Hydrol. Earth Syst. Sci., 16, 2219–2231, 2012www.hydrol-earth-syst-sci.net/16/2219/2012/doi:10.5194/hess-16-2219-2012© Author(s) 2012. CC Attribution 3.0 License.

Hydrology andEarth System

Sciences

A new approach to model the spatial and temporal variability ofrecharge to karst aquifers

A. Hartmann 1, J. Lange1, M. Weiler1, Y. Arbel2, and N. Greenbaum2,3

1Institute of Hydrology, Freiburg University, Germany2Department of Geography and Environmental Studies, University of Haifa, Israel3Department of Natural Resources and Environmental Management, University of Haifa, Israel

Correspondence to:A. Hartmann (andreas.hartmann@hydrology.uni-freiburg.de)

Received: 7 February 2012 – Published in Hydrol. Earth Syst. Sci. Discuss.: 23 February 2012Revised: 22 May 2012 – Accepted: 19 June 2012 – Published: 20 July 2012

Abstract. In karst systems, near-surface dissolution of car-bonate rock results in a high spatial and temporal variabilityof groundwater recharge. To adequately represent the dom-inating recharge processes in hydrological models is still achallenge, especially in data scarce regions. In this study, wedeveloped a recharge model that is based on a conceptualmodel of the epikarst. It represents epikarst heterogeneity asa set of system property distributions to produce not only asingle recharge time series, but a variety of time series rep-resenting the spatial recharge variability. We tested the newmodel with a unique set of spatially distributed flow andtracer observations in a karstic cave at Mt. Carmel, Israel. Wetransformed the spatial variability into statistical variablesand apply an iterative calibration strategy in which more andmore data was added to the calibration. Thereby, we couldshow that the model is only able to produce realistic resultswhen the information about the spatial variability of the ob-servations was included into the model calibration. We couldalso show that tracer information improves the model perfor-mance if data about the spatial variability is not included.

1 Introduction

For a sustainable groundwater management, detailed quan-titative knowledge about groundwater recharge is required(Vries and Simmers, 2002). In karst regions, the epikarst,which develops due to higher dissolution activity of thecarbonate rock near the surface (Williams, 1983), controlsrecharge dynamics. Field research (Aquilina et al., 2006;Williams, 1983, 2008) as well as modeling approaches

(Kiraly et al., 1995; Perrin et al., 2003) revealed that theepikarst acts as a temporary storage and distribution systemfor infiltrating water into karst systems.

Karst aquifer recharge can be estimated by different ap-proaches. The water-balance method (e.g. in Carter andDriscoll, 2006; Sheffer et al., 2011; Jocson et al., 2002), em-pirical methods (e.g. in Andreo et al., 2008; Kessler, 1967)and tracer techniques (e.g. in Lange et al., 2010; Plummeret al., 1998; Aquilina et al., 2005) are based on direct mon-itoring and, strictly speaking, only valid for the time of ob-servation. Information about past recharge conditions can beobtained using environmental tracers like chlorofluorocar-bons (CFSs),3H/3He relationships (e.g. Cook and Solomon,1997; Dunkle et al., 1993) or chloride (e.g. Johnston, 1987;Wood and Sanford, 1995). However, estimates about futurerecharge conditions are only possible with numerical model-ing approaches (Scanlon et al., 2002).

Physically based approaches, on the one hand, are de-scribed by Hughes et al. (2008), Kiraly et al. (1995),Martınez-Santos and Andreu (2010) and Perrin et al. (2003).They require extensive data collection to characterize systemproperties (Le Moine et al., 2008), but may provide spatialinformation about recharge rates (Martınez-Santos and An-dreu, 2010). Lumped approaches, on the other hand, wereused by Fleury et al. (2007), Geyer et al. (2008), Jukic andDenic-Jukic (2009b) and Tritz et al. (2011), mostly as asubroutine of a model of an entire karst system. These ap-proaches are based on a set of equations transferring input tooutput, conceptually representing physical processes (Hart-mann et al., 2012). Because they are easy to implement,they are widely used in karst modeling (Tritz et al., 2011).

Published by Copernicus Publications on behalf of the European Geosciences Union.

2220 A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers

Unfortunately, both approaches have deficiencies. Due to thecomplexity of hydrogeological characteristics, the parame-terization of physically based models is usually not possi-ble (Jukic and Denic-Jukic, 2009a). In contrast, lumped ap-proaches include karst-specific processes with strong simpli-fications and only provide one single recharge time series forthe entire system (Scanlon et al., 2002).

