Assessing the role of uncertain precipitation estimates on the robustness of hydrological model parameters under highly variable climate conditions

Contents lists available atScienceDirect

Journal of Hydrology: Regional Studies

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / e j r h

Assessing the role of uncertain precipitation estimates on the robustness of hydrological model parameters under highly variable climate conditions

B. Bisselink

, M. Zambrano-Bigiarini

, P. Burek

, A. de Roo

aEuropeanCommission,JointResearchCentre(JRC),DirectorateforSustainableResources,Italy

bFacultyofEngineeringandSciences,UniversidaddeLaFrontera,Temuco,Chile

cInternationalInstituteforAppliedSystemsAnalysis(IIASA),Laxenburg,Austria

a r t i c l e i n f o

Articlehistory:

Received6April2016

Receivedinrevisedform1September2016 Accepted2September2016

Keywords:

Satellite-basedrainfallestimates Highlyvariableclimateconditions Differentialsplit-sample Calibration

Modelparameterrobustness Hydrologicalmodelling SouthernAfrica

a b s t r a c t

Studyregion:FourheadwatersinSouthernAfrica.

Studyfocus:ThestreamflowregimesinSouthernAfricaareamongstthemostvariablein theworld.Thecorrespondingdifferencesinstreamflowbiasandvariabilityallowedusto analyzethebehaviorandrobustnessoftheLISFLOODhydrologicalmodelparameters.A differentialsplit-sampletestisusedforcalibrationusingsevensatellite-basedrainfallesti- mates,inordertoassesstherobustnessofmodelparameters.Robustmodelparameters areofhighimportancewhentheyhavetobetransferredbothintimeandspace.Forcali- bration,themodifiedKling-Guptastatisticwasused,whichallowedustodifferentiatethe contributionofthecorrelation,biasandvariabilitybetweenthesimulatedandobserved streamflow.

Newhydrologicalinsights:Resultsindicatelargediscrepanciesintermsofthelinearcorrela- tion(r),bias(ˇ)andvariability()betweentheobservedandsimulatedstreamflowswhen usingdifferentprecipitationestimatesasmodelinput.Thebestmodelperformancewas obtainedwithproductswhichingestgaugedataforbiascorrection.However,catchment behaviorwasdifficulttobecapturedusingasingleparametersetandtoobtainasingle robustparametersetforeachcatchment,whichindicatethattransposingmodelparam- etersshouldbecarriedoutwithcaution.Modelparametersdependontheprecipitation characteristicsofthecalibrationperiodandshouldthereforeonlybeusedintargetperiods withsimilarprecipitationcharacteristics(wet/dry).

©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCC BYlicense(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Hydrologicalmodelsarewidelyusedforwaterresourcesmodelling,bothdroughtandfloodforecasting,andclimate changeimpactassessmentstudies,amongothers.Beforeapplyingthesemodelstheirrobustnessneedstobetestedvis-à-vis withthespecificmodellingobjectivetobuildmodelcredibilityandensuremodelapplicability(Klemeˇs,1986).Operational modelsoftenneedtobecalibratedtoobtainnumericalvaluesofmodelparameters.Theaimofacalibrationprocessisto obtainparameterswhichallowanacceptablerepresentationofthehydrologicalbehavioroftheselectedcatchment,and moreovertoobtainparameterswhicharerobustand,therefore,betransposabletowardsothertimeperiodsaswell.This

∗ Correspondingauthor.

E-mailaddress:bernard.bisselink@jrc.ec.europa.eu(B.Bisselink).

http://dx.doi.org/10.1016/j.ejrh.2016.09.003

2214-5818/©2016TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/

4.0/).

assumptionmightonlybevalidiftheuncertaintyintheobtainedmodelparametersislowand/ortheconditionsbetween thecalibrationandvalidationperiodaresimilar(stationaryconditions).However,therearemultiplereasonsthatmightlead tochangesinmodelparametersintimeand,therefore,raisealackofmodelrobustness.Themostobviouscausemightbe aninappropriatemodelstructure(Buttsetal.,2004;BulyginaandGupta,2009;ReusserandZehe,2011;LinandBeck,2012;

Seilleretal.,2012).Recently,Coronetal.(2014)showedtheinabilityofthreemodelsofincreasingcomplexityinreproducing thewaterbalanceondifferentsub-periods.Anotherexplanationforthelackofmodelrobustnesscanbemiscalibration(i.e.

pooroptimizationalgorithm)orovercalibration(i.e.insufficientcalibrationperiod,toomanyparameters,wrongobjective function)ofmodelparameters,asshownbyWageneretal.(2003),HartmannandBárdossy(2005),Sonand Sivapalan (2007),Guptaetal.(2009),Ebtehajetal.(2010),EfstratiadisandKoutsoyiannis(2010),Andréassianetal.(2012),Gharari etal.(2013)andZhanetal.(2013).Inaddition,changesintimeofsomecatchmentfeatures(e.g.,landusechangeand management,operationalrulesofreservoirs,changesingroundwaterlevel)arereflectedinthemodelinputdata,andmight alsoleadtolackofmodelrobustness.For example,Feniciaetal.(2009)showedthemajorroleofchangesinlanduse managementandforestageonthecatchments’behavior.

Toassessthemodel’srobustnessunderhighlyvariableclimateconditionsthestandardsplit-sampletest,usedtocalibrate themodelinoneperiodandtestthemodelinanotherperiod,isnotsufficientenough.Klemeˇs(1986)proposedamore powerfultest,thesocalleddifferentialsplit-sampletest,wherecalibrationandvalidationperiodsarechosentorepresent markedlydifferenthydro-meteorologicalconditionsofthecatchment.Thisdifferentialsplit-sampletestshouldbeapplied wheneveramodelistobeusedtosimulateflowsinabasinunderconditionsdifferentfromthosecorrespondingtothe availableflowrecord(Klemeˇs,1986).Arobustmodelshoulddemonstrateitsabilitytoperformequallywellintheselected calibrationandvalidationperiods.Studiesthatperformedadifferentialsplit-sampletestarerelativelyscarce,becausemost modelsfailthistest(Seibert,2003).ThestudiesofRefsgaardandKnudsen(1996),Donnelly-MakoweckiandMoore(1999), Xu(1999),Seibert(2003),Wilby(2005)andChiewetal.(2009)allappliedadifferentialsplit-sampletest.Mostofthese studiesfoundadecreaseinmodelperformanceduetothesensitivityofthemodelparametersinrelationtodifferentclimate conditions.Morerecently,Merzetal.(2011)foundinatestfor273Austriancatchmentsthattheparameterscontrolling snowandsoilmoisturewerestronglyinfluencedbyclimaticconditions.Vazeetal.(2010)andCoronetal.(2012)conducted studieswithfourandthreehydrologicalmodels,respectively,onsoutheasternAustraliancatchments.Theyalsofounda strongclimateinfluenceintheirmodels.AccordingtoLietal.(2012)dryperiodscontainmoreinformationformodel calibrationcomparedtowetperiods,whentheyinvestigatedthetransposabilityofmodelparametersfordryand wet conditions.

Forsuccessfulstreamflowpredictionsthemodelshouldbeforcedwithaccurateprecipitationdata(Beven,2004).The impactofprecipitationinputonmodelperformanceiswelldocumentedinerroranalyses(Kavetskietal.,2003,2006),asa functionofcatchmentsize(Moulinetal.,2009),raingaugedensity(BárdossyandDas,2008)orusingvariousgeostatistical methods(Sunetal.,2000).However,modelrobustnessproblemsduetoincorrectestimationsofprecipitationamountsare rarelyreportedinhydrologicalmodelling,whileitiswellknownthatsucherrorsmighthaveasignificanteffectonthefinal valuesofmodelparameters(Oudinetal.,2006).

