A large-scale simulation model to assess karstic groundwater recharge over Europe and the Mediterranean


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A large-scale simulation model to assess karstic groundwater recharge over Europe and the Mediterranean

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Title:
A large-scale simulation model to assess karstic groundwater recharge over Europe and the Mediterranean
Series Title:
GMD
Creator:
Hartmann, A.
Gleeson, T.
Rosolem, R.
Pianosi, F.
Wada, Y.
Wagener, T.
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Copernicus Publications
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English

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Karst ( local )
Karstic Groundwater Recharge ( local )
Carbonate Rock ( local )
Europe ( local )
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serial ( sobekcm )

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Abstract:
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 > 1 m a−1 in humid regions. The majority of recharge rates range from 20 to 50% of precipitation and are sensitive to subannual climate variability. Simulation results are consistent with independent observations of mean annual recharge and significantly better than other global hydrology models that do not consider karst processes (PCR-GLOBWB, WaterGAP). Global hydrology models systematically under-estimate karst recharge implying that they over-estimate actual evapotranspiration and surface runoff. Karst water budgets and thus information to support management decisions regarding drinking water supply and flood risk are significantly improved by our model.
Original Version:
GMD, Vol. 8, no. 6 (2015-06-11).

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K26-05114 ( USFLDC: LOCAL DOI )
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Geosci.ModelDev.,8,1729–1746,2015 www.geosci-model-dev.net/8/1729/2015/ doi:10.5194/gmd-8-1729-2015 Authors2015.CCAttribution3.0License. Alarge-scalesimulationmodeltoassesskarsticgroundwater rechargeoverEuropeandtheMediterranean A.Hartmann 1,3 ,T.Gleeson 2 ,R.Rosolem 1 ,F.Pianosi 1 ,Y.Wada 4 ,andT.Wagener 1 1 DepartmentofCivilEngineering,UniversityofBristol,Bristol,UK 2 CivilEngineering,McGillUniversity,Montreal,Canada 3 FacultyofEnvironmentandNaturalResources,UniversityofFreiburg,Freiburg,Germany 4 DepartmentofPhysicalGeography,UtrechtUniversity,Utrecht,theNetherlands Correspondenceto: A.Hartmannaj.hartmann@bristol.ac.uk Received:25September2014–PublishedinGeosci.ModelDev.Discuss.:19November2014 Revised:7May2015–Accepted:12May2015–Published:11June2015 Abstract. Karstdevelopsthroughthedissolutionofcarbonaterockandisamajorsourceofgroundwatercontributingup tohalfofthetotaldrinkingwatersupplyinsomeEuropean countries.PreviousapproachestomodelfuturewateravailabilityinEuropeareeithertoo-smallscaleordonotincorporatekarstprocesses,i.e.preferentialowpaths.Thisstudy presentstherstsimulationsofgroundwaterrechargeinall karstregionsinEuropewithaparsimoniouskarsthydrology model.Anovelparameterconnementstrategycombinesa prioriinformationwithrecharge-relatedobservationsactual evapotranspirationandsoilmoistureatlocationsacrossEuropewhileexplicitlyidentifyinguncertaintyinthemodelparameters.Europe'skarstregionsaredividedintofourtypicalkarstlandscapeshumid,mountain,Mediterraneanand desertbyclusteranalysisandrechargeissimulatedfrom 2002to2012foreachkarstlandscape.Meanannualrecharge rangesfromnegligibleindesertsto > 1ma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 inhumidregions.Themajorityofrechargeratesrangefrom20to50% ofprecipitationandaresensitivetosubannualclimatevariability.Simulationresultsareconsistentwithindependent observationsofmeanannualrechargeandsignicantlybetter thanotherglobalhydrologymodelsthatdonotconsiderkarst processesPCR-GLOBWB,WaterGAP.Globalhydrology modelssystematicallyunder-estimatekarstrechargeimplyingthattheyover-estimateactualevapotranspirationandsurfacerunoff.Karstwaterbudgetsandthusinformationtosupportmanagementdecisionsregardingdrinkingwatersupply andoodriskaresignicantlyimprovedbyourmodel. 1Introduction Groundwateristhemainsourceofwatersupplyforbillions ofpeopleintheworldGleesonetal.,2012.Carbonaterock regionsonlyconstituteabout35%ofEurope'slandsurface WilliamsandFord,2006,yetcontributeupto50%ofthe nationalwatersupplyinsomeEuropeancountriesCOST, 1995becauseoftheirhighstoragecapacityandpermeabilityFordandWilliams,2007.ClimateconditionshaveaprimarycontrolongroundwaterrechargedeVriesandSimmers,2002.Climatesimulationssuggestthatinthenext90 yearsMediterraneanregionswillbeexposedtohighertemperaturesandlowerprecipitationamountsChristensenetal., 2007.Inaddition,shiftsinhydrologicalregimesMillyet al.,2005andhydrologicalextremesDai,2012;Hirabayashi etal.,2013canbeexpected.Toassesstheimpactofclimatechangeonregionalgroundwaterresourcesasgroundwaterdepletionordeteriorationsofwaterquality,large-scale simulationmodelsarenecessarythatgobeyondthetypical scaleofaquifersimulationmodels 10000km 2 Additionally,weexpectthefuturevariabilityofclimatetobebeyondthatreectedinhistoricalobservations,whichmeans thatmodelpredictionsshouldderivecredibilityviamoreindepthdiagnosticevaluationoftheconsistencybetweenthe modelandtheunderlyingsystemandnotfromsomecalibrationexerciseWageneretal.,2010. Currentlyavailableglobalhydrologymodelsdiscretizethe landsurfaceingridswitharesolutiondownto0.25.5 . Partsoftheverticaluxesarewellrepresented,e.g.theenergybalanceEk,2003;Mirallesetal.,2011.ButgroundwaPublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.

