Assessing the performance of the FAO Aquacrop model to estimate maize yields and water use under full and deficit irrigation with focus on model parametrization

ContentslistsavailableatScienceDirect

Agricultural

Water

Management

j o ur na l h o me pa g e : w w w . e l s e v i e r . c o m / l o c a t e / a g w a t

Assessing

the

performance

of

the

FAO

AquaCrop

model

to

estimate

maize

yields

and

water

use

under

full

and

deficit

irrigation

with

focus

on

model

parameterization

P.

Paredes,

J.P.

de

Melo-Abreu,

I.

Alves,

L.S.

Pereira

CEER—BiosystemsEngineering,InstitutoSuperiordeAgronomia,UniversidadedeLisboa,TapadadaAjuda,1349-017Lisboa,Portugal

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received5March2014 Accepted1June2014 Availableonline26June2014 Keywords:

Cropgrowthmodel Yield–waterrelations Canopycover

Biomassandyieldpredictions SIMDualKcmodel

Dualcropcoefficients

a

b

s

t

r

a

c

t

Severalmaizefieldexperiments,includingdeficitandfullirrigation,wereperformedinRibatejoregion, PortugalandwereusedtoassesswaterstressimpactsonyieldsusingtheAquaCropmodel.Themodel wasassessedafteritsparameterizationusingfieldobservationsrelativetoleafareaindex(LAI),crop evapotranspiration,soilwatercontent,biomassandfinalyielddataandalsousingdefaultparameters.LAI datawereusedtocalibratethecanopycover(CC)curve.ResultsshowedthatwhentheCCcurveisproperly calibrated,withrootmeansquareerrors(RMSE)smallerthan7.4%,modelsimulations,namelyrelativeto cropevapotranspirationanditspartition,showanimprovedaccuracy.Themodelperformancerelativeto soilwaterbalancesimulationrevealedabiasinestimationbutlowestimationerrors,withRMSE<13%of thetotalavailablesoilwater.Howeverthemodeltendstooverestimatetranspirationandunderestimate soilevaporation.Agoodmodelperformancewasobtainedrelativetobiomassandyieldpredictions,with RMSElowerthan11%and9%oftheaverageobservedbiomassandyield,respectively.Overallresultsshow adequacyofAquaCropforestimatingmaizebiomassandyieldunderdeficitirrigationconditions,mainly whenanappropriateparameterizationisadopted.Themodelshowedlessgoodperformancewhenusing thedefaultparametersbuterrorsarelikelyacceptablewhenfielddataarenotavailable.

©2014ElsevierB.V.Allrightsreserved.

1. Introduction

Selectingthebestirrigationscheduleisrequiredforimproved

useoftheavailablewaterandforachievingthebestyields.That

selectionimpliesappropriatepredictionoftheyieldresponseto

water,whichisintheoriginofnumerousstudiesonwater-yield

responsestoavarietyofwaterstressesimposedthroughoutthe

cropseason.

Severalstudieshave been performedonmaize showingthe

impacts of water deficitsby reducing cropgrowth and canopy

development(NeSmithandRitchie,1992),changing

morpholog-icalcharacteristicsoftheplants(Traoreetal.,2000;Stoneetal.,

2001a,b;C¸akir,2004),reducingthenumberandweightofkernels (Weerathawornetal.,1992;Karametal.,2003),andthusreducing

yields(Stewartetal.,1977;DoorenbosandKassam,1979).

IntheextensiveworkbyStewartetal.(1977)resultsshowed

differentmaizeyieldresponseswhenwaterstresswasimposed

∗ Correspondingauthor.Tel.:+351213653480;+351213653339. E-mailaddresses:[email protected],[email protected], [email protected](L.S.Pereira).

atdifferentgrowthstages,withhigherimpactswhenwaterstress

occurredduringthefloweringperiod.Othersensitiveperiodsare

those of grain filling and the end of the vegetative stage. The

sameconclusionwasreportedbyDenmeadandShaw(1960)and

WestgateandGrant(1989).Formaize,loweryieldlossesdueto

mildstressduringfloweringaretobeexpectedwhenthecrophas

alreadybeensubjecttostressduringthevegetativestage(Stewart

et al., 1977). Alves et al. (1991) also noticed this conditioning

behaviourwhenreportingresultsofanextensivefieldworkon

determiningimpactsofwaterstressonmaize.

