Spatially distributed modelling of surface water-groundwater exchanges during overbank flood events – a case study at the Garonne River

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Spatially distributed modelling of surface

water-groundwater exchanges during overbank flood events – a case study at the Garonne River

Léonard Bernard-Jannin, David Brito, Xiaoling Sun, Eduardo Jauch, Ramiro Neves, Sabine Sauvage, Jose-Miguel Sanchez-Perez

To cite this version:

Léonard Bernard-Jannin, David Brito, Xiaoling Sun, Eduardo Jauch, Ramiro Neves, et al.. Spatially distributed modelling of surface water-groundwater exchanges during overbank flood events – a case study at the Garonne River. Advances in Water Resources, Elsevier, 2016, vol. 94, pp. 146-159.

�10.1016/j.advwatres.2016.05.008�. �hal-01348632�

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To link to this article : DOI :10.1016/j.advwatres.2016.05.008 URL : http://dx.doi.org/10.1016/j.advwatres.2016.05.008

To cite this version : Bernard-Jannin, Léonard and Brito, David and Sun, Xiaoling and Jauch, Eduardo and Neves, Ramiro and Sauvage,

Sabine and Sanchez-Pérez, José-Miguel Spatially distributed modelling of surface water-groundwater exchanges during overbank flood events – a case study at the Garonne River. (2016) Advances in Water Resources, vol. 94. pp.

146-159. ISSN 0309-1708

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Spatially distributed modelling of surface water-groundwater

exchanges during overbank flood events – a case study at the Garonne River

LéonardBernard-Jannin^a,∗,David Brito^b, Xiaoling Sun^a, Eduardo Jauch^b,Ramiro Neves^b, Sabine Sauvage^a,José-Miguel Sánchez-Pérez^a,∗

aECOLAB, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France

bMARETEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Keywords:

Floodplain

Hydrological modelling Water exchanges River-aquifer interface 3D model

a b s t ra c t

Exchangesbetweensurfacewater(SW)andgroundwater(GW)areofconsiderableimportancetoflood- plainecosystemsandbiogeochemicalcycles.Floodeventsinparticularareimportantforriparianwater budgetandelementexchangesandprocessing.HoweverSW-GWexchangespresentcomplexspatialand temporalpatternsandmodellingcanprovideusefulknowledgeabouttheprocessesinvolvedatthescale ofthereachand itsadjacentfloodplain.Thisstudyused aphysically-based,spatially-distributedmod- ellingapproach for studyingSW-GW exchanges. The modelling inthisstudy is basedon the MOHID Landmodel,combiningthemodellingofsurfacewaterflowin2DwiththeSaint-Venantequationand themodellingofunsaturatedgroundwaterflowin3DwiththeRichards’equation.Overbankflowdur- ingfloodswas alsointegrated,aswellaswaterexchangesbetweenthetwodomainsacrosstheentire floodplain.Conservativetransportsimulationswerealsoperformedtostudyandvalidatethesimulation ofthemixingbetweensurfacewater andgroundwater.The modelwas appliedtothe well-monitored studysiteofMonbéqui(6.6km²)intheGaronnefloodplain(south-westFrance)forafive-monthperiod andwasabletorepresentthehydrologyofthestudyarea.Infiltration(SWtoGW)andexfiltration(SW toGW)werecharacterisedoverthefive-monthperiod.Resultsshowedthatinfiltrationandexfiltration exhibitedstrongspatiotemporalvariations,andinfiltrationfromoverbankflowaccountedfor88%ofthe totalsimulated infiltration, corresponding tolarge flood periods.The results confirmed thatoverbank floodeventsplayedadeterminantroleinfloodplainwaterbudgetandSW-GWexchangescomparedto smaller(belowbankfull)floodevents.Theimpactoffloodsonwaterbudgetappearedtobesimilarfor floodeventsexceedingathreshold correspondingtothefive-yearreturnperiodeventduetothestudy area’stopography.Simulationofoverbankflowduringfloodeventswasanimportantfeatureintheac- curateassessmentofexchangesbetweensurfacewater andgroundwaterinfloodplainareas, especially whenconsideringlargefloodevents.

1. Introduction

Exchanges at the interface between surface water (SW) and groundwater (GW) are known to play a key role in floodplain ecosystems (Amoros and Bornette, 2002, Sophocleous, 2002, Thoms,2003). Areas of mixingbetweenSW andGW are regions of intensified biogeochemical activity (Grimm and Fisher, 1984, McClain et al., 2003). These processes include denitrification,

∗ Corresponding author at: Avenue de l’Agrobiopole, 31326 Castanet Tolosan Cedex, France.