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1730A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge terrechargeandgroundwaterowarerepresentedsimplyby heuristicequationsDllandFiedler,2008orassumptions oflinearityWadaetal.,2010,2014.Theydonotexplicitlysimulateadynamicwatertableorregionalgroundwaterow.Globalmodelsalsoassumehomogenousconditions ofhydrologicandhydraulicpropertiesineachoftheirgrid cells,ratherthanvariableowpaths,andtheycompletely omitthepossibilityofpreferentialow.Thiswascriticizedin therecentscienticdiscourseabouttheneedforlarge-scale hyper-resolutionmodelsBevenandCloke,2012;Woodet al.,2011. Theassumptionofhomogeneityiscertainlyinappropriate forkarstregions.Chemicalweatheringofcarbonaterockand otherphysicalprocessesdeveloppreferentialpathwaysand strongsubsurfaceheterogeneityBakalowicz,2005.Flow andstorageareheterogeneousrangingfromveryslowdiffusiontorapidconcentratedowatthesurface,inthesoil,the unsaturatedzoneandtheaquiferKiraly,1998.Arangeof modellingstudieshavedevelopedandappliedkarstspecic modelsatindividualkarstsystemsatthecatchmentoraquifer scaleDoummaretal.,2012;Fleuryetal.,2007;Hartmann etal.,2013b;LeMoineetal.,2008butalackofaprioriinformationofaquiferpropertiesandobservationsofgroundwaterdynamicshaveprohibitedtheirapplicationonlarger scalesHartmannetal.,2014a. Comparedtothelimitedinformationaboutthedeeper subsurfacethereismuchbetterinformationaboutthesurfaceandshallowsubsurface,includingmapsofsoiltypes andpropertiesFAO/IIASA/ISRIC/ISSCAS/JRCv,2012, observationsofsoilmoistureInternationalSoilMoisture Network;Dorigoetal.,2011andoflatentheatuxes FLUXNET;Baldocchietal.,2001,aswellasriverdischargeGRDC,2004.Surfaceandshallowsubsurfaceinformationisusedfortheparameterizationandevaluationofthe surfaceroutinesofpresentlarge-scalemodels.But,although thesedataalsocoverEurope'skarstregions,ithasnotbeen usedforthedevelopmentoflarge-scalemodelstosimulate karsticsurfaceandshallowsubsurfaceowandstoragedynamics. Theobjectiveofthisstudyistodeveloptherstlargescalesimulationmodelforkarsticgroundwaterrechargeover EuropeandtheMediterranean.Despitemuchbroaderdefinitionsofgroundwaterrechargee.g.Lerneretal.,1990, wefocusonpotentialrecharge,thatis,verticalpercolation fromthesoilbelowthedepthaffectedbyevapotranspiration.Weuseanoveltypeofmodelstructurethatconsiders thesubgridheterogeneityofkarstpropertiesusingstatistical distributionfunctions.Toachievearealisticparameterization ofthemodelweidentifytypicalkarstlandscapesbycluster analysisandbyacombineduseofaprioriinformationabout soilstoragecapacitiesandobservationsofrecharge-related uxesandstoragedynamics.ApplyingaparameterconnementstrategybasedonMonteCarlosamplingweareableto providelarge-scalesimulationofannualrechargeincluding aquanticationoftheiruncertainty. Figure1.a Schematicdescriptionofthemodelforonegridcell includingthesoilyellowandepikarststoragesgreyandthesimulateduxes, b itsgriddeddiscretizationoverkarstregionsand c thesubsurfaceheterogeneitythatitsstructurerepresentsforeach gridcell. 2Dataandmethods Duetochemicalweatheringkarsticationkarstsystems haveastrongsubsurfaceheterogeneityofowandstorage processesBakalowicz,2005thathavetobeconsideredto producerealisticsimulationsHartmannetal.,2014a.In thisstudy,large-scalekarstrechargeisestimatedbyamodiedversionoftheVarKarstmodelHartmannetal.,2013a, 2014b.Themodelhasshowntobeapplicableatvarious scalesandclimatesoverEuropeHartmannetal.,2013b.To simulatekarstrechargewediscardthegroundwaterroutines butweuseexactlythesamesurfaceandshallowsubsurface routines.Theresultingrechargesimulationmodel,VarKarstR,isdescribedintheproceedingsubsection.Thenewfeature ofthelarge-scaleapplicationoftheVarKarst-Rmodelisthe estimationofitsparameters.Whilepreviousapplicationsof themodelcouldrelyoncalibrationbyobservationsatthe karstsystemoutletthesimulationoflarge-scalerechargerequiresadifferentapproach.Wedevelopedanewparameter estimationprocedurethatseparatesthestudyareaintofour karstlandscapesbyclusteranalysisandestimatesmodelparametersandtheiruncertaintybyastep-wiseparameterconnementprocessexplainedinSect.2.3. 2.1Themodel ThestructureoftheVarKarst-RmodelFig.1aisbasedon theconceptualunderstandingofthesurfaceandshallowsubsurfaceprocessesofkarstregionsFig.1c.Theirmostcharacteristicfeatureistheexistenceoftheepikarstthatevolves closetothesurfacebecauseofstrongercarbonaterockdissolution.Itcanbeseenasatemporalstorageanddistribution systemforkarstrechargeAquilinaetal.,2006;Williams, 1983a.Dependingontheratesofinltration,variabilityof soilthicknessesandhydraulicconductivities,itcanproduce slowanddiffuseverticalpercolationintothecarbonaterock oritcanconcentrateinltrationlaterallytowardsdissolutionwidenedssuresorconduitsHartmannetal.,2012.ApGeosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1731 pliedona0.25 0.25 gridFig.1b,VarKarst-Rsimulates potentialrecharge,whichisthewatercolumnverticallypercolatedfromthesoilandepikarst.Hence,thepreviousversionofthemodelisreducedtoincludeonlythesoilandthe epikarstsimulationroutinesbutstillusingthesamestatisticaldistributionfunctionsthatallowforvariablesoildepths, variableepikarstdepthsandvariablesubsurfacedynamics Fig.1.Thisleadstoaparametricallyefcientprocessrepresentation.Comparisonswithindependentlyderivedelddata showedthatthesedistributionfunctionsareagoodapproximationofthenaturalheterogeneityHartmannetal.,2014b. Heterogeneityofsoildepthsisrepresentedbyameansoil storagecapacity V soil [mm]andavariabilityconstant a [–]. Thesoilstoragecapacity V S ;i [mm]foreverycompartment i isdenedby V S ;i D V max ; S i N a ; where V max,S [mm]isthemaximumsoilstoragecapacityand N isthetotalnumberofmodelcompartments.Fortheapplicationofaprioriinformationonmeansoilstoragecapacities Sect.2.3 V max,S hastobederivedfromthemeansoilstoragecapacity V soil byHartmannetal.,2013b V max ; S D V soil 2 a a C 1 : PrecedingworkHartmannetal.,2013ashowedthatthe samedistributioncoefcient a canbeusedtoderivethe epikarststoragedistribution V E ;i fromthemeanepikarststoragecapacity V epi [mm]viathemaximumepikarststorage V max,E ,likewiseto V max,S inEq.2: V E ;i D V max ;E i N a : Ateachtimestep t ,theactualevapotranspirationfrom eachsoilcompartment E act ;i isderivedbyreducingpotentialevaporationaccordingthesoilmoisturedecit: E act ;i . t / D E pot . t / min V Soil ;i . t / C P eff . t / C Q Surface ;i . t / ;V S ;i V S ;i ; where E pot [mm]isthepotentialevapotranspirationderivedbythePriestley–TaylorequationPriestleyandTaylor,1972, P eff [mm]isthesumofliquidprecipitationand snowmelt, Q surface ;i [mm]isthesurfaceinowarrivingfrom compartment i )]TJ/F64 9.9626 Tf 9.431 0 Td [(1seeEq.9,and V soil ;i [mm]thewaterstoredinthesoilattimestep t .Snowfallandsnowmelt arederivedfromdailysnowwaterequivalentavailablefrom GLDAS-2GlobalLandDataAssimilationSystem;Table1. Duringdayswithsnowcoverweset E act .t/ D 0.Flowfrom