In this study we aim to combine the advantages of dis-tributed and lumped recharge modeling approaches. We hy-pothesize that recharge spatial and temporal variability is dueto the physical variability of the epikarst, which can be rep-resented by distribution functions of system properties. Ourmodel produces not only a single recharge time series butalso a variety of time series representing the spatial vari-ability of epikarst recharge. To test the model we used mea-surements of stalactite drips in a karstic cave at Mt. Carmel,Northern Israel (Arbel et al., 2010; Lange et al., 2010).

2 The epikarst and study area

2.1 General conceptual model of the epikarst

The epikarst develops close to the surface due to higher so-lution activity of infiltrating water with higher carbon diox-ide concentrations. It is regarded as a temporary storage anddistribution system for infiltrating water into karst systems(Williams, 1983; Aquilina et al., 2006). Temporarily, perchedaquifers can develop (Mangin, 1975) to allow lateral flows tothe proximate enlarged fissure or conduit (Williams, 2008).Hence, recharge to the lower karst system is (1) slow anddiffuse into the fissured porous matrix and (2) fast and con-centrated into the conduits (Fig. 1a). The interplay betweenconcentrated and diffuse recharge depends on the variabilityof system properties, such as lateral and vertical hydraulicconductivities as well as soil and epikarst thickness.

2.2 Study area

The Orenin Cave (Fig. 1b and c) is a karstic cave, which de-veloped in crystalline limestone located at the western es-carpment of Mt. Carmel – a triangular-shaped, anticlinal, up-lifted block up to 546 m above sea level. It is located closeto the northwestern coast of Israel and composed of up-per Cretaceous limestone, dolomites, chalks and marls. Thearea is intensively fractured and jointed, and characterizedby various karstic features (Guttman, 1998; Karczs, 1959).The cave is located 28 m below an almost horizontal sur-face covered with∼ 48 % rock outcrops and shallow soilpockets of reddish-brown, silty-clay, stony Terra Rossa soilup to 110 cm deep (Arbel et al., 2008; Wittenberg et al.,2007). The regional water table is located about 120 m belowthe cave within the Upper Cretaceous Judea Group Aquiferof Mt. Carmel. Aquifer recharge by freshwater is indicatedby a seasonal rise in water table with a decline in chloride

Fig. 1. (a)Conceptual model of the epikarst (after Williams, 1983,modified, blue: temporarly stored water, yellow: soil and dissolutionresiduals),(b) location of the study site, and(c) schematic descrip-tion of the study site (after Arbel et al., 2010, modified).

concentrations (Guttman, 1998) occurring after significantrainstorms during winter.

The climate in Mt. Carmel is typically Mediterranean withcool rainy winters, dry hot summers, and average daily po-tential evapotranspiration rates of 5–6 mm. The mean annualrainfall above the cave is about 550 mm a−1. The rainy sea-son lasts from October to April, but most rainfall occursbetween November and March. Rainfall intensities exceed30 mm h−1 during short and localized convective rainstormsin autumn, whereas in winter the storms are frontal events,lasting a few days with lower intensities. Significant win-ter rainstorms have total rainfall amounts between 40 and180 mm (Wittenberg et al., 2007). Above the cave, vegetationcover is a typical Mediterraneangarrigue, i.e. shrubs (Arbelet al., 2010).

Most recent findings about the spatial and temporalrecharge variability at the cave can be found in Lange etal. (2010) and Arbel et al. (2010). The former studied dripand tracer responses of several stalactites following a sprin-kling experiment (Fig. 2a and b), while the latter observeddripping rates and tracer concentrations at a seasonal timescale (Fig. 2c). Both highlight the presence of large waterstorages in the soil of the epikarst, which need to becomesaturated before the drips activate. Hydrochemical analysisindicated that the drip water was largely composed of pre-event water with variable but generally low event water frac-tions. Even though several tracers were used in both studies,we only consider artificially enriched water with high elec-tric conductivity (EC) since it was the only tracer that wasapplied uniformly over the whole area.

