Green-blue water accounting in a soil water balance

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ContentslistsavailableatScienceDirect

Advances

in

Water

Resources

journalhomepage:www.elsevier.com/locate/advwatres

Green-blue

water

accounting

in

a

soil

water

balance

Arjen

Y. Hoekstra

University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands

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Keywords: Crop production Irrigation eﬃciency Water footprint Water productivity Water use eﬃciency

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Ithasbecomecommonpracticetospeakabout‘green’versus‘blue’waterconsumption,inordertodistinguish betweenconsumptionofrainwaterversusgroundwaterorsurfacewater.Thetwosourcesofwaterdifferinterms ofpossibilitiesforstorageanduse.Whereasindustrial,municipalandlivestockwatersupplyprimarilydepend onbluewater,cropcultivationreliesonbothgreenandbluewater.Discriminatingbetweengreenandblue waterconsumptioninacropfieldisnotstraightforward:consumptionreferstoevapotranspiration(ET)and watercontainedintheharvestedcrop,whichbothappearinundifferentiatedform.Onecannotseewhichpart ofETorthewaterinaplantoriginatesfromrainwaterandwhichpartfromirrigationwater.InthispaperI proposeagenericandphysicallybasedmethodtodifferentiategreenandblueevaporation(E)andgreenand bluetranspiration(T)bydailyaccountingofthefractionsgreenandbluewaterineachsoilandvegetationlayer. Thegreenandbluefractionsofallwaterfluxesleavingasoilorvegetationlayerinadaydependontheaverage greenandbluewaterfractionsinthatsoilorvegetationlayerduringthatday.Thismethodallowsforanaccurate assessmentofirrigationefficiency(theratioofbluewatertranspirationtotheirrigationwaterapplied),andfor apreciseestimationofgreenandbluewaterfootprintsofcropproduction(theratioofeithergreenETorblue ETtothecropyield).

1. Introduction

Freshwateravailabilityessentiallydependsontheprecipitationover land.On land,precipitation partitionsinto two components: evapo-transpirationandrunoff.Thetraditionalfocusofwaterresources plan-ningandmanagementhasbeenonhowtobestdivert,storeand redis-tributetherunoff flowforuseinagriculture,industriesandhouseholds (FalkenmarkandRockström,2006).This,however,hasproventobea limitedfocus,becauseitignorestheotherwaterflowthatishighly rel-evanttooureconomyaswell(Schynsetal.,2019).Theconventional engineeringapproachofoptimizingtheallocationanduseof ground-waterandsurfacewaterresources (therunoff flow)results inaform ofsub-optimizationiftheefficientallocationanduseofthe evapora-tiveflowis notincludedin theconsiderationsaswell.Anestimated 67%oftheworld’scropproductionstillcomesfromrainfedagriculture (Portmannetal.,2010),wherecropstakeuprainwaterthatisstored inthesoiltosubsequentlytranspiremost ofit.Incroplandsthereis, nexttothebeneficialtranspirationbycrops,whichcontributestotheir biomassgrowth,unproductiveevaporationofwateraswell,from rain-fallthatfallsontheleavesandfromthesoilsurface.Efficientuse of rainwaterisasimportantasefficientuseofirrigationwater.Inorder togeneratethenecessarydebateontheefficientuseoftheevaporative flowfromrainwaterstoredinthesoilversustheefficientuseof ground-waterandsurfacewaterresources,Falkenmark(1995)coinedtheterms

E-mailaddress:a.y.hoekstra@utwente.nl

greenversusbluewateruse.Greenwaterusereferstotheuseof rainwa-terinthesoilandbluewaterusetotheuseofgroundwaterandsurface waterresources.

Eventhoughthedistinctionsbetweengreenandbluewaterresources andbetweengreenandbluewaterusearecommonlyemployedthese days,westillstruggletousetheminpreciseunambiguousways. Re-garding green water, as Schynset al.(2015) pointout, the termis oftenlooselyused,sometimestorefertorainwaterstorageinthesoil, whileothertimestorainwaterevaporation(FalkenmarkandRockström, 2006; Falkenmark, 2013).Furthermore, the term‘green water flow’ isusuallydefinedas‘theevaporativeflowfromland’,butoftenit re-mainsunclearwhetherthisincludesonlyevapotranspiration(ET)from rain storedinthesoil ortotalET,which includesETfrom irrigation water and evaporation from otherforms of blue water use as well. Falkenmark(2007) speaksabouttheblue-to-greenredirectionthat oc-curswhenpartofbluewaterresourcesthatareabstractedsubsequently evaporate.Thisideaofbluewaterflowbecominggreenwaterflow con-trasts withthecommonandlogicalusagetospeakaboutbluewater consumptionwhenreferringtoevaporationofabstractedbluewater re-sources. Furthermore,thetermsgreenandbluewateraresometimes usedtorefertowaterresourcesavailability,whileothertimestowater resourcesuse.Alltheseambiguitiesmayplayaroleinthehesitancein thehydrologicalcommunitytousethegreen-bluewaterterminology, sinceweshouldusecleardefinitionsofstocksandflowsandkeeptrack