Consideringtheimportanceoftheprecipitationinputonthereliabilityofmodelpredictions,itisextremelychallengingto performreliableapplicationsofhydrologicalmodelsinungaugedordata-scarseareas.ForAfrica,“groundtruth”precipitation isverysparseand,thereforeremotesensingcanbeanidealtechniqueforobtainingtimeseriesofprecipitationtobeused asinputdataforhydrologicalmodellingstudies.Applicationsofsatellite-basedrainfallestimates(SRFE)forhydrological modelingarewelldocumented(fore.g.,Thiemigetal.,2013;Artanetal.,2007;Behrangietal.,2011;Gourleyetal.,2011;

StisenandSandholt,2010;CohenLiechtietal.,2012),observinglargedifferencesinparametervaluesobtainedfromdifferent rainfallinputs(BitewandGebremichael,2011).However,mostofthesestudiesperformthestandardsplit-sampletestanddo notdiscusstherobustnessoftheobtainedmodelparametersandhowthemodelstructurecompensatefortheprecipitation inaccuracy,andmoreoveriftheyaretransposabletotimeperiodsotherthanthesinglevalidationperiod.

TheaimofthisstudyistodeterminetherobustnessofthefullydistributedLISFLOODhydrologicalmodelbyusingdif- ferentprecipitationestimatesasmodelinput.Toachievethisaim,thisresearchfocusesonfivemainresearchquestions:(i) Howaccuratearethedifferentprecipitationdatasetsforstreamflowsimulations?(ii)Whatistheeffectofuncertaininput data(precipitation)ontheestimatesofmodelparameters?(iii)Howwillthemodelparametersobtainedbycalibration compensateforprecipitationinaccuracy?(iv)Canadifferentsourceofprecipitationovercomerobustnessproblems?(v) Isasinglecalibrationparametersetsufficientforhydrologicalforecastingorclimatescenariomodelling?Theseresearch questionsareansweredperformingadifferentialsplit-sampletesttocalibratetheLISFLOODhydrologicalmodelusingdif- ferentprecipitationsources,toshowdifferencesinmodelparametersandtoensureaminimumstandardforoperational validationofthissimulationmodel.SouthernAfricaisselectedasacasestudybecauseofitshighlyinterandintra-annual hydrologicalvariability,mainlyduetorainfallpatternscharacterizedbyeventsofshortdurationandhighintensities.There- fore,theprecipitationestimatesmightpresentlargedifferenceswithgroundobservations,i.e.,theycanbehighlyinaccurate.

Thecorrespondingdifferencesinstreamflowbiasandvariabilitywillallowustoassessdifferencesinmodel’sbehaviorand robustnessofmodelparameters.

Thepaperisorganizedasfollows.Section2presentstheprecipitationestimatesandotherhydrologicalmodeldataused inthisresearch,providingadescriptionofthesensitivityanalysis,calibrationprocedureandclimatecharacteristicsduring thehydrologicalsimulations.Section3containsadescriptionofthecalibrationandvalidationresultsofthedifferentialsplit-

sampletest,whileSection4givesadescriptionofthemodelparameters,theirrobustnessanduncertainty.Theconclusions arefinallypresentedinSection5.

2. Methodology

2.1. Hydrologicalmodel

LISFLOODisaGIS-basedspatially-distributedhydrologicalrainfall-runoffmodel(DeRooetal.,2000;VanDerKnijffetal., 2010;Bureketal.,2013).Drivenbymeteorologicalforcingdata,LISFLOODcalculatesacompletewaterbalanceatadaily timestepandeverygrid-celldefinedinthemodeldomain.Processessimulatedforeachgridcellincludesnowmelt,soil freezing,surfacerunoff,infiltrationintothesoil,preferentialflow,redistributionofsoilmoisturewithinthesoilprofile, drainageofwatertothegroundwatersystem,groundwaterstorage,andgroundwaterbaseflow.Runoffproducedforevery gridcellisroutedthroughtherivernetworkusingakinematicwaveapproach.Lakes,reservoirsandretentionareasor polderscanbesimulatedbygivingtheirlocation,sizeandin-andoutflowboundaryconditions.LISFLOODiscurrently usedforstudiesdealingwithwaterresources(Mubarekaetal.,2013;Sepulcre-Cantoetal.,2012),climatechangeimpact assessment(DankersandFeyen,2008,2009;Feyenetal.,2009;Rojasetal.,2012),flashfloodforecasting(Alfierietal.,2012) andfloodforecastingforEurope(Bartholmesetal.,2009;Pappenbergeretal.,2011;Ramosetal.,2007;DeRooetal.,2011;

Thielenetal.,2009)andrecentlyforAfrica(Thiemigetal.,2015).

Spatiallyvariableinputparametersandvariableswereobtainedfromdifferentdatabases.Soilpropertieswerederived fromtheHarmonizedWorldSoilDatabase(HWSD).ForestfractionandlandusecoverwereobtainedfromtheGlobalLand Cover2000(GLC2000)dataset(Bartholoméetal.,2003).Inadditiontolandcover,thevegetativepropertieswereobtained fromtheVGT4AFRICAProject.AmoredetaileddescriptionofthestaticinputmapsforAfricaisgivenby(Bódis,2009).Water useinformationfromtheGlobalCropWaterModel(GCWM–SiebertandDöll,2008,2010)isdynamicallycoupledwith LISFLOOD.Itisassumedthatwaterissubtractedsolelyfromthestreamflowandnotfrominternalstorages.

ThedrainagenetworkoftheAfricanriverbasinswereobtainedusingasequenceofupscalingoperationsperformedon therivernetworkderivedfromaShuttleRadarTopographyMission(SRTM;Jarvisetal.,2008)elevationmodelwithspatial resolutionof90m.Withtheupscalingfromafinetowardsacoarserscaletheaccuracyofthedrainagenetworkdatacan belostandmanualcorrectionsshouldbeapplied.However,inthecurrentpan-Africansetupweappliedanewalgorithm developedbyWuetal.(2011)forautomaticupscalingofrivernetworks,whichsuccessfullyaddressesmostoftheupscaling issues.

Meteorologicalforcingdataforthepan-AfricandomainoftheLISFLOODmodelwereobtainedfromtheERA-Interim reanalysisdataset(Simmons etal.,2007).GriddeddataproductsofERA-Interiminclude alargevarietyofsurface and upper-airparameters.Hereweretrieved3-hourlyordailyestimatesofwindspeed,minimumandmaximumtemperature, dewpointtemperature,andsolarandthermalradiationatagridof0.25^◦fromtheoriginalGaussianreducedgrid(about 0.7^◦).Afterwards,thePenman-Monteithformulawasusedtocomputepotentialevapotranspiration,evaporationratesfor openwaterandbaresoilsurfaces,tobeusedasinputdataforthehydrologicalmodel.Thecurrentpan-Africansetupof LISFLOODusesa0.1^◦grid,whichmeansthatallthedatasetswerere-sampledto0.1^◦ofspatialresolution.

2.2. Data

2.2.1. Precipitationsources

TheprecipitationproductsusedinthisworkaretheNationalAeronauticsandSpaceAdministration(NASA)Tropical RainfallMeasuringMission(TRMM)3B42version6(hereafter3B42V6)andthelatestversion7(3B42V7),theNational OceanicandAtmosphericAdministration(NOAA)ClimatePredictionCentermorphingtechniqueversion1.0(CMORPHV1.0), ERA-InterimprecipitationcorrectedusingtheGlobalPrecipitationClimatologyProject(GPCP)dataset(ERAIGPCP),theGlobal SatelliteMappingofPrecipitationmovingvectorwithKalmanfilter(GSMaP),ThePrecipitationEstimationfromRemotely SensedInformationUsingNeuralNetworksproduct(PERSIANN)andTheNOAAAfricanPrecipitationEstimationAlgorithm (RFE2.0).Abriefdescriptionofeachproductisgivenbelow.

