Karst develops through the dissolution of carbonate rock and is a major
source of groundwater contributing up to half of the total drinking water
supply in some European countries. Previous approaches to model future water
availability in Europe are either too-small scale or do not incorporate
karst processes, i.e. preferential flow paths. This study presents the first
simulations of groundwater recharge in all karst regions in Europe with a
parsimonious karst hydrology model. A novel parameter confinement strategy
combines a priori information with recharge-related observations (actual
evapotranspiration and soil moisture) at locations across Europe while
explicitly identifying uncertainty in the model parameters. Europe's karst
regions are divided into four typical karst landscapes (humid, mountain,
Mediterranean and desert) by cluster analysis and recharge is simulated from
2002 to 2012 for each karst landscape. Mean annual recharge ranges from
negligible in deserts to
Groundwater is the main source of water supply for billions of people in the
world (Gleeson et al., 2012). Carbonate rock regions only constitute about
35 % of Europe's land surface (Williams and Ford, 2006), yet contribute up
to 50 % of the national water supply in some European countries (COST,
1995) because of their high storage capacity and permeability (Ford and
Williams, 2007). Climate conditions have a primary control on groundwater
recharge (de Vries and Simmers, 2002). Climate simulations suggest that in
the next 90 years Mediterranean regions will be exposed to higher
temperatures and lower precipitation amounts (Christensen et al., 2007). In
addition, shifts in hydrological regimes (Milly et al., 2005) and
hydrological extremes (Dai, 2012; Hirabayashi et al., 2013) can be expected.
To assess the impact of climate change on regional groundwater resources as
groundwater depletion or deteriorations of water quality, large-scale
simulation models are necessary that go beyond the typical scale of aquifer
simulation models (
Currently available global hydrology models discretize the land surface in
grids with a resolution down to 0.25–0.5
The assumption of homogeneity is certainly inappropriate for karst regions. Chemical weathering of carbonate rock and other physical processes develop preferential pathways and strong subsurface heterogeneity (Bakalowicz, 2005). Flow and storage are heterogeneous ranging from very slow diffusion to rapid concentrated flow at the surface, in the soil, the unsaturated zone and the aquifer (Kiraly, 1998). A range of modelling studies have developed and applied karst specific models at individual karst systems at the catchment or aquifer scale (Doummar et al., 2012; Fleury et al., 2007; Hartmann et al., 2013b; Le Moine et al., 2008) but a lack of a priori information of aquifer properties and observations of groundwater dynamics have prohibited their application on larger scales (Hartmann et al., 2014a).
Compared to the limited information about the deeper subsurface there is much better information about the surface and shallow subsurface, including maps of soil types and properties (FAO/IIASA/ISRIC/ISSCAS/JRCv, 2012), observations of soil moisture (International Soil Moisture Network; Dorigo et al., 2011) and of latent heat fluxes (FLUXNET; Baldocchi et al., 2001), as well as river discharge (GRDC, 2004). Surface and shallow subsurface information is used for the parameterization and evaluation of the surface routines of present large-scale models. But, although these data also cover Europe's karst regions, it has not been used for the development of large-scale models to simulate karstic surface and shallow subsurface flow and storage dynamics.
The objective of this study is to develop the first large-scale simulation model for karstic groundwater recharge over Europe and the Mediterranean. Despite much broader definitions of groundwater recharge (e.g. Lerner et al., 1990), we focus on potential recharge, that is, vertical percolation from the soil below the depth affected by evapotranspiration. We use a novel type of model structure that considers the subgrid heterogeneity of karst properties using statistical distribution functions. To achieve a realistic parameterization of the model we identify typical karst landscapes by cluster analysis and by a combined use of a priori information about soil storage capacities and observations of recharge-related fluxes and storage dynamics. Applying a parameter confinement strategy based on Monte Carlo sampling we are able to provide large-scale simulation of annual recharge including a quantification of their uncertainty.
