shallow aquifer and that almost no leakage is induced when 1 million m3 is injected.

The impacts of afforestation and a new ditch are illustrated in Fig. 8. Afforestation of the neighboring fields (see Fig. 4c for location) has almost no impact on the groundwater level in the old town. The reduction in groundwater recharge seems to only affect the locations where the forest is introduced. The effect is slightly higher when more trees are planted in the town, but the impact is still small.

Fig. 8
figure 8

The left panel shows the impact of planting a new forest on the change in depth to phreatic surface (dtps; 95th percentile): a forest around town, b forest around and in the town. The right panel shows the impact of a new ditch on the change in dtps (95th percentile): c low and d high leakage coefficient of river bottom

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In Fig. 8c,d (scenarios D1 and D2), the effects of an open ditch with a low and a high leakage coefficient, respectively, are shown. In both cases, the ditch has a significant impact on the water table in a zone of 150–200 m on each side of the ditch, with the scenario with the higher leakage coefficient yielding the largest drawdown in a much larger area than the scenario with the small leakage coefficient (Fig. 8c, scenario D1). Table 3 shows the statistics for the 95th percentile of the depth to phreatic surface (dtps) and the mean exceedance probability for the adaptation measures.

Table 3 Statistics for 95th percentile of the depth to phreatic surface (dtps) for the different scenarios, for present time (B0) and for the climate model (IPSL) for the far future period (FF)
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Robustness of adaptation measures to climate change

The robustness of the four adaptation measures is examined through a climate change test. Figure 9a (scenario A3 ff) shows the scenario with the third pipe, from which the results from the base scenario with no climate change and no adaptation measures are subtracted. Larger negative numbers correspond to larger depths to the phreatic surface. In Figure 9a, scenario A3 ff can be compared directly to Fig. 7c, scenario A3, the only difference being the wetter climate (ff). The two results are somehow similar; however, the difference is that the area encompassing the lowest water table is confined to a smaller area defined by the location of the third pipe.

Fig. 9
figure 9

Climate change robustness of the four adaptation measures, showing the change in depth to phreatic surface (dtps; 95th percentile) for a wet climate scenario in far future (2081–2100): a third pipe, b pumping/injection, c new ditch, and d new forest

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The results presented in Fig. 9b, scenario B2 ff, are similar to those in Fig. 7e, scenario B2. Here, results from the present period are subtracted from the scenario with groundwater pumping from the shallow aquifer and subsequently injected into the deep aquifer (Bastrup Fm.). The increasing groundwater recharge produced according to the selected climate model almost compensates for the original drawdown. Only in the north-western part of the old town is a small area with a reduction of more than 10 cm observed. In the remaining area, the increase in precipitation neutralizes the effect of the pumping.

The robustness of the forest scenario is found to be relatively weak, Fig. 9d, scenario C2 ff. The phreatic surface in the old town rises by the order of 40–50 cm, so even in the more extreme case where the forest is planted inside the town, the effect is small. It is seen from Table 3 that the forest scenario for the wet future climate is the only one that shows a higher exceedance probability (34%) than the base scenario B0 in present time (32%).

The results presented in Fig. 9d, scenario D2 ff are similar to those illustrated in Fig. 8d, D2. The lowering of the water table obtained by the ditch (Fig. 8d, scenario D2) is to a large degree compensated by climate changes. The only remaining impact of the ditch is found in the upper north-western corner of the old town (Fig. 9c, scenario D2 ff).

Discussion

Based on the results presented in Figs. 7 and 8, the third pipe solution (Fig. 7c, scenario A3) seems to be the most effective adaptation measure since the area affected and the magnitude by which the phreatic surface is reduced exceeds the other solutions. In the implementation in the presented model, the third pipe is located in the entire area (red polygon in Figs. 7, 8 and 9) and the quantity of water removed is proportional to the elevation of the water table (when exceeding the drain level). Hence, this measure is flexible as it may adapt to periods with dryer or wetter climate, as shown in Fig. 9a, A3 ff. The pumping solution (Fig. 7b scenarios B1, B2, B3) is not as effective as the third pipe. However, it should be noted that the extraction rate was kept constant at 1 million m3 per season throughout the entire simulation period irrespective of precipitation and groundwater level. In reality, it would be expected that the extraction rate would be adjusted locally and temporally to the actual need for reducing the water table. It would be a natural next step of the evaluation of the different adaptation measures to design and carry out a sensitivity analysis on the amount of water that is abstracted. However, the pumping solution has the potential to be highly flexible as the pumping rate can be managed both temporally and spatially.

The effect of the ditch is constrained to the depression in the north-western part of the old town; hence, this solution is only effective in its direct surroundings, while the impact in the remaining area is relatively small. The robustness to climate change is also relatively low as most of the old town is unaffected by the ditch in a future more wet climate. The least effective adaptation measure is the afforestation, as the reduction of the phreatic surface in the town is less than 20 cm. This measure also lacks robustness as it is not able to reduce the water table in a future more wet climate. Hence, based on effectiveness, flexibility and robustness, the third pipe solution is found to be the best solution; although, it should, however, be mentioned that neither the cost associated with installation nor running the facilities has been quantified here, as it is beyond the scope of this study. Furthermore, a combination of the four methods may show to be the best solution in reality; this option has, however, not been explored in this work as it opens up an almost infinite number of possible solutions.

