Impacts of rising sea level on the hydraulic balance between aquifers and the ocean threaten fresh water resources and aquatic ecosystems along many world coastlines. Understanding the vulnerability of groundwater systems to these changes and the primary factors that determine the magnitude of system response is critical to developing effective management and adaptation plans in coastal zones. We assessed the vulnerability of two types of groundwater systems, recharge-limited and topography-limited, to changes caused by sea-level rise over a range of hydrogeologic settings. Vulnerability in this context is defined by the rate and magnitude of salinization of coastal aquifers and changes in groundwater flow to the sea. Two-dimensional variable-density groundwater flow and salt transport simulations indicate that the response of recharge-limited systems is largely minimal, whereas topography-limited systems are vulnerable for various combinations of permeability, vertical anisotropy in permeability, and recharge. World coastlines were classified according to system type as a vulnerability indicator. Results indicate that approximately 70% of world coastlines may be topography-limited, though variability in hydrogeologic conditions strongly affects classification. Future recharge and sea-level rise scenarios have much less influence on the proportion of vulnerable coastlines than differences in permeability, distance to a hydraulic divide, and recharge, indicating that hydrogeologic properties and setting are more important factors to consider in determining system type than uncertainties in the magnitude of sea-level rise and hydrologic shifts associated with future climate change.
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 Nearly a quarter of the world's population lives within 100 km of a coastline and 100 m of sea level [Small and Nicholls, 2003]. Fresh water is essential for sustaining these dense populations and critical ecosystems, yet coastal water resources are threatened by salinization due to overpumping and climate change. The combined effects of sea-level rise and hydrologic shifts predicted to occur due to climate change, including changes in rainfall and evapotranspiration [Earman and Dettinger, 2011; Intergovernmental Panel on Climate Change, 2007], will alter hydraulic gradients between land and sea. Changes in this hydraulic balance affect aquifer-ocean water fluxes, with implications for both water resources and ecosystems. When sea level rises relative to hydraulic heads on land, salinization of fresh groundwater can occur. Salinization mechanisms include lateral saltwater intrusion at depth and vertical infiltration at the surface due to coastline transgression and storm surge overtopping [Kooi et al., 2000]. The land-sea hydraulic balance also affects groundwater flow to the sea: both fresh groundwater discharge and circulation of saltwater through the offshore subsurface. Alteration of this submarine groundwater discharge (SGD) can have important implications for coastal aquatic ecosystems and chemical ocean budgets. Fresh groundwater contributes nutrients to estuarine environments, resulting in increased ecosystem productivity and in many cases eutrophication [Hu et al., 2006; Johannes, 1980; Kim et al., 2011; Valiela et al., 1990]. Both fresh and saline groundwater discharge contribute constituents that affect ocean chemistry [Bone et al., 2007; Johannesson and Burdige, 2007; Windom et al., 2006]. Despite the importance of groundwater as a resource and a transport vector, it has received little attention relative to surface flooding in climate change vulnerability assessments [Kundzewicz et al., 2007]. Potential effects of climate change on groundwater resources are important to assess as coastal adaptation and management strategies are developed now and in the coming decades [Green et al., 2011; Milly et al., 2008; Werner et al., 2013].
 The geologic and hydrologic settings of coastal groundwater systems are critical to assessing vulnerability of groundwater resources to salinization. These factors have been considered at particular sites [e.g., Hughes et al., 2009; Loaiciga et al., 2012; Oude Essink et al., 2010; Vandenbohede et al., 2008], providing insights into local impacts. More general studies [e.g., Masterson and Garabedian, 2007; Webb and Howard, 2011; Werner and Simmons, 2009; Werner et al., 2012] improve mechanistic understanding, and large-scale analyses [Ferguson and Gleeson, 2012; Ranjan et al., 2006, 2009] assess worldwide impacts. Due to the long timescale over which changes in climate and sea level occur, the majority of studies focused on groundwater impacts involve model predictions. Model analyses that have explored controls of hydrogeologic characteristics on groundwater salinization due to climate change simulated the difference between the steady-state position of the freshwater-saltwater interface before and after a rise in sea level [Sherif and Singh, 1999; Werner and Simmons, 2009] as well as transient saltwater intrusion using sharp [e.g., Ranjan et al., 2009] or dispersed [e.g., Chang et al., 2011; Watson et al., 2010; Webb and Howard, 2011] interface models with varying hydrogeologic properties. These modeling studies suggest that important hydrogeologic factors affecting salinization due to sea-level rise are recharge, hydraulic gradient, and permeability; less important are specific yield, specific storage, and dispersivity. Perhaps the most important control on the extent and rate of seawater intrusion in simulations is the nature of the freshwater boundary condition: specified flux or specified head [Werner and Simmons, 2009]. Despite the finding that in steady state, systems with specified head experience a greater magnitude of salinization [Werner and Simmons, 2009], the majority of studies investigate system response using specified flux boundary conditions.