Due to chemical weathering (karstification) karst systems have a strong subsurface heterogeneity of flow and storage processes (Bakalowicz, 2005) that have to be considered to produce realistic simulations (Hartmann et al., 2014a). In this study, large-scale karst recharge is estimated by a modified version of the VarKarst model (Hartmann et al., 2013a, 2014b). The model has shown to be applicable at various scales and climates over Europe (Hartmann et al., 2013b). To simulate karst recharge we discard the groundwater routines but we use exactly the same surface and shallow subsurface routines. The resulting recharge simulation model, VarKarst-R, is described in the proceeding subsection. The new feature of the large-scale application of the VarKarst-R model is the estimation of its parameters. While previous applications of the model could rely on calibration by observations at the karst system outlet the simulation of large-scale recharge requires a different approach. We developed a new parameter estimation procedure that separates the study area into four karst landscapes by cluster analysis and estimates model parameters and their uncertainty by a step-wise parameter confinement process (explained in Sect. 2.3).
The structure of the VarKarst-R model (Fig. 1a) is based on the
conceptual understanding of the surface and shallow subsurface processes of
karst regions (Fig. 1c). Their most characteristic feature is the
existence of the epikarst that evolves close to the surface because of
stronger carbonate rock dissolution. It can be seen as a temporal storage
and distribution system for karst recharge (Aquilina et al., 2006; Williams,
1983a). Depending on the rates of infiltration, variability of soil
thicknesses and hydraulic conductivities, it can produce slow and diffuse
vertical percolation into the carbonate rock or it can concentrate
infiltration laterally towards dissolution-widened fissures or conduits
(Hartmann et al., 2012). Applied on a 0.25
Heterogeneity of soil depths is represented by a mean soil storage capacity
Preceding work (Hartmann et al., 2013a) showed that the same distribution
coefficient
At each time step
Data availability, data properties and sources.
The temporal water storage of the epikarst is drained following an
assumption of linearity (Rimmer and Hartmann, 2012), which is controlled by
the epikarst storage coefficients
When infiltration exceeds the soil and epikarst storage capacities, surface
flow to the next model compartment
To summarize, the model is completely defined by the four parameters
Parameter description and initial ranges for Monte Carlo sampling based on previous field studies and large-scale model applications.
Forcing for the VarKarst-R model is derived through GLDAS-2, which assimilates satellite- and ground-based
observational data products to obtain optimal fields of land surface states
and fluxes (Rodell et al., 2004; Rui and Beaudoing, 2013). While
precipitation, temperature and net radiation are mainly merged from
satellite and gauge observations, snow water equivalent is derived using
data assimilation as well as the snow water equivalent simulations of the
NOAH land surface model v3.3 (Ek, 2003) driven by GLDAS-2 forcing. Europe's
and the Mediterranean's carbonate rock areas are derived from a global map
(vector data) of carbonate rock (Williams and Ford, 2006). Each cell of the
0.25
Carbonate rock areas over Europe and the Mediterranean, and location of the selected FLUXNET and ISMN stations.
A lack of a priori information and observations of discharge and groundwater levels that can be used for calibration are the primary reasons why karst models have not been applied on larger scales yet (Hartmann et al., 2014a). The parameter assessment strategy we present in the following is meant to overcome this problem by using a combination of a priori information and recharge-related variables. We define typical karst landscapes over Europe and the Mediterranean and apply this combined information to a large initial sample of possible model parameter sets. In a stepwise process we then discard all parameter sets that produce simulations inconsistent with our a priori information and our recharge-related observations.