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A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers 2221

3 Methodology

3.1 Transforming spatial variability intostatistical variables

Instead of considering individual hydrographs and tracerconcentration curves for each single drip, integrated hydro-dynamic and hydrochemical responses,Q [l h−1] andC[–],of all measured drips are calculated:

Q(t) =

N∑i=1

Qi (t) (1)

C (t) =

N∑i=1

Qi (t) · C′

i (t)

Q(t). (2)

The coefficients of variation CVC [–] and CVQ [–] specifytheir spatial variability:

CVQ (t) =

√1

N−1

N∑i=1

[Qi (t) −

Q(t)N

]2

Q(t)N

(3)

CVC (t) =

√1

N−1

N∑i=1

[C′

i (t) − C (t)]2

C (t)(4)

whereQi(t) [l h−1] is the individual drip rate, andC′

i (t) [–]is the normalized tracer concentration of the dripi, i = 1...N ,at timet . Concentrations are normalized by the tracer inputconcentrationCin [µS cm−1]:

C′

i (t) =Ci (t)

Cin(5)

whereCi(t) [µS cm−1] is the originally observed tracer con-centration at dripi. Note that in Eq. (3) Q is divided byN in order to obtain its mean from the sum (Eq. 1). UsingEqs. (1)–(5) observations at the individual drips were trans-formed into three time series of integrated responsesQexp,Cexp, andQseas, and three time series of coefficients of vari-ation, CVQ,exp, CVC,exp, and CVQ,seas, for the experimenthydrodynamic and tracer observations, and the seasonal hy-drodynamic observations, respectively (Fig. 2).

3.2 The model

3.2.1 Model structure

The developed model structure (Fig. 3) follows the generalconceptual epikarst model of Williams (1983) (Fig. 1a) andshould reproduce the typical epikarst features. Its geometry

is defined by a lengthL [m], representing the average flowdistance between the shallowest and the deepest part of theepikarst, and an areaA [m2]. To account for spatial variabil-ity, N model compartments are connected horizontally. Theirequal areas,Ai [m2], and lengths,Li [m], are derived by di-viding A andL by N . Similar to the Probability DistributedModel PDM (Moore, 2007) a variable soil and epikarst thick-ness are defined:

dsoil,i = dmax,soil ·

(i

N

)adepth

(6)

depi,i = dmax,epi ·

(i

N

)adepth

(7)

wheredsoil,i [m] anddepi,i [m] are the soil and epikarst thick-nesses of reservoiri, dmax,soil [m] and dmax,epi [m] are themaximum soil and epikarst thicknesses, andadepth [–] isthe depth variability coefficient. Defining soil and epikarstporositiesnsoil [–] andnepi [–], respectively, the storage vol-umesSsoil,i [m3] andSepi,i [m3] are defined by:

Ssoil,i = Ai · dsoil,i · nsoil (8)

Sepi,i = Ai · depi,i · nepi. (9)

3.2.2 Water fluxes

Infiltration into the soil originates from precipitation andsurface flow arriving from the neighboring reservoir. Waterleaves the soil either as actual evaporation or as percolationto the epikarst when its storage volumeSsoil,i is exceeded.Similar to many other models (HBV, Bergstrom, 1995;TOP-MODEL, Beven and Kirby, 1979), actual evaporationEact,i[mm h−1] is derived from:

Eact,i (t) = Epot(t) ·Vsoil,i (t)

Ssoil,i(10)

where Epot(t) [mm h−1] is the potential evaporation, andVsoil,i(t) [m3] is the water volume stored in soil compart-menti at time stept . Inflow to the epikarst either originatesfrom soil percolation or from the neighboring epikarst com-partment as a consequence of water level difference1hi(t)

[m], which is calculated by

1hi (t) =Vepi,i−1 (t) − Vepi,i (t)

Ai · nepi(11)

whereVepi,i(t) [m3] is the water volume stored in the epikarstat compartmenti. Lateral flowQlat,i [l h−1] is described bythe Dupuit-Forchheimer assumption, which proved to be anadequate representation of lateral flows in perched aquiferdelivery (Freeze and Cherry, 1979):

Qlat,i (t) = Ti (t) ·1hi (t)

Li

· Wi (12)

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2222 A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers

Fig. 2. Individual observations, integrated response and coefficient of variation of(a) drip rates during the sprinkling experiment (Lange etal., 2010),(b) drips’ normalized EC concentrations during the sprinkling event (Lange et al., 2010), and(c) drip rates at the seasonal timescale (Arbel et al., 2010).