 Physically, a specified flux boundary condition represents a system that has sufficient thickness of unsaturated zone to accommodate any water-table rise. The elevation of the water table is limited only by the flux of water to the system, or its recharge: a flux-controlled system [Werner and Simmons, 2009] or in this work, a recharge-limited system (Figure 1). The piezometric rise in recharge-limited systems caused by an increase in sea level has been called a “lifting” effect [Chang et al., 2011]. Recharge-limited systems are less vulnerable to sea-level rise because the hydraulic gradient between land and sea can be maintained (Figure 1). Conversely, in topography-limited systems the water table is near to land surface such that an increase in base level results in intersection of the water table with land surface and increased runoff. Topography-limited systems are more vulnerable to sea-level rise because the hydraulic head on the freshwater, landward side cannot rise in response to a rise on the seaward side (Figure 1). Conditions which would produce these types of systems are similar to conditions for topography-controlled and recharge-controlled water tables described by Haitjema and Mitchell-Bruker  and mapped over the contiguous United States by Gleeson et al. [2011a]. Recharge-limited systems tend to be more arid, more mountainous, and/or more permeable, whereas topography-limited systems are humid, low-lying, and/or less permeable. However, the criterion developed by Haitjema and Mitchell-Bruker  indicates the tendency of the water table to follow the shape of the topography, which determines the nature of the flow system, whereas the distinction in this work relates to the capacity of the system to accommodate water-table rise due to an elevated sea level.
 Because the type of system impacts the land-sea hydraulic balance, it will also affect the response to sea-level rise of groundwater flow to the sea. Topography-limited systems will experience a reduction in fresh SGD relative to recharge-limited systems due to a reduced hydraulic gradient [Werner et al., 2012]. The change in the saline component of SGD expected in each system with a rise in sea level is not obvious, however. While a global typology for the importance of SGD has been proposed [Bokuniewicz et al., 2003], the relationship between system type and sea-level rise induced changes in fresh and saline SGD has not been well studied.
 The objectives of this study are to explore the vulnerability of a range of coastal groundwater systems to effects of sea-level rise and to consider the distribution of system type, recharge-limited and topography-limited, over world coastlines. We isolate effects on the natural system by neglecting anthropogenic effects, such as pumping or mitigation measures. We define and evaluate vulnerability by the magnitude of three primary effects: salinized aquifer volume, seawater intrusion rates, and changes in fresh and saline groundwater flow to the sea. We use transient advective-dispersive flow and transport models to characterize the extent to which hydrogeologic factors (permeability, vertical anisotropy in permeability, and recharge) control the magnitude of these effects for recharge-limited and topography-limited systems. We show that the transient response to sea-level rise is greater for topography-limited systems compared to recharge-limited systems over the range of parameter values explored for both salinization and changes in SGD. We then use an analytical model to classify world coastlines by system type as a first indicator of geographic vulnerability to sea-level rise.
 Two sets of analyses were performed. The first was a generic assessment of aquifer response to sea-level rise. We used 2-D variable-density numerical models to assess effects of aquifer properties and recharge rate on the magnitude and rate of salinization as well as changes in groundwater discharge to the sea for the two types of hydrogeologic systems: recharge-limited and topography-limited. We then classified world coastlines by system type for a range of hydrogeologic characteristics to assess global vulnerability.
2.1. Vulnerability Assessment
 Numerical modeling of the transient response of flow and salinity distributions in response to a sea-level change was carried out using the U.S. Geological Survey SUTRA (Saturated-Unsaturated TRAnsport) code [Voss and Provost, 2002]. SUTRA is a finite-element model capable of simulating variable-density groundwater flow and advective-dispersive solute transport. We chose this numerical modeling approach rather than steady-state or sharp-interface modeling approaches in order to incorporate rates of interface movement and the inland extent of low-salinity groundwater. The rate of interface movement, which is not estimated in steady-state approximations, may be slow (occurring over millennia), so salinization over management timescales may be small. Thus, the rate of movement is an important management consideration. Sharp-interface models can simulate transient movement, but the full width of the interface is not simulated, potentially leading to overestimation of the freshwater resource since only water containing <2% seawater is generally considered potable.
 Simulations were run using a 2-D, cross-section model domain (Figure 2a). After a steady-state flow simulation to obtain an initial pressure distribution, simulations were run to steady state (1000 years) with current sea level to obtain pressure and concentration distributions prior to sea-level rise. A 1 m instantaneous rise in global sea level was considered without coastline transgression, assuming fortification that would maintain the position of the coastline. This assumption allows isolation of the lateral component of seawater intrusion because vertical infiltration of seawater above inundated coastline [e.g., Kooi et al., 2000] is not simulated. Only salinization due to lateral movement of the freshwater-saltwater interface was considered, infiltration due to saltwater overtopping on land was not. A 1 m rise is within the range of 0.5–1.4 m predicted by the Intergovernmental Panel on Climate Change (IPCC) for the period 1990–2100 [Rahmstorf, 2007]. Simulations were run for a period of 200 years post sea-level rise, a length of time considered relevant for management. To evaluate aquifer vulnerability, the area salinized (volume salinized per meter length of coastline), salinization rate (the rate of movement of the 2% seawater contour at the model base, or toe), and changes in fresh and saline SGD over the 200 year period were analyzed.