Simulationmodelsmaybehelpfulforassessingtheimpactsof

waterstressincropyield.Thereareseveralstudiesusing

mechanis-ticmodelsthatallowdeterminingbiomassandyieldsandthatmay

alsobeusedforevaluatingcropandirrigationmanagement

prac-tices.Examplesofapplicationsofthesemodelstomaizeincludethe

useofCERES-Maize(Pandaetal.,2004;DeJongeetal.,2012),

Crop-Syst(Stöckleetal.,2003),EPIC(Caveroetal.,2000;Koetal.,2009)

andSTICS(Katerjietal.,2010).Acombinationofthewaterbalance

modelSIMDualKc(Rosaetal.,2012)withthephasicStewart’swater

yieldmodel(Stewartetal.,1977)wasrecentlytestedwhenusing

maizetranspirationasdrivingvariable(Paredesetal.,2014a).The

cropgrowthmodelrecentlyproposedbyFAO,AquaCrop(Steduto

http://dx.doi.org/10.1016/j.agwat.2014.06.002 0378-3774/©2014ElsevierB.V.Allrightsreserved.

AAE averageabsoluteerror(sameunitsasobservations)

ASW availablesoilwater(mm)

B abovegrounddrybiomass(tha−1)

b regressioncoefficient(non-dimensional)

BWP* Biomass(water)productivityadjustedforEToand

CO2(gm−2)

CC* actual crop canopy cover adjusted for

micro-advectiveeffects(%)

CCo canopycoverat90%emergence(cm2perplant)

CCx maximumcanopycover(%)

CDC canopydeclinecoefficient(%GDD−1)

CGC canopygrowthcoefficient(%GDD−1)

CN curvenumber(non-dimensional)

D irrigationdepths(mm)

EF modellingefficiency(non-dimensional)

Es soilevaporation(mm)

ETc standard (non-stressed) crop evapotranspiration

(mm)

ETc adj adjustedoractualcropevapotranspiration(mm)

ETo referenceevapotranspiration(mm)

fc fraction of soil cover by vegetation

(non-dimensional)

fHI adjustmentfactorintegratingfivewaterstress

fac-tors(non-dimensional)

HI harvestindex(%)

HIo referenceharvestindex(%)

Kcb basalcropcoefficient(non-dimensional)

Kcbadj adjustedbasalcropcoefficient(non-dimensional)

Kcbmid basal crop coefficient for the mid season

(non-dimensional)

KcTr,x maximum standard croptranspirationcoefficient

(non-dimensional)

Kex maximum soil evaporation coefficient

(non-dimensional)

Kr evaporation reduction coefficient

(non-dimensional)

Ks waterstresscoefficient(non-dimensional)

Ksat saturatedhydraulicconductivity(cmd−1)

LAI leafareaindex(cm2_cm−2₎

Pe precipitation(mm)

R2 _{determinationcoefficient(non-dimensional)}

REW readilyevaporablesoilwater(mm)

RMSE rootmeansquareerror(sameunitsasobservations)

Ta actual(oradjusted)transpiration(mm)

TAW totalavailablesoilwater(mm)

Tc croptranspiration(mm)

TEW totalevaporablewater(mm)

Y actualyield(tha−1)

Zr rootdepth(m)

FC volumetricwatercontentatfieldcapacity(m3m−3)

sat volumetricwatercontentatsaturation(m3m−3)

WP volumetricwatercontentatwiltingpoint(m3m−3)

etal.,2012),wasselectedforthepresentstudybecauseofits

nov-eltyand yetalready wide applicationnot onlytomaize (Hsiao

etal.,2009;Hengetal.,2009;Katerjietal.,2013),butalso cot-ton(Farahanietal.,2009),barley(Arayaetal.,2010),andwheat (Andarzianetal.,2011).