TheTRMM3B42V6producthasbeenproducedsince1998andtheestimatesareproducedinfourstages(Huffman etal.,2007):(1)themicrowaveestimates(TMI,AMSR-E,SSM/IandAMSU-B)precipitationarecalibratedandcombined, (2)infrared(IR)precipitationestimatesarecreatedusingthecalibratedmicrowaveprecipitation,(3)themicrowaveand IRestimatesarecombined,and(4)rescalingtomonthlydataisappliedusingmonthlygaugedata.Thelatestversion,the 3B42V7,isareprocessedversionof3B42V6withchangesinthealgorithmandincludesadditionaldatasets(Huffmanetal., 2010;HuffmanandBolvin,2012).Both3B42V6and3B42V7productestimatesareavailableapproximately2monthsafter observation,butaremoreaccurateandsuitableforresearchcomparedtothenear-real-timeproducts(Huffmanetal.,2007, 2010).Theyarereleasedona0.25^◦by0.25^◦gridata3-hourlytemporalresolutionandcoveralllatitudesbetween50^◦Nand 50^◦S.

ThemaininputsfortheCMORPHV1.0arethecombinedIRandmicrowaveestimates.Thepassivemicrowaveestimates areinterpolatedusingatmosphericmotionvectorsfromtwosuccessiveIRimagesat30-minintervals(Joyceetal.,2004).

Thefinalproductincludestheraw,satelliteonlyprecipitationestimatesaswellasbiascorrectedandgauge-satelliteblended precipitationproducts.Theoriginalproducthasaveryhighspatialresolution:8kmgridandhalf-hourlytimestep.However,

Fig.1. ElevationmapofSouthernAfricaincludingthefourheadwaterswiththeoutletsmarkedasblackdots.

bothradarandsatelliteprecipitationdatasetsaregriddedtothe0.25^◦ gridandaggregatedtoa3-htimesteptoensure commonspatialandtemporalscalesinaglobalbeltextendingfrom60^◦Nto60^◦S.

TheERAIGPCPisestimatedbythenumericalmodelbasedontemperatureandhumidityinformationderivedfromassim- ilatedobservationsoriginatingfrompassivemicrowaveandinsitumeasurements(Deeetal.,2011).Balsamoetal.(2010) reportedonsystematicbiasesintheERA-Interimprecipitationdata.Tocorrectforthesebiases,theERA-Interimprecipitation iscorrectedusingtheGPCPdataset.DetailsoftherescalingmethodcanbefoundinBalsamoetal.(2010).

ThemaindatasourcesfortheGSMaPalgorithmareTRMM/TMI,Aqua/AMSR-E,DMSP/SSMI,andIRdata.Inadditionto these,AMSU-B’sareincludedintheGSMaPproduct.ThealgorithmusestheKalmanfiltertoretrievetheprecipitationrate (Ushioetal.,2009)andrefinestheprecipitationateach0.1^◦pixelusingtherelationbetweentheIRbrightnesstemperature andsurfaceprecipitationrates.

PERSIANNisdevelopedwithartificialneuralnetworksestimatingprecipitationratesusingIR.Theaccuracyisimproved withadjustmentsinthenetworkparametersusingprecipitationestimatesfrommicrowaveandgroundrainrateswhere available(Hsuetal.,1997).

TheRFE2.0product(Hermanetal.,1997)isbasedonacombinationofpassivemicrowaveandIRprecipitationestimates.

DailyraingaugestationdatafromGlobalTelecommunicationSystem(GTS)recordsisusedforbiascorrection.Thespatial resolutioncorrespondstoa0.1^◦gridwhichextendsfrom40^◦Nto40^◦Sand20^◦Wto55^◦E.

Forthisstudy,eachprecipitationsourceisresampled(nearestneighboralgorithm)ontoa0.1^◦commongrid,fromJuly 2001untilJune2010atadailytimesteptodrivetheLISFLOODhydrologicalmodel.

2.2.2. Observedstreamflow

TheclimateoftheSouthernAfricanregionischaracterizedashighlyvariable,bothtemporallyandspatially.Manyrivers passthroughdifferentclimatezonesfromtropicaltoextremelyarid,andthestreamflowregimesareamongstthemost variableintheworld(GorgensandHughes,1982).WaterresourcemanagementisofhighimportanceforSouthAfricato maintainreliablewatersuppliesattimesofwaterstress.Therefore,allmajorriversarebeingregulatedtosomedegree (Walmsleyetal.,1999).

Fourheadwaterswereselected(Fig.1)forthemostimportantriversinSouthernAfrica,tryingtoexcludetheunnatural flowregimesdownstreamasmuchaspossible.Dailystreamflowrecordswerecollectedfrom4gaugingstations(Fig.1), providedbytheDepartmentofWaterAffairsinSouthAfrica(www.dwaf.gov.za),fortheperiodJuly2001untilJune2010.

2.3. Selectionofstudyarea

Asdescribed inSection2.2.2,fourheadwatersin SouthernAfricawithnear-undisturbedhydrologicalregime were selectedforanalysis.However,man-madereservoirsexistinbothregionsA2andA3,buttheirsmallregulationcapac- ityhavelittleimpactonstreamflowamount,asobservedintheflowdurationcurves(notshownhere).Thelocationsof

Table1

Physiographiccharacteristicsforthestudyarea.ThecharacteristicsarecalculatedbasedontheERA-Interimforevapotranspiration(PET)andtemperature (TA),andERA-interimcorrectedwithGPCPfortheprecipitation(P).

Type Variable A1 A2 A3 A4

Station Name Roodewal Oranjedraai TugelaFerry Overvloed

River Kraai Orange Tugela WhiteMfolozi

Catchment Orange Orange Tugela Mfolozi

Topography Area(km²) 8667 24960 12987 3917

Elevation(m) 1848 2297 1291 1047

Climate HI(−) 0.56 0.70 0.67 0.69

P(mmyear⁻¹) 748 832 875 876

PET(mmyear⁻¹) 1342 1186 1310 1267

CORR(−) 0.29 0.47 0.49 0.53

TA(^◦C) 12.6 10.5 16.8 17.0

Q(m³s⁻¹) 23.4 105.6 43.4 5.8

theheadwatersareshowninFig.1,whileTable1liststheclimaticandtopographicalattributesoftheselectedcatchments.

ThefourheadwatersarelocatedinorontheEasternplainsoftheDrakensbergmountainrangewherethemostimportant riversoriginate.Thesizeoftheheadwatersrangefromabout3917km²forA4toabout24960km²forA2,andtheaverage elevationrangesfrom1047(A4)to2297(A1)metersa.s.l.(seeTable1).

Accordingtothecalculatedhumidityindex(HI=P/PET),theclimateintheselectedheadwatersissub-humidwithan averageannualprecipitation(P)rangingfrom748(A1)to876(A4)mmyr⁻¹(accordingtoERAIGPCP).Theaverageannual evapotranspiration(PET)rangesfrom1186(A1)to1342(A4)mmyr⁻¹.ThePearsonproduct-momentcorrelationcoefficient (CORR)betweenmonthlymoisture(P)andenergy availability(PET)rangesfrom0.29 to0.53showingagood positive correlationinA2,A3andA4(>0.4)which,accordingtoPetersenetal.(2012),representsareaswithastrongseasonal precipitationregime.Precipitationoccursmainlyduringthesummermonths(i.e.OctobertoMarch)andthemajorsources ofrainfallduringsummerarethunderstorms,orographicallyinducedstorms(Tysonetal.,1976),andoccasionallytropical cyclones(DysonandVanHeerden,2001;ReasonandKeibel,2004).Althoughthesesystemsmayresultindevastatingfloods, theyareanimportantsourceofwatertosupplytheincreasingwaterdemandinthisarea.Theaverageannualtemperature (TA)rangesfromabout10.5^◦Cinthemountainousareas(A2)to17^◦Cintheheadwaterwiththelowestelevation(A4).The averagemonthlystreamflow(Q)rangesfrom5.8(A4)upto105.6m³s⁻¹(A2),butthehighrainfallvariabilityresultsinlarge fluctuationsofthestreamflowregime.