 The model domain was 500 m deep and extended 50 km landward and 25 km seaward of the coastline. Mesh size was 100 m in the x direction (horizontal) and 20 m in the y direction (vertical), except for the region 10 km landward and 5 km seaward of the coastline in which horizontal mesh size was 50 m. Vertical side and bottom boundaries were zero flux. The offshore top boundary was specified pressure, initially hydrostatic mean sea level at the elevation of the coastline node. We note that this configuration does not allow for an increase in aquifer thickness with higher sea level or water tables, an effect that would tend to cause landward movement of the interface toe [see Werner et al., 2012]. However, in this case, the ratio of the change in thickness to the total thickness is very low (1:500), so the effect is probably minimal.
 A specified flux representing average annual recharge was applied to the landward top boundary for recharge-limited simulations, which produced a pressure distribution increasing landward that could change with changes in sea level. Topography-limited systems were represented by specifying the pressure distribution developed along the landward boundary from the steady-state recharge-limited simulation with the same set of hydrogeologic parameters; this distribution represents an unmoving water table limited in elevation by the topographic surface. These boundary conditions ensured that each set of recharge-limited and topography-limited simulations was hydrologically comparable. To simulate response to sea-level rise, the specified pressure on the offshore top boundary was increased by the equivalent of 1m of seawater, with the position of the coastline assumed stationary. Solute transport boundary conditions were zero flux along the vertical sides and bottom, concentration C = 0 along the top landward boundary and C = Cseawater = 0.0357 kg salt kg seawater−1 along the top offshore boundary for inflow, and zero concentration gradient for outflow.
 Aquifer permeability (k) and vertical anisotropy (ratio of horizontal to vertical permeability, kx:kz) were considered to be the primary aquifer characteristics affecting system response to sea-level rise; these were varied in the analysis. The range of simulated k values was chosen based on the permeability of common unconsolidated aquifer materials from well-sorted gravel (10−10 m2) to silt (10−14 m2) [e.g., Fetter, 2001]. Vertical anisotropy was achieved by using the same value of kx, 10−10 m2, while decreasing kz by factors of 10, 100, and 1000.
 Freshwater recharge (R) was considered the primary hydrologic factor affecting system response. Recharge categories were chosen based on a global analysis of recharge rates [Döll, 2009]. The global recharge distribution was separated into seven quantiles, each represented in simulations by the median value. The base-case model represents an isotropic, well-sorted sand aquifer receiving a moderate amount of recharge (R = 300 mm yr−1, kx = kz = 10−10 m2).
 Model sensitivity to changes in dispersivity was found to be minimal, and so the dispersivity was chosen to minimize numerical instability (longitudinal = 50 m, transverse = 5 m). Specific storage was 10−4 m−1; this parameter has been found to have little effect on salinization processes in this study and other studies [e.g., Ranjan et al., 2009; Webb and Howard, 2011], likely because pressure equilibrates much faster than the salinity distribution.
2.2. Global Classification
 ARCMAP 10.0 [Environmental Systems Research Institute, 2011] geographic information system (GIS) software was used to classify coastlines as either recharge-limited or topography-limited for different values of k, R, and shore-perpendicular distance to a hydraulic divide (L). This classification was achieved by comparing topographic slope, as calculated in the GIS from a digital elevation model (DEM) [U.S. Geological Survey (USGS), 1996], to the average slope of the phreatic surface with vector analyses at points equally spaced every 1 km along world coastlines. The average slope of the phreatic surface was calculated using global data sets of current and future recharge, permeability, and an analytical solution for the elevation of freshwater head [Custodio, 1987]:
where h is the freshwater head, qo is the discharge per unit length of coastline, x is the distance inland from the coast, R is the uniform net recharge, K is the hydraulic conductivity, and α is the density ratio, ρf/(ρs − ρf), where ρf and ρs are the freshwater and saltwater end-member densities, respectively. The discharge qo was conceptualized as the recharge rate multiplied by the shore-perpendicular distance to a hydraulic divide. The Custodio  solution was chosen because it accounts for the freshwater-saltwater interface of coastal systems, provides a similar pressure profile to that obtained by numerical modeling for the same input parameters, and has been similarly applied in recent coastal hydrogeology literature [e.g., Werner and Simmons, 2009].
 In order to describe a curved surface in terms of a simple linear slope (the slope of the phreatic surface), the average slope over 1 km was considered. This definition of average slope is arbitrary and was chosen to match the 1 km resolution of the elevation raster data. To preserve distance values in geographical calculations, the global shoreline line file was clipped and reprojected into files corresponding to each of the 60 unique UTM (Universal Transverse Mercator) zones. In each file, a line was buffered 1 km shoreward of the coastline along which points were picked at 1 km intervals. By working in UTM projections, we maintained precision and reduced distance and angular distortion that would have resulted from performing these buffer calculations in the original geographic projection. Following point delineation, the 60 point files were merged back into a global data set. Elevation [USGS, 1996] and current and future recharge values [Döll, 2009] were extracted at each point location from the nearest raster cell, which allowed calculation of the phreatic surface for each point with the Custodio solution. Because each point was 1000 m from the shoreline (assumed head = 0 m), the average slope of the phreatic surface could be calculated and compared to the average topographic slope at each point. Points where the average slope of the phreatic surface exceeded the topographic slope were considered to be topography-limited, whereas points where the average slope was less than the topographic slope were considered to be recharge-limited. The effects of sea-level rise on system type classification were evaluated by subtracting 1 m from all terrestrial elevation values; this is equivalent to adding 1 m to the elevation of mean sea level.