Our definition of typical karst landscapes is based on the well-known
hydrologic landscape concept (Winter, 2001), which describes hydrological
landscapes based on their geology, relief and climate. Constraining
ourselves to karst regions that mainly develop on carbonate rock, we assume
that differences among the karst landscapes are due to differences in relief
and climate, and the consequent processes of landscape evolution including
the weathering of carbonate rock (karstification). The carbonate rock
regions in Europe and the Mediterranean are divided into typical landscapes
using simple descriptors of relief (range of altitude RA) and climate
(aridity index AI and mean annual number of days with snow cover DS) within
each of 0.25
We initially sample 25 000 possible model parameter sets from independent uniform distributions using parameter ranges derived from previous catchment-scale applications of the VarKarst-R model over Europe and the Mediterranean (Table 2). We use a priori information and recharge-related observations to assess parameter performance for each karst landscape. A priori information consists of spatially distributed information about mean soil storage capacities as provided by several preceding mapping and modelling studies (Ek, 2003; FAO/IIASA/ISRIC/ISSCAS/JRCv, 2012; Miralles et al., 2011). Recharge-related variables are (1) soil moisture observations and (2) observations of actual evaporation at various locations over the modelling domain (Table 1, Fig. 2). Soil moisture is related to recharge because it indicates the start and duration of saturation of the soil during which diffuse and preferential recharge can take place. Actual evaporation is related to recharge because usually no surface runoff occurs in karst regions due to the high infiltration capacities (Jeannin and Grasso, 1997). The difference of monthly precipitation and actual evaporation is therefore a valid proxy for groundwater recharge at a monthly timescale or above. The new parameter confinement strategy is applied to each of the karst landscapes in three steps:
Bias rule: retain only the parameter sets that produce a bias between observed and simulated actual evaporation lower than 75 % at all FLUXNET locations within the chosen karst landscape: where Correlation rule: retain only the parameter sets that produce a positive coefficient of (Pearson) correlation between observations and simulations of both actual evaporation and soil moisture, at all locations: where AET Application of a priori information: retain only parameter sets in which
Each step reduces the initial parameter sample differently for each of the karst landscapes. The posterior parameter distributions within the confined samples should be different among the karst landscapes if the karst landscapes are properly defined. The rather weak thresholds in step 1 and 2 were chosen to take into account the uncertainties resulting from the differences in scales of observations (point) and simulations (grid cell), and from the indirect observation of recharge (actual evaporation and soil moisture as recharge-related variables).
Recharge is simulated over the carbonate regions of Europe and the Mediterranean from 2002/03 to 2011/12 using the confined parameter samples for each of the identified karst landscapes and the available forcings (Table 1). The mean and standard deviation of simulated recharge for each grid cell and time step are calculated by uniform discrete sampling of a representative subset of 250 parameter sets from each of the confined parameters sets which we regarded to be large enough to provide a reliable measure of spread.
To assess the realism of simulated groundwater recharge we compare simulated with observed mean annual recharge volumes derived independently from karst studies over Europe and the Mediterranean (Table 3). In addition, we compare our results to the simulated mean annual recharge volumes of two well-established global simulation models: PCR-GLOBWB (Wada et al., 2010, 2014) and WaterGAP (Döll and Fiedler, 2008; Döll et al., 2003).
Independent observations of mean annual recharge from field and modelling studies over Europe and the Mediterranean.
We furthermore apply a global sensitivity analysis strategy, called regional sensitivity analysis (Spear and Hornberger, 1980), to evaluate the importance of the four model parameters at different simulation timescales ranging from 1 month up to 10 years. This analysis shows (1) which simulated process and characteristics are dominant at a given timescale and (2) which parameters will need more careful calibration when the model is used in future studies. We use the same sample of 25 000 parameter sets that was created for the parameter estimation strategy (Sect. 2.3.2) and assess the sensitivity of four model outputs representative of different timescales: coefficient of variation (CV) of simulated monthly recharge volumes (monthly), CV of simulated 3-month recharge volumes (seasonal), CV of annual recharge volumes (annual), and total recharge over the entire 10-year simulation period (decadal). We do not consider temporal resolutions of less than a month given the assumption that the difference of precipitation and actual evapotranspiration can be a proxy for groundwater recharge and due to uncertainties related to differences in simulation (grid cell) and observation (point).
For each of the identified karst landscapes we choose the 10 locations that
are closest to their cluster means (Euclidean distances to relief and
climate descriptors; Sect. 2.3.1) as representative locations. In the
regional sensitivity analysis approach, we split the parameter sets into two
groups, those that produce simulations above the simulated median of one of
the four model outputs and those that produce simulations below. We then
calculate the maximum distance
Schematic elaboration of the regional sensitivity analysis procedure.
