Integrating storage and spatial variability into shallow groundwater balances: moving towards water security in hard rock coastal areas

In terrains with limited soil cover and groundwater storage, groundwater resource management is governed by the spatial nature of storage, recharge and distributed local extraction. Local soils act as important groundwater reservoirs for residents who have no other feasible water supply. A novel heuristic methodology is presented which accounts for the spatial distribution of storage and extraction, using existing topographical and geological databases in addition to well data to construct an applied conceptual groundwater model with assumed stratigraphy. The method uses a geographic information systems (GIS) environment and allows for modelling climate and land-use scenarios. Several scenarios were examined, demonstrating that average reservoir volumes meet demand but at the local levels depletion of reservoirs occurs. Groundwater abstraction in excess of 50% of the approximate freshwater storage was observed in the model, particularly near the coast. Soil-filled valleys may act as local hydraulic barriers by maintaining a higher pressure head as they are less susceptible to large-level fluctuations than the hard rock and may aid in preventing contamination from saline water provided no direct hydraulic connection is present. The method demonstrates the importance of a spatial approach in managing groundwater resources and could be used as a tool in increasing water security.


INTRODUCTION
Identifying sustainably extractable volumes of water from a groundwater system is vital from a regional planning viewpoint, particularly in regions which experience water scarcity. In Europe, the Water Framework Directive (EU WFD ) specifies that abstraction in excess of the overall recharge 'not needed by the ecology' be avoided. The Swedish Parliament established an environmental goal in 1999 ensuring public access to groundwater of good quality. However, extremely limited storage due to lack of soil cover and the inherently low-storage characteristics of the hard rock (Engqvist & Fogdestam ; Knutsson & Morfeldt ) implies that the timing of recharge throughout the year will play an important role in how the local reservoirs are influenced by spatially distributed, private water-supply wells. Thus, tools which account for the limited storage capacity which is prevalent in many of these areas are needed in order to manage groundwater resources appropriately and identify areas which are vulnerable.
Quantifying overall recharge, let alone the portion needed by the ecological system, is problematic and prone to error (Gaye & Edmunds ; Gleeson et al. ; Chesnaux ). However, in terrains with hard crystalline bedrock and limited soil cover, such as much of Scandinavia, the issue becomes much more problematic where field and regional estimates of recharge (Jie et al. ) may not be representative of local settings in terrains with elevated levels of heterogeneity (Earon & Olofsson ) and deterministic models may be too uncertain and resource-heavy to calibrate locally (Dripps & Bradbury ; Earon ).
Often lacking traditional productive aquifers (e.g. glacio- As this soil cover is often isolated to valleys and the surrounding hydraulic conductivity of the bedrock is very low (Engqvist & Fogdestam ; Chesnaux et al. ; Earon et al. ), these soil-filled valleys provide an extremely important function for local residents with privately drilled wells. Due to the low-population density in Swedish, periurban areas and the difficulty in connecting residences in these areas to municipal water systems due to limited soil cover, local drilled wells are often the only viable source of sustainable drinking water for many residents. It is thus exceedingly important to account for these small reservoirs both quantitatively and spatially in water balance calculations, as kinematic (or effective) porosity values are often several orders of magnitude higher in common soils (e.g. till) than in crystalline rock (Freeze & Cherry ). Thus, as a reservoir, a 1 m thick layer of glacial till could serve equally as well as 100 m of granitic bedrock and will likely act as a recharging reservoir which balances volumes extracted from local drilled wells. Hydraulic heterogeneity and anisotropy in crystalline bedrock make regional characterization based on point data, such as well tests, extremely difficult (Shapiro & (Müller et al. ) and geostatistics (Wang et al. ). Due to the limited storage capabilities of recently glaciated terrains, precipitation during spring and autumn months could potentially fill such aquifers very quickly, causing any excess precipitation to be lost as either baseflow runoff or overland runoff. While runoff volumes in hard rock terrains are often very high (Spence & Woo ), these runoff volumes will usually accumulate in topographically lower pockets of soil, where they likely infiltrate causing these soil pockets to act as a recharging reservoir to the surrounding area, which could mean that simple models for recharge such as precipitation-evapotranspiration balances might be an adequate approximation.
The purpose of this paper is to present a straightforward methodology for integrating a storage parameter with high levels of heterogeneity into a spatial, shallow (∼0-200 m) water balance with the intended application being as a heuristic surrogate for numerical groundwater modelling to aid in groundwater resources management and increase water security in hard rock coastal terrains. Specific aims include identifying how spatial heterogeneity in storage and extraction parameters will influence hydrogeological response in coastal areas. Additionally, the effects of varying the storage parameter, residency and groundwater flow will be investigated in order to assess the sensitivity of these parameters.