 A global map of permeability developed by Gleeson et al. [2011b] was used as the base-case spatial distribution. Current and future recharge rates were based on the analysis of Döll . The climate change scenario based on the IPCC B2 greenhouse gas emission scenario and ECHAM4 global climate model predicted the greatest change to global recharge values. This scenario was used to calculate future values of expected recharge from the current recharge estimate and ECHAM4 B2 future recharge multiplier given by Döll .
 Sensitivity of system type characterization to permeability, recharge, and shore-perpendicular distance to a hydraulic divide were evaluated. Permeability was varied across a range of reasonable values from 10−14 to 10−10 m2, and recharge rates were varied by a factor of two above and below the base-case distribution. The base-case divide distance was considered 10 km and was varied between 1 and 50 km.
3.1. Vulnerability Assessment
 Three vulnerability criteria were considered for recharge-limited and topography-limited systems: salinization rate, salinized area, and changes in SGD. These were assessed for an instantaneous rise in sea level over a 200 year management time period. Recharge-limited systems exhibited little to no salinization, whereas the response of topography-limited systems was substantial and dependent on hydrogeologic factors.
 The initial salinity distributions, which were identical for both system types, and salinized portion of the aquifer for selected topography-limited simulations are shown in Figure 2. In recharge-limited systems, the elevation of the water table rose with a rising sea level, nearly maintaining the position of the freshwater-saltwater interface and largely preventing salinization. In topography-limited systems, the water table remained stationary, allowing the interface to move inland at a rate dependent on model parameters. In both systems, low recharge conditions (Figure 2f) and high values of vertical anisotropy in permeability (Figure 2d) resulted in highly dispersed interfaces with great landward extent; these tended to move more slowly than the sharp interfaces exhibited by systems with greater throughflow of fresh groundwater. Vertical anisotropy in permeability also affected the interface position. Lower values of kz relative to a constant kx resulted in wider offshore freshwater discharge zones and salinity transition zones that were farther offshore (Figure 2d).
3.1.1. Salinization Rate
 The rate of movement of the 2% seawater contour, the approximate potable water limit, on the interface toe (the intersection of the interface and the model bottom boundary) for each topography-limited simulation is shown in Figure 3. Although the salinized area in recharge-limited systems was negligible compared to topography-limited systems (Table 1), the interface moved in response to sea-level rise, consistent with previous studies [Chang et al., 2011; Werner et al., 2012]. The 2% seawater toe initially oscillated, eventually stabilizing in its initial location, usually within the 200 year simulation period. Salinization rates for topography-limited systems (Figure 3 and Table 1) were generally highest after the initial sea-level perturbation and tended to decrease with time. In some cases, there was a time lag between the perturbation and the peak rate of movement of the toe. This effect was most pronounced in simulations with low recharge, with the peak salinization rate for a recharge rate of 90 mm yr−1 occurring 50 years after sea-level rise, and the 2% toe only beginning to noticeably move after about 100 years for the 35 mm yr−1 recharge rate. The time lag in peak rate only occurred (within the 200 year simulation period) for the isotropic case and the highest value of permeability simulated, 10−10 m2.
Table 1. Model Simulation Results for Topography-Limited and Recharge-Limited Boundary Conditionsa
Salinized Area (m2)
Toe of 2% Seawater Contour
Change in SGD
% Change in SGD
Peak Salinization Rate (m yr−1)
Equilibration Time (yr)
Inland Toe Movement (m)
Saline (m3 d−1)
Fresh (m3 d−1)
Parameter values are base case (bold; R = 300 mm yr−1, kx = 10−10 m2, kx:kz = 1:1) unless otherwise specified; recharge (R) in mm yr−1 and permeability (k) in m2. Salinized area and toe movement (maximum salinization rate, equilibration time, and distance toe moved inland) over the 200 year sea-level rise response period are given for topography-limited/recharge-limited systems. Change in SGD is negligible for recharge-limited systems and is not shown. Salinization and change in SGD are negligible for low-permeability (kx = 10−13 to 10−14 m2) simulations and are not shown.
 The peak salinization rate was highest in simulations with high permeability, decreasing with lower horizontal and vertical permeability values (higher-anisotropy ratios; Figures 3b and 3c). The effect of recharge rate on peak salinization rate was nonlinear: maximum peaks occurred for intermediate recharge rates of 146 and 300 mm yr−1 (Figure 3a and Table 1). Equilibration occurred quickly at higher recharge rates, but the extent of intrusion was lower due to high hydraulic gradients and freshwater throughflow. At low recharge rates there was a lag in response and lower rates of intrusion over a longer timeframe, resulting in greater overall salinization than occurred at higher recharge rates.