thesoiltotheepikarst R epi ;i [mm]takesplacewhenthesoil storagesarefullysaturated.Itiscalculatedby R epi ;i . t / D max V Soil ;i . t / C P eff . t / C Q Surface ;i . t / )]TJ/F23 9.9626 Tf 7.771 0 Td [(E act ;i . t / )]TJ/F23 9.9626 Tf 9.432 0 Td [(V S ;i ; 0 : ThetemporalwaterstorageoftheepikarstisdrainedfollowinganassumptionoflinearityRimmerandHartmann, 2012,whichiscontrolledbytheepikarststoragecoefcients K E ;i [d]: Q epi ;i . t / D min V epi ;i . t / C R epi ;i . t / ;V E ;i K E ;i 1t K E ;i D K epi N )]TJ/F23 9.9626 Tf 9.431 0 Td [(i C 1 N a ; where V epi ;i [mm]isthewaterstoredincompartment i of theepikarstattimestep t .Again,thesamedistributioncoefcient a isappliedtoderive K E ;i fromthemeanepikarst storagecoefcient K epi .Thelatterisobtainedfromthemean epikarststoragecoefcient K epi using N K mean,E D N R 0 K max ;E x N a d x; m K max ; E D K epi . a C 1 / : Wheninltrationexceedsthesoilandepikarststorage capacities,surfaceowtothenextmodelcompartment Q Surf ;i C 1 [mm]initiates: Q Surf ;i C 1 . t / D max V Epi ;i . t / C R Epi ;i . t / )]TJ/F23 9.9626 Tf 9.431 0 Td [(V E ;i ; 0 : Tosummarize,themodeliscompletelydenedbythefour parameters a , K epi , V soil ,and V epi Table2. 2.2Dataavailability ForcingfortheVarKarst-Rmodelisderivedthrough GLDAS-2,whichassimilatessatellite-andground-basedobservationaldataproductstoobtainoptimaleldsoflandsurfacestatesanduxesRodelletal.,2004;RuiandBeaudoing,2013.Whileprecipitation,temperatureandnetradiationaremainlymergedfromsatelliteandgaugeobservations,snowwaterequivalentisderivedusingdataassimilationaswellasthesnowwaterequivalentsimulationsof theNOAHlandsurfacemodelv3.3Ek,2003drivenby GLDAS-2forcing.Europe'sandtheMediterranean'scarbonaterockareasarederivedfromaglobalmapvectordata ofcarbonaterockWilliamsandFord,2006.Eachcellof the0.25 simulationgridintersectingacarbonaterockregionwasconsideredakarstregion.Themodelwascalibrated andevaluatedwithobservationsofactualevapotranspiration fromFLUXNETBaldocchietal.,2001andwithsoilwater contentdatafromtheInternationalSoilMoistureNetwork ISMN;Dorigoetal.,2011.Onlystationswithincarbonate www.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1732A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge Table1. Dataavailability,datapropertiesandsources. VariableSpatialresolutionTimeperiodFrequencySourceReference Precipitation0.25 2002dailyGLDAS-2Rodelletal.,RuiandBeaudoing Temperature0.25 2002dailyGLDAS-2 Netradiation0.25 2002dailyGLDAS-2 Snowwaterequivalent0.25 2002dailyNOAHv3.3/GLDAS-2Ek,Rodelletal. Carbonaterockareasvectordata––WilliamsandFord Elevation3 00 ––SRMTV2.1USGS Rockpermeabilityvectordata––Gleesonetal.a ActualevaporationindividuallocationsindividualperiodsdailyFLUXNETBaldocchietal. SoilmoistureIndividuallocationsindividualperiodsdailyISMNDorigoetal. Table2. ParameterdescriptionandinitialrangesforMonteCarlosamplingbasedonpreviouseldstudiesandlarge-scalemodelapplications. ParameterUnitDescriptionLowerUpperReferences limitlimit a [–]Variabilityconstant06Hartmannetal.b,2014b,2015 V soil [mm]Meansoilstoragecapacity01250Mirallesetal., FAO/IIASA/ISRIC/ISSCAS/JRCv, Ek V epi [mm]Meanepikarststoragecapacity200700Perrinetal.,Williams K epi [d]Meanepikarststoragecoefcient050Gleesonetal.b,Hartmannetal.b Figure2. CarbonaterockareasoverEuropeandtheMediterranean, andlocationoftheselectedFLUXNETandISMNstations. rockregionsandwith 12monthsofavailabledatawere usedFig.2.Monthswith < 25daysofobservationswere discarded.Inaddition,monthswith 50%mismatchintheir energyclosurewerediscardfromtheFLUXNETdataset similartoMirallesetal.,2011. 2.3Parameterestimation Alackofaprioriinformationandobservationsofdischarge andgroundwaterlevelsthatcanbeusedforcalibrationare theprimaryreasonswhykarstmodelshavenotbeenapplied onlargerscalesyetHartmannetal.,2014a.Theparameterassessmentstrategywepresentinthefollowingismeant toovercomethisproblembyusingacombinationofapriori informationandrecharge-relatedvariables.WedenetypicalkarstlandscapesoverEuropeandtheMediterraneanand applythiscombinedinformationtoalargeinitialsampleof possiblemodelparametersets.Inastepwiseprocesswethen discardallparametersetsthatproducesimulationsinconsistentwithouraprioriinformationandourrecharge-related observations. 2.3.1Denitionoftypicalkarstlandscapes Ourdenitionoftypicalkarstlandscapesisbasedonthe well-knownhydrologiclandscapeconceptWinter,2001, whichdescribeshydrologicallandscapesbasedontheirgeology,reliefandclimate.Constrainingourselvestokarstregionsthatmainlydeveloponcarbonaterock,weassumethat differencesamongthekarstlandscapesareduetodifferences inreliefandclimate,andtheconsequentprocessesoflandscapeevolutionincludingtheweatheringofcarbonaterock karstication.ThecarbonaterockregionsinEuropeand theMediterraneanaredividedintotypicallandscapesusing simpledescriptorsofreliefrangeofaltitudeRAandclimatearidityindexAIandmeanannualnumberofdayswith snowcoverDSwithineachof0.25 gridcellsandastandard clusteranalysisscheme k meansmethod.Wetestthequalityofclusteringfor2clustersbycalculatingthesumsof squaredinternaldistancestotheclustermeans.Theso-called “elbowmethod”identiesthepointwhereaddingadditional clustersonlyleadstoamarginalreductionintheinternal distancemetric,i.e.thepercentageofvarianceexplainedby addingmoreclusterswouldnotincreasesignicantlySeber, 2009. Geosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1733 2.3.2Modelparametersforeachkarstlandscape Weinitiallysample25000possiblemodelparametersets fromindependentuniformdistributionsusingparameter rangesderivedfrompreviouscatchment-scaleapplications oftheVarKarst-RmodeloverEuropeandtheMediterranean Table2.Weuseaprioriinformationandrecharge-related observationstoassessparameterperformanceforeachkarst landscape.Aprioriinformationconsistsofspatiallydistributedinformationaboutmeansoilstoragecapacitiesas providedbyseveralprecedingmappingandmodellingstudiesEk,2003;FAO/IIASA/ISRIC/ISSCAS/JRCv,2012;Mirallesetal.,2011.Recharge-relatedvariablesaresoil moistureobservationsandobservationsofactualevaporationatvariouslocationsoverthemodellingdomainTable1,Fig.2.Soilmoistureisrelatedtorechargebecauseit indicatesthestartanddurationofsaturationofthesoilduringwhichdiffuseandpreferentialrechargecantakeplace. Actualevaporationisrelatedtorechargebecauseusuallyno surfacerunoffoccursinkarstregionsduetothehighinltrationcapacitiesJeanninandGrasso,1997.Thedifference ofmonthlyprecipitationandactualevaporationisthereforea validproxyforgroundwaterrechargeatamonthlytimescale orabove.Thenewparameterconnementstrategyisapplied toeachofthekarstlandscapesinthreesteps: 1.Biasrule:retainonlytheparametersetsthatproducea biasbetweenobservedandsimulatedactualevaporation lowerthan75%atallFLUXNETlocationswithinthe chosenkarstlandscape: min i . bias i / D min i sim ;i )]TJ/F23 9.9626 Tf 9.431 0 Td [( obs ;i obs ;i W < 75% ; where m sim ;i and m obs ;i arethesumofsimulatedand observedactualevapotranspirationatlocation i ,respectively.Thevalue75%wasfoundbytrial-and-error, whichreducedtheinitialsampletoareasonablenumber.Thebiasrulewasnotappliedonthesoilmoisture sinceporositiesofthesoilmatrixwerenotavailable, prohibitingacomparisonofsimulatedandobservedsoil watercontents. 