https://doi.org/10.1016/j.advwatres.2019.05.012

Received29December2018;Receivedinrevisedform13April2019;Accepted16May2019 Availableonline17May2019

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ofwaterbalancesovertime.Whatevercolourtermsareused,itshould alwaysbeclearhowatermmatchesanidentifiablestockorflowinthe watercycle.Infact,forunderstandinghydrologywecansufficeworking withwell-establishedhydrologicalterms;wedon’tneedcolourcoding forthat.Thecolourcoding,however,fulfilsapracticalfunctionin dis-cussionsontheefficientallocationanduseofdifferentwatersources (Rostetal.,2008;Hoekstra,2014).Whatisneededthoughisastricter formalizationoftheuseofthegreen-bluewaterterminology,inaway clearlylinkedtohydrologicalterminology.

Anotherchallengeisthatdifferentiatingbetweengreenandblue wa-terconsumptionisnotthatsimpleasitmayseem.Consumptionrefers toETandwatercontainedin theharvestedcrop,whichbothappear inundifferentiatedform;onecannotseewhichpartofETorthe wa-terinaplantoriginatesfromrainwaterandwhichpartfromirrigation water.Thisraisesthequestionthenhowtoestimateirrigationwater consumption.Eventhoughmanyscholarsreportfiguresonirrigation waterconsumption(e.g.Haddelandetal.,2014;Hoff etal.,2010),it oftenremainsunclearwhatpreciselytheyreferto,sincehydrological orcrop growthmodelshelp tosimulatethesoil waterbalance,thus providingestimatesoftotalET,possiblydistinguishingbetween evap-oration(E)andtranspiration(T),butthesemodelsdonotdistinguish betweengreenandblueET.Sinceirrigationwaterconsumptionrefers toblueET,thequestionishowthesescholarshandlethisproblem.

OnemethodthathasbeenpractisedistoestimateblueETasthe differencebetweenETunderirrigatedconditionsandETunder rain-fedconditions(e.g.MekonnenandHoekstra,2010,2011;LiuandYang, 2010;SiebertandDöll,2010;Hoogeveenetal.,2015).Thisapproachis problematicsincetherootingdepthunderrainfedconditionscan sub-stantiallydifferfromtherootingdepthunderirrigatedconditions, af-fectingthewateruptakebyplants,sothatwhatisgreenEandTunder rainfedconditionsisnotthesameasgreenEandTunderirrigated con-ditions.MekonnenandHoekstra(2010,2011) partiallysolvedthisby simulatingtherainfedcasewitharootingdepthasitwouldbeunder ir-rigatedconditions,butthisapproachisstillunsatisfactory,because irri-gationaffectstheoverallsoilmoisturedynamicsovertime,sothatgreen EandgreenTunderirrigationarenotnecessarilythesameasgreenE andTunderrainfedconditions.Anotherproblemwiththis approach isthatinmanyregions,rainfedagricultureisnotevenanalternative toirrigatedagriculture,sothatthereferencerainfedcaseisnot avail-able.Theapproachofestimating blueETastotalETunderirrigated conditionsminustotalETunderrainfedconditionshasalsobeen fol-lowedbyRomagueraetal.(2014),whousedremotesensingproducts forestimatingtotalETunderirrigationconditionsandmodel simula-tionswithoutirrigation.Thisapproachfacesthesameproblemasthe studiesthatcomparetwodifferentmodelsimulations.