2.4. Sensitivityanalysis

Beforeusingacalibrationproceduretoobtainparametervaluesforthehydrologicalmodel,weidentifiedparameters withthehighestinfluenceinsimulatedstreamflow.InthecurrentLISFLOODversion,experienceofthemodeldevelopment teamsuggeststhefollowingparameterstobecalibrated.TheUpperZoneTimeConstant(UZTC)andLowerZoneTime Constant(LZTC)reflecttheresidencetimeofwaterintheupperandlowergroundwaterzone,respectively.Assuch,they controltheamountandtimingofoutflowfromthegroundwaterreservoir.TheGroundwaterPercolationValue(GwPV) controlstheflowfromtheupperandlowergroundwaterzone.TheGroundWaterLossFraction(GwLoss)istherateofflow outofthelowergroundwaterzone,expressedasafractionoftheinflow,GwPV.TheXinanjiangparameter(bXinan)isan empiricalshapeparameterintheXinanjiangmodel(ZhaoandLiu,1995)thatisusedtosimulateinfiltration.Itcontrolsthe fractionofsaturatedareawithinagridcellthatiscontributingtorunoff;henceitisinverselyrelatedtoinfiltration.The PowerPreferentialFlowParameter(PPrefFlow)isalsoanempiricalshapeparameterofthefunctiondescribingtheflowthat bypassesthesoil-matrixanddrainsdirectlytothegroundwater.TheChannelManningparameter(CCM)isamultiplierthat isappliedtotheManning’sroughnessmapsofthechannelsystem.Thehigherthevaluethemorefrictionthewaterwill experienceandresultinginalowerspecificstreamflow.Theevaporationinputdoesnothavealargespatialvariationand issubjecttoerrorsinSouthernAfrica(Hughes,2006;Hughesetal.,2010).Moreover,therearelargedifferencesbetween actualevaporationestimatespartiallydependentonprecipitation(Trambaueretal.,2014).Topartiallyconsideruncertainties onthemagnitudeoftheevaporation,relatedtothedifferentprecipitationsources,amultipliertotheevaporationinput (CalEvap)isalsocalibrated.Inaddition,forcatchmentswithupstreamreservoirs(A2andA3,with2reservoirseach)aset offourreservoirparametersareincludedtodescribetheinflowandoutflowstreamflows.Finally,thetwelveparameters selectedfortheglobalsensitivityanalysesarelistedinTable2.

Thevariance-basedmethodofSobol(Sobol’,2007)wasselectedasaglobalsensitivityanalysistechniquetoidentifythe relevantmodelparameters.Here,theSobol’salgorithmproposedbySaltellietal.(2010)isusedtoquantifythefirst-and total-orderindicesofeachmodelparameterdescribedintheprevioussection.Thefirst-ordersensitivityindex(Si)measures thedirectcontributionofeachmodelparametertothetotalmodeloutputvariance.Bydefinition,thesumofthefirst-order indicesofeachsinglecalibrationparameterissmallerorequalto1.Thefirst-orderindexprovidesameasureofthedirect importanceofeachparameter,andthelargerthefirst-ordersensitivityindexthemoreimportanttheparameter.Onthe otherhand,thetotal-ordersensitivityindex(Sti)isameasureofthetotaleffectofeachparameter,i.e.,itsdirecteffectand alltheinteractionswithotherparameters.Ifthefirst-ordersensitivityindexisequaltothetotal-ordersensitivityindexfor

Table2

LISFLOODcalibrationparameterswithbothupperandlowerbound.

Parameter Unit Min Max

UZTC days 5 40

LZTC days 50 2500

GwPV mmday⁻¹ 0.5 2

GwLoss – 0.01 0.70

b Xinan – 0.01 1

PPrefFlow – 1 4

CCM – 0.1 15

CalEvap rnlim rflim rnormq rndq

– – – m³s⁻¹ m³s⁻¹

0.8 0.10^* 0.81^* 0.1^* 12^*

1.2 0.80^* 1.0^* 20^* 1200^*

*RangesarereservoirdependentandonlyusedforregionA2andA3intheglobalsensitivityanalysis.

Fig.2. Barplotsofthesensitivityindiceswithrespecttothecalibrationparametersforeachprecipitationsourcebasedontheperiod2002–2006.Foreach precipitationsource,twobarsaredisplayed:theleftoneisforfirst-ordersensitivityindicesandtherightoneisforthetotal-ordersensitivityindices.

agivenparameter,itmeansthatthisparameterdoesnotinteractwiththeotherparameters.Conversely,ifthefirst-order sensitivityindexislowerthanthetotal-ordersensitivityindex,itindicatesstronginteractionsbetweenthisparameterand otherparameters(highcomplexitymodel).Notethatthesumofthetotal-ordersensitivityindicesmaybelargerthan1 (becausesomeeffectsarecountedmorethanonceinthesum).

TheSobol’smethodwasusedtoidentifythemostimportantparameterswhentheLISFLOODmodelwasforcedwith eachoneofthesevenSRFEdescribedinSection2.2.1.Theevaluationofboththefirst-andtotal-ordersensitivityindices isshowninFig.2.ForregionA1(Fig.2a),themostsensitiveparametersarerelatedtoinfiltration(PPrefFlow,bXinan), groundwaterprocesses(GwLoss)and evaporation(CalEvap). BothGwLossand bXinanareclearlythemostimportant variablesforeveryprecipitationsource.TheparameterPPrefFlowisfoundtohaveaveryweakdirectinfluence,butahigh

interactionwiththeotherparameters.ForregionA2(Fig.2b),themostinfluentialparameterisGwLossformostofthe SRFEs,exceptfortheRFE2.0precipitationproduct.GwLossexplainsbyitselfmorethan50%ofthemodeloutputvariance.

Severalprecipitationproductsledtomodelparametershighlyrelatedamongstthem(i.e.,theyarenotindependent),as shownbytheheightdifferenceoftheverticalbarsrepresentingthesumofallfirst-ordersensitivityindices:50%ormore.

ForregionA3(Fig.2c),onlythreeparameters(GwLoss,PPrefFlowandCalEvap)areinfluentialforthemodeloutputvariance.

Theinteractionbetweentheparametersis variable,withweakinteractionforCMORPHV1.0and stronginteractionfor RFE2.0.Fig.2dshowssimilarresultsforregionA4,butwithastrongerdirectinfluenceandaweakerinteractionamongst thosethreeparameters.Notethattheparametersrelatedtothereservoirs(regionsA2andA3)areofnoimportanceat allforthemodeloutputvariance.Theaforementionedresultsshowthatonlyparametersrelatedtoevaporation(CalEvap), infiltration(PPrefFlow)andgroundwaterprocesses(GwLoss)arethemostimportantforthenextcalibrationstep.Thestrong interactionsobservedamongstthemclearlyindicatethattryingtooptimizeoneparameteratatimewouldbeinefficient.

Althoughanindependentcalibrationofonlythemostimportantparameterscouldbeattempted,wecalibratedjointlythe 8parameters(UZTC,LZTC,GwPV,GwLoss,bXinan,PPrefFlow,CCMandCalEvap).Theparameterstobecalibratedandtheir respectivephysically-reasonablerangesarelistedinTable2.Theparametersrelatedtothereservoirsareneglectedinthe calibrationprocedureastheywerenotidentifiedasimportantduringtheglobalsensitivitystep.

2.5. Calibrationprocedure

TheopensourcehydroPSORpackagev0.3-3(Zambrano-Bigiarini,2013;Zambrano-BigiariniandRojas,2013)wasused forcalibratingtheLISFLOODmodelinthefourselectedcatchments.hydroPSOisanewglobaloptimisation/calibrationtool basedontheParticleSwarmOptimisation(PSO)algorithm.hydroPSOisaneffectiveandefficientcalibrationtool,asshown inrecentapplicationswithdifferenthydrologicalandenvironmentalmodels(Thiemigetal.,2013;Braueretal.,2014a,b;

AbdelazizandZambrano-Bigiarini,2014;Silaletal.,2015).MoredetailsabouthydroPSOcanbefoundinZambrano-Bigiarini andRojas(2013)andZambrano-Bigiarinietal.(2013).

Thedifferentialsplit-sampletestwasperformedovertwotimeperiodsoffouryears(Jul2002–Jun2006andJul2006–Jun 2010),runningtheLISFLOODmodelwithadailytimestep.Foreachmodelsimulationapre-runisperformedtoinitializethe groundwaterstorageandsubsequentlyanadditionalwarm-upperiodofsixmonthsisusedtoinitializethewaterstorage componentsofthemodel.