2.Correlationrule:retainonlytheparametersetsthatproduceapositivecoefcientofPearsoncorrelationbetweenobservationsandsimulationsofbothactualevaporationandsoilmoisture,atalllocations: min i corr . AET sim ;i ; AET obs ;i ^ min j corr . sim ;j ; obs ;j W > 0 ; whereAET sim ;j andAET obs ;j ,and sim ;j and obs ;j ,are themonthlymeansofsimulatedandobservedactual evapotranspiration,andsoilwatercontentatlocations i=j ,respectively. 3.Applicationofaprioriinformation:retainonlyparametersetsinwhich V soil fallswithinthefeasibleranges thatcanbederivedfromaprioriinformationaboutthe maximumsoilstoragecapacityindifferentkarstlandscapesEk,2003;FAO/IIASA/ISRIC/ISSCAS/JRCv, 2012;Mirallesetal.,2011.Weaddlessthantheusuala prioriinformationatthelaststeptoevaluateiftheposteriordistributionsof V soil alreadyadapttotherangesdenedinthisconnementstep.Iftheydonot,wewould concludethattherecharge-relatedinformationapplied inconnementsteps1and2isbiased.Iftheydo,we haveindicationthatthedataappliedinallthreestepsis complementary. Eachstepreducestheinitialparametersampledifferently foreachofthekarstlandscapes.Theposteriorparameter distributionswithintheconnedsamplesshouldbedifferentamongthekarstlandscapesifthekarstlandscapesare properlydened.Theratherweakthresholdsinstep1and 2werechosentotakeintoaccounttheuncertaintiesresultingfromthedifferencesinscalesofobservationspointand simulationsgridcell,andfromtheindirectobservationof rechargeactualevaporationandsoilmoistureasrechargerelatedvariables. 2.4RechargesimulationsoverEuropeandthe Mediterranean RechargeissimulatedoverthecarbonateregionsofEurope andtheMediterraneanfrom2002/03to2011/12usingthe connedparametersamplesforeachoftheidentiedkarst landscapesandtheavailableforcingsTable1.Themean andstandarddeviationofsimulatedrechargeforeachgrid cellandtimesteparecalculatedbyuniformdiscretesamplingofarepresentativesubsetof250parametersetsfrom eachoftheconnedparameterssetswhichweregardedto belargeenoughtoprovideareliablemeasureofspread. 2.5Modelevaluation Toassesstherealismofsimulatedgroundwaterrechargewe comparesimulatedwithobservedmeanannualrechargevolumesderivedindependentlyfromkarststudiesoverEurope andtheMediterraneanTable3.Inaddition,wecompareour resultstothesimulatedmeanannualrechargevolumesoftwo well-establishedglobalsimulationmodels:PCR-GLOBWB Wadaetal.,2010,2014andWaterGAPDllandFiedler, 2008;Dlletal.,2003. Wefurthermoreapplyaglobalsensitivityanalysisstrategy,calledregionalsensitivityanalysisSpearandHornberger,1980,toevaluatetheimportanceofthefourmodel parametersatdifferentsimulationtimescalesrangingfrom1 monthupto10years.Thisanalysisshowswhichsimulatedprocessandcharacteristicsaredominantatagiven timescaleandwhichparameterswillneedmorecareful calibrationwhenthemodelisusedinfuturestudies.Weuse www.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1734A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge Table3. IndependentobservationsofmeanannualrechargefromeldandmodellingstudiesoverEuropeandtheMediterranean. LocationLatitudeLongitudeMeanannualMethodAuthor recharge country,province[ ][ ][mm] AustriaSiebenquellenspring,Schneeaple47.6915.6694observedwaterbalanceMaloszewskietal. CroatiaJadrospring,Dugopolje43.5816.6795simulatedwaterbalanceJukicandDenic-Jukic CroatiaStIvan,Mirna45.2213.6386observedwaterbalanceBonacci FranceBonnieure,LaRouchefoucauld-Touvre45.80.44250simulatedwaterbalanceLeMoineetal. FranceDurzonspring,LaCavalerie44.013.16378observedwaterbalanceTritzetal. FranceFontaine-de-Vaucluse43.925.13568observedwaterbalanceFleuryetal. FranceStHippolyte-du-Fort,Vidourle43.933.85287observedwaterbalanceVauteetal. GermanyBohmingspring,Rieshofen48.9311.3130observedwaterbalanceEinsiedl GermanyGallusquellespring,SwabianAlps48.219.15351observedwaterbalanceDoummaretal. GermanyHohenfels49.211.8200observedwaterbalanceQuinnetal. GreeceArvi,Crete35.1324.55241observedwaterbalanceKoutroulisetal. GreeceAitoloakarnania38.6021.15484empiricestimationmethodZaganaetal. ItalyCerellaspring,Latina41.8812.9416empiricestimationmethodAlloccaetal. ItalyForcellaspring,Sapri41.0514.55559empiricestimationmethodAlloccaetal. ItalyGranSasso,Teramo42.2713.34700observedwaterbalanceBarbierietal. ItalySanit40.7815.13974observedwaterbalanceVitaetal. ItalyTaburnospring39.915.81693empiricestimationmethodAlloccaetal. LebanonAnjar-Chamsine33.7335.93278observedwaterbalanceBakalowiczetal. LebanonZarka34.0836.30205observedwaterbalanceBakalowiczetal. LebanonAfka34.0535.95842observedwaterbalanceBakalowiczetal. PalestineMountainAquifer 32.00 35.30144simulatedwaterbalanceHughesetal. PortugalAlgarve,minimumvalue 37.10 )]TJ/F64 8.9664 Tf 15.482 0 Td [(7.90130notmentioneddeVriesandSimmers PortugalAlgarve,maximumvalue 37.10 )]TJ/F64 8.9664 Tf 15.482 0 Td [(7.90300notmentioneddeVriesandSimmers SaudiArabiaeasternArabianPeninsula 26.50 46.5044naturaltracersHoetzl SpainCazorla,SierradeCazorla37.9 )]TJ/F64 8.9664 Tf 6.994 0 Td [(3.03244empiricestimationmethodAndreoetal. SpainLaVillaspring,ElTorcel36.93 )]TJ/F64 8.9664 Tf 6.994 0 Td [(4.52463observedwaterbalancePadillaetal. SpainSierradelasCabras,ArcosdelaFrontera36.65 )]TJ/F64 8.9664 Tf 6.994 0 Td [(5.72318empiricestimationmethodAndreoetal. SwitzerlandRappenuhSpring47.877.67650simulatedwaterbalanceButscherandHuggenberger TurkeyAydincik,Mersin36.9733.22552observedwaterbalanceHatipoglu-BagciandSazan TurkeyHarmankoy,Beyyayla40.1530.6532observedwaterbalanceAydinetal. UKMarlboroughandBerkshireDownsand South-WestChilterns,minimumvalue 51.53 )]TJ/F64 8.9664 Tf 6.994 0 Td [(1.15146simulatedwaterbalanceJacksonetal. UKMarlboroughandBerkshireDownsand South-WestChilterns,maximumvalue 51.53 )]TJ/F64 8.9664 Tf 6.994 0 Td [(1.15365simulatedwaterbalanceJacksonetal. UKDorset50.75 )]TJ/F64 8.9664 Tf 6.994 0 Td [(2.45700observedwaterbalanceFoster UKNorfolk52.600.88260observedwaterbalanceFoster UKGretaspring,Durham54.52 )]TJ/F64 8.9664 Tf 6.994 0 Td [(1.87690observedwaterbalanceArnell UKR.Teme,TenburyWells52.3 )]TJ/F64 8.9664 Tf 6.994 0 Td [(2.58355observedwaterbalanceArnell UKLambourn51.5 )]TJ/F64 8.9664 Tf 6.994 0 Td [(1.53234observedwaterbalanceArnell UKHampshire51.1 )]TJ/F64 8.9664 Tf 6.994 0 Td [(1.26348observedwaterbalanceWellings thesamesampleof25000parametersetsthatwascreated fortheparameterestimationstrategySect.2.3.2andassessthesensitivityoffourmodeloutputsrepresentativeof differenttimescales:coefcientofvariationCVofsimulatedmonthlyrechargevolumesmonthly,CVofsimulated 3-monthrechargevolumesseasonal,CVofannualrecharge volumesannual,andtotalrechargeovertheentire10-year simulationperioddecadal.Wedonotconsidertemporal resolutionsoflessthanamonthgiventheassumptionthatthe differenceofprecipitationandactualevapotranspirationcan beaproxyforgroundwaterrechargeandduetouncertainties relatedtodifferencesinsimulationgridcellandobservationpoint. Foreachoftheidentiedkarstlandscapeswechoosethe 10locationsthatareclosesttotheirclustermeansEuclidean distancestoreliefandclimatedescriptors;Sect.2.3.1asrepresentativelocations.Intheregionalsensitivityanalysisapproach,wesplittheparametersetsintotwogroups,those thatproducesimulationsabovethesimulatedmedianofone ofthefourmodeloutputsandthosethatproducesimulationsbelow.Wethencalculatethemaximumdistance D.x/ betweenmarginalcumulativedistributionfunctionsCDFs producedbythesetwodistributionsforeachoftheparameters–alargedistance D.x/ suggeststhattheparameteris importantforsimulatingthisparticularoutputFig.3. 