Wi =Ai

Li

(13)

whereTi(t) is the transmissivity, andWi [m] is the width offlow. Since a decrease of the lateral hydraulic conductivityKlat,i [mm h−1] with depth can be expected (Perrin et al.,2003), a decay coefficientalat [–] is introduced:

Klat (z) = Klat,max · e(−alatz) (14)

whereKlat,max [mm h−1] is the lateral hydraulic conductivityat the surface, andz is the depth below surface. As describedin more detail in Wigmosta and Lettenmaier (1999),Ti(t) iscalculated by:

Ti (t) =

hepi,i (t)∫depi,i

Klat (z)dz (15)

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Fig. 3. Model structure and parameters; parameteralat controls thedecay ofKlat,max with depthz, and parametersavert and adepthcontrol the variability ofKvert,max, Vold, max, dsoil,maxanddepi,maxamong theN compartments.

hepi,i (t) =Vepi,i (t)

Ai · nepi. (16)

Outflow from the saturated zone either occurs by lateral flowto the next reservoir (Eqs. 12 to 16) or in the form of verticalrecharge which is represented by a simple linear relationship:

Ri (t) = Kvert,iVepi,i (t)

Ai

(17)

where Ri [l h−1] is the vertical recharge, andKvert,i[mm h−1] is the vertical hydraulic conductivity. This sim-ple relationship does not take into account that water move-ment is also gravity driven, it only considers flow due towater pressure. However, trying different equations describ-ing the vertical percolation, this simple relationship wasfound to perform best. Following the conceptual model ofWilliams (1983), the variability of vertical hydraulic conduc-tivity is included by:

Kvert,i = Kvert,max ·

(i

N

)avert

(18)

whereKvert,max [mm h−1] is assumed to be the hydraulicconductivity at the uppermost part of the epikarst (Fig. 2b),and avert [–] is a coefficient describing the variability ofKvert,i . When inflows simultaneously exceed theSsoil,i andSepi,i , surface flow is produced. Based on a doline structure(Fig. 1a), a surface gradient towards the doline centre canbe assumed. Hence, surface flow is routed from outer com-partments with low soil and epikarst thickness to the innercompartments with higher thickness:

Qout,surf,i (t) = Qin,surf,i+1 (t) (19)

whereQout,surf,i [l h−1] is the surface flow produced at com-partmenti, andQin,surf,i+1 is the surface flow reaching com-partmenti+1 from the neighboring compartment with lowersoil and epikarst thickness.

3.2.3 Solute transport

The solute transport in all reservoirs is based on the assump-tion of complete mixing. Since preceding studies (Arbel etal., 2010; Lange et al., 2010) found evidence for consider-able amounts of old water in the cave drips, a maximum oldwater volumeVold,max [mm] and its solute concentrationCold[–] are defined as initial conditions. It is assumed that theold water storage is stored below the epikarst (Fig. 3) andthat compartments with a lower soil and epikarst thicknesshave larger old water storage beneath them than regions withhigher soil and epikarst depths. Therefore, the same distribu-tion function as for the soil and epikarst thickness is applied,but this time in the opposite direction:

Vold,i = Vold,max ·

(N − i + 1

N

)adepth

. (20)

With Eqs. (6) to (20), the model producesN series ofrecharge rates and tracer concentrations on which Eqs. (1)to (5) can be applied.

3.3 Calibration approach

Including solute transport, the model consists of 13 parame-ters (Table 1) that have to be determined by calibration, sinceno field information is available. To identify parameter val-ues, the Shuffled Complex Evolution Metropolis algorithmSCEM (Vrugt et al., 2003) was chosen, which has provento reliably find optimal parameter sets including informationabout their uncertainty (e.g. in Feyen et al., 2007; Schoupset al., 2005; Vrugt, 2004). As a measure of model perfor-mance, the Nash Sutcliffe Efficiency NS (Nash and Sutcliffe,1970) was used. In order to show the influence of differentinformation sources, an iterative calibration strategy was ap-plied (Table 2). Four individual efficiencies were calculatedand equally weighted. More and more information was itera-tively added to the optimization procedure until all availabledata was included.

3.4 Stability of simulation time series

The number of compartmentsN was arbitrarily set to 15,which is larger than the number of observed drip locations inthe cave (in total 9). To investigate whether this number waslarge enough to provide numerically stable results, we ran themodel using calibration step (4) but with different numbers ofcompartments (N = 3...50). Calculating NSQ,exp, NSQ,seas,NSC,exp, and NSCV for the differentN indicated which mini-mum number forN was necessary to have stable mean valuesand coefficients of variation. The results were considered sta-ble as long as their relative deviations remained below 20 %.

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2224 A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers

Table 1.Parameter table, calibration ranges, optimized parameter sets and their efficiencies for all four calibration steps.