TheobjectivefunctionchosentodrivetheoptimizationwasthemodifiedKling-Guptaefficiency(KGE)betweensimulated andobservedstreamflows(Klingetal.,2012),whichwasmaximizedtowardsanoptimalvalueof1.

KGE=1−

K+L+M, (1)

whereKisthecorrelationterm

K=(r−1)² (2)

Lthebiasterm L=

ˇ−1

(3) andMthevariabilityterm

M=(−1)² (4)

withristhePearsonproduct-momentcorrelationcoefficient,ˇisthebiasratio:

ˇ= s

o

(5) andisthevariabilityratio:

= CV_s CVo =

s s o o

(6) whereisthemeanstreamflow(m³s⁻¹),CVisthecoefficientofvariationandisthestandarddeviationofthestreamflow (m³s⁻¹),andtheindicessandorepresentsimulatedandobservedstreamflow,respectively.KGE,r,ˇ,andhavetheiropti- mumatunity.ThehydrologicalperformanceisclassifiedasmentionedinThiemigetal.(2013)andaccordingKling’sreview comment(2016):excellent(KGE≥0.9),good(0.9>KGE≥0.75),intermediate(0.75>KGE≥0.5),poor(0.5>KGE>0.0)and verypoor(KGE≤0.0).MoreinformationaboutKGEinrelationtootherobjectivefunctionscanbefoundinGuptaetal.

(2009).Althoughthemodelwasrunwithdailytimesteps,theresultsofthecalibrationareanalyzedonamonthlybasis.

2.6. Climatecharacteristicsof2002–2006and2006–2010

ThecalibrationofLISFLOODiscarriedoutforeachofthesevenprecipitationproductsdescribedinSection2.2.1,using twocalibrationperiodswithhighlydifferentclimatecharacteristics:2002–2006and2006–2010.Fig.3summarizesthe

Fig.3.Barplotswiththechangeincorrelation(panelsa,d,g,j),mean(panelsb,e,h,k)andvariation(panelse,f,i,l)between2002–2006and2006–2010 foreachprecipitationsourceandobservedstreamflowineachstudyareaA1(panelsa,b,c),A2(panelsd,e,f),A3(panelsg,h,i),andA4(panelsj,k,l).The valueof2002–2006istheupperorlowervalueoftheverticalbaraccompaniedwiththeblackdot.

climatecharacteristicsofeachselectedcatchment,byshowingtherelationbetweenmonthlyprecipitationandobserved streamflowduringthetwocalibrationperiods.Fig.3willbeusedasaguidelinetoexplaintheresultswhicharepresented inthefollowingsection.

ForregionA1,thelowestcorrelationbetweentheobservedstreamflowandprecipitationisobservedforCMORPHV1.0in 2002–2006andPERSIANNin2006–2010.Thehighestcorrelationbetweenobservedstreamflowandprecipitationisfound usingthe3B42V7productforbothcalibrationperiods(Fig.3a).Thedifferenceintheamountofobservedstreamflow(Q, Fig.3b)between2002–2006and2006–2010isnegligiblewhereasthestreamflowin2002–2006isslightlylowercompared to2006–2010.Thedifferenceinprecipitationamountfromdifferentproductsisdispersed,withtheCMORHPV1.0asthe wettestandtheRFE2.0asthedriestproductfor2002–2006,whilefor2006–2010GSMaPisthewettestandRFE2.0isthe driest.NotethattheprecipitationmeanfortheCMORPHV1.0,ERAIGPCPandPERSIANNproductsin2002–2006arelarger comparedto2006–2010,whichisincontrastwiththeobservedstreamflowwhichislargerin2006–2010comparedto 2002–2006.Thevariabilityoftheobservedstreamflowislargerin2002–2006comparedto2006–2010(Fig.3c),whichis also,buttoalesserextent,observedfromthe3B42V6,CMORPHV1.0,3B42V7,ERAIGPCPandRFE2.0products.Incontrast, thevariabilityfromtheGSMaPandthePERSIANNproductislargerin2006–2010comparedto2002–2006.

ForregionA2,thedistributionofthecorrelation,meanandvariabilitybetweentheprecipitationproductsandobserved streamflowin2002–2006and2006–2010isquitesimilarasforregionA1.Thelowestcorrelationbetweentheobserved streamflowandprecipitationisagainobservedforCMORPHV1.0in2002–2006andPERSIANNin2006–2010.Thehighest correlationbetweenobservedstreamflowandprecipitationisfoundwiththeERAIGPCPproductforthe2002–2006period and3B42V7forthe2006–2010period(Fig.3d).Theamountofobservedstreamflowishigherforthe2006–2010period comparedtothe2002–2006period(Fig.3e).Fortheprecipitation,theCMORPHV1.0productisthewettestandtheRFE2.0 productthedriestoutofallproductsforthe2002–2006period.For2006–2010,theGSMaPproductisthewettestand theRFE2.0isthedriestproduct.Thevariabilityoftheobservedstreamflowisin2002–2006slightlylargercomparedto 2006–2010(Fig.3f).ThePERSIANNprecipitationproducthasthelargestvariabilityinbothperiodsbutacontradicting distributioncomparedtotheobservedstreamflowbetween2002–2006and2006–2010.Therestoftheproductshavea similarprecipitationvariabilitydistributionbutamuchlowervaluecomparedtotheobservedstreamflow.

ForregionA3,thelowestcorrelationbetweentheobservedstreamflowandprecipitationisobservedforCMORPHV1.0 in2002–2006andPERSIANNin2006–2010.Thehighestcorrelationbetweenobservedstreamflowand precipitationis foundwiththeERAIGPCPproductfor2002–2006and3B42V7for2006–2010(Fig.3g).Theamountofobservedstreamflow ishigherforthe2006–2010periodcomparedtothe2002–2006period(Fig.3h).Fortheprecipitation,theCMORPHV1.0 productisthewettestandtheRFE2.0productthedriestoutofallproductsforthe2002–2006period.For2006–2010,the 3B42V7productisthewettestandtheRFE2.0isthedriestproduct.Thevariabilityoftheobservedstreamflowislargerin

Fig.4.BarplotsofcalibrationresultsintermsofKGEinthetwoperiodsofthedifferentialsplitsampletest:2002–2006and2006–2010,foreachprecipitation product.Panelsa),b),c)andd)correspondtoregionA1,A2,A3andA4,respectively.

2002–2006comparedto2006–2010(Fig.3i).ThePERSIANNprecipitationproducthasthelargestprecipitationvariability inbothperiods,whileERAIGPCPhasthelowest.

ForregionA4,thecorrelationbetweentheobservedstreamflowandprecipitationisquitesimilarforallprecipitation productsforbothcalibrationperiodswithahighercorrelationforthe2002–2006period(Fig.3j).Thedifferenceintheamount ofobservedstreamflowbetween2002–2006and2006–2010isnegligible(Fig.3k).Forprecipitation,theCMORPHV1.0 productisthewettestandRFE2.0isthedriestforthe2002–2006period.For2006–2010,PERSIANNisthewettestand RFE2.0isthedriestproduct.Thevariabilityoftheobservedstreamflowisin2002–2006muchlowercomparedto2006–2010 (Fig.3l).ThePERSIANNprecipitationproducthasthelargestvariabilityinbothperiods.

3. Results

3.1. Calibration

Fig.4showsthebestvaluesofKGEobtainedinthetwocalibrationperiodsofthedifferentialsplitsampletest:2002–2006 and2006–2010,whentheLISFLOODmodeliscalibratedwitheveryprecipitationproductforeachstudyarea.Inaddition, takingintoaccountthathighvaluesofK,LandM(Eqs.(2)–(4))leadtolowvaluesofKGE(Eq.(1)),wecomputedtherelative contributionsofK,L,andMtotheKGEvaluesobtainedineachcalibration(100·K,LorMK+L+M),inordertoidentifythe limitingfactorthatpreventsKGEtoachieveanidealvalueof1.0.Fig.5showstherelativecontributionofeachlimitingfactor totheKGEvalue:K,L,M(Eqs.(1)–(4)),whichrepresenttheimpactofthelinearcorrelation(r),bias(ˇ)andvariability() betweensimulatedandobservedstreamflowonthecalibrationresults.