AnothermethodtodistinguishbetweengreenandblueETisto es-timateblueETbasedontherelativeadditiontothesoilofirrigation waterandrainfallovertime(Rostetal.,2008;Hanasakietal.,2010; Faderetal.,2011).Thisisabetterwaytopursue,butthewaythishas beenimplementedhasthusfarbeenabitsimplistic,ignoringthefull dynamicswithinthesoil.Dropsofirrigationwaterorrainwaterarenot reallyfollowedalongtheirpathwaysthroughthesoilmoistureand fi-nallytoEorT.Rostetal.(2008) andFaderetal.(2011),forexample, distinguishdifferentsoillayerswithoutaccountingthegreen-blue ra-tiointhelayersseparately,andlackafullaccountingofallgreenand bluewaterfluxesleavingeachsoillayer.Hanasakietal.(2010)consider evapotranspirationasawhole,notdistinguishingtranspiration specifi-cally,thusunabletoestimatethepartofirrigationwaterappliedthat benefitsthecrop.Furthermore,allthreestudiesneglectthecontribution ofcapillaryrisetosoilwater.

InthispaperIproposeagenericandphysicallybasedmethodfor greenandbluewateraccountingincropcultivation.Thebasisisformed bytheunderlyingsoil hydrologythat determinesthechangesinsoil waterstocksandﬂowsovertime.Themethodcomprisesapartitioning ofsoilmoistureandallwaterﬂuxesleavingthesoilintoagreenand bluecomponent,forinstanceonadailybasiswhenthatisthetimestep

considered inthehydrological orcrop growthmodel. Inthegeneric frameworkIwill alsoincludecapillaryriseasa particularsourceof waterforcropgrowth,whichcomesinadditiontorainwaterand irri-gationwater.Thegreen-bluewateraccountsformanextensiontothe usualhydrologicalwateraccountsofchangesinstocksandflows.The essenceisthatwetracethedifferentoriginsofthewatercontainedin thesoilandineachflowleavingthesoil.Thenoveltyofthepaperisthat itproposesatheoreticallysoundmethodtodistinguishbetweengreen andbluetranspirationandbetweengreenandbluesoilevaporation,by trackingthepathwaysofrainwaterandirrigationwater,toreplacethe proximalmethodsasdiscussedaboveandemployeduntilnow.

First,Iwilladdressthequestionwhyhavingsuchgreen-bluewater accountingsystemisusefulatall.Second,Iintroducetheprincipleof tracinggreenandbluewaterinthesoilwaterbalance.Third,Iprovide anillustrativeexampleofgreen-bluewateraccounting,inasimplecase ofaone-soil-layermodel.Fourth,Ireﬂectonthepracticaluse ofthe accountingmethodfortheestimationofirrigationwaterconsumption, irrigationeﬃciencyandgreenandbluewaterfootprints.Iwillconclude byshowinghowthemethodpresentedheresolvestheambiguitiesin green-bluewateraccountingasmentionedabove,andIwillrecommend tointegrategreen-bluewateraccountinginsoil-waterbalancemodels asastandardroutine.

2. Whydiﬀerentiatebetweengreenandbluewaterconsumption?

Themainreasontoexplicitlydistinguishbetween‘green’and‘blue’ waterconsumption– thatisconsumptionofrainwaterversus groundwa-terorsurfacewater– isthatthetwosourcesofwaterdifferintermsof possibilitiesforstorageanduse.Whereasrainwaterisstoredinthesoil andisprimarilyusedin-situforbiomassgrowth(food,feedorenergy crops,productionforest),groundwaterandsurfacewaterarestoredin naturalaquifers,lakesandrivers,butcanalsobeabstractedordiverted, transported,andstoredinartificialreservoirs,andcanbeusedfora va-rietyofpurposes,fromirrigatingcropsortrees(tosupplement rainwa-ter)towatersupplyforhouseholds,municipalpurposesandindustries. Therangeofbeneficialusesforbluewateristhuslargerthanforgreen water,butthisdoesnotmeanthatgreenwaterisnotbeneficiallyused foroureconomy.Therearevariousreasonswhywewanttoknowhow muchgreenandbluewaterresourcesweconsume,forwhat,andhow efficient.

Letmestartwiththerelevanceofirrigationefficiency.Whenweare interestedinthequestionwhichpartoftheirrigationwaterappliedto thefieldbenefitsthecrop,weneedtoknowblueT.Theirrigation ef-ficiencyatfieldlevelisdefinedasthefractionoftheappliedirrigation watervolumethatbenefitstheplant(Burtetal.,1997).Thevolumeof irrigationwaterthatbenefitstheplantisblueT,henceweneedtobe abletoestimatethat.Totalwaterconsumptionincropproductionis de-finedastheEToverthegrowingperiod(fromplantingtoharvest).In irrigatedcropproduction,thesourceofsoilmoistureandETispartly rainwater,partlyirrigationwater,andpartlycapillaryrise.With hydro-logicalorcropgrowthmodelsweareusedtoestimatetotalEandtotal T,butforassessingirrigationefficiencywereallyneedtoknowblueT, thepartofTthatstemsfromirrigation.