Parameter Description UnitParameter ranges Calibration step

lower upper 1 2 3 4

adepth depth variability coefficient [–] 0.5 5 0.5 2.3 2.6 2.6dsoil,max maximum soil depth [m] 0 1 0.16 0.10 0.22 0.10depi,max maximum epikarst depth [m] 0 28 1.4 17.8 24.8 25.1nsoil effective porosity of soil [–] 0.35 0.45 0.4 0.4 0.4 0.4nepi effective porosity of epikarst [–] 0.1 0.3 0.16 0.12 0.30 0.19avert variability of vertical hydraulic conductivity [–] 0.5 5 5.0 4.6 3.0 3.5logKvert,max log of maximum vertical hydraulic conductivity [mm h−1] 0 3 1.99 1.89 1.72 1.75logKlat,max log of maximum lateral hydraulic conductivity [mm h−1] 0 3 1.29 0.40 1.48 1.70alat decay coeffcient of lateral hydraulic conductivity [m−1] 0 10 2.6 3.0 5.3 8.4L average lateral flow length [m] 0 15 5.5 9.9 10.6 14.3A contributing area [m2] 0 20 9.4 9.1 9.3 8.6Cold old water concentration∗ [–] 0.5 0.6 0.56 0.60 0.54 0.60Vold maximum old water volume [mm] 0 2000 786 909 1271 1048

Objective functions

NSQ,exp 0.96 0.85 0.83 0.81NSQ,seas 0.72 0.69 0.68 0.68NSC,exp −35.68 0.55 −8.35 0.54NSCV 0.26 0.39 0.62 0.61

∗ Normalized, see Eq. (3),

Table 2. Description of calibration steps and weights associated with the Nash Sutcliffe efficiencies concerning the drip rates observedduring the experiment, NSQ,exp, the drip rates during the seasonal times scale, NSQ,seas, the drip water concentration during the experiment,NSC,exp, and their coefficients of variation, NSCV.

Calibration DescriptionWeights [–]

step NSQ,exp NSQ,seas NSC,exp NSCV

1 only drip rates 1/2 1/2 – –2 drip rates and tracer 1/3 1/3 1/3 –3 drip rates and variability 1/3 1/3 – 1/3∗

4 drip rates, tracer and variability 1/4 1/4 1/4 1/4

∗ In this calibration step only the variability of CVQ,exp and CVQ,seasare considered.

4 Results

The model was run with a six-hour time step. For each cal-ibration step, SCEM was performed until convergence wasreached (see Vrugt et al., 2003). Parameter ranges were setto physically reasonable values according to preceding stud-ies. Table 1 shows the optimized parameters and the resultingNS efficiencies for all the calibration steps. The parameterswere normalized by their range and compared (Fig. 4). Atcalibration step 1 the modeledQexp andQseasclosely com-pared with the observations, which was expressed by highNSQ,exp andNSQ,seasvalues. However, simulated CV andCexp showed a strong bias from the observations and NSC,expand NSCV had low values. In calibration step 2, tracer infor-mation consequentially improved the simulated tracer con-centrations, even though a moderate decrease in NSQ,expwas observed. NSCV improved slightly. In calibration step 3,the information about spatial variability strongly improved

NSCV, while there was also a small improvement of tracersimulations evident by an increase of NSC,exp. Only whentracer and variability information were added in calibrationstep 4, an acceptable simulation was reached forQexp, Cexp,Qseasand CV with all NS values exceeding 0.5.

For calibration steps 1 and 2, some parameters were simi-lar, e.g.nsoil, avert andalat, but some parameters had unreal-istic and contradicting values when only information aboutdrip rates and tracer concentration was used (e.g.,adepthanddepi,max). When the information about spatial variabil-ity was added in calibration step 3, the majority of the pa-rameters changed and plotted almost at the same location incalibration step 4, e.g.depi,max, avert and logKvert. In manycases, calibration step 2 parameters plotted between calibra-tion step 1 and calibration step 3 and 4 parameters. Excep-tions were the hydrochemical parameters,Vold,max andCold,and the parameters describing the lateral flow,alat andL. Thehydrochemical parameters grouped together in calibration

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A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers 2225

Fig. 4. (a) Normalized optimized parameter sets for the four cali-bration steps and(b) the resulting NS efficiencies.

steps 2 and 4 when information about the tracer data wasconsidered. The lateral flow parameters did not show any sys-tematic pattern between the calibration steps.