ThecalibrationresultsforA1(Fig.4a)weredeemedtobesatisfactory(intermediateorgood)forthesimulationswith products3B42V6,3B42V7,ERAIGPCPandRFE2.0inbothcalibrationperiods.Ontheotherhand,calibrationresultsforthe CMORPHV1.0andPERSIANNwerepoorfortheperiod2002–2006calibrationbutintermediatefor2006–2010.Theopposite wastrueforsimulationsforcedbytheGSMaPproduct.Fig.5ashowswithverticalbarstherelativecontributionofK,Land MtotheKGE,makingclearthatthepoorperformanceofmodelsimulationsforcedbyCMORPHV1.0andPERSIANNduring 2002–2006wasmainlyduetoapoorcorrelationbetweensimulatedandobservedstreamflow(highKvalue).Thesefindings areinagreementwiththeresultsofFig.3a,wherebothCMORPHV1.0andPERSIANNpresentedthelowestcorrelationwith

Fig.5. Barplotswiththerelativecontribution(in%)ofthecorrelation(K),bias(L)andvariability(M)whichpreventtheKGEtoachieveanoptimum valueof1.0.Foreachprecipitationproduct,K,LandMwerecomputedinthetwocalibrationperiodsofthedifferentialsplitsampletest:2002–2006and 2006–2010.Panelsa),b),c)andd)correspondtoregionA1,A2,A3andA4,respectively.

observedstreamflowduring2002–2006.However,thisrelationisnotalwaysvalidasthemodelperformancefor2006–2010 withPERSIANNisreasonablygoodinspiteofPERSIANNhavingthelowestcorrelationwiththeobservedstreamflowout ofallprecipitationproducts.Ontheotherhand,Fig.4ashowsthatsimulationsforcedbyGSMaPweretheworstforthe 2006–2010period,whichwasmainlyduetothehighrelativecontributionofthebiastermL(Fig.5a).Thepreviousresultisin agreementwiththefactthatGSMaPwasthewettestprecipitationproductduringthatperiod(seeFig.3b).Calibrationresults forA2(Fig.4b)areintermediateorgoodforthesimulationsdrivenbyproducts3B42V6,3B42V7,ERAIGPCP,GSMaPand RFE2.0forbothcalibrationperiods.ThepoorperformanceoftheCMORPHV1.0andPERSIANNsimulationsinthe2002–2006 periodwascausedbya lowcorrelationbetweenobservedand simulatedstreamflow(Fig.5b).Fig.3dshowsalsolow correlationsbetweenprecipitationandobservedstreamflowin2002–2006,forbothCMORPHV1.0andPERSIANN.Fig.5b showsthatthepoorperformanceofthePERSIANNsimulationsin2006–2010wasthelowcorrelationbetweenobservedand simulatedstreamflow,possiblyrelatedtothepoorestcorrelationbetweenprecipitationandobservedstreamflowobtained byPERSIANNoutofallproductsin2006–2010(Fig.3e).

ThecalibrationresultsforA3(Fig.4c)aresatisfactory(excellent,intermediateorgood)forthe3B42V6,3B42V7,CMOR- PHV1.0,ERAIGPCPandRFE2.0simulationsforbothcalibrationperiods.TheresultsoftheGSMaPandPERSIANNsimulations wereintermediatein2002–2006andpoorforthe2006–2010period,mainlyduetotheweakcorrelationbetweensimulated andobservedstreamflow(Fig.5c).ThepreviousresultispossiblyduetothelowcorrelationbetweenGSMaPandPERSIANN precipitationandtheobservedstreamflow,whichwerethepoorestoutofallproductsin2006–2010(Fig.3g).

InregionA4(Fig.4d),thecalibrationresultsforthe2002–2006periodwereintermediateorgoodonlyforthe3B42V6, 3B42V7andERAIGPCPproducts.ThepoorresultsobtainedwithCMORPHV1.0,GSMaP,PERSIANNandRFE2.0productswere mainlycausedbythedifferenceinthevariabilityterm(MinEqs.(1)and(4))betweensimulatedandobservedstreamflow, whichisapparentlyrelatedtohighvariabilityofthoseprecipitationproducts(Fig.3l).TheCMORPHV1.0,GSMaP,PERSIANN andRFE2.0arematchingthevariabilityofthestreamflowmorecloselycomparedtothethreeremainingproducts.Con- troversially,highprecipitationvariabilityofthesefourprecipitationproductsresultsinstreamflowoverestimationdueto overestimationofbothrainfallamountandduration.ThecalibrationresultsofthesimulationsforcedbyERAIGPCPand PERSIANNin2006–2010werepoorduetothecontributionofcorrelation(KterminEqs.(1)and(2))andbias(LterminEqs.

(1)and(3))betweensimulatedandobservedstreamflow,respectively.ThisisinagreementwithFig.3j,wherethecorre-

Fig.6.BarplotsofthevalidationresultsintermsofthevariationofKGE(KGE=KGEcalibrationrun2002–2006(2006–2010)minusKGEvalidationrun 2002–2006(2006–2010)withoptimumparametervaluesobtainedfrom2006–2010(2002–2006))inthetwoperiodsofthedifferentialsplitsampletest foreachprecipitationproduct.Panelsa),b),c)andd)correspondstoregionA1,A2,A3andA4,respectively.

lationbetweenERAIGPCPprecipitationandobservedstreamflowisthelowest,andwithFig.3kwherethemeanmonthly precipitationofPERSIANNishighestoutofallproducts.

3.2. Robustnessofmodelparameters

Inordertotesttherobustnessofthemodelparametersobtainedineachcalibrationperiod,allthe“optimum”parameter setswerevalidatedonanindependenttimeperiodwithadifferentclimatologicalregime,asexplainedinSection2.6,for eachheadwaterandprecipitationproduct.Inparticular,whenusingthedifferentialsplit-sampleapproach,theperformance ofmodelparametersobtainedduringthecalibrationin2002–2006(2006–2010)wascomparedagainsttheperformance ofavalidationrunobtainedwithmodelparameterscalibratedintheothertimeperiod2006–2010(2002–2006).Fig.6 showstheKGEvaluesofthevalidationperiodrunin2002–2006(2006–2010)usingtheoptimumparametersetobtained duringthecalibrationrunin2006–2010(2002–2006)withthelatterreference(KGE=KGECAL−KGEVAL).Ontheother hand,Fig.7showsforeveryprecipitationproduct,studyareaandcalibrationperiod,therelativecontributionofK,Land MtotheobtainedKGEofthevalidationrun.Modelparametersobtainedduringcalibrationareconsideredrobustifthe modelperformsequallywellinthevalidationrunusingmodelparametersderivedinadifferentprecipitationregime,i.e., theKGE shouldbesmall.NotethatinasmallnumberofcasestheKGE valuesobtainedduringthevalidationrunare higherthantheKGEvaluesobtainedduringthecalibrationruninthesameperiod(e.g.,PERSIANNinA4).Thisisduetothe aggregationfromdailytomonthlyvaluestocomputetheKGE.

Fig.6ashowsthat“optimum”parametersetsobtainedforalmostalltheproductsinthestudyareaA1weredeemedrobust, asshownbythesmallvalueofKGE.TheonlyexceptionwastherundrivenbytheERAIGPCPprecipitation,whichshowed animportantreductioninmodelperformancewhenrunningthemodelin2002–2006withparametersobtainedforthe 2006–2010timeperiod.TheverticalbarsinFig.7ashowthattheKGEinthe2002–2006validationperiodfortheERAIGPCP productsismainlylimitedbythebias(L)betweensimulatedandobservedstreamflow.Thecomparisonofobservedand simulatedhydrographs(notshownhere)revealsthattheobservedstreamflowinthevalidationperiod2002–2006isslightly lowercomparedtothecalibrationperiod2006–2010.Controversially,theaverageERAIGPCPprecipitationin2002–2006is wettercomparedto2006–2010,whichresultsinanoverestimationoftheobservedstreamflow.