Despite the existence of a large number of publications on

applicationsofAquaCrop,informationrelativetoparameterization,

calibrationandvalidationprovidedbythemodelauthors(Hsiao

etal.,2009)andthereferencemanual(Raesetal.,2012),aswellas

byotherauthors,isinsufficient.Usersmayhaveahardtaskwhen

tryingtocorrectlyusethemodel,whichbecomesevenharderwhen

cropshavenotbeenpreviouslyparameterizedbyFAO(Raesetal.,

2012).Inaddition,availablepublicationsoftendonotassessthe

performanceofthemodelinsimulatingtheavailablesoilwater,or

indescribingthecanopycovercurve.Thereareafewstudiesthat

discussmodellimitations(Farahanietal.,2009;Andarzianetal.,

2011;Katerjietal.,2013;Paredesetal.,2014b,c).Difficultieswere

referredbyHengetal.(2009)andKaterjietal.(2013)relativeto

theAquaCropapplicationtomaizewhenhighwaterstressis

con-sidered.Farahanietal.(2009)referredtolimitationsinestimating

thewaterbalancecomponentsinapplicationstocotton.

Consideringthatsomeofthestudiesreferredabovehaveshown

theneedforabetterparameterizationofthemodel,particularly

forconditionsofwaterstress,thepresentstudyaimsattesting

AquaCropforbiomassandyieldpredictionsofmaizeundervarious

deficitirrigationlevelsandtimings,andtoassesstheperformance

ofthemodelusingdifferentparameterizationapproaches,

includ-ingtheadoptionofthedefaultparametersprovidedbyRaesetal.

(2012).Inaddition,theparameterizationisanalyzedrelativetothe

canopycovercurve,thesimulationoftheavailablesoilwater,and

thepredictionofbiomassandharvestableyield.

2. Materialandmethods

2.1. Casestudies

2.1.1. Realfarmingmaizeproduction

Observationswereperformedinfarmer’sfieldsat“Quintada

LagoalvadeCima”,locatedinAlpiarc¸a,centralPortugal.Thisfarm

has a total of 200ha cropped with maize. Dailyweather data

wereobservedinameteorologicalstationlocatednearby(39.28◦N;

8.55◦Wand 24m elevation)and includedmaximum and

mini-mumtemperatures(◦C),windspeed(ms−1),globalsolarradiation

(Wm−2), relative humidity(%)and precipitation (mm).Climate

intheregionhasMediterraneancharacteristics,withmild rainy

wintersanddryhotsummers.Dailyweatherdatarelativetothe

observationsperiodof2010–2012areshowninFig.1including

thereferenceevapotranspiration(ETo,mmd−1)determinedwith

theFAO-PMmethod(Allenetal.,1998).

FieldswerecroppedwithZeamaysL.hybridPR33Y74(FAO600)

withadensityofapproximately82,000plantsha−1.Management

practices, includingfertilization and irrigation, wereperformed

accordingtothestandardpracticesintheregionandweredecided

bythefarmer.Directsowingwasused.Alongthethreeirrigation

seasonsseveralfieldswerefollowed-up:twofieldsin2010and

2012,respectively,fields1and2,andfields2and3;in2011only

field1wasobserved.Thesefieldswereapproximately30ha(fields

1and2)and40ha(field3).Furtherinformation,includingcrop

stages,isgivenbyParedesetal.(2014a).

Themainsoilhydraulicpropertiesofthethreefieldsobserved

arepresentedinTable1.Threeundisturbedsoilsamplesof100cm3

foreachsoillayertoamaximumdepthof1mwerecollectedprior

tothebeginning oftheexperiment todeterminethesoilwater

retentioncurveand thedry bulkdensity. Thesoilwater

reten-tioncurveforeachlayerwasdeterminedinthelaboratoryusing

suctiontableswithsandforsuctionsbelow−10kPa,anda

pres-sureplateapparatusforsuctionsof−10,−33,−100and−1500kPa

(Ramosetal.,2011;Morenoetal.,2013).Thesaturatedhydraulic

conductivity(Ksat,cmd−1)valueswereobtainedusing

pedotrans-fer functionsof texture and bulk density (Ramos et al., 2014).