Map with clusters and typical karst landscapes that were attributed to them.
Cluster means of the four identified karst landscapes (AI: aridity index, DS: mean annual number of days with snow cover, RA: range of altitudes).
Cluster analysis resulted in four clusters, which are generally spatially
contiguous (Fig. 4) and have quantitatively distinct cluster means (Table 4). We can attribute particular characteristics to each cluster using the
mean values of the clustering descriptors (Table 4): (1) humid hills and
plains (HUM) are characterized by an aridity index
The three steps of the new parameter confinement strategy resulted in a
significant reduction of the initial sample of 25 000 parameter sets (Fig. 5). Each step has a different impact on the reduction among the identified
landscapes. For the humid karst landscapes, the correlation rule appears to
have the strongest impact while for the mountain and Mediterranean
landscapes the bias rule results in the strongest reduction. For the desert
landscape only step 3, i.e. application of a priori information, reduces the initial
sample because no data were available to apply steps 1 and 2. Considering the
parameter ranges for each landscape after the application of the confinement
strategy (Table 5), we only achieved a confinement of the distribution
parameter
Evolution of the initial sample of 25 000 parameter sets (each including the four model parameters sampled from within their initial ranges) along the different confinement steps for the four karst landscapes.
The impact of the three confinement steps becomes more obvious when
considering their posterior distributions (Fig. 6). The distributions of parameters
Evolution of posterior probabilities of the four model parameters for the four karst landscapes along the steps of the parameter confinement strategy.
The parameter confinement strategy allows us to apply VarKarst-R over all of
Europe and the Mediterranean and to obtain recharge simulations for the
hydrological years 2002/03–2011/12. Thanks to the 250 parameter sets that we
sampled from the posterior parameter distributions we can include an estimate of
uncertainty for each grid cell (Fig. 7). Mean annual recharge ranges from
almost 0 to
Minima and maxima of the confined parameter samples for each of the identified landscapes.
* in parentheses: a priori information used for step 3 of the parameter confinement strategy.
We compare the simulated recharge volumes of our model with recharge volumes
assessed from independent and published karst studies over Europe and the
Mediterranean (Fig. 9a). Even though there is a considerable spread across
the simulations, their bulk plots well around the
Mean deviations of the VarKarst-R, the PCR-GLOBWB model and the WaterGAP model from all observations and the individual regions.
Observations of mean annual recharge from independent studies (Table 3) versus the simulated mean annual recharge by the VarKarst-R and PCR-GLOBWB models (no data for the DES region available).
Sensitivity of simulated recharge to the model parameters at different timescales and in the different karst landscapes. Sensitivity is measured by the maximum distance (D) between the distribution of parameter sets that produce “low” recharge (i.e. below the median) and the distribution producing “high” recharge (above the median). Parameter sets are initially sampled from the ranges in Table 2.
In addition to comparing simulated and observed annual averages, sensitivity
analysis on the model output gives us insight into the realism of the model
and the importance of individual model parameters at different timescales
(Fig. 10). Our results show that parameters
The identification of different karst landscapes is a crucial step within
our new parameter estimation strategy. The four karst landscapes we
identified depend mostly on the choice of climatic and topographic
descriptors (Table 4) and the selected number of clusters. Even though
neglecting several factors as depositional environments, fracturing by
tectonic processes or regional variations in rain acidity, our choice of
descriptors is well justified from our understanding of dominant hydrologic
process controls as formalized in the hydrologic landscape concept (Winter,
2001) and applied similarly at many other studies (Leibowitz et al., 2014;
Sawicz et al., 2011; Wigington et al., 2013). The appropriate choice of
clusters for the
The borders of these hydrologic landscapes are also uncertain. Natural systems usually do not have straight borders that fall on a grid, as assumed by this analysis. Typical transitions between landscape types are continuous and hence transitions from a parameter set representing one landscape to another parameter set of another cluster should be graded, as well. This will be discussed in the following subsection.