Fig.7.Barplotswiththerelativecontribution(in%)ofthecorrelation(K),bias(L)andvariability(M)whichpreventKGEtoachieveanoptimumvalueof 1.0.Foreachprecipitationproduct,K,LandMwerecomputedinthetwovalidationperiodsofthedifferentialsplitsampletest:2002–2006and2006–2010.

Panelsa),b),c)andd)correspondtoregionA1,A2,A3andA4,respectively.

AfterthevalidationinregionA2(Fig.6b)themodelperformancewiththeparametersforcedwiththe3B42V6,3B42V7, ERAIGPCPandRFE2.0productsaredeemedrobustforboth periods.Notethat,incomparison withthecalibration,the contributionofthebias(L)becomesamorepronouncedvariableinreducingtheKGEinmostoftheproducts.Thisiseven morepronouncedinregionA3(Fig.6c).Inbothcalibrationperiods(Fig.4c)thelimitingfactorismostlydominatedbythe correlation(K)orvariability(M),whereasinthevalidationthelimitingfactoristhebias(L)betweensimulatedandobserved streamflow(Fig.7c)sometimesresultinginlargereductionsoftheKGE.InFig.3hisfoundthattheaverageprecipitationof theCMORPHV1.0,ERAIGPCP,PERSIANNandRFE2.0productsishigherin2002–2006comparedto2006–2010.However,the oppositeistruefortheobservedstreamflowandconsequentlythisresultinbiasissuesandthereforealackofrobustness betweencalibrationandvalidation.Calibratingtheseprecipitationproductsin2006–2010(dry)andvalidatingthemin 2002–2006(wet)resultinanoverestimationoftheobservedstreamflowastheaverageobservedstreamflowislower andtheaverageprecipitationishigherinthevalidationperiodcomparedtothecalibrationperiod.Theoppositeisalso valid.Calibratingtheseprecipitationproductsin2002–2006(wet)andvalidatingthemin2006–2010(dry)resultinan underestimationoftheobservedstreamflowastheaveragestreamflowishigherandtheaverageprecipitationislowerin thevalidationperiodcomparedtothecalibrationperiod.

ThelimitingfactorforpoorcalibrationresultsinregionA4wasmostlydominatedbythevariabilityterm(M).However, poorvalidationresultsareobservedinFig.6dduetoboththevariability(M)andbias(L)termaslimitingfactors(Fig.7d).

OnlythereductioninKGEofthevalidationoftheERAIGPCPsimulationsislowinbothperiods,butthecalibrationresults in2006–2010werealreadypoorduetopoorcorrelationbetweenobservedandsimulatedstreamflow.Forthisreason,no robustmodelparametersarefoundinregionA4nomatterwhichprecipitationproduct.

4. “Optimum”parametersetsunderhighlyvariableclimateconditions

AsseeninFig.7thebias(L)betweenobservedandsimulatedstreamflowisanimportantfactorinthelossofmodel performanceinthevalidationperiod.Apparently,themodelparametersarecompensatingthebiasbetweensimulatedand observedstreamflowduringthecalibrationbutthesemodelparametersfailtocapturetheobservedstreamflowduringthe

Fig.8.Barplotswiththerelativechange(in%)inthemagnitudeofthebestparametersetfoundinthe2002–2006and2006–2010calibrationperiods, whereasthevalueof2002–2006istheupperorlowervalueoftheverticalbaraccompaniedwiththeblackdot.Thelowerandupperboundvaluesforthe parameters(Table2)represent0and100%respectivelyandonlytheparameterswithatotal-ordersensitivityindexlargerthan0.1areincluded(Fig.2).

validationperiod.Compensationforcorrelationandvariabilityfailurebetweenobservedandsimulatedstreamflowisless pronouncedastheyarethedominantlimitingfactorsinthecalibrationperiods.

InFig.8thelengthoftheverticalbarsshowtherelativechangeinthemagnitudeofthebestparametersetfoundinthe twocalibrationperiods.Ingeneralitcanbeobservedthatthe“optimum”parametersetsdiffersignificantlybetweenthe calibrationperiods.Differentvaluesfoundfortheoptimumparametersetsindifferenttimeperiodsareaclearindication ofparametricuncertaintyintheobtainedmodelparameters(Beven,1993).

ForregionA1(Fig.8a),thedifferenceinthemodelparametersbetweenthecalibrationperiodsisnegligibleformost precipitationproductsexceptforRFE2.0.ThemodelparametersGwLossandCalEvaparereachingtheuppervaluesofthe calibrationrangeforalmostallprecipitationproductsinbothcalibrationperiods.Thismeansthatthemodelparameters arecompensatingtheexcessofrainfallbyeliminatingwaterbothtodeepergroundwaterandbyincreasingtheevaporation ratetomatchtheobservedstreamflow.Typically,theseparametervaluesresultinbiasproblemsbetweensimulatedand observedstreamflowdependingonwhetheronecalibrationperiodisdrierorwettercomparedtotheotherperiod.For example,Fig.8ashowsthattheoptimumvaluefortheGwLossandCalEvapparameterswerefoundintheupperboundary oftheircalibrationrange,whenLISFLOODwascalibratedwithERAIGPCPin2006–2010.However,validatingtheprevious optimumparametersetduringawetterperiod(Fig.3b)resultsconsequentlyinanoverestimationoftheobservedstreamflow (Fig.5a).AlthoughtheresultsforboththecalibrationandvalidationinbothperiodsfortheRFE2.0precipitationproduct aresatisfactory(Figs.4aand6a),theobtainedmodelparametersarequitedifferent.However,therangeofthetwomost sensitiveparameters,GwLossandbXinan(Fig.3a)issmall.

ForregionA2(Fig.8b),largedifferencesinthebestparametersobtainedinthetwocalibrationperiodsareobserved.As seeninFig.2bthemodelperformanceisthemostsensitivetotheGwLossparameterformostoftheprecipitationproducts.

AlargevariationintheGwLossvaluebetweenthetwocalibrationperiodsisneededtocompensatefortheprecipitation differencebetweenthetwoperiods,resultingmostlyinareductioninmodelperformanceintheindependentvalidation periods(Fig.6b).ThemodelparametervaluesfromthePPrefflowandCalEvapareconsiderablydifferentfortheRFE2.0 productbetweenthecalibrationperiodswhilethemodelperformanceandrobustnesswasjudgedtobegood.Apparently,

thehighinteractionbetweenthemodelparametersforcedwithRFE2.0producedgoodresultsevenwithadifferentsetof parameters.

ThesmallreductioninKGEinthevalidationperiodsforthe3B42V6,3B42V7andERAIGPCPprecipitationproductsin regionA3isprobablyrelatedtothelowmodelparameterrangesofthemostsensitivemodelparametersfortheseproducts (Fig.8c).Moreover,thesearealsotheproductswithsmalldifferencesbetweenthemeanprecipitationinbothcalibration periodsandthereforecompensationishardlyneeded.

ForregionA4,themodelparametersreachtheupperboundariesoftheparameterrangestoeliminatewatertomatchthe observedstreamflowforthewetterCMORPHV1.0,GSMaPandPERSIANNproducts(Fig.8d).Althoughthemodelparameter rangesforthe3B42V6,3B42V7andERAIGPCParerelativelysmall,themodelparameterswerenotcapabletocompensate forthehighvariabilityofthestreamflowandmatchtheobservedstreamflow.