3Results 3.1Parameterassessment 3.1.1Denitionoftypicalkarstlandscapes Clusteranalysisresultedinfourclusters,whicharegenerally spatiallycontiguousFig.4andhavequantitativelydistinct Geosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1735 Figure3. Schematicelaborationoftheregionalsensitivityanalysis procedure. Table4. ClustermeansofthefouridentiedkarstlandscapesAI: aridityindex,DS:meanannualnumberofdayswithsnowcover, RA:rangeofaltitudes. DescriptorUnitNumberofcluster/karstlandscape 1.HUM2.MTN3.MED4.DES AI[–]0.800.983.1820.00 DS[a )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 ]8576161 RA[m]2281785691232 clustermeansTable4.WecanattributeparticularcharacteristicstoeachclusterusingthemeanvaluesoftheclusteringdescriptorsTable4:humidhillsandplainsHUM arecharacterizedbyanaridityindex < 1,asignicantnumberofdayswithsnowcoverandlowelevationdifferences. HighrangemountainsMTNhaveanaridityindexof 1,theyalsohaveasignicantnumberofdayswithsnow coverandtheyshowverylargetopographicelevationdifferences.MediterraneanmediumrangemountainsMED showhigharidityindex,onlyfewdayswithsnowcoverand highelevationdifferences.DeserthillsandplainsDES aredescribedbysimilaraltituderangesasthehumidhills andplainsbuttheyhaveahigharidityindicesandalmostno dayswithsnowcover.Thekarstlandscapesorderfromnorth HUMtosouthDESbasedonincreasingtemperaturesand decreasingprecipitationamounts.WhileHUMandDESappeartobeseparatedclearly,MTNandMEDmixinsome regions,forinstanceGreeceandTurkeywheremountainous regionsareincloseproximitytothecoast. 3.1.2Modelparameterestimatesforeachkarst landscape Thethreestepsofthenewparameterconnementstrategyresultedinasignicantreductionoftheinitialsampleof25000 parametersetsFig.5.Eachstephasadifferentimpacton thereductionamongtheidentiedlandscapes.Forthehumidkarstlandscapes,thecorrelationruleappearstohavethe strongestimpactwhileforthemountainandMediterranean landscapesthebiasruleresultsinthestrongestreduction.For thedesertlandscapeonlystep3,i.e.applicationofaprioriinformation,reducestheinitialsamplebecausenodata wereavailabletoapplysteps1and2.Consideringtheparameterrangesforeachlandscapeaftertheapplicationofthe connementstrategyTable5,weonlyachievedaconnementofthedistributionparameter a ,thesoilstoragecapacity V soil ,andslightconnementoftheepikarststoragecoefcient K epi . Theimpactofthethreeconnementstepsbecomes moreobviouswhenconsideringtheirposteriordistributions Fig.6.Thedistributionsofparameters a , K epi and V soil evolvesignicantlyawayfromtheirinitialuniformdistributionsalongtheconnementsteps.Ingeneral,changesofthe posteriordistributionsofeachlandscape'sparametersamplesareinaccordancewiththereductionsintheirnumber Fig.5,thoughchangesarepronounceddifferentlyamong theparameters.While a and V soil changestronglyforHUM, MTNandMED, V epi maintainsauniformdistributionacross allsteps. K epi alsoexhibitsstrongchangesforHUMbutthey arelesspronouncedforMTNandMED.TheposteriordistributionsoftheDESlandscapedonotchangeexceptforstep 3duetothelackofinformationtoapplyconnementsteps1 and2.Step3resultsinatailoringofthedistributionof V soil foralllandscapes.ForHUM,MTNandMEDitcanbeseen thatconnementsteps1and2alreadypushedtheparameterdistributionstowardstheirnalshape,meaningthatthe changesinparameterdistributionsinducedbythecomparisonwithobservationsareconsistentwiththeaprioriinformationaboutthephysicalcharacteristicsofthekarst. 3.2RechargesimulationsoverEuropeandthe Mediterranean Theparameterconnementstrategyallowsustoapply VarKarst-RoverallofEuropeandtheMediterraneanand toobtainrechargesimulationsforthehydrologicalyears 2002/03/12.Thankstothe250parametersetsthat wesampledfromtheposteriorparameterdistributionswe canincludeanestimateofuncertaintyforeachgridcell Fig.7.Meanannualrechargerangesfromalmost0to > 1000mma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 withthehighestvolumesfoundinnorthernUK,theAlpsandformerYugoslavia.ThelowestvaluesarefoundinthedesertregionsofNorthernAfrica.The vastmajorityofrechargeratesrangefrom20to50%ofprecipitation.Consideringthesimulationsindividuallyforeach karstlandscaperevealsthatthemountainlandscapesproducethelargestrechargevolumesfollowedbythehumid andMediterraneanlandscapesFig.8a.Thedesertlandscapesproducethelowestrechargevolumes.However,the rechargeratesrevealthatonaveragetheMediterraneanlandscapesshowthelargestrechargerates,followedbythehighly variablemountainsFig.8c.Humidanddesertlandscapes exhibitlowerrechargerates.Uncertainties,expressedbythe www.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1736A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge Figure4. Mapwithclustersandtypicalkarstlandscapesthatwereattributedtothem. Figure5. Evolutionoftheinitialsampleof25000parametersets eachincludingthefourmodelparameterssampledfromwithin theirinitialrangesalongthedifferentconnementstepsforthe fourkarstlandscapes. standarddeviationofthe250simulationsforeachgridcell, areratherlow,seldomexceeding35mma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 Fig.8b.However,expressedascoefcientsofvariation,mostofthem rangefrom5to25%forthehumid,mountainandMediterraneanlandscapesbutforthedesertlandscapetheycanreach upto50%ofthemeanannualrechargeFig.8d. 3.3Modelevaluation Wecomparethesimulatedrechargevolumesofourmodel withrechargevolumesassessedfromindependentandpublishedkarststudiesoverEuropeandtheMediterranean Fig.9a.Eventhoughthereisaconsiderablespreadacross thesimulations,theirbulkplotswellaroundthe1 V 1line achievinganaveragedeviationofonly )]TJ/F64 9.9626 Tf 7.771 0 Td [(58mma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 Table6.Consideringtheindividualkarstlandscapes,there isanover-estimationofrechargeforthehumidlandscapes andanunder-estimationforthemountainlandscapes.The bestresultsareachievedfortheMediterraneanlandscapes withonlyslightunder-estimationFig.9a.WhenwecomparethesameobservationstothesimulatedrechargevolumesofthePCR-GLOBWBFig.9bandWaterGAPmodFigure6. Evolutionofposteriorprobabilitiesofthefourmodelparametersforthefourkarstlandscapesalongthestepsoftheparameterconnementstrategy. elsFig.9cwendastrongtendencyofunder-estimation