E-mail addresses: l.bernardjannin@gmail.com (L. Bernard-Jannin), jose- miguel.sanchez-perez@univ-tlse3.fr (J.-M. Sánchez-Pérez).

whichhasbeenrecognisedasthemostimportantnitrateremoval process in GW (Rivett et al., 2008) and can lead to significantly reducednitrate concentrations inaquifers supporting agricultural activities (Sánchez-Pérez and Tremolières, 1997, Correll et al., 1992). Denitrification is known to be influenced by hydrological connectivity between SW and GW, and denitrification hotspots have been relatedto activation of the processes through the or- ganicmatterfluxcomingfromsurfacewater(Sánchez-Pérezetal., 2003,Bernard-Janninetal.,2016).Thisnaturalmitigation process is reinforced by the dilution of contaminant concentrations due to the mixingbetweenSW andGW (Pinay etal., 1998,Baillieux etal., 2014). Infloodplains,flood eventsarean importantfeature forecosystems.Thepulsingofriverdischargeisthemajordriving http://dx.doi.org/10.1016/j.advwatres.2016.05.008

force determining the exchange processes of organic matter and organismsacrossriver-floodplaingradients(Junketal.,1989,Tock- ner etal., 1999). Furthermore it is recognised that the overbank flow component has to be included in SW-GW exchanges for a comprehensive water balance assessment (Rassam et al., 2008).

An accurate quantification anddescription of SW-GW exchanges, includingoverbank floods, isthereforea key factorwhen dealing withwaterqualityinalluvialaquifersasitcanhelpassessthepat- terns ofactivationofnaturalmitigation biogeochemicalprocesses and dilution effects. However SW-GW interactions often present complexspatialandtemporalpatterns(Sophocleous,2002,Krause etal.,2007)andastudyatthescaleofthestreamanditsadjacent floodplain(Woessner,2000)isrequiredtounderstandthemfully.

As they allow characteristics of the environment to be taken into consideration ona detailedscale, physically-based, spatially- distributedmodels arevaluable toolsforimprovingknowledgeof SW-GWexchangesandassessing thethree-dimensional natureof the problem (Sophocleous, 1998, Bradford and Acreman, 2003).

NumerousstudiesfeaturingdistributedmodelsandincludingSW- GW exchangesin floodplainareashave beencarriedout, encom- passing SW-GW exchange patterns and biogeochemical zonation induced by meander sinuosity (Boano et al., 2006, Boano et al., 2010),heattransport (Brookfieldetal., 2009,Horrittetal., 2006), 3D-flow patternsin relation to riverlevel variations (Derx et al., 2010,Nützmannetal.,2013),hydrofaciesheterogeneityimpacton SW-GWexchanges(Freietal., 2009),SW-GWexchangeimpacton floodplainwaterbalance(Krauseetal.,2007,KrauseandBronstert, 2007, Wenget al., 2003), solute transport through riparianareas (Wengetal.,2003,Hoffmannetal.,2006,Peyrardetal.,2008)and contributionofGWtostreamwater(Partingtonetal.,2011).While allthesemodellingstudiesintegrateasurfaceandsubsurfacecom- ponent aswell asSW-GWexchanges, overbankfloodeventshave not beenincludedintheanalysis.Thiscanpresentaproblemfor assessingSW-GWexchangesinthefloodplainaccurately,especially duringlargefloodeventswhereinfiltrationfromsurfacerunoff can occuracrossthefloodplain(Batesetal.,2000)andinundatedareas candriveaquiferrechargepatterns(Helton etal., 2014).Although overbank flood infiltration is not considered importantwhen the riverandaquiferaredisconnected(Morinetal.,2009),itisrecog- nisedthatthelackofanoverbankflowcomponentinmodelsleads toanunderestimationofinfiltrationofriverwaterintotheaquifer (Doppleretal., 2007,Engeler etal.,2011). Inanotherstudy,over- bankflow duringflooding hasbeensimulatedtostudyfloodplain contamination,butonlyverticalinfiltrationhasbeentakenintoac- count to evaluate pollutantdeposition andsubsurfaceflows have not been simulated (Stewart et al., 1998). In this case it is the simulation of subsurface flow returning to the river that is lack- inginordertoprovideacomprehensiverepresentationofSW-GW exchanges.