 Equilibration of the system, indicated by a salinization rate of zero, occurred within decades for some systems and much longer than 200 years for others. Equilibration time was greatest for low recharge rates and higher anisotropy ratios, which were also scenarios with more dispersed interfaces (Figure 2). Rates of movement for the 90% seawater toe were similar to those of the 2% toe, though generally of slightly lesser magnitude, indicating a widening interface after sea-level rise. Under low recharge conditions (<146 mm yr−1), the 90% toe initially moved offshore in response to increased sea level, which may have been an artifact of the instantaneous sea-level rise. Within the 200 year management timeframe, the interface toe moved inland between 0 and 2 km depending on the hydrogeologic scenario, 1 km in the base case (Table 1).
3.1.2. Salinized Area
 The area salinized after 200 years of equilibration with a 1 m sea-level rise for topography-limited and recharge-limited systems is shown in Figures 4a–4c. Salinization was not observable in recharge-limited systems except under conditions of very low recharge (35 mm yr−1), for which effects were minimal. In topography-limited systems, salinized area tended to decrease with increasing recharge (Figure 3a). This was not apparent in the lowest recharge case (35 mm yr−1) for salinized area after 200 years (Figure 4a) because the time lag between sea-level rise and interface movement was large (Figure 3a), and a new equilibrium was not reached within that timeframe.
 In topography-limited systems, aquifer permeability was a major control on interface movement. The area salinized increased with permeability: values typical of fine to coarse sandy aquifers exhibited orders of magnitude more salinization than lower-permeability systems (Figure 4b). System vertical anisotropy greatly affected the position of the interface (the initial salinity distribution; Figure 2) but had only a minor effect on salinized area (Figure 4c). An exception is highly anisotropic systems (anisotropy ratio of 1:1000 in our simulations), in which the interface position near the surface was far offshore and seawater intruded through another mechanism: seawater infiltrated into the previously fresh outflow face seaward of the initial coastline, creating a lobe of dense saltwater (Figure 2e).
3.1.3. Changes in SGD
 Changes in the hydraulic balance between land and sea can affect groundwater fluxes to the sea as well as seawater fluxes to aquifers (salinization). We analyzed the change in fresh and saline SGD as a result of sea-level rise for each of the simulations. For recharge-limited systems in this analysis, the model setup prescribed the fresh flux through the system, so fresh SGD could not change. Saline recirculation could be affected, but the minimal changes in the nature of the interface in recharge-limited systems resulted in negligible changes in saline SGD driven by the density gradient along the interface. No other mechanisms for saltwater exchange were simulated; thus, changes were not evaluated. In topography-limited systems, both the fresh throughflow and the position and thickness of the interface changed with changes in sea level: in nearly all cases a rise in sea level resulted in a reduction of both fresh and saline SGD.
 The reduction in SGD (defined as discharge seaward of the armored coastline) rate varied among topography-limited systems with different recharge rates. In systems with low recharge rates (35–146 mm yr−1), a 1 m rise in sea level caused the salinity interface to move entirely onshore. This means that the fresh and saline water that discharged offshore prior to sea-level rise discharged landward of the armored coastline after the rise (as into streams), resulting in 100% reduction and a linear reduction in the magnitude of discharge with increasing recharge rate (Figure 4d, open symbols). In simulations with greater recharge, the interface remained at least partially offshore, allowing some fresh offshore discharge to occur: fresh SGD reduction increased with recharge rate, though the relative reduction decreased (Figure 4d, closed symbols, and Table 1). In the higher-recharge cases, saline SGD was reduced; this was also due to partial movement of the interface landward across the shoreline. Simulations with the highest recharge rates have less reduction in saline discharge than intermediate recharge simulations.
 Low-permeability systems exhibited minimal changes in SGD and very low initial SGD, but in systems with permeability values typical of sandy aquifers, reduction was pronounced and initial values were greater. The salinity interface was offshore for low k values (10−12 to 10−14 m2) and the hydraulic gradient was high enough (determined by the recharge rate) that there was little change in fresh SGD; the same was true for saline SGD. For a permeability of 10−11 m2 the interface was partially onshore: the shoreline intersected the 2% salinity contour 200 years after the sea-level rise. In this case, fresh discharge was reduced by about one third, while saline SGD remained approximately constant because nearly all of the saline part of the interface remained offshore throughout the simulation. The highest permeability base case exhibited the greatest change in offshore discharge. Initially, the shoreline bisected the interface. After 200 years the interface migrated almost completely onshore, resulting in nearly 100% reduction in offshore discharge.
 The effect of vertical permeability, or anisotropy ratio, was similar to that of horizontal permeability: higher-anisotropy systems exhibited a lower reduction in discharge. The primary reasons for this are the position of the interface relative to the shoreline and its rate of movement. Higher-anisotropy systems display offshore interfaces that move more slowly than those with a lower-permeability contrast. In the isotropic system, the shoreline initially approximately intersected the 90% seawater salinity contour, meaning that most fresh and saline groundwater discharged onshore initially, and nearly all of it discharged onshore after the rise in sea level when the interface moved landward of the shoreline. The simulated interface for anisotropy ratios of 10 and 100 also straddled the shoreline but did not migrate completely onshore after 200 years; thus, the reduction in SGD is slightly less than the isotropic case for both fresh and saline SGD. The interface in the highly anisotropic case remained offshore throughout the simulation. The reduction in fresh SGD occurred due to the reduced hydraulic gradient, while the increase in saline SGD was a result of the development of a saline circulation cell near the shoreline (Figure 2e).