How the three steps of the parameter confinement strategy reduce the initial sample shows which type of data provides the most relevant information for each of the karst landscapes. While the timing of actual evapotranspiration and soil saturation that is expressed by the correlation rule appears to be most relevant for the humid landscapes, the bias rule, which represents the volumes of monthly evapotranspiration, is more relevant for the mountain and Mediterranean landscapes. Swapping the order of the correlation rule and the bias rule would provide the same results for HUM and MTN. But for MED the alternative order increases the importance of timing expressed by the correlation rule, indicating the similar importance of both confinement steps.
The thresholds we set in confinement steps 1 and 2 are not very strict, and
the ranges of soil storage capacity we used as a priori information in step 3 are
quite large. This compensates for the fact that (1) only recharge-related
variables are available rather than direct recharge observations, (2) these
variables are not available at the simulation scale (0.25
All model parameters, except for
The little changes that occur to the initial distributions of the DES
parameter sets elaborate the flexibility of our parameter assessment
strategy. The posterior distribution evolves only where information is available (for
this landscape on
Simulated mean annual recharge amounts for the period 2002/03–2011/12 show a
wide range of values, from 0 to
Mountain ranges are considered to be the water towers of the world (Viviroli et al., 2007). Here the MTN landscapes also show the largest recharge volumes due to the large precipitation volumes they receive, though with a considerable spread in our study. HUM and MED landscapes behave similarly with significantly less recharge than MTN. Not surprisingly, there is not much recharge in the desert landscapes at all. But the differences among the clusters shift when considering recharge rates. Due to their thin soils and therefore low soil storage for evaporation (Table 5), the DES karst landscapes transfer up to 45 % of the little precipitation they receive into recharge. The MED landscapes show similarly high recharge rates. Though since their soils are generally thicker than the DES soils, the typical seasonal and convective rainfall patterns of the Mediterranean climate (Goldreich, 2003; Lionello, 2012) might have an important impact, too.
Even though there is still considerable spread in our confined parameter
sets, the uncertainty in simulated mean annual recharge volumes is quite
low. The uncertainties that follow the limited information contained in the
observations are revealed more clearly when we relate the standard deviation
of simulated recharge to its mean volumes with the coefficient of variation.
The uncertainty for the DES landscape is the largest among the clusters
because a priori information is only available for
The mean annual water balance of a hydrological system is dominated by the
separation of precipitation into actual evapotranspiration and discharge
(Budyko and Miller, 1974; Sivapalan et al., 2011). Actual evapotranspiration
is controlled by the soil storage capacity
Furthermore, the results of the regional sensitivity analysis show which
parameters are most important at a given timescale. Depending on the
purpose, a new study may start with the initial ranges of the model
parameters or it might continue with the confined parameter ranges that we
found here. The latter would result in slightly different sensitivities
(Fig. A2). For both cases, the epikarst parameters will require more
attention when applying the VarKarst-R model for simulations at seasonal or
monthly timescales. When working at a smaller spatial scale, combined
analysis of spring discharge and its hydrochemistry may provide such
additional information (Lee and Krothe, 2001; Mudarra and Andreo, 2011).
When working at a timescale of
Even though some deviations occur among the individual karst landscapes, the general simulations of the VarKarst-R model follow well the observations of mean annual recharge rates over Europe and the Mediterranean (Fig. 9). On the other hand, the widely used large-scale simulation models PCR-GLOBWB (Wada et al., 2010, 2014) and WaterGAP (Döll and Fiedler, 2008; Döll et al., 2003) generally under-estimate groundwater recharge (Table 6). The reason for this is the representation of karstic subsurface heterogeneity within the VarKarst-R model, i.e. the inclusion of preferential flow paths and of subsurface heterogeneity. Based on the conceptual understanding of soil and epikarst storage behaviour (Fig. 1c) it allows (1) for more recharge during wet conditions because surface runoff is not generated, and (2) for more recharge during dry conditions because the thin soil compartments will always allow for some water to percolate downwards before it is consumed by evapotranspiration. During wet conditions, both PCR-GLOBWB and WaterGAP will instead produce surface runoff that is subsequently lost from groundwater recharge. During dry conditions, due to its non-variable soil storage capacity, the PCR-GLOBWB model will not produce any recharge when the soil water is below its minimum storage. Separating surface runoff and groundwater recharge by a constant factor, the WaterGAP model will produce recharge during dry conditions, but a constant fraction of effective precipitation will always become fast surface/subsurface runoff resulting in reduced recharge volumes.