Overbankflood eventsareknownto bevery importantforel- ementprocessingandwaterbudgetinfloodplainareas,buttothe authors’knowledgetheyarenotusuallyincludedinSW-GWstud- ies.Themainobjectiveofthisstudywastoassesstheimportance of overbank flood eventson SW-GWinteractions in a floodplain area. Using a distributed model, two domains – SW and GW – were simulated and coupled through infiltration/exfiltrationpro- cesses. These processes were simulated across the entire flood- plainareainordertoincludetheimpactofoverbankfloodevents on SW-GWexchange dynamic.The modelwasapplied toa well- monitoredstudysite,providingastrongdatasetformodelvalida- tion, whereSW-GWexchangeswere analysed. Atransport model wasalsoincluded andthemodelwasthenused toevaluate SW- GW exchanges spatially andtemporally fordifferent flood condi- tionsinthestudyarea.Thisstudyisalsoaprerequisiteforfuture workinvolvingthesimulationofbiogeochemicalprocessessuchas denitrificationinfloodplainareas.

2. Materialsandmethods 2.1. Modellingapproach

Themodelling strategyfora completesurface-subsurface flow systemshouldincludesurfaceandsubsurfacecomponentsandthe couplingbetweenthem(Furman,2008).Numerousmodelsbelong tothiscategorythatdifferintermsoftheformulationofthecom- ponent governing equations (including dimensionality) and their coupling strategy and technical solution (Maxwell et al., 2014).

Forsubsurfaceflow, mostofthemodelssolvetheRichards’equa- tion (one, two or three dimensions) and solve a formulation of the Saint-Venantequation (kinematic, diffusive or dynamicwave in one or two dimensions) for the surface component (Furman, 2008). The models differ in terms of their coupling strategy in- volvingasynchronouslinking(CondonandMaxwell,2013),sequen- tial iteration (Dagès et al., 2012) or a globally implicit scheme (Kollet and Maxwell, 2006), andthe technical solution involving boundaryconditions(BC)switching(Dagèsetal.,2012),first-order exchange (Panday and Huyakorn, 2004) or pressure continuity (Maxwell etal., 2014,KolletandMaxwell,2006). Inastudycom- paring seven models with the different characteristics described above,itwasfoundthatthemodels demonstratethe samequali- tativeagreementalthoughtheyusedifferentapproaches(Maxwell etal.,2014).

Out of the open-source models able to simulate SW-GW ex- changes, MOHID Land was applied in this study. This model in- cludesall featuresrequiredtosimulateimpactofflood eventson SW-GWexchanges.Subsurfaceflowwascomputedwiththethree- dimensional Richard’s equation needed to represent spatial vari- abilityoftheflowintheunsaturatedmediaofthefloodplainarea in detail. Surface flow was computed with the two-dimensional dynamicwave formulationoftheSaint-Venantequation,allowing the correct representation of the rapidly changing stream stages duringflooding. The couplingbetween the two components was produced through asynchronous linking andfirst-order exchange andrealisedacrosstheentiremodelleddomain(i.e.notlimitedto theriverbed location).Inaddition,themodelincludedatransport module. While these features are shared by several models, the noveltyoftheapproachistoapplythistypeofmodeltosimulate floodplainhydrology.

2.1.1. OverviewoftheMOHIDmodel

MOHIDLandis apartof theMOHID WaterModellingSystem (Neves et al., 2013) (www.mohid.com). It is a physically-based, spatially-distributed model designed to simulate the water cycle inhydrographic basins, including SW-GWinteractions. It uses an object-oriented approach to facilitate the integration of different processesandmodules,andafinitevolumeapproachwithaflux- driven strategy to facilitate the coupling of processes and verify the conservationof mass andmomentum (Trancoso et al., 2009, Braunschweigetal.,2004,Britoetal.,2015).

Although it was originally designed to model river network systems and watersheds (Trancoso et al., 2009), the modularity ofMOHIDLandallowsthemodelto meetthespecificfeatures of a floodplainarea. The modelset-up used in this studyconsisted oftwo domains: thesurface water(SW) domain andthe porous media (PM) domain (Fig. 1). The hydrology of the SW domain was calculated according to the two-dimensional Saint-Venant equation(dynamicwave).The rivergeometrywasincludedinthe SWdomain toensure thecontinuity ofsurfacerunoff simulation overthefloodplain duringoverbank floodevents.Waterfluxesin thePMdomainwerecalculatedinthreedimensionsforsaturated andunsaturatedmediausingtheBuckingham-Darcyequation.The spatially-distributed structure allowed interactions between the two domains – infiltration from SW to PMand exfiltration from

Fig. 1. Presentation of the modelling approach. Water flows are modelled in and between PM and SW domains. Overbank flow is taken into account during flood events.