thatisstrongestforthemountainandMediterraneanlandscapesbutstillsignicantforthehumidlandscapesTable6. Forthehumidlandscapesabsolutedeviationsaresimilarfor PCR-GLOBWBandVarKarst-R. Inadditiontocomparingsimulatedandobservedannual averages,sensitivityanalysisonthemodeloutputgivesus insightintotherealismofthemodelandtheimportanceof individualmodelparametersatdifferenttimescalesFig.10. Ourresultsshowthatparameters a and V soil havetheoverall strongestinuenceonthesimulatedrechargefromamonthly toa10-yeartimescale,buttheirinuencedecreasestoward shortertimescales.Simultaneously,theepikarstparameter K epi gainsmoreimportance.ThisbehaviourismostpronouncedfortheMediterraneananddesertlandscapes.The Geosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1737 Figure7.a Observedprecipitationand d potentialevaporationversusthesimulated b meanannualrechargeand e meanannual rechargeratesderivedfromthemeanofall250parametersets,and c thestandarddeviationand f coefcientsofvariationofthesimulationsduetothevariabilityamongthe250parametersets. Table5. Minimaandmaximaoftheconnedparametersamplesforeachoftheidentiedlandscapes. ParameterUnitHUMMTNMEDDES minmaxminmaxminmaxminmax a [–]1.13.30.32.90.86.00.16.0 V soil *[mm]900.11248.9500.4899.951.7498.40.249.1 V epi [mm]204.3694.8201.6699.4200.1696.7202.3695.7 K epi [d]0.035.87.349.90.048.410.449.9 *inparentheses:aprioriinformationusedforstep3oftheparameterconnementstrategy. Table6. MeandeviationsoftheVarKarst-R,thePCR-GLOBWB modelandtheWaterGAPmodelfromallobservationsandtheindividualregions. Region Meandeviation[mma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 ] VarKarst-RPCR-GLOBWBWaterGAP All )]TJ/F64 8.9664 Tf 6.994 0 Td [(58.3 )]TJ/F64 8.9664 Tf 6.994 0 Td [(230.4 )]TJ/F64 8.9664 Tf 6.994 0 Td [(264.2 HUM65.5 )]TJ/F64 8.9664 Tf 6.994 0 Td [(90.2 )]TJ/F64 8.9664 Tf 6.994 0 Td [(151.6 MTN )]TJ/F64 8.9664 Tf 6.994 0 Td [(202.8 )]TJ/F64 8.9664 Tf 6.994 0 Td [(427.5 )]TJ/F64 8.9664 Tf 6.994 0 Td [(446.4 MED )]TJ/F64 8.9664 Tf 6.994 0 Td [(4.3 )]TJ/F64 8.9664 Tf 6.994 0 Td [(217.3 )]TJ/F64 8.9664 Tf 6.994 0 Td [(211.4 sameistruefor V epi ,butitsoverallimportanceremainsmuch lower,whichwasalsofoundintheparameterconnement strategyFig.6. 4Discussion 4.1Reliabilityofparameterestimation 4.1.1Identicationofkarstlandscapes Theidenticationofdifferentkarstlandscapesisacrucial stepwithinournewparameterestimationstrategy.Thefour karstlandscapesweidentieddependmostlyonthechoice ofclimaticandtopographicdescriptorsTable4andtheselectednumberofclusters.Eventhoughneglectingseveral factorsasdepositionalenvironments,fracturingbytectonic processesorregionalvariationsinrainacidity,ourchoiceof descriptorsiswelljustiedfromourunderstandingofdominanthydrologicprocesscontrolsasformalizedinthehydrologiclandscapeconceptWinter,2001andappliedsimilarlyatmanyotherstudiesLeibowitzetal.,2014;Sawiczetal.,2011;Wigingtonetal.,2013.Theappropriate www.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1738A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge Figure8.a Simulatedmeanannualrecharge,amongthefourkarst landscapes, b theirstandarddeviations, c rechargerates,and d coefcientsofvariationobtainedbythenalsampleofparameters. choiceofclustersforthe k meansmethodislessunambiguousKetchenandShook,1996.Thechangeinnumberof clusterswhenthesumofsquareddistancestoourcluster centresonlyreducesmarginallywasnotclearlydenable Fig.A1.However,choosingonlythreeclustersinsteadof fourwouldhaveresultedinunrealisticspatialdistributionof clusters.TheattributionofnorthAfricanregionswithnorthernEuropetothesameclusteroccurredbecauseoftheirsimilarityofaltituderangesTable4.Ontheotherhand,aselectionofveclusterswouldhaveresultedinaclusterwith propertiesjustbetweentheMTNandtheMEDclustersand, becauseofamuchstrongerscattering,weakerspatialdistinctionbetweenthem.Withfourclusters,ourkarstlandscapes aresimilartotheKppen–GeigerclimateregionsKotteket al.,2006,inparticulartotheoceanicclimateHUM,the hotandwarmsummerMediterraneanclimateMED,and thehotdesertclimatesDES.However,weseedeviations whencomparingthepolarandAlpineclimateregionsofthe Kppen–Geigerwithourhighrangemountainkarstlandscape,sinceourlandscapesarealsodenedbytheirelevation ranges. Thebordersofthesehydrologiclandscapesarealsouncertain.Naturalsystemsusuallydonothavestraightborders thatfallonagrid,asassumedbythisanalysis.Typicaltransitionsbetweenlandscapetypesarecontinuousandhence transitionsfromaparametersetrepresentingonelandscape toanotherparametersetofanotherclustershouldbegraded, aswell.Thiswillbediscussedinthefollowingsubsection. 4.1.2Connementofparameters Howthethreestepsoftheparameterconnementstrategy reducetheinitialsampleshowswhichtypeofdataprovides themostrelevantinformationforeachofthekarstlandscapes.Whilethetimingofactualevapotranspirationand soilsaturationthatisexpressedbythecorrelationruleappearstobemostrelevantforthehumidlandscapes,thebias rule,whichrepresentsthevolumesofmonthlyevapotranspiration,ismorerelevantforthemountainandMediterranean landscapes.Swappingtheorderofthecorrelationruleand thebiasrulewouldprovidethesameresultsforHUMand MTN.ButforMEDthealternativeorderincreasestheimportanceoftimingexpressedbythecorrelationrule,indicating thesimilarimportanceofbothconnementsteps. Thethresholdswesetinconnementsteps1and2arenot verystrict,andtherangesofsoilstoragecapacityweusedas aprioriinformationinstep3arequitelarge.Thiscompensatesforthefactthatonlyrecharge-relatedvariablesare availableratherthandirectrechargeobservations,these variablesarenotavailableatthesimulationscale.25 grid butatapointscale,andthetransitionbetweenthelandscapesismorecontinuousthandiscrete.Despitetheserather weakconstraints,theinitialparametersampleof25000reducestoquitelownumbersbetween679HUMand2731 MED.Allposteriorparametersoverlapexceptforthesoil storagecapacitiesthataretailoredbytheaprioriinformationconnementstep3.Hence,asmallnumberofparametersetsforonelandscapeisalsoacceptableforsomeofthe otherlandscapes,therebytakingintoaccountthecontinuous transitionbetweenthem. Allmodelparameters,exceptfor V epi ,showdifferent shapesintheircumulativedistributionfunctionsacrossthe karstlandscapes.Thedesertlandscapeparametersonlydifferfromtheinitialsampleforthe V soil parameterduetothe lackofinformationtoapplyconnementsteps1and2.The distributionparameter a isfoundatthelowervaluesofits feasiblerangeforthehumidandmountainlandscapes,indicatingasignicantcontributionofpreferentialrecharge. SincealtituderangesareratherlowforHUMthismaybeattributedtoasignicantepikarstdevelopmentPerrinetal., 2003;Williams,1983b.ForMTN,amixtureofepikarstdevelopmentandtopographydriveninterowatthemountain hillslopesandvalleyscanbeexpectedtocontrolthedynamicsofkarsticrechargeScanlonetal.,2002;Tagueand Grant,2009.AttheMediterraneanlandscapesthe a