Figure 5 shows the cumulative parameter distributions ob-tained by SCEM for each calibration step. If a parameter issensitive, it would significantly differ from a uniform dis-tribution (grey diagonals). Using this criterion, many of theparameters seemed sensitive already at calibration step 1.However, the lateral flow parameters, logKlat,max, alat andL, the hydrochemical parameters,Vold,max andCold, and theporosities,nsoil andnepi revealed low sensitivities.Vold,maxandCold became sensitive in calibration steps 2 and 4 whentracer data was added. logKlat,max, alat and L, as well asnsoil andnepi, remained non-sensitive among all calibrationsteps, which means that they could adapt to any value with-out changing the simulation results. The grouping of param-eters that occurred at calibration steps 3 and 4 was also re-flected by a shift of the cumulative parameter distributions,which changed when the information about spatial variabil-ity of drip rates and tracer concentrations was added, e.g. forlogKvert,maxor avert.

The ability of the model to produce a realistic spatial vari-ability of recharge rates and tracer concentrations is visual-ized in Fig. 6. Some model compartments react delayed, oth-ers rapidly to rainfall events. On the other hand, the delayedcompartments sustain flow long after water input, while therapidly reacting compartments fall dry shortly after rain-fall events. Regarding the tracer concentrations, the delayedcompartments almost do not react to the input. More rapidlyreacting compartments change their concentration, while themost rapid totally adapted to the input concentration.

The water balances in Fig. 7 show the simulated sum ofinternal model fluxes for calibration step 4, with separategraphs for the sprinkling experiment (Fig. 7a) and the sea-sonal time scale (Fig. 7b). Even though all compartments re-ceive the same amount of precipitation, the remaining waterbalance components of the individual compartments show ahigh spatial variability. At both time scales, the first five com-partments produce surface flow, while noteworthy amounts

of actual evaporation are visible from the fourth compart-ment at the seasonal scale, increasing towards compartment15. While the sprinkling experiment produces the largestrecharge amounts for the last five compartments, major partsof the water are recharged by compartment four to seven atthe seasonal time scale.

Increasing the number of model compartments (Fig. 8) in-dicates that the simulated drip rates were stable atN = 3,both for the experiment and for the seasonal time scale. TheCV stabilized forN ≥ 5. Tracer concentrations stabilized forN > 10 and diverged again forN ≥ 25. The drip rates as wellas the CVs remained stable even forN = 50.

5 Discussion

5.1 Model performance along the iterative calibration

Considering only integrated recharge rates, calibration step 1provided acceptable predictions of mean recharge rates, butunacceptable results for the spatial variability and hence in-ternal process dynamics (Table 1, Fig. 4). When tracer datawas added in calibration step 2, the tracer and also the predic-tions of spatial recharge variability improved slightly. How-ever, only information about the spatial variability in calibra-tion step 3 adequately reproduced the observed variability.Using both tracer and variability data in calibration step 4, nofurther significant improvement could be reached. Thus, theinformation about spatial variability of recharge rates had thestrongest impact on the optimized parameters and on the re-sulting simulations, while tracer data alone had a slight pos-itive impact on the representation of variability and, in addi-tion, gave evidence of proper process representation and pa-rameter choice. Including information about spatial variabil-ity resulted in small reductions of NSQ,exp and NSQ,seasinfavor of an overall acceptable multi-objective fit and more re-alistic results. Similar conclusions can also be found in Kucz-era and Mroczkowski (1998), Seibert and McDonnell (2002),and Son and Sivapalan (2007).

5.2 Water balance

Figure 7 indicates that there is almost no lateral subsurfaceflow during the sprinkling experiment as well as at the sea-sonal time scale. This suggests that lateral flow processes arenot important at the study site. This is supported by tracers inpreceding field research that showed that even though lateralflow processes exist, only minimum lateral flow concentra-tion occurs during infiltration and percolation (Arbel et al.,2010; Lange et al., 2010), majorly due to a previously verti-cal fissure orientation (Karczs, 1959). There are also no sig-nificant amounts of actual evaporation during the sprinklingexperiment, because the observation time was too short toevaporate the newly stored sprinkled water. At the seasonaltime scale, actual evaporation constitutes a large part of the

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2226 A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers

Fig. 5.Cumulative parameter distributions for all four calibration steps.

outflows, which is comparable to other studies (e.g. Andreoet al., 2008).

Due to the variability of soil and epikarst thickness, sur-face flow is only produced at the first six compartments dur-ing the experiment at the seasonal time scale (Fig. 7), whichis 40 % of the modeled area. This fraction closely compareswith 48 % of rock outcrops (Arbel et al., 2008; Wittenberg etal., 2007) that are found at the surface. During the sprinklingexperiment, the largest recharge amounts can be found in thelast five model compartments, whereas at the seasonal scale,compartments five to seven produce the largest amounts ofrecharge. That indicates that major parts of the recharge arerather slow. Only during strong events, as artificially pro-duced by the sprinkling experiment, fast flow paths activateand produce much recharge in a very short time. Using wa-ter isotopes and lumped parameters models, Maloszewski etal. (2002) arrived at similar results for a karst system in theAustrian Alps.