STUDY AREA AND DATA
The study area, Östhammar Municipality, lies roughly    (Figure 1) showing the assumed relationship between surface elevation and acceptable reservoir depth for avoiding water quality issues (i) in bedrock (light grey). Soil depth (dark grey) was obtained from the Geological Survey of Sweden's (SGU) soil depth model (ii). Surface water with connection to saline water (iii) and approximate groundwater pressure surface interpolated from the SGU well archive (iv) shown for reference. This profile shows the basis for the conceptual model used in the spatial groundwater balance, where each cell is given a reservoir height (i) and assigned a soil depth if surface soil was present (ii).    Using the storage and extraction layers as continuous raster surfaces, the groundwater balance was then calculated, in this study using an extraction radius of 250 m and 50% permanent residency rate, unless otherwise stated.
Recharge was assumed to be very limited, especially during summer months when evapotranspiration rates exceed precipitation (Engqvist & Fogdestam ; where n k is the kinematic porosity in each cell, h is hydraulic head, t is time, P is precipitation, ET is evapotranspiration, Q is extraction (Figure 4(b)) and G is the groundwater flow which can either be positive or negative.
where K is the hydraulic conductivity and is assumed to be where T is transmissivity, Δt is the time step, S is storativity, Δx is cell size and n k is kinematic porosity. While kinematic porosity is often roughly similar to storativity, in fracture rock reservoirs, dead-end but drainable pores may be present which may subsequently contain entrapped air after initial drainage. These pores would then give a higher value for storativity than would likely contribute to the actual pore network involved in the water-supply flow regime.  extraction reservoirs will dip below 50% in particularly vulnerable areas.

Water balance calculations from
Increasing permanent residency rates within the model scenario had fairly evenly distributed effects. An increase to 50% from 15% residency leads to extensive decreases in reservoir volumes remaining after 8 months by 15-20% ( Figure 6). More extreme impacts were found to be localized to areas which were already at risk, increasing the extent of these risk zones. Increasing permanent residency rates amplified the extent and intensity of problematic areas identified at lower rates. While the model results may appear quite similar, local comparisons of the model showed that differences between the models could be greater than 75% ( Figure 6). As residency changes may often occur as conversions of seasonal domiciles (cottages) to permanent residences, additional environmental impacts due to increased water use will likely also be constrained to these localized areas. The effect of subsurface flows within the model was also examined by direct comparison of two scenarios with identical parameters with the exception of medium (K ¼ 1 × 10 À8 m/s) or low (K ¼ 5 × 10 À11 m/s) regional hydraulic conductivities, with a third baseline scenario with no subsurface flows, in addition to evaluating model stability ( Figure 7). Average differences between the models were zero and À2%, with a modelled remaining storage standard deviations of 1 and 10%, for low and medium K scenarios, respectively. Model stability criteria were not fulfilled for higher estimates of hydraulic conductivity (2 × 10 À6 m/s).
Results indicate that subsurface recharge to depleted reservoirs has limited influence at great horizontal distances from the soils. The most substantial effects were seen in close proximity to pockets of soil or till, where groundwater reservoir levels were largely unaffected by the extraction whereas the surrounding bedrock were markedly affected.
In these areas, reservoirs could be replenished by 20-50% and in some cases much more. However, the spatial extent Östhammar, coastal regions using 495 l/d water usage, 100% permanent residency over 8 months with a 100 m extraction radius of influence, K ¼ 5 × 10 À11 m/s (b) and K ¼ 10 À8 m/s (c). Note that model stability criteria are not fulfilled for models in the higher ranges of hydraulic conductivity (K ¼ 2 × 10 À6 m/s). Differences in models (b,c) are direct differences between the two scenarios (groundwater flow vs. no groundwater flow) in percent of total storage in each cell at the end of August.
extraction, due to the large differences in kinematic porosity between the local soils and bedrock.
Varying different parameters within the model in order to assess parametric sensitivity was also carried out. Comparisons were made between soil-depth models estimated from well archive and geological data (SGU ) and a soil-depth model estimated from the slope of outcropping bedrock (Karlsson et al. ). Differences between the storage models, using either the simplified regolith model  hydrogeological models will likely greatly benefit from surrogate tools such as this one which identify areas of likely environmental stress. Identification of these areas could allow for more resilient resource management strategies and/or a better allocation of limited resources to decrease uncertainty in vulnerable areas.
The model results also clearly illustrate the importance of a spatial approach in water resource management questions where soil cover is limited, seen in the spatial variability of the remaining reservoir ratio in 8-month scenarios ( Figure 5), largely due to heterogeneity in the hydraulic parameters, in agreement with Batelaan & De Smedt ().
As reservoir volumes on a regional scale are often largely unaffected by the extraction made in a few local housing areas and a limited number of private wells, if a spatial approach or a too-coarse model resolution is adopted the erroneous conclusion could be made that the water resources in a given region are capable of supporting far greater numbers of residents than would be possible in reality. Water resources in terrains where soil cover is limited must be considered at quite a local scale, as even after a few hundred metres resources which are present may not be obtainable due to low bedrock transmissivities. Exacerbating the problem is the observation of non-uniform spatial distribution of extraction. Contrary to watershedand subwatershed-based mass-balance approaches where usage is assumed to be dispersed equally over the study area, houses will often be clustered within a specific and limited area. Thus, the extraction from the reservoirs in the centres of these areas will be greater than if residents were uniformly distributed over the area. Increasing permanent residency rates may not influence the regional water balance particularly heavily, but instead the effects may be constrained to local areas and may amplify stresses in areas which are already the cause for some concern. If water use is more evenly distributed, these effects might be avoided. In the model, reintroduction of untreated water reserves. While the overall groundwater levels will not be as low as those which were modelled, the water quality situation will likely be significantly worsened in the areas with greatest impact. Volumes of water which were shown to be inflowing from cells surrounding the area of influence of extraction would be less (due to a lower hydraulic gradient), meaning that freshwater is not replacing the water which was being extracted, but rather grey water or worse is being introduced. Due to the low porosity of the bedrock and limited soil depths, this in turn leads to local reservoirs which are highly vulnerable.