SoilsareEutricFluvisols(FAO,2006).Infields1and2soilshave

loamysand textureand in field 3 thesoil hasa silt loam

tex-ture.Thetotalavailablewater(TAW),differencebetweenthesoil

waterstoredatfieldcapacityandatthewiltingpointtoadepth

Fig.1. DailyweatherdataofAlpiarc¸aduringthecroppingseasonsof2010(a),2011(b)and2012(c):onleftmaximum(–)andminimum( )temperaturesandrelative humidity( );onrightprecipitation( )andreferenceevapotranspiration(ETo)( ).

Table1

SelectedsoilhydraulicpropertiesoftheAlpiarc¸afields.

Soillayer(m) FC(m3m−3) WP(m3m−3) sat(m3m−3) Ksat(cmd−1)

Field1 Field2 Field3 Field1 Field2 Field3 Field1 Field2 Field3 Field1 Field2 Field3

0.00–0.10 0.32 0.25 0.35 0.08 0.08 0.22 0.48 0.56 0.45 442 891 71 0.10–0.20 0.25 0.17 0.36 0.06 0.05 0.24 0.35 0.39 0.41 129 157 46 0.20–0.40 0.22 0.17 0.36 0.06 0.04 0.20 0.33 0.36 0.42 93 117 50 0.40–0.60 0.22 0.26 0.37 0.04 0.09 0.12 0.34 0.32 0.43 87 40 59 0.60–0.80 0.22 0.16 0.36 0.05 0.04 0.10 0.34 0.36 0.43 93 86 61 0.80–1.00 0.17 0.32 0.37 0.04 0.14 0.12 0.24 0.39 0.45 92 66 77

FCisvolumetricwatercontentatfieldcapacity;WPisvolumetricwatercontentatwiltingpoint;satisvolumetricwatercontentatsaturation;Ksatissaturatedhydraulic

Fig.2.DailyweatherdataobservedatSorraiaValleystationduringthe1989maizecropseason:onleftmaximum(–)andminimum( )temperatures,andrelative humidity( );onrightprecipitation( )andreferenceevapotranspiration(ETo)( ).

andTAW=209mmm−1forfield3.Thesaturatedhydraulic con-ductivity(Ksat,cmd−1)wasmoderatefortheentireprofileexcept

forthetop0.10m(Table1)where highervalues areassociated

withmoderatetohighorganicmattercontent,averaging25,30and

26mgg−1forfields1,2and3,respectively.Thisisduetomanure

additionsperformedtwoweekspriortosowingandalsotocrop

residuesfromthepreviouscropseasonbecausedirectsowingis

practiced.TheKsatvalues(Table1)areneartherangeproposedby

Rawlsetal.(1998)andRaesetal.(2012)forloamysandandsilt

loamsoils.Afulldescriptionofthesoilstexturalpropertiesis

pre-sentedbyParedesetal.(2014a).Groundwaterisbelow10mand

thereforecapillaryrisedoesnotinfluencethemoistureconditions

inthemaizerootzone.

Fieldobservationsincluded:

(i)datesofmostrelevantcropgrowthstages;

(ii)rootingdepths,observedusinga1mprobeinrandompoints

betweenemergenceandmaximumcanopycover;

(iii)leafareaindex(LAI,m2_m−2_{),measuredalongthecropseason,}

usuallywitha7-dayinterval,atthreelocationsperfieldusinga

ceptometer(DecagonDevicesInc.USA,modelAccuPARLP-80)

andfollowingtherecommendationsproposedbyJohnsonetal.

(2010).LAImeasurementsin2010werelostduetoproblems

withtheloggerincorporatedintheceptometer;

(iv)biomasssamplesandthefinalactualyieldobservedat

harvest-ing:sampleswerecomposedof10plantsharvestedneareach

soilwaterprobeaccesstube(see(vi)below).Sampleswere

placed inrefrigeratorcontainersfortransportingtothelab,

wheretheywereseparatedintoleaves,stem,cobandgrains