Transport is considered in both domains.

PMtoSW– tooccuracrossthefloodplainareaateach timestep.

Thepossibilityofimposingboundaryconditionsforthesimulated domaininSWandPMwasimplementedinthemodelforthepur- posesof thisstudy. Transport of chloride (Cl⁻) asa conservative element was also simulated. Input data construction and output datavisualisation were facilitated using the graphical user inter- faceMOHIDStudio.Dueto itsobject-oriented modellingstrategy, MOHID Land can provide a basis for further modelling studies in alluvial plains by facilitating the incorporation of modules designedtosimulatebiogeochemicalprocessesforexample.

2.1.2. GoverningequationsofMOHIDLand

MOHIDLandisagrid-basedmodelwithanArkawaC-gridtype (Purser and Leslie,1988) inwhich flows andvelocities are com- puted atthe cell interfaces, while propertiessuch aswater con- tentarecomputedatthecentreofeachcell.Unsaturatedandsat- uratedflowsarecomputedinthreedimensionsinthePMdomain, andsurfaceflowintwodimensions(horizontal)intheSWdomain wherehorizontalPMandSWgridsarematching.Processesineach domainarecalculatedusinga finitevolumemethodto guarantee massconservation,andsolvedwithanexplicitscheme.Themodel firstcomputesPMprocesses,includinginfiltration/exfiltration,fol- lowedbySWprocesses.

Porous media flow. First, water velocity is computedin each cell interface of the saturated and unsaturated medium using the Buckingham-Darcyequation(Swartzendruber,1969)(1):

vi=−K(θ) ∂^H

∂^xi

(1)

wherev_i [m s⁻¹] isthe watervelocity atthe cellinterface along directioni, x_i [m] is the distance along direction i, K [m s⁻¹] is hydraulicconductivityandθ ^{[-]isthecellwatercontent.H[m]is}

thehydraulicheadcomputedineachcellcentreasshowninEq.2:

H=h+ψ^{+z (2)}

whereh[m]is thesuction head,ψ^{[m]is thestaticpressurehead}

andz[m]istheelevationofthecentreofthecell.

The governing equation for flow in the porous media result from the combination of the Buckingham-Darcy Eq. (1) and the continuity equation and is known as Richards’ equation (Brito etal.,2015,Richards,1931)(3).

∂θ∂^{t =} ∂

∂^xi

K(θ)∂^H

∂^xi

. ⁽³⁾

The model uses the combination of the Mualem model (Mualem, 1976), which calculates the hydraulic conductivity in unsaturated soils (4 and 5), andthe van Genuchten model (van Genuchten,1980)forcomputingwaterretentioninsoils(6):

K(θ)^=Ks.SEL.

1−

1−SE1/(^1−N1)1−1/N2

(4)

SE=(θ−θr)^/(θs−θr) ⁽⁵⁾

h(θ)=−

S_E^{(−1/(1−1/N))}−1 ^1/N

/α ⁽⁶⁾

whereθr [-]istheresidual watercontent,θs[-]is thesaturated watercontent,α^{[cm−1]isatermrelatedtotheinverseoftheair}

entrypressure,N(dimensionless)isameasureofthepore-sizedis- tribution,S_E [-]istheeffectivesaturation,Lisan empiricalpore- connectivity parameterand Ks [m s⁻¹] isthe saturated hydraulic conductivity.

PMfluxesarecalculated inthethree-spacedirection,andver- ticalinfiltration betweenSWandGWisthencomputedbyapply- ingtheDarcyequation betweenSWandthetopPMlayer(Fig.2,

Fig. 2. Schematic of the vertical infiltration flux (q inf) calculation between SW cells (i,j) and the top PM cells (i,j,k top). WC is the surface water column in SW and z soilis the elevation of the soil surface. DWZ is the thickness, H is the hydraulic head and K sis the saturated hydraulic conductivity of the top PM cell. i and j are the hori- zontal cell coordinates, k toprepresents the vertical coordinate of the upper layer.