5.3 Optimized parameters and water balance

The final parameters derived from calibration step 4 canonly be interpreted when their sensitivity is considered. Theparameter distributions in Fig. 5 show that all parameterswere sensitive when all available information was used forthe calibration procedure, except for lateral flow parameters,logKlat,max, alat andL, and the porosities,nsoil andnepi. Thiscan be interpreted as an indicator for over-parameterization(Perrin et al., 2001). However, since lateral subsurface flowwas found to be not significant at the study site, a non-sensitivity of these parameters is rather due to the non-importance of the lateral flow processes. The non-sensitivityof the porosity parameters derives from Eqs. (8) and (9). Thesame storage volume can be generated by different combi-nations of area, depth, and porosity. Since the ranges of area

and depth are much wider than those of porosities (see dis-cussion below), the porosities appear non-sensitive becausetheir variations can be totally compensated by variations ofarea and depth. Similar results were obtained with a split-sample test and multiple bootstrapping of subsets of the ob-servation period (see the Supplement).

The sensitive parameters of calibration step 4 suggestedthat the maximum soil depthdsoil,max was quite low (14 cm)compared to measurements in the field (up to 110 cm, Arbelet al., 2008; Wittenberg et al., 2007). The soil porositynsoilwas set to 35 % to 45 % and did not consider the stoniness.Stoniness may drastically reduce overall porosity and wouldtherefore result in a larger calibrateddsoil,max. However, thecorrectness of the final soil volumesSsoil,i was corroboratedby the realistic amounts of actual evaporation. A part of themaximum measured soil thickness might also be attributedto the epikarst. In the model, its thicknessdepi,maxwas closeto the rock thickness above the cave (27 m). Due to thedepth variability coefficientadepth, very small storagesSsoil,iandSepi,i can be found at the first compartments, which re-sulted in noteworthy rates of surface flow (see Sect. 5.2). Theepikarst porositynepi, although non-sensitive, was calibratedto a realistic value (19 %) compared to other studies (e.g.Williams, 2008). The hydrologically small contributing areaA of ∼ 9 m corresponded to the findings of the sprinklingexperiment (Lange et al., 2010), which showed that onlysmall parts of the sprinkling water finally reached the cave.The maximum vertical hydraulic conductivityKvert,maxwascalibrated to 55 mm h−1 (1.46× 10−5 m s−1), which corre-sponds with other studies (Williams, 1985; Perrin et al.,2003).

The calibrated old water concentrationCold was foundto remain at the uppermost part of the predefined range(Fig. 4). A widening of theCold calibration ranges resulted

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A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers 2227

Fig. 6.Simulation results of all individual model compartments for calibration step (4) and the integrated responses and CVs of all calibrationsteps for(a) drip rates during the sprinkling experiment,(b) drips’ concentrations during the sprinkling event, and(c) drip rates at the seasonaltime scale.

in slightly better model results for NSC,exp, but since theoriginal ranges were set according to the old water concen-trations determined for all the drips prior to the sprinkling(Lange et al., 2010), physical realism was prefered insteadof an optimal fit. The maximum old water volumeVold,maxof ∼ 1000 mm is in accordance with Lange et al. (2010) andArbel et al. (2010), who discovered large old water contribu-tions in the rock above the cave.

5.4 Representation of spatial variability

Our model reproduces the spatial variability of recharge ratesevery time step because distribution functions are included.They control the variability of soil and epikarst depth, ver-tical hydraulic conductivity and old water storage. The as-sumption that the observed drip rates in the cave show thereal spatial variability of recharge rates raises the questionwhether one drip really represents one individual flow path.Since the calcite precipitation, which formed the stalactite,produces a less permeable layer on the cave ceiling, it is

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2228 A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers

Fig. 7. Water balance for each model compartment:(a) sprinklingexperiment and(b) seasonal observations for calibration step 4 (thechange of storage within the compartments is attributed to the out-put).

reasonable to expect an accumulation of several flow pathsbefore the water finally reaches the cave. For that reasonwe used integrated responses and coefficients of variation in-stead of directly comparing individual model compartmentswith individual drip observations, and we chose a numberof model compartments (15) that is considerably larger thanthat of observed drips (9). Varying the number of modelcompartments (Fig. 8) showed thatN = 15 model compart-ments were enough for stable results for both integrated flowrates and their coefficients of variation. Only hydrochemicalpredictions diverged for compartment numbers> 25, whichwas most probably due to their dependence on the flow pre-dictions. Small changes inQexp might result in very largechanges ofCexp.