This does not mean that the representation of recharge processes in models like PCR-GLOBWB or WaterGAP is generally wrong, but that it can be limited since our analysis shows that the structures of such models need more adaption to the particularities of different hydrologic landscapes. In particular, it adds to the need for incorporating subgrid heterogeneity in our large-scale simulation models (Beven and Cloke, 2012). Karst regions comprise about 35 % of Europe's land surface and our results indicate that presently their groundwater recharge is under-estimated, while surface runoff and actual evaporation are over-estimated. Given the expected decrease of precipitation in semi-arid regions, such as the Mediterranean, and an increase of extreme rainfall events at the same time in the near future (2016–2035, Kirtman et al., 2013), current large-scale simulation models will over-estimate both the vulnerability of groundwater recharge and the flood hazard in karst regions in Europe and the Mediterranean. The same is true for the long-term future (end of 21st century; Collins et al., 2013). Of course, an over-estimation of vulnerability and hazard might be the “lesser evil” compared to an over-estimation. But, at times of limited financial resources, excessive investments in ensuring the security of drinking water supply and flood risk management for potential future changes may unnecessarily aggravate the socio-economic impacts of climate change.
In this study we have presented the first attempt to model groundwater recharge over all karst regions in Europe and the Mediterranean. The model application was made possible by a novel parameter confinement strategy that utilized a combination of a priori information and recharge related observations on four typical karst landscapes that were identified through cluster analysis. Handling the remaining uncertainty explicitly as posterior parameter distributions resulting from the confinement strategy, we were finally able to produce recharge simulations and an estimate of their uncertainty. We found an adequate agreement with our new model when comparing our results with independent observations of recharge at study sites across Europe and the Mediterranean. We further show that current large-scale modelling approaches tend to significantly under-estimate recharge volumes.
Overall, our analysis showed that the subsurface heterogeneity of karst regions and the presence of preferential flow paths enhances recharge. It results in high infiltration capacities prohibiting surface runoff and reducing actual evapotranspiration during wet conditions. On the other hand it allows for recharge during dry conditions because some water can always percolate downwards passing the thin fraction of the distributed soil depths. This particular behaviour suggests that karstic regions might be more resilient to climate change in terms of both flooding and droughts. Drinking water and flood risk management is liable to be based on erroneous information for at least 35 % of Europe's land surface since this is not considered in current large-scale modelling approaches.
However, using recharge directly as a proxy for “available” groundwater resources may not be good in all cases, neither in karst regions nor in other types of aquifers (Bredehoeft, 2002). To precisely estimate the sustainable usable fraction of groundwater the aquifer outflow should be known rather than just the inflow. Furthermore, pumping strategies should consider the geometry and transmissivity of the aquifer. Hence, recharge estimation can be considered only as a first proxy of available groundwater and future studies should focus on the large-scale simulation of karst groundwater flow and storage to further improve water resources predictions in karst regions.
Elbow plot of sum of squared distances to cluster centres for
Sensitivity of simulated recharge to the model parameters at different timescales and in the different karst landscapes, as in Fig. 10 but with sampling parameters from the confined parameter ranges of Table 5.
We want to thank Juergen Strub, research associate at the Chair of
Hydrology, Freiburg, Germany, for designing some of the figures and Thomas
Godman for collecting references to independent recharge studies. This work
was supported by a fellowship within the Postdoc Programme of the German
Academic Exchange Service (Andreas Hartmann, DAAD) and by the UK Natural
Environment Research Council (Francesca Pianosi, CREDIBLE Project; grant
number NE/J017450/1). The sensitivity analysis was carried out by the SAFE
Toolbox (