Eq.7):

q_{in f}(ⁱ,j)=Ks(ⁱ,j,ktop) ^A(ⁱ,j)

H_SW(ⁱ,j)−H(ⁱ,j,ktop) WC (ⁱ,j)+0.5DWZ(ⁱ,j,ktop)

(7) whereq_inf istheverticalinfiltrationflux[m³s⁻¹],Aistheareaof thecell[m²],HSWisthesurfacewaterelevation[m],WCisthesur- facewatercolumn[m],DWZisthe PMcellverticalheight,i,jare thecellhorizontalcoordinatesandktopisthetopPMlayercoordi- nate.

ToavoidnegativevolumeinSW,theinfiltrationfluxq_infislim- ited to the available water volume in SW domain. Then θ^{t+dt is}

updatedineachcellofthePMdomainaccordingtothecontinuity (Eq.(8)):

θ^t+dt=

θ^tV+(^qx+qy+qz+q_{in f})^dt /V (8) whereθ^{t+dt istheupdatedcellwatercontentattimestept}+dt[-],

θ^{t isthecellwatercontentattimestept [-],Visthecellvolume}

[m³],dtisthetime step[s],andqx,qy,qz arethefluxesalong the threespacedirectionsx,yandz[m³s⁻¹].

Finally,foreachcellthewatercontentθ^{t+dt iscomparedtothe}

saturatedwatercontentθ^s.Ifθ^t+dt>θS theexcessofthecellwa- ter volume (θ^t+dt−θS) ^istransferred firstto theunderlying cells ifspaceisavailableandthentotheuppercells.Whenallthecells ofthecolumnaresaturated,theeventual remainingexcesswater volumeisreallocatedtotheSWdomain(exfiltration).Thismeans that massconservation issatisfiedandθ^t+dt≤θS inevery cellof thePMdomain.

Surface water flow. Surface waterflow is then computed, solving the 2D Saint-Venantequation (dynamic wave) inits conservative form,accountingforadvection,pressureandfrictionforces(Chow et al., 1988) for the two horizontaldirections of the grid (9 and 10):

∂^Qx

∂^{t +}vx∂^Qx

∂^{x +}vy∂^Qx

∂^{y =−g.A} ∂^H

∂^{x +}|^Q|^.Qx.n2

A².R⁴_h^/3

(9)

∂^Qy

∂^{t +}vx∂^Qy

∂^{x +}vy∂^Qy

∂^{y =−g.A} ∂^H

∂^y+|^Q|^.Qy.n2

A².R⁴_h^/3

(10)

Fig. 3. Schematic of time step management (see text for explanations).

whereQ[m³ s⁻¹]istheflowatacellfacealongthetwohorizon- tal directions ofthe gridsx and y, v [m s⁻¹] is the flow velocity alongthe xandy directions,g [ms⁻²] isthegravitationalaccel- eration,A[m²]is thecross-sectionofthewatercolumn, Histhe watercolumn[m],n[sm^−1/3]istheManningcoefficient,R_h[m]is thehydraulic radius,andxandy[m]are thedistancesalong the twohorizontaldirectionsofthegrid.Thewatervolumeandwater columnineachcell arethen updatedaccordingto thecontinuity equation.

Transport. Transport of properties is computed in SW and PM throughtheadvection-diffusionEqs.(11and10):

∂β∂^{t =−}∂(β^.v₎

∂^{xi +}∂ γ ∇ β

∂^{xi (11)}

γ=αi.vi (12)

where β ^{is the property} concentration in [gm⁻³], x_i [m] is the distancealong thedirectioni,γ ^isthediffusivity[m² s⁻¹]andαi

isthedispersivityalongthedirectioni[m].

2.1.3. Timestepcontrolandstability

MOHIDLanduses anadaptivetime step(Fig.3). Startingfrom aninitialtimestepdefinedforthewholemodel(dt_model),aniter- ativeprocess isperformed within eachdomain (PM andSW) for whichastabilitycriterion isdefined.InPM,itcorresponds tothe maximumwatervolumevariationallowedinacell.InSWthetime stepiscontrolledbylimitingtheCourantnumber.Ineachdomain the time step is reducedand thenumber of iterationsincreased untilthe criterionis met.Thefluxesare thenintegratedforeach domain over dt_model. At the endof the iterativeprocess, a time stepiscalculatedforeachdomain(dtPM anddtSW).Thistimestep corresponds to an increased value of the dt_model ifone iteration is enough to meetthe stability criterion ora decreased value of