5. Conclusion

Inthisstudy,weappliedthedifferentialsplit-sampletesttoinvestigatetherobustnessofmodelparametersofafully distributedhydrologicalmodel,bycalibratingthemodelforcedbysevensatellite-basedprecipitationestimates.Formodel calibrationweusedthemodifiedKling-Guptaefficiency(KGE)asobjectivefunction,whichallowedustodifferentiatethe relativecontributionoflinearcorrelation(r),bias(ˇ)andvariability()betweenthesimulatedandobservedstreamflowto theobtainedKGEvalue.WeselectedfourregionsinSouthernAfricawithhighlyvariableclimateconditions,whichresulted inlargeprecipitationdifferencesbetweenthesevenprecipitationproducts.Largediscrepanciesintermsofther,ˇand betweenthesimulatedandobservedstreamflowwereobservedwhenusingSRFEsasmodelinput.Followingadifferential split-sampleapproachtotesttherobustnessofthebestparametersetsoftheLISFLOODmodel,theobservedstreamflowtime seriesweresplitintwoperiodswithhighlydifferentclimaticcharacteristic:2002–2006and2006–2010,andthenmodel parametersobtainedduringcalibrationinoneperiodweretransferredtotheotherperiodtoassessitsperformance.Thus, twooptimizedparametersetswerevalidatedontwoindependenttimeperiods,whichisessentialinhighlyvariableclimate andnon-stationaryconditions(Xu,1999).FromtheresultsobtainedinthisworkitcanbeconcludedthataSRFEproduct whichisaccurateenough(incomparisontogroundobservations)canhelptoavoidfuturemodelrobustnessproblems.

Therefore,accurateprecipitationestimatesareessentialforobtainingrobustmodelparametersbeforeextrapolatingthem intimeandspace.However,thisstatementiscatchmentandtimeperiodspecific,asthecatchmentbehaviorinhighly variableclimateisdifficulttocaptureandonthelimitofmodel’scapability.Therefore,hydrologicalanalysesorpredictions whicharebasedontransferredmodelparametersinhighlyvariableclimateornon-stationaryconditionsshouldbetaken withcare.Notethatreasonsforthelackofmodelrobustnesscanbemultiple(seeIntroduction)andweonlytakeuncertain precipitationestimatesintoaccount.

Wesummarizeourfindingsasfollows:

•The(lackof)modelperformanceintermsofKGEdifferssubstantiallybetweenmodelrunsdrivenbythesevendifferent precipitationproductsandispartiallyreflectedbytheirprecipitationcharacteristics.Ahighpositivecorrelationbetween theupstreammonthlyprecipitationestimateandtheobservedstreamflowprovedtobea goodaprioriindicatorfor obtaininggoodmodelperformanceinaposteriorcalibrationprocess,aslongastheprecipitationvariability(CV)isnottoo high.Highprecipitationvariabilityoftenresultsinoverestimationofthedurationoftherainfalleventsand,therefore,an overestimationofthetotalamountsaswell(e.g.,ther(P,Q)betweenPERSIANNandobservedstreamflowinregionA4for 2002–2006is0.56(significant),buttheCVoftheprecipitationhasavalueof1.21whichresultinapoorKGEof0.24).

•Modelparametersrelatedtoinfiltration(PPrefFlowandbXinan)andwaterlossesintermsofgroundwater(GwLoss)and evaporation(CalEvap)arethemostsensitiveparametersfortheLISFLOODmodelinSouthernAfrica.Theseparameters aremostlyimportanttocompensatethebiasedprecipitationinputs.Mostlikely,forwetprecipitationproducts(e.g., CMORPHV1.0)theinteractionbetweenthemodelparametersislessimportantcomparedtodryproducts(e.g.,RFE2.0).

Tocompensatetheprecipitationbiasthisparametersfindtheiroptimumvalueintheupperorlowerboundsoftheir calibrationrange.Thesensitivemodelparametersofdryprecipitationproductsinteractmuchmorewitheachother,as thetimingandshapeofthehydrographbecomesimportantifcompensatingtheprecipitationbiasislessdominant.

•Parametersetsobtainedduringcalibrationcompensate,uptoacertainextent,thebiasintheprecipitationestimateto matchtheobservedsteamflow,asthebiasishardlyalimitingfactorfortheobtainedKGE inthecalibrationprocess.

Therefore,tominimizethelackofmodelperformanceinthevalidationperiods,thedry/wettrendoftheprecipitation estimateshouldbeingeneralagreementwiththedry/wettrendoftheobservedstreamflow.

•Thecompensationoftheprecipitationcharacteristicsbetweenthecalibrationperiodsleadstodifferentoptimumparam- etersetsunlessthemodelparametersreachtheupperlimits,whichmeansthatthecatchmentsbehaviorisnotcaptured withintheparameterranges.Thisoftenhappenedifthesimulatedstreamflowoverestimatestheobservedstreamflow andtheparametersGwLossandCalEvapreachtheirupperlimittomatchtheobservedstreamflow.

•TheCMORPHV1.0,GSMaPandPERSIANNproductsare–ingeneral–notsuitabletodrivehydrologicalmodelingstudiesin theSouthernAfricanregionwiththeLISFLOODmodelastheseproductsoftenhaveapoorcorrelationwiththeobserved streamflowandgeneratemuchmorerainfallcomparedwiththeotherproducts,whichresultsinlargedifferencesbetween simulatedandobservedstreamflows.Thebestmodelperformanceisobtainedwithproductswhichingestgaugedatafor

biascorrection(3B42V6,3B42V7,ERAIGPCPandRFE2.0products)resultinginthebestconditionsintermsofther,ˇand betweensimulatedandobservedstreamflow.

•AccordingtoVazeetal.(2010)andLietal.(2012),modelscalibratedoverdryperiodsperformbetterinwetperiodsthan theotherwayround.Thesefindingsmightbetrue(notexhaustivelyverifiedhereduetolowsamplesize)becauseof thecommonoverestimationofobservedstreamflowin(semi-)aridareasinhydrologicalmodelling(Vazeetal.,2010;

Gallartetal.,2007;Perrinetal.,2007;LidénandHarlin,2000;Ganetal.,1997;Hughes,1997).However,thesefindings donotruleoutrobustmodelparameters.Accordingtoourfindings,modelparametersobtainedfordrycatchmentswith occasionalrainfalleventsandthereforeahighintra-andinterannualvariabilityinstreamflow(e.g.,A4)arenotableto capturethecatchments’behavior.Thismaybeduetothefactthatthemodelparametersarehighlyinfluencedbyafew eventsandthereforehaveahigherriskforerrorswhentransferredtoadifferentperiod.Moreover,thespatialresolution oftheprecipitationproductsmightbetoocoarse(0.1or0.25^◦)foranaccuratedetectionoflocalheavyprecipitationevents and,therefore,theydonotcapturewellthevolumeandtimingofthepeakflowsespeciallyinasmallcatchmentlikeregion A4.

•Differentcalibrationperiodsrelatedtoprecipitationorstreamflowvariability(wet/dry)resultindifferentoptimumparam- etersobtainedinthecalibrationphase,whichreflectstheeffectofnon-stationarityconditionsontheparameterestimates (Beven,1993).However,theparameterdistributiontendstoshowmorespreadwith“insensitive”modelparameterscom- paredto“sensitive”parametersinthetimeperiodsusedforcalibration(Fig.8).Forthisreasonalongwiththeinteraction betweenparameters,themodelisabletoproducegoodresultswithadifferentsetofparameters,i.e.equifinality(Beven, 1993).Therefore,anestimationofparameteruncertaintyandtheirlackofrobustnesswouldonlymakesenseon“sensitive”

modelparameters.

•ThebehaviorofcatchmentsinSouthernAfrica,butprobablyalsoinotherareaswithhighlyvariableclimateconditions (e.g.,AustraliaortheIberianPeninsula)isdifficulttocaptureusingasinglemodelparametersetforthewholesimulation period.Transposingtheseparameterstoothertimeperiods(scenariosinclimateimpactstudies)orareas(inregionalization studies)shouldbecarriedoutwithcaution.WeagreewiththeconclusionofVazeetal.(2010)thatmodelparameters obtainedfromawet(dry)calibrationperiodshouldbeusedforperiodswhereawetter(drier)futureispredicted,which doesnotmeanthattheparametersarerobust.

Conflictofinterest

Theauthorsdeclarethattherearenoconflictofinterest.

Acknowledgments

ThisworkwascarriedoutwithintheframeworkoftheFP7EUprojectGLOWASIS.Observedstreamflowdatainthisstudy havebeenobtainedfromtheDepartmentofWaterAffairsinSouthAfrica.

WethankHaraldKlingandananonymousreviewerforprovidingvaluablecommentstoimprovethemanuscript.

AppendixA. Supplementarydata

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ejrh.2016.09.003.

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