parameteradaptstorangesthatareratherfoundatthehighervalues ofitsinitialrange,indicatingthatthereisastrongerdifferentiationbetweendiffuseandconcentratedrecharge.Thismay beduetothegenerallythinnersoilsTable5thatlimitthe availabilityofCO 2 forkarstevolutionFordandWilliams, 2007.Instead,localsurfacerunoffchannelsthewatertothe nextenlargedssureorcrackinordertoreachthesubsurface asconcentratedrechargeLangeetal.,2003.Theepikarst storagecoefcient K epi forHUMandMEDisatlowervaluesoftheinitialrange,indicatingrealisticmeanresidence timesofdaystoweeksAquilinaetal.,2006;Hartmannet al.,2013a.TheMTNlandscapesshowlarger K epi valuesindicatingslowerepikarstdynamicsmostprobablyduetothe reasonsmentionedabove.Theapplicationofaprioriinformationinconnementstep3automaticallytailorsthevalues Geosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1739 Figure9. ObservationsofmeanannualrechargefromindependentstudiesTable3versusthesimulatedmeanannualrechargebythe VarKarst-RandPCR-GLOBWBmodelsnodatafortheDESregionavailable. Figure10. Sensitivityofsimulatedrechargetothemodelparametersatdifferenttimescalesandinthedifferentkarstlandscapes.SensitivityismeasuredbythemaximumdistanceDbetweenthedistributionofparametersetsthatproduce“low”rechargei.e.below themedianandthedistributionproducing“high”rechargeabove themedian.Parametersetsareinitiallysampledfromtherangesin Table2. of V soil torangesthatweassumetoberealistic.Thefactthat connementsteps1and2alreadypushtheshapeoftheir posteriorstowardstheapriorirangescorroboratesthatassumption. Thelittlechangesthatoccurtotheinitialdistributionsof theDESparametersetselaboratetheexibilityofourparameterassessmentstrategy.Theposteriordistributionevolves onlywhereinformationisavailableforthislandscapeon V soil / .Thisisalsoevidentinthebehaviourofparameter V epi .Theavailableinformationisjustnotpreciseenoughto achieveidenticationbeyonditsaprioriranges.Forparameter a inHUM,MTNandMED,alotofinformationisderived fromtheavailabledataanditsposteriorsdifferstronglyfrom itsinitialdistribution,whilethereislessinformationtodetermine K epi .Thisexplicithandlingofuncertaintiesintheparameteridenticationprocessallowsustoproviderecharge simulationsoverEurope'skarstregionswithuncertaintyestimatesthatrepresentcondenceforeachoftheidentied karstlandscapes. 4.2SimulationofkarstrechargeoverEuropeandthe Mediterranean 4.2.1Realismofspatialpatterns Simulatedmeanannualrechargeamountsfortheperiod 2002/03/12showawiderangeofvalues,from0to > 1000mma )]TJ/F64 7.5716 Tf 5.906 0 Td [(1 Fig.7.Totalwateravailabilitymeanannualprecipitationappearstobethemaindriverforitsspatialpatterninmanyregions,forinstanceintheformerYugoslaviaornorthernUK.Thisisconsistentwithndingsof otherstudiesHartmannetal.,2014b;Samuelsetal.,2010. Whenwenormalizetherechargeratesbytheobservedprecipitationamountswendthatwateravailabilityisnotthe onlycontrolonmeanannualrechargevolumes.Astrong relationofevapotranspirationandkarstcharacteristicsand processeswasshowninmanystudiesandisalsofoundhere Heilmanetal.,2014;JukicandDenic-Jukic,2008.Potentialevaporationisgenerallyincreasingfromnorthtosouth andhasanimportantimpactonrechargeratesaswell,for instanceintheArabianPeninsulaandtheAlps. Mountainrangesareconsideredtobethewatertowersof theworldVivirolietal.,2007.HeretheMTNlandscapes alsoshowthelargestrechargevolumesduetothelargeprecipitationvolumestheyreceive,thoughwithaconsiderable spreadinourstudy.HUMandMEDlandscapesbehavesimilarlywithsignicantlylessrechargethanMTN.Notsurprisingly,thereisnotmuchrechargeinthedesertlandscapesat all.Butthedifferencesamongtheclustersshiftwhenconwww.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1740A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge sideringrechargerates.Duetotheirthinsoilsandtherefore lowsoilstorageforevaporationTable5,theDESkarst landscapestransferupto45%ofthelittleprecipitationthey receiveintorecharge.TheMEDlandscapesshowsimilarly highrechargerates.Thoughsincetheirsoilsaregenerally thickerthantheDESsoils,thetypicalseasonalandconvectiverainfallpatternsoftheMediterraneanclimateGoldreich,2003;Lionello,2012mighthaveanimportantimpact, too. Eventhoughthereisstillconsiderablespreadinourconnedparametersets,theuncertaintyinsimulatedmeanannualrechargevolumesisquitelow.Theuncertaintiesthat followthelimitedinformationcontainedintheobservations arerevealedmoreclearlywhenwerelatethestandarddeviationofsimulatedrechargetoitsmeanvolumeswiththecoefcientofvariation.TheuncertaintyfortheDESlandscapeis thelargestamongtheclustersbecauseaprioriinformationis onlyavailablefor V soil .TheuncertaintyreducesfortheMED andMTNlandscapes.ThelowuncertaintiesforthecoefcientofvariationofourrechargesimulationsfortheHUM landscapeindicatethattheavailabledatacontainedsignicantinformationforconningthemodelparameterranges. 4.2.2Relevanceofdifferentrechargeprocessesto simulationtimescales Themeanannualwaterbalanceofahydrologicalsystemis dominatedbytheseparationofprecipitationintoactualevapotranspirationanddischargeBudykoandMiller,1974;Sivapalanetal.,2011.Actualevapotranspirationiscontrolledby thesoilstoragecapacity V soil andthedistributioncoefcient a withintheVarKarst-Rmodel.Regionalsensitivityanalysis showsthatbothparametersaremostsensitivetothe10-year andannualtimescalesFig.10.Bothparametersloosesome impactathighertemporalresolutionsseasonalormonthly timescaleinfavouroftheparametersthatcontrolthedynamicsoftheepikarst.Thisbehaviourisconsistentwithevidencefromeldandothermodellingstudiesthatshowed thattheepikarstcanbeconsideredasatemporarystorage anddistributionsystemforkarsticrechargeHartmannetal., 2012;Williams,1983b–potentiallystoringwaterforseveraldaystoweeksAquilinaetal.,2006;Hartmannetal., 2013a.Parameter V epi doesnotshowmuchsensitivityacross alllandscapesassuggestedbytheposteriordistributionsof theconnementstrategy.Firstofall,thisndingindicates thatthedataweusedforourconnementstrategydonot biasthegeneralmodelbehaviour.Italsoshowsthatforthe epikarststorageandowdynamics, K epi ismuchmoreimportantwhensimulatingatmonthlyorseasonalresolutions. Furthermore,theresultsoftheregionalsensitivityanalysisshowwhichparametersaremostimportantatagiven timescale.Dependingonthepurpose,anewstudymaystart withtheinitialrangesofthemodelparametersoritmight continuewiththeconnedparameterrangesthatwefound here.Thelatterwouldresultinslightlydifferentsensitivities Fig.A2.Forbothcases,theepikarstparameterswillrequire moreattentionwhenapplyingtheVarKarst-Rmodelforsimulationsatseasonalormonthlytimescales.Whenworking atasmallerspatialscale,combinedanalysisofspringdischargeanditshydrochemistrymayprovidesuchadditional informationLeeandKrothe,2001;MudarraandAndreo, 2011.Whenworkingatatimescaleof > 1year,thevariabilityconstant a andthesoilstoragecapacity V soil require mostattentionifonestartsfromtheinitialranges.Thedistributionparameterismostimportantwhenusingtheconnedranges.Again,springdischargeanalysismayhelpin understandingthedegreeofkarsticationKiraly,2003and thedistributionofconcentratedanddiffuserechargemechanismsthatarecontrolledby a .Inaddition,moreprecisedigitalelevationmodelsorsoilmapsmayhelpinbetteridenticationof a and V soil .Alimitationoftheregionalsensitivity analysisapproachusedhereisthatparameterinteractionsare onlyincludedimplicitly,consideringparameterinteractions withmoreelaboratemethodsSaltellietal.,2008mayrevealevenmorecharacteristicsoftheVarKarst-Rmodelat differentsimulationtimescales.Butthisisbeyondthescope ofthispaper. 