3.2. Global Classification
 The results of section 3.1 illustrate the dependence of aquifer vulnerability to sea-level rise on system type: recharge-limited or topography-limited. This means that type classification of coastlines may serve as a first indicator of potential vulnerability. The relationship between the topographic slope and water-table elevations determines whether a system is recharge-limited (low vulnerability) or topography-limited (high vulnerability).
 The calculated global distribution of topography-limited coastlines for the base-case parameter values (permeability distribution from Gleeson et al. [2011b], recharge rate from Döll , and shore-perpendicular distance to a hydraulic divide of 10 km) is shown in Figure 5. In this best-estimate scenario, 67.8% of world coastlines are topography-limited (Table 2). Low-sloping coastal areas and those that receive plentiful rainfall, such as the US Gulf Coast and coastal Bangladesh, are more likely to be topography-limited, and thus more vulnerable sea-level rise, than coasts with high slopes or in drier climates, such as the US West Coast and northern Africa.
Table 2. Percentage of Topography-Limited World Coastlines Calculated for Different Values of Permeability and Current and Future Recharge Scenariosa
Varied Parameter (m2)
Current Sea Level
1 m Sea-Level Rise
Current base-case results are in bold. Parameter values are base case unless otherwise specified. Permeability values in “distributed” scenario are from Gleeson et al. [2011b].
k = 10−10 m2
k = 10−12 m2
k = 10−14 m2
L = 1 km
L = 50 km
 System type is dependent on the hydraulic gradient, which develops from the balance of recharge, permeability, and sea level. Sensitivity to permeability, recharge rate, and divide distance is shown in Table 2 and Figure 6. The percentage of topography-limited coastlines varies from 15.9% to 77.9% over the range of values considered for current conditions. Over all current and future scenarios, 15.5% of coastlines are always recharge-limited, and 14.1% are always topography-limited.
 The sensitivity of system classification to permeability, which is highly variable both globally and locally (subpixel scale), was assessed (Figure 6a and Table 2). Between 15.9% and 75.4% of coastlines are topography-limited for the range of permeability values considered (other parameters held at base-case values); in other words, 15.9% of world coastlines are always topography-limited, and 24.6% of world coastlines are always recharge-limited. Systems with higher permeability require a lower hydraulic gradient to transmit a given fresh discharge per unit coastline; thus, higher-permeability systems are less likely to be topography-limited. The shore-perpendicular distance to a hydraulic divide determines in part the fresh discharge for a given recharge rate, so this is also an important parameter. The percentage of topography-limited shorelines ranges from 46.8% to 77.9% if divide distance is changed from 1 to 50 km (Figure 6b and Table 2; other parameters held at base-case values). Recharge has a lesser effect on classification because the assumed uncertainty associated with recharge estimates is less than the uncertainty in coastal aquifer permeability and geometry globally. The percentage of topography-limited coastlines varies from 63.1% to 72.2% if recharge is halved and doubled, while other parameters are held at base-case values (Figure 6c and Table 2).
 Increases in recharge due to climate change have the potential to convert previously recharge-limited systems to topography-limited systems. A future scenario (scenario ECHAM4 B2) [Döll, 2009] in which 55.1% of world shoreline locations are predicted to experience enhanced recharge causes a 0.14% decrease to 0.64% increase in topography-limited world coastlines, while a 1 m sea-level rise will increase the percentage of topography-limited coastlines by between 0.0% and 8.3% (across tested k, L, and R values; Table 2). This indicates that sea-level rise has a potentially greater impact than changes in recharge, but effects will be more strongly controlled by the hydrogeologic properties (k, L, and R; Table 2). If both sea-level rise and recharge changes occur, the percentage of global coastlines that are topography-limited will increase by 0.0%–8.3%. These results suggest that values of and uncertainties in hydrogeologic characteristics (such as permeability, recharge, and watershed size) are more critical to quantify than uncertainties in predicted changes in recharge and sea-level rise for improving estimates of the distribution of world coastlines highly vulnerable to effects of sea-level rise.
 The difference in response to sea-level rise between topography- and recharge-limited coastal groundwater systems highlights the importance of this distinction in assessing vulnerability, as defined by the rate and magnitude of aquifer salinization and changes in groundwater discharge to the sea. In the first part of this study, we analyzed changes in idealized 2-D hydrogeologic systems with a range of hydrogeologic characteristics (horizontal and vertical permeability) and hydrologic settings (recharge rates). We focused on seawater flux into the aquifer (salinization extent and rate) as well groundwater flux to the sea (changes in fresh and saline SGD) over a 200 year management timescale for an instantaneous 1 m rise in sea level. In all cases, recharge-limited systems experienced nearly negligible changes in response to sea-level rise. Only topography-limited systems changed measurably.