AnotherreasonforourinterestinblueT,aswellasblueE,isthe impact ofbluewater useon groundwatertables,river flowsand re-mainingbluewateravailabilityinacatchment,whichisnotcaptured bythemeasureofirrigationefficiency(Perry,2007;ContorandTaylor, 2013;Graftonetal.,2018).Whenweareinterestedinthequestionhow muchoftheirrigationwatergetslostfromthecatchment– thatisthe partoftheirrigationwaterthatevaporatesortranspiresanddoesnot infiltratetogroundwaterorrunoff tostreamsagain– weneedtoknow blueET.Bluewaterabstractionsarenotchangingthewateravailable inthecatchmentaslongaswereturnthewaterafterusetowherewe abstractedit.Bluewaterscarcityinacatchmentdependsonthevolume ofbluewaterconsumptionincomparisontobluewateravailability.

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Wearealsointerestedinbluewaterconsumption(blueET),aswell asingreenwaterconsumption(greenET),toevaluatehowmuchwater weconsumeperunitofcropproduced.Inotherwords,wemaybe inter-estedtoquantifytheblueandgreenwaterfootprintofcropproduction andanalysetheextenttowhichwecanreducetheblueandgreen wa-terfootprintperunitofproductbyeitherconsuminglesswaterwhile producingthesameorproducingmorewiththesameamountofwater (Hoekstraetal.,2011).Notethatreducingthegreenandbluewater footprintperunitofcropisthesameasincreasingwaterproductivity, whichisexpressedastheamountofcropproducedperunitofwater consumed(Molden,2007).Inirrigatedcropproduction,onemayaim toincreaseproductionpertotalamountofgreenandbluewater con-sumed,whileinrainfedfarming,thefocuscansimplybetheincrease ofproductionperdropofgreenwaterconsumed.

Yetanotherreasonwhywemaybeinterestedinestimatinggreen andbluewaterconsumptionistoanalysethetrade-off betweenthetwo. Addingirrigationwatertoacropfieldchangesthewaterbalanceasa whole,affectingtheevaporationandwateruptakeandtranspirationby plantsaswell.Chukallaetal.(2015),forinstance,showhowadding someirrigationwatertoanoriginallyrainfedcropcanincreasegreen ET,butincreasecropyieldevenmore,thusreducingthegreenwater footprintperunitofcropproduced.Perryetal.(2009)refertothecase wherebyonecrop isreplacedbyanothercropwithadeeperrooting depth,sothatmorewatercanbetappedfromthesoilprofile.Ifthecrop wasirrigated,lessirrigation(bluewater)willbeneededtoachievethe sameyield,butthevolumeofrainwater(greenwater)thatwillbe con-sumedwillincrease.Therearealsotrade-offsatlargerscale,typically whenshiftinginariverbasinfromrainfedtoirrigatedproductionor viceversa,orwhenshiftingproductionfromabasinwithmainly rain-fedagriculturetoanotherbasinwithmostlyirrigatedfarmingorvice versa.Yetanotherexampleofshiftingbetweengreentobluewater con-sumptioniswhenchangingfromthecultivationofarainfedwintercrop togrowinganirrigatedspringcroportheotherwayaround.

ForvariousreasonswemaythusbeinterestedinknowingblueT, blueEorblueETasatotal,tobedistinguishedfromgreenT,greenE andgreenETasatotal.Inreality,however,EandTappear undifferen-tiated,sogreenandblueEandgreenandblueTcannotbemeasured directly;theycanonlybeinferredindirectly.GreenandblueEandgreen andblueTaren’tconventionalhydrologicalconcepts,becausefor un-derstandinghydrologyit’slogicandsufficienttoworkwithtotalEand totalT.SeparatingEandTintotheirgreenandbluecomponentsis use-fulthough,asthissplitunveilstheoriginofthewaterthatevaporates ortranspires.Green-bluewateraccountsasextensiontohydrological accountsthustellsomethingabouttheoriginofstocksandflows.Most inparticularforEandTorforETasatotalitishighlyrelevanttoknow whichpartscomeforrainwaterandwhichpartsfromaddedirrigation water.

3. Theprincipleoftracinggreenandbluewaterinthesoilwater

balance

Theaccountingmethodproposedhereisbuiltontheideathatavalid questionforanywaterfluxleavingthesoilandvegetationis:whatisthe source?Particularlyfor(nonbeneficial)soilevaporationand(beneficial) croptranspirationwemaywanttoknowhowmuchofthatwas irriga-tionwaterandhowmuchrainwaterorcapillaryrisefromthe ground-water.