The problem with both the third pipe and the well-pumping solutions is the disposal of the water. If the quality of the shallow groundwater is acceptable, it may be possible to discharge or pump it to a nearby stream. This will, however, increase stream discharge, and this will become especially problematic if the method is applied in several urban areas in a catchment. The risk of flooding downstream areas will increase and this solution may not be accepted at the downstream end of the catchment. Using the rivers and streams as sinks for the excess shallow groundwater could be managed in a way that only allows discharge in periods where the rivers have excess capacity. This would leave a lowered water table coming into the periods where water tables and discharge to the rivers usually are higher. If the geological settings allow it, the abstracted water may also be pumped down into a deep aquifer reservoir. During the summer, when dry conditions are prevailing, the injected water can be extracted again and used for irrigation. Or the water can be pumped to streams that may suffer from low water levels and, hence, poor ecological conditions. In cases where the shallow groundwater has poor quality, this energy-demanding pumping solution is less obvious as an effective solution, since, depending on the actual quality problem, cleaning or dilution may be possible.

The mechanisms behind the lowering of the groundwater level are different for the four measures, which also becomes apparent in a water balance evaluation of the hydrological model for the town (area outlined in black in Fig. 3). The most effective adaptation measure, the third pipe scenario (A), also shows the most significant changes in the water balance. The baseline scenario (B0) simulates an average of 84 mm/year of subsurface drainage. This amount is increased to 203 mm/year in scenario A1 and up to 629 mm/year in scenario A3. In comparison, even scenario C2, i.e. afforestation in and around the town, only increases actual evapotranspiration from 399 mm/yr in the base scenario to 409 mm/year in C2 (with a higher increase of evapotranspiration in the forest). The added ditch leads to an increase in baseflow to the streams in the town compared to the base scenario by 69 and 118 mm/year for scenarios D1 and D2, respectively. All solutions have in common that, along with lowered water tables, the lateral inflow of groundwater to the town area is increased. The inflow amounts are considerable, with up to 471 mm/year additional inflow compared to the baseline for the most effective adaptation measure A3. This means that adaptation measures implemented in the town effectively also have to handle groundwater from outside the town; however, the study area with its sand-dominated geology, represents a case where the potential for lateral inflows is high. Other areas with lower hydraulic conductivities will experience less lateral inflow, potentially increasing the effects of the adaptation measures.

An alternative method to remove water from the system is to use the water in Power-To-X production (Foit et al. 2017). This technology is able to split water into oxygen and hydrogen using “green” energy produced by, e.g., windmills or solar panels. The produced hydrogen is stored and can be used when needed. The solution depends on the excess production of green electricity in the area with too-high groundwater levels. The water pumped from the shallow aquifer could also be used for aquifer thermal energy storage (ATES) where heat exchangers make it possible to increase the temperature in water pumped from the aquifers before it is pumped down and used later. However, in contrast to the Power-To-X technology, the amount of water is not reduced in ATES and therefore not immediately interesting in relation to rising water tables. Irrigation of surrounding fields with water from the shallow aquifer is also a possible methodology for removal of excess water and at the same time serves a purpose for industry in the community.

The findings of this work are derived from an area with a small terrain slope where precipitation is increasing, especially during winter, probably as a result of climate changes. Such conditions are found in many places in Europe, e.g., in northern France, Belgium, the UK, Ireland, The Netherlands, northern Germany and southern Sweden. Here, the required geographical conditions exist for the development of problems with rising shallow groundwater. Additionally, the hydrogeology at Sunds is characterized by a relatively high transmissivity of the secondary aquifer, mainly as a result of relatively high hydraulic conductivities from the glacial outwash and sandy sediments. The larger the transmissivity, the more water should be removed to obtain the drawdown required to avoid problems with high water tables. For areas with low permeability settings, e.g., moraine clay, the horizontal flow will be limited which might change the suitability of some of the adaptation solutions presented here. With low hydraulic conductivities in the uppermost profile, e.g. clay tills, some of the less effective adaptation measures such as afforestation could be a competitive adaptation strategy. The low horizontal conductivity in clayey areas most likely results in poor performance of the ditch measure because it relies on the horizontal spreading of the drawdown or local depression of the water table around the ditch to neighbouring areas. The pumping strategy also relies on the horizontal spreading of the introduced local depression of the water table around the pumping well and would most likely fail in clayey areas. Pumping from clayey or low permeability formations is generally not possible (the well will run dry). In the tested hydrogeological set-up with a water table that is close to the terrain surface and that is dominated by sediments of high hydraulic conductivity, the third pipe measure is not only the most effective strategy, but also most likely the most effective in areas dominated by sediments with low hydraulic conductivity. A third basic hydrogeological set-up is fissured sediments, e.g., fractured chalk or limestone, as opposed to the porous media (sand or clay). In the fissured sediments situation, the horizontal as well as the vertical connectivity are dominated by the exact fracture orientation and groundwater flow would also be affected. The effects of the different adaptation measures under fissured conditions would therefore depend on the exact groundwater flow conditions and this is beyond what can be assessed based on this study.

Conclusions

The following conclusions may be derived from the study:

  • Four adaptation measures (third pipe, ditch, afforestation, and pumping) were tested and evaluated. The third pipe was found to be the most effective, and to a certain degree, it was also more flexible than the other solutions.

  • With respect to robustness, the third pipe was also found to be superior to the other measures. However, it should be noted that the pumping solution was not designed to cope with changes in precipitation of either short- or long-term periods.

  • Water balance evaluations for the four scenarios illustrate that each measure affects the flow differently, where the two grey (third pipe, pumping) and the one blue (new ditch) measures remove groundwater (to drains, streams and pumps), where the third pipe and the ditch are passive in nature compared to the pump solution where water is actively removed from the aquifer. The green measure (forest) generates a reduction in groundwater recharge resulting in a lowering of the water table.

  • Disposal of water that is captured by the adaptation methods is a problem in three out of the four methods, with only the forest scenarios being able to remove the water effectively. For the three remaining scenarios, it would be ideal to combine the method with a water-consuming activity like Power-to-X or irrigation of agricultural fields.