 Our GIS analyses show that under present and future scenarios, over half of the world's coastlines may be topography-limited and thus vulnerable to sea-level rise. There is no dominant characteristic that alone indicates whether a system is topography-limited or recharge-limited. Instead, it is the combination of hydrologic and physical features that determines vulnerability. For example, areas with high recharge rates or high fresh discharge rates may be more likely to be topography-limited, but high gradients may cause offshore salinity interfaces, which are much less vulnerable to salinization inland. Similarly, while low-permeability systems may exhibit lower rates of salinization and SGD changes, they are also more likely to be topography-limited for a given recharge rate.
 This analysis indicates that the 15.5% of coastlines that are consistently recharge-limited for all values of permeability and divide distance, for current and future sea level, and all recharge scenarios are robust with respect to vulnerability. Other areas may have more uncertain responses to effects of climate change. The 14.1% of coastlines that are topography-limited for all scenarios and should be considered most vulnerable to climate change. While recharge rates and their changes are fairly homogeneous on a regional scale in most areas, aquifer permeability can vary by orders of magnitude over short distances. This means that locally, aquifer characteristics may be most important to characterize for vulnerability assessment and that vulnerability varies locally to a much greater extent than indicated by Figures 5 and 6. The very small difference in the extent of topography-limited coastlines between current and future recharge and sea-level scenarios also indicates that local hydrogeologic characteristics are more critical in vulnerability assessment than uncertainties in climate predictions.
 Although topography-limited areas have the potential to be greatly affected by sea-level rise, the magnitude of system response and its implications depend on the hydrogeologic setting. The timescale over which salinization occurs is highly variable: some conditions would produce significant salinization at equilibrium, but salinization occurs so slowly that it is no longer relevant for management. These are systems that may not be in equilibrium with present-day sea level; thus, managing to minimize impacts of pumping on salinization, rather than sea-level rise, is a greater priority [i.e., Yu et al., 2010]. Additionally, some aquifers are less likely to be used for water supply, particularly those with low permeability; thus, groundwater salinization is not a primary resource concern in those areas.
4.1. Assumptions and Limitations
 The aim of this work is to improve understanding of basic controls on coastal aquifer vulnerability to aspects of changes in climate and to assess the global distribution of areas at risk. In order to gain such general insights, we have considered very simple systems and avoided site-specific complexity. We considered homogeneous hydrogeologic parameters within 2-D shore-perpendicular cross-sectional models and over world coastlines. This approach allows illustration of overall effects of changes in parameters but ignores the true spatial distribution of these properties and 3-D effects. In the vulnerability analysis, we consider only one aquifer geometry. However, effects of geometric variations may be inferred from the analysis. Shorter aquifers will respond similarly to long aquifers with lower recharge rates for this model setup, and thinner aquifers will respond similarly to thick, lower-permeability aquifers (analogous to a reduction in transmissivity).
 The global analysis does not consider variability in system response: heterogeneous rates of seawater intrusion and SGD due to both geologic and geomorphic heterogeneity. Terrestrial drains such as rivers and lakes that occur on smaller scales than the DEM resolution are also not represented. Finer-scale representation would likely increase the proportion of topography-limited regions because the topographic lows are determining factors in the maximum water-table height. Clearly higher resolution regional- to local-scale efforts are essential to assess true vulnerability of coastal aquifer systems.
 The analysis also assumes that armored shorelines prevent transgression and overtopping that would cause salinization from the aquifer top rather than lateral intrusion. In cases where transgression occurs, overtopping and resulting vertical infiltration would accelerate the salinization modeled in this work. Results of the SGD analysis would also change, since discharge onshore of an armored coastline would occur offshore under transgression. Overtopping by storm surge inundation is also not considered, but has the potential to cause groundwater salinization. Under some conditions, this salinization may be more pronounced in recharge-limited compared to topography-limited systems because of greater unsaturated zone thickness.
 This analysis is limited to unconfined aquifer systems, which may be more vulnerable than deeper systems, but which also may not be the primary groundwater resource in some areas. It can be difficult to assess the vulnerability of deep fresh resources, which may not be in equilibrium with present-day sea level [e.g., Kooi and Groen, 2001; Person et al., 2003; Yu et al., 2010], suggesting that future sea-level rise may not have a great impact on the slow salinization rate. Though deep, confined groundwater resources may be less vulnerable to sea-level rise, the cost of deep drilling may be prohibitive, and so domestic pumping in many regions of the world and irrigation pumping may commonly occur from unconfined aquifers.
 Though groundwater pumping has been shown to be an important factor contributing to salinization and changes in land-ocean fluxes [Ferguson and Gleeson, 2012; Loaiciga et al., 2012; Yu et al., 2010], we consider only natural hydrogeologic factors in this analysis in order to isolate effects of climate change. If considered in a distributed manner, pumping effectively reduces the net recharge by an amount less than the total amount extracted (since irrigation return flows may occur and pumping may induce more recharge). This would shift our estimates toward lower recharge rates and greater vulnerability. The importance of pumping in driving salinization would depend on the relative rates of recharge to and pumping from the unconfined aquifer.