5.5 Transferability of the new approach

Even if the introduced model performs well and is physi-cally reasonable under the study site’s conditions, the ques-tion about the transferability of the approach to other siteshas to be addressed. In detail one has to ask whether themodel is able to cope with differences in system propertiesand whether the model can be applied without informationabout the spatial variability of recharge dynamics. We the-oretically consider two different caves (1) the Soreq cave,Israel, and (2) the Vers-chez-le-Brandt cave, Switzerland, todiscuss this question.

The Soreq cave is located in a semi-arid climate 10–50 mbelow the surface at a sloping terrain. Using drip rate obser-vations at several observation points within the cave and en-vironmental tracers, it was found that, depending on the de-gree of fractures, distance to the surface, and rainfall durationand intensity, fast flow can occur (Even et al., 1986; Ayalon

Fig. 8.Maximum relative deviation of NS efficiencies with varyingnumber of compartments from the NS efficiencies usingN = 15compartments.

et al., 1998). However, most recharge water travels severaldecades in small fissures before it reaches the cave (Kauf-man et al., 2003). Our model already proved that it is able tocope with fast as well as with slow flow paths. However, dueto the sloping terrain, lateral flow processes that have shownto be not as important at our study site may be of higher sig-nificance at the Soreq cave. On such terrain, surface runoffshould also be accounted for, as it has been shown on a slopenearby (Lange et al., 2003).

The Vers-chez-le-Brandt cave is located below relativelyflat pasture land in a humid environment, 30 m below thesurface with 1–2 m deep soil on top. Drip rate observationsat one observation point in the cave and artificial and envi-ronmental tracers showed that its typical dynamics duringa rain event are characterized by five phases (Pronk et al.,2009): saturation of the soil, initiation of pressure pulse byperched water, arrival of first event water at the cave, in-creased amounts of event water at the cave, and recessionperiod. Since our model includes a soil layer and allows forperched water tables, we are confident that our approach willmost probably be able to reproduce these five characteristicphases. Compared to our site, the soils are much thicker anddistributed more evenly. Hence, allowing a deeper soil in themodel setup will address this difference. The lack of informa-tion about the spatial variability of recharge could be reducedby directly measuring soil depth distributions (as for examplein Tromp-van Meerveld and McDonnell, 2006). However, in-formation about the distribution of vertical conductivity, wa-ter storage, and decrease of lateral conductivity with depth isdifficult to obtain. To compensate for this, we see a high valuein karst evolution studies and models, which provide aper-ture width distributions depending on climate and degree offractures before karstification began (e.g. Bloomfield et al.,2005; Hubinger and Birk, 2011).

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A. Hartmann et al.: Spatial and temporal variability of recharge to karst aquifers 2229

6 Conclusions

In this study we hypothesize that the spatial variability ofepikarst recharge is due to the variability of system proper-ties, which can be represented by simple distribution func-tions. Based on our conceptual understanding of the epikarst,we developed a model structure that includes the variabilityof selected system properties. Our results indicate that ourmodel is able to realistically produce the spatial variabilityof recharge and tracer fluxes. The proposed iterative calibra-tion strategy reveals that these results are realistic only wheninformation about spatial variability was included into modelcalibration.

The use of simple parametric distribution functions ofmodel properties and parameters in an otherwise lumpedmodel may allow reproduction of the temporal and spatialvariability of karstic recharge if variability is considered inthe model structure and calibration. However, before moregeneral statements on the performance of the newly devel-oped model for practical applications can be made, it has tobe compared with other already existing approaches. Withthe information provided by this study, we can only confirmthat the model works well under the observed conditions anddata. The model should be applied to other sites with differ-ent controls of climate, processes and epikarst properties toevaluate its transferability before it can finally be applied forpractical purposes, e.g. water resources management. Thiswill be the scope of further research.

Supplementary material related to this article isavailable online at:http://www.hydrol-earth-syst-sci.net/16/2219/2012/hess-16-2219-2012-supplement.zip.

Acknowledgements.This study was carried out in the framework ofthe GLOWA Jordan River Project, funded by the German Ministryof Education and Research (BMBF), Grant No. 01LW0507G1.In addition we want to thank Jurriaan Spaaks from AmsterdamUniversity for his helpful support in using SCEM and Jurgen Strubfrom the Institute of Hydrology, Freiburg University, for designingsome of the figures.

Edited by: E. Zehe

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