CONCLUSIONS
In heterogeneous terrains with low inherent storage and non-uniformly distributed water use, a spatial approach to groundwater resources inventory and management is needed to avoid excessive overextraction and/or potential water quality problems which may arise (e.g. from seawater intrusion). Spatial heterogeneity in extraction and subsurface storage characteristics result in local variations from regional averages, which may have negative environmental impacts but also may be missed if a model resolution is used which is too coarse. Variability in groundwater reservoir levels at a 100 m 2 resolution implies that vital information will be missed should regional groundwater balance estimates be applied rather than incorporating a higher spatial resolution, although more research is needed regarding the effects of spatial resolution on model results in different geological settings.
Incorporating limited storage within groundwater balance models and heuristic solutions for groundwater management has vital implications for resilient groundwater resources management in terrains with limited soil cover.
Storage in terrains with such limited hydraulic conductivity values has an important role in this setting in governing the volumes of water which will be sustainably extractable by residents who are not reasonably able to connect to municipal water supplies. Given the heterogeneous spatial distribution of extraction, rock type and soil cover, it is therefore essential that groundwater balance methods be adapted with a limited storage component to compensate for these conditions where possible.
The approach presented in this study shows promise as a tool for successful management of groundwater resources in hard rock coastal terrains with limited soil cover, particularly in regions where municipal planners may have limited resources to apply. Results of this study imply that identification of extraction rates and storage volumes on a local scale can be accomplished using available geological, topographical and land-use GIS databases, which could lower the demand for expensive hydraulic tests and computational models which require extensive amounts of input data. This will lead to lower time and resource costs needed to identify and mitigate areas which may be susceptible to environmental stress and may have sparse hydraulic measurement data. The use of existing datasets which are available for most of Sweden and obtainable in many other countries in digital form is an enticing aspect of this approach to groundwater modelling. This allows the method presented in this study to be readily applied to all regions in Sweden and with little modification and to be applied to any region with general physical and geological information where storage in the subsurface may be the limiting factor in groundwater balance questions, such as in large parts of Canada or Scandinavia.