 The primary implications of aquifer salinization modeled in this work are associated with human uses: reduction in the sustainable rate of pumping, deterioration of drinking water quality, and agricultural soil salinization by applied irrigation water. These threats are particularly acute in highly populated areas, which comprise a substantial portion of world coastlines. A secondary threat of this salinization, particularly in the near surface, is mobilization of land-based anthropogenic contaminants from soils in urban and agricultural areas, industrial sites, and waste disposal facilities, many of which are located along highly populated coastlines [Danielopol et al., 2003; Pope et al., 2011].
4.2.2. Changes in Saline SGD
 In many cases considered in this analysis, the freshwater-saltwater interface moved from an offshore or partially offshore position to a new location inland of the shoreline, despite the assumption that the coastline would remain stationary with sea-level rise (as by construction of a sea wall, for example). The onshore discharge of saline water across the constant-head boundary is equivalent to discharge into surface water bodies: the increase in on-land saline groundwater discharge is nearly equivalent to the reduction in saline SGD reported in section 3.1. Increased flow of brackish or saline groundwater into previously fresh surface water bodies can have severe ecological effects. Even in the absence of surface flooding, freshwater wetlands may convert to salt marsh, salinity-sensitive species may die, and aquatic ecosystems hosting freshwater species may be permanently altered [e.g., Baldwin and Mendelssohn, 1998; James et al., 2003].
4.2.3. Changes in Fresh SGD
 Changes in direct offshore discharge of fresh groundwater can have important effects, both positive and negative. Reduction in fresh SGD due to sea-level rise can result from an increase in rejected recharge or landward movement of the freshwater-saltwater interface causing increased discharge into onshore surface water bodies, as discussed previously. This means that if onshore discharge is occurring to streams connected to coastal surface water bodies, the volume of water that eventually reaches the coast is the same before and after sea-level rise. However, the discharge path (via surface water, wetlands, or directly by groundwater) can impact processes that attenuate nutrients or immobilize contaminants. Therefore, changing distributions of groundwater discharge to streams, wetlands, and offshore water bodies are likely to impact chemical fluxes to estuaries and the ocean.
4.2.4. Rising Water Tables
 Topography-limited systems are assumed in this work to experience no change in elevation of the water table. In reality, there is likely to be some depth of unsaturated zone, at least in some areas during some of the year. These previously aerated areas would be subject to more frequent flooding or poor drainage with rising sea level or increases in recharge. Problems associated with rising water tables may be more pronounced in recharge-limited systems, despite their relative resistance to salinization. In areas with water tables sufficiently below land surface, storage or disposal of wastes in the unsaturated zone is common. Proper functioning of these systems, such as septic tanks, land-based wastewater disposal sites, and landfills, requires, often by law, a minimum thickness of the unsaturated zone. A systematic rise in the water table may render this infrastructure ineffective or illegal. Moreover, saturation of soils previously under oxic conditions may cause a change in redox state to more reducing conditions. These geochemical changes have the potential to mobilize contaminants, such as phosphate or toxic trace metals bound to iron or manganese oxides [e.g., Borch et al., 2010].
 This two-part analysis establishes the relative vulnerability of recharge-limited and topography-limited coastal hydrogeologic systems to sea-level rise and explores the prevalence and spatial distribution of highly vulnerable world coastlines. A series of 2-D variable-density groundwater flow and salt transport simulations establish that topography-limited systems are more vulnerable than recharge-limited systems to salinization rates, salinized aquifer volume, and changes in groundwater flow to the sea. This is true for a wide range of two critical hydrogeologic factors, aquifer permeability and recharge rate. Global analysis indicates that more than half of world coastlines are topography-limited. Local hydrogeologic properties (permeability, recharge, and aquifer geometry) are the primary determinant: the proportion of highly vulnerable coastlines for current conditions ranges from 15.7% to 77.9% over values of hydrogeologic parameters typical of natural systems. This range is much greater than the uncertainty due to estimates of climate change induced sea-level rise and changes in recharge; differences between an estimated current and predicted future scenario differ by less than 8.3%. Thus, local hydrogeologic characteristics are the primary indicators of vulnerability of coastal groundwater systems to sea-level rise and should be prioritized over reduction of uncertainty in predicted changes for adaptation, management, and planning purposes. Because the response of coastal groundwater systems to sea-level rise depends strongly on system type, classification of topography-limited and recharge-limited systems may be an important first indicator of vulnerability. Improved assessment of this indicator can be accomplished on local and regional scales by incorporating site-specific hydrogeologic characteristics.
 This work was funded in part by the University of Delaware Research Foundation and the National Science Foundation (EAR-0910756 and EAR-1151733). The authors thank Petra Döll and Tom Gleeson for groundwater recharge and permeability data sets, respectively. The authors also thank Clifford Voss for helpful discussions and comments on this manuscript, Lawrence Feinson for assistance with analysis of model results, and Tracy DeLiberty and Luc Claessens for assistance with the GIS analysis. The helpful comments of Daniel Fernandez-Garcia, Tom Gleeson, Adrian Werner, Diana Allen, and an anonymous reviewer substantially improved this manuscript.