4.3Impactofkarsticsubsurfaceheterogeneity Eventhoughsomedeviationsoccuramongtheindividual karstlandscapes,thegeneralsimulationsoftheVarKarst-R modelfollowwelltheobservationsofmeanannualrecharge ratesoverEuropeandtheMediterraneanFig.9.Onthe otherhand,thewidelyusedlarge-scalesimulationmodels PCR-GLOBWBWadaetal.,2010,2014andWaterGAP DllandFiedler,2008;Dlletal.,2003generallyunderestimategroundwaterrechargeTable6.Thereasonfor thisistherepresentationofkarsticsubsurfaceheterogeneitywithintheVarKarst-Rmodel,i.e.theinclusionofpreferentialowpathsandofsubsurfaceheterogeneity.Based ontheconceptualunderstandingofsoilandepikarststoragebehaviourFig.1citallowsformorerechargeduringwetconditionsbecausesurfacerunoffisnotgenerated, andformorerechargeduringdryconditionsbecausethe thinsoilcompartmentswillalwaysallowforsomewaterto percolatedownwardsbeforeitisconsumedbyevapotranspiration.Duringwetconditions,bothPCR-GLOBWBand WaterGAPwillinsteadproducesurfacerunoffthatissubsequentlylostfromgroundwaterrecharge.Duringdryconditions,duetoitsnon-variablesoilstoragecapacity,thePCRGLOBWBmodelwillnotproduceanyrechargewhenthe soilwaterisbelowitsminimumstorage.Separatingsurface runoffandgroundwaterrechargebyaconstantfactor,the WaterGAPmodelwillproducerechargeduringdryconditions,butaconstantfractionofeffectiveprecipitationwill alwaysbecomefastsurface/subsurfacerunoffresultinginreducedrechargevolumes. ThisdoesnotmeanthattherepresentationofrechargeprocessesinmodelslikePCR-GLOBWBorWaterGAPisgenerGeosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1741 allywrong,butthatitcanbelimitedsinceouranalysisshows thatthestructuresofsuchmodelsneedmoreadaptiontothe particularitiesofdifferenthydrologiclandscapes.Inparticular,itaddstotheneedforincorporatingsubgridheterogeneityinourlarge-scalesimulationmodelsBevenandCloke, 2012.Karstregionscompriseabout35%ofEurope'sland surfaceandourresultsindicatethatpresentlytheirgroundwaterrechargeisunder-estimated,whilesurfacerunoffand actualevaporationareover-estimated.Giventheexpected decreaseofprecipitationinsemi-aridregions,suchasthe Mediterranean,andanincreaseofextremerainfallevents atthesametimeinthenearfuture,Kirtmanet al.,2013,currentlarge-scalesimulationmodelswilloverestimateboththevulnerabilityofgroundwaterrechargeand theoodhazardinkarstregionsinEuropeandtheMediterranean.Thesameistrueforthelong-termfutureendof21st century;Collinsetal.,2013.Ofcourse,anover-estimation ofvulnerabilityandhazardmightbethe“lesserevil”comparedtoanover-estimation.But,attimesoflimitednancial resources,excessiveinvestmentsinensuringthesecurityof drinkingwatersupplyandoodriskmanagementforpotentialfuturechangesmayunnecessarilyaggravatethesocioeconomicimpactsofclimatechange. 5Conclusions Inthisstudywehavepresentedtherstattempttomodel groundwaterrechargeoverallkarstregionsinEuropeandthe Mediterranean.Themodelapplicationwasmadepossibleby anovelparameterconnementstrategythatutilizedacombinationofaprioriinformationandrechargerelatedobservationsonfourtypicalkarstlandscapesthatwereidentied throughclusteranalysis.Handlingtheremaininguncertainty explicitlyasposteriorparameterdistributionsresultingfrom theconnementstrategy,wewerenallyabletoproduce rechargesimulationsandanestimateoftheiruncertainty.We foundanadequateagreementwithournewmodelwhencomparingourresultswithindependentobservationsofrecharge atstudysitesacrossEuropeandtheMediterranean.Wefurthershowthatcurrentlarge-scalemodellingapproachestend tosignicantlyunder-estimaterechargevolumes. Overall,ouranalysisshowedthatthesubsurfaceheterogeneityofkarstregionsandthepresenceofpreferentialow pathsenhancesrecharge.Itresultsinhighinltrationcapacitiesprohibitingsurfacerunoffandreducingactualevapotranspirationduringwetconditions.Ontheotherhanditallowsforrechargeduringdryconditionsbecausesomewatercanalwayspercolatedownwardspassingthethinfraction ofthedistributedsoildepths.Thisparticularbehavioursuggeststhatkarsticregionsmightbemoreresilienttoclimate changeintermsofbothoodinganddroughts.Drinkingwaterandoodriskmanagementisliabletobebasedonerroneousinformationforatleast35%ofEurope'slandsurface sincethisisnotconsideredincurrentlarge-scalemodelling approaches. However,usingrechargedirectlyasaproxyfor“available”groundwaterresourcesmaynotbegoodinallcases, neitherinkarstregionsnorinothertypesofaquifersBredehoeft,2002.Topreciselyestimatethesustainableusable fractionofgroundwatertheaquiferoutowshouldbeknown ratherthanjusttheinow.Furthermore,pumpingstrategiesshouldconsiderthegeometryandtransmissivityofthe aquifer.Hence,rechargeestimationcanbeconsideredonly asarstproxyofavailablegroundwaterandfuturestudies shouldfocusonthelarge-scalesimulationofkarstgroundwaterowandstoragetofurtherimprovewaterresources predictionsinkarstregions. www.geosci-model-dev.net/8/1729/2015/Geosci.ModelDev.,8,1729–1746,2015

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1742A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge AppendixA A1Resultsoftheclusteranalysis FigureA1. Elbowplotofsumofsquareddistancestoclustercentresfor k meansmethod. A2Resultsoftheregionalsensitivityusinginitial ranges FigureA2. Sensitivityofsimulatedrechargetothemodelparametersatdifferenttimescalesandinthedifferentkarstlandscapes,as inFig.10butwithsamplingparametersfromtheconnedparameterrangesofTable5. Geosci.ModelDev.,8,1729–1746,2015www.geosci-model-dev.net/8/1729/2015/

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A.Hartmannetal.:Alarge-scalesimulationmodeltoassesskarsticgroundwaterrecharge1743 Acknowledgements. WewanttothankJuergenStrub,research associateattheChairofHydrology,Freiburg,Germany,for designingsomeoftheguresandThomasGodmanforcollectingreferencestoindependentrechargestudies.Thisworkwas supportedbyafellowshipwithinthePostdocProgrammeofthe GermanAcademicExchangeServiceAndreasHartmann,DAAD andbytheUKNaturalEnvironmentResearchCouncilFrancesca Pianosi,CREDIBLEProject;grantnumberNE/J017450/1. ThesensitivityanalysiswascarriedoutbytheSAFEToolbox http://bristol.ac.uk/cabot/resources/safe-toolbox/.WethankPetra DllforprovidingthemeanannualrechargevolumesofWaterGAP,andFannySarazinforcheckingtheresultsoftheregional sensitivityanalysis.Thearticleprocessingchargewasfundedby theopen-accesspublicationfundoftheAlbertLudwigsUniversity Freiburg. 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