InordertoestimategreenandblueEandTweneedtotracethe originofEandT.TheEandTﬂowsoriginatefromsoilwaterorwater interceptedbyvegetation.These waterstocks inturn originatefrom eitherprecipitationorirrigation,andsometimespartlyfromcapillary riseaswell.Ifwe knowhowmuchofthewaterinthesoilandhow muchofthewaterinterceptedbyvegetationcomesfromprecipitation orirrigation,wealsoknowthefractionsofgreenandbluewaterinEand T.ThereforeIproposeasimpleaccountingmethodtokeeptrackofthe fractionsgreenandbluewaterinthediﬀerentsoilandvegetationlayers,

onadailybasis,asabasistoestimategreenandbluewaterfractionsin allﬂuxesleavingeachlayer.Themethodisasfollows:

1. Asystematicrecordingofthegreen-bluewatercompositionisdone persoilandvegetationlayer.Theamountofgreenwaterinasoil orvegetationlayerincreaseswhenrainwaterentersthatlayer.The amountofbluewaterinalayerincreaseswhenirrigationwateror capillaryriseentersthatlayer.Thegreen-bluecompositionof the waterstorageinalayeriscontinuouslyupdatedbasedonthecolours ofthevariousinﬂows.

2. Atacertainpointintime,eachwaterﬂux(e.g.EorT)fromaspeciﬁc soilorvegetationlayeriscomposedofagreenandabluefraction equaltothegreen-bluecompositionofthewaterstorageinthatlayer atthatpointintime.Thisassumesahomogeneousdistributionof greenandbluewaterinalayer.

Theextendedaccountsarenotnecessarilylimitedtogreenandblue water. Thebluewateraccounts canbe doneseparatelyforblue wa-teroriginatingfromdifferentsources(Hoekstraetal.,2011),including forexample:irrigationwaterfromsurfacewater;irrigationwaterfrom renewablegroundwater;irrigationwaterfromfossilgroundwater; irri-gationwaterfromharvestedrainwater;irrigationwaterfromdomestic wastewater;irrigationwaterfromdesalinatedseawater;andcapillary risefromrenewablegroundwater.Atcatchmentscaleitcouldbe inter-estingtoknowhowmuchbluewaterisconsumedincropproduction fromthesedifferentwatersources.Attheminimumlevel– becauseof theessentiallydifferentsoilwaterdynamics– itisrecommendedto dis-tinguishbetweenbluewaterfromirrigationwateraddedtothefieldand bluewaterenteringthesoilwaterfrombelowthroughcapillaryrise.

Letmemakeanotehereonthetreatmentofharvestedrainwater. Rainwaterharvestingreferstothelocalcaptureandstorageof rainwa-ter,directlywhenitfallsonthegroundorshortlyafteritalreadyhas becomerunoﬀ.Harvestedrainwateristhusbluewater(whichmaybe confusinggiventheuseofthetermrainwater),becauseitisnot con-tainedinthesoilbutinsteadcollectedinawaterreservoirfromwhich thewatercanbedistributedtoanyuse.Usingthisharvestedrainwater isthusbluewateruseandanyconsumptionfollowingfromitwillbea formofbluewaterconsumption.

Theaccountingmethodpresentedhereisphysicallybased;the out-comescouldbeempiricallytestedusingtracermethods.Forexample, ifwewouldaddatracersubstancetoirrigationwaterandmeasurethe occurrenceofthattracerinthesurfacerunoff,evaporativeflowsand groundwaterrecharge,wecouldestablishwhichfractionsofthese wa-terflowsoriginatefromtheaddedirrigationwater.Thesameistruefor thesoilwaterindifferentsoillayers:atanymomentintimeonecould measuretheoccurrenceofthetracerinthesoilmoistureinaparticular soillayerandestablishwhichfractionofthesoilmoistureinthatlayer apparentlyoriginatesfromirrigationwater(versusothersourceslike rainandcapillaryrise).

4. Thepracticeoftracinggreenandbluewaterinasoilwater

balancemodel

Howtheaccountingofgreenandbluewaterincropcultivationis donepreciselydependsontheschematizationoftheverticalintooneor moresoilandvegetationlayersandtheschematizationofwaterfluxes enteringandleavingthevariouslayers.HereIgiveasimpleexamplefor thecaseofonesoillayer,whiledistinguishingbetweenthreeinflows (in-filtrationofrainwater;infiltrationofirrigationwater;andcapillaryrise fromthegroundwater)andthreeoutflows(evaporation;transpiration; andpercolationtothegroundwater).Besides,wedistinguishan over-landrunoff flow,whichsubtractsfromrainwaterandirrigationwater beforeinfiltrationintothesoil(Fig.1).Notethatwaterenteringthesoil throughcapillaryriseisbluewaterbecausethewateroriginatesfrom groundwater.

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Fig. 1. Green-bluewateraccountingofsoilmoistureandwaterﬂuxesenteringandleavingthesoilmoistureincaseofonesoillayer.The‘colourcodes’intheform ofsubscriptsrefertotheoriginofthewater.

InthesoilwaterbalancemodelasshowninFig.1,thechangesin thediﬀerentcomponentsofthesoilmoisturearegivenby:

𝑑𝑆𝑔 𝑑𝑡 =𝑃−( 𝑃𝑃+𝐼 ) 𝑅𝑂−𝑆𝑔 𝑆(𝐺𝑊𝑅+𝐸+𝑇) (1) 𝑑𝑆𝑏,𝑖 𝑑𝑡 =𝐼−( 𝐼𝑃+𝐼 ) 𝑅𝑂−𝑆𝑏,𝑖 𝑆 (𝐺𝑊𝑅+𝐸+𝑇) (2) 𝑑𝑆𝑏,𝑐 𝑑𝑡 =𝐶𝑅− 𝑆𝑏,𝑐 𝑆 (𝐺𝑊𝑅+𝐸+𝑇) (3)

ThesymbolsrefertothestocksandﬂowsasshowninFig.1.When implementedinanumericalmodel,thisgives;

𝑆𝑔(𝑡)=𝑆_𝑔(𝑡−𝑑𝑡)+𝑃(𝑡)− ( _𝑃 (𝑡) 𝑃(𝑡)+𝐼(𝑡) ) 𝑅𝑂(𝑡) − (_𝑆 𝑔(𝑡−𝑑𝑡) 𝑆(𝑡−𝑑𝑡) ) (𝐺𝑊𝑅(𝑡)+𝐸(𝑡)+𝑇(𝑡)) (4) 𝑆𝑏,𝑖(𝑡)=𝑆𝑏,𝑖(𝑡−𝑑𝑡)+𝐼(𝑡)− ( 𝐼(𝑡) 𝑃(𝑡)+𝐼(𝑡) ) 𝑅𝑂(𝑡) − (_𝑆 𝑏,𝑖(𝑡−𝑑𝑡) 𝑆(𝑡−𝑑𝑡) ) (𝐺𝑊𝑅(𝑡)+𝐸(𝑡)+𝑇(𝑡)) (5) 𝑆𝑏,𝑐(𝑡)=𝑆_𝑏,𝑐(𝑡−𝑑𝑡)+𝐶𝑅(𝑡)− (_𝑆 𝑏,𝑐(𝑡−𝑑𝑡) 𝑆(𝑡−𝑑𝑡) ) (𝐺𝑊𝑅(𝑡)+𝐸(𝑡)+𝑇(𝑡)) (6) Atimestepdtofonedaywillgenerallybesuﬃcienttocapturethe dynamicsofthesoilmoisture,andispracticalalsogiventhatthevarious inputdataaregenerallyavailableonadailybasis.

ForanyoutﬂowFfromthesoilmoisture(E,T,GWR),thepartofF

thathasoriginx(precipitation,irrigationorcapillaryrise)followsat anytimefrom:

𝐹𝑥(𝑡)= (_𝑆 𝑥(𝑡) 𝑆(𝑡) ) 𝐹(𝑡) (7)

Theexampleprovidedhereisforthecaseofasimplesoilwater bal-ancemodelwithonlyonesoillayerandhasbeensuccessfullyapplied

inafewcasestudiesalready(Chukallaetal.,2015;Zhuoetal.,2016; KarandishandHoekstra,2017;Nourietal.,2019).Inthecaseof var-ioussoillayers,theaccountingprincipleremainsthesame:thecolour compositionofeachsoillayeristoberecordedovertimebasedonthe colourcompositionsofincomingandoutgoingwaterﬂuxes.Themodel presentedherealsodoesn’tdistinguishbetweenevaporationfromthe soilandevaporationofwaterinterceptedbytheleavesandstemsofthe vegetation.Ifavegetationlayerandtheprocessofinterceptionisadded, thegreen-bluewateraccountingprinciplewillneedtobeappliedtothis layeraswell.

Thegreen-bluewater accountingasproposedhere doesnotneed anydataontopofthedataalreadyrequiredforthesoilwaterbalance modelused.Thedatarequireddependonthechosensoilwaterbalance model,nottheextendedgreen-blueaccounting.Theonlypractical is-suewhenapplyingtheproposed accountingmethodis thataninitial green-bluecompositionofthesoilwaterneedstobeassumed(foreach layerwhenmorethanonelayerisdistinguished),justlikeanoverallsoil moisturecontentneedstobeassumed.Insimulationstudies, initializa-tionisawell-knownproblemandthegeneralsolutionsoftenchosenin hydrologicalstudiescanalsobeappliedforinitialisingthegreen-blue compositionofthesoilwater.Oneoptionistoiterativelydeterminea realisticinitialcondition(seee.g.Chukallaetal.,2015);anotheroption is torunamodelfortwoormoresubsequentyearsjustfor initializ-ing(wherebytheoriginalassumptiondoesnotmattermuch,because anyerrorwillnotworkthroughmorethanafewyears)anduseonly thesimulatedyearsaftertheinitializationperiod(seee.g.Nourietal., 2019).

5. Fromthegreen-bluewateraccountstoestimatingirrigation

waterconsumption,irrigationeﬃciencyandgreenandblue

waterfootprints

Thegenericprincipleintroducedheretodistinguishbetweengreen andblueEandbetweengreenandblueTallowsustomoreaccurately estimateirrigationwaterconsumption,irrigationeﬃciencyandgreen andbluewaterfootprintsofcropproductionthanbefore.Earlier

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assess-mentsofblueETinirrigatedcropproductionwereroughestimations basedontherelativeadditiontothesoilofirrigationwaterandrainfall overtime(Rostetal.,2008;Faderetal.,2011;Hanasakietal.,2010) orontakingthediﬀerencebetweenETunderrainfedconditionsand ETunderirrigatedconditions(MekonnenandHoekstra,2010;Siebert andDöll,2010).AnearlierassessmentofblueETfromcapillaryrisein productionforestswassimilarlybasedonaroughassumptionregarding thecontributionofcapillaryrisewithoutproperlykeepingtrackofthe compositionofthesoilmoisture(Schynsetal.,2017).

Theaccountingmethodpresentedoffersanunambiguouswayto esti-mateirrigationwaterconsumption,whichreferstowhatintheaccounts comesas‘blueevapotranspirationfromirrigationwater’(E_b,i+T_b,i).It isimportanttoknowirrigationwaterconsumption,becauseitisthepart oftheirrigationwaterappliedtothefieldthatdoesnotreturntothe catchment(througheitherrunoff fromthefieldordrainage).Itisthe consumptivepartofirrigationthatcontributestobluewaterscarcity, soitishighlyrelevanttoestimateitaccurately.

Theaccountingmethodalsoenablesthecalculationofirrigation eﬃ-ciency(IE)astheratioofbluetranspirationfromirrigationwater(T_b,i) totheappliedirrigationwater(I)overthegrowingperiodofthecrop (ZhuoandHoekstra,2017):

𝐼𝐸= 𝑇𝑏,𝑖

𝐼 (8)

Itistobenotedherethatifnexttotheharvestedcropthereareweeds orotherformsofvegetation(e.g.thecoverunderproductiontrees)as well,oneshoulddistinguishbetweentotalcropTandweed/otherTand computeIEbasedoncropT.

ByprovidingthedistinctionbetweengreenandblueEandTover thegrowingperiod,theproposedaccountingschemeeasilyallowsthe estimationofgreenandbluewaterfootprints(WF)perunitofcrop har-vestedbydividingtherightcomponentsofEandToverthegrowing periodbythecropyield(Y):

𝑊𝐹𝑔=𝐸𝑔 +𝑇_𝑔 𝑌 (9) 𝑊𝐹𝑏,𝑖= 𝐸𝑏,𝑖 +𝑇_𝑏,𝑖 𝑌 (10) 𝑊𝐹𝑏,𝑐=𝐸𝑏,𝑐 +𝑇_𝑏,𝑐 𝑌 (11)

Allwaterfootprintsarecalculatedbasedonthesumofthebeneficial consumptionofwater(T)andthenonbeneficialconsumptionofwater (E)becausethewaterfootprintmetricintendstoshowtotalwater con-sumptionrelatedtoproduction,andthisincludesthe‘wastefraction’ ofconsumption,thatistheunproductiveevaporationfromthesoil.For theblueWFofirrigationthismeansthatitgetssmallerwhenthe un-productiveconsumptionofwatergetsreduced;measurestoshiftsome ofthenonbeneficialEtobeneficialT(e.g.throughsoilmulching),thus increasingY,willreducetheblueWF(Chukallaetal.,2015).Theblue WFrelatedtoconsumptionofirrigationwatercanbesplitupinto dif-ferentcomponentsifdifferentsourcesofirrigationwaterareusedand explicitlydistinguished(e.g.fossilgroundwater,renewable groundwa-ter,rivers/lakes,andharvestedrainwater).TheblueWFcanbesplitup accordingtothesesourcesprovidedthatseparatetracingisdoneinthe accountingforeachofthesesources.

6. Conclusion

Theconfusionintheliteratureonwhether‘greenwater’refersto rainwaterinthesoilortoevapotranspirationofrainwater– aswas men-tionedintheintroduction– hasbeensolvedherebyacknowledgingthat ‘green’and‘blue’donotrefertooneparticularstockorﬂowinthe wa-tercycle,butareratherlabelsthattellsomethingabouttheoriginof water.Greenandbluearelabelsthatcanbeusedbothforwaterstored inasoilorvegetationlayerandforawaterﬂuxthatleavesfromthesoil

orvegetation(liketheevaporationortranspirationflow).‘Green’thus means‘originatingfromrainwater’and‘blue’means‘originatingfrom groundwaterorsurfacewater’.Inbothcaseswerefertotheorigininthe short-termpast,becausewaterkeepscirculating,sointheendallwater canbetracedbackinsomestagetobothrainwaterandrunoff flows.The issuehereiswhether,whenwetraceforinstanceE,Torsoilmoisture backtowhereitcomesfrom,weeitherendupfirstwithrainfallorwith groundwaterorsurfacewater.

Theproposedgreen-bluewateraccountingmethodhelpstoimprove theestimationofirrigationwaterconsumption,irrigationeﬃciencyand greenandbluewaterfootprintsinagriculture.Althoughtheemphasis hasbeenoncropproduction,thegreen-bluewateraccountingmethodis equallyapplicableforforestryandgardening.Forallthesepurposeswe needanaccuratepartitioningofEandTintoagreenandblue compo-nent.Theproposedmethodprovidesinagenericandaccurateroutine forthat,whileallpreviousapproachesreliedonsimplisticroutinesthat didnotdojusticetothesoilwaterdynamics.

Thenumberofpaperspublishedinthefieldofgreenandblue wa-terconsumptioninagricultureandforestryisgrowingquickly;itwould behelpfulifresearchers– insteadofrelyingonsimplisticassumptions – adoptthehereproposedphysicallybasedtracingmethod,which al-lowsthepreciseassessmentofgreenandbluefractionsofsoilmoisture andwaterfluxesleavingthesoil.Theminimumrequirementisthatthe hydrologicalorcropgrowthmodelusedincludesadailysoilwater bal-ance.Currentlytheredoesnotexistanyhydrologicalorcrop growth modelthatincludesgreen-bluewatertracing,henceresearchershave torelyonpost-processingofthetimeseriesoutputsfromtheirmodelto simulatethecolourcompositionofsoilmoistureandwaterfluxes leav-ingthesoil(seee.g.Chukallaetal.,2015).Itistobe recommended tointegrategreen-bluewateraccountinginsoil-waterbalancemodels, which requireslittleeffortotherthanaddsome additionalcoding to systematicallykeeptrackofthecolourcompositionofsoilmoistureand soilwaterfluxes.

Theinterestintracingtheoriginsofwaterconsumedincrop produc-tionincreases.Wadaetal.(2014)forinstanceestimatedirrigationwater consumptiondistinguishingbetweenirrigationfromsurfacewaterand irrigationfromgroundwaterataglobalscale,ataspatialresolutionof 0.5arcdegree.Thenextstepistosystematicallydiﬀerentiatebetween irrigationfromfossilversusrenewablewaterresources.Itwillbe inter-estingalsotomapirrigationwaterconsumptionfrominter-basinwater transferschemes.Sinceirrigationwaterconsumptionisthelargest con-tributortobluewaterscarcitythroughouttheworld(Mekonnen and Hoekstra,2016)andsinceincreasingwater-useeﬃciencyand reduc-ingbluewaterscarcityaretargetsintheUNSustainableDevelopment Goals(Vanhametal.,2018),properlyestimatingirrigationwater con-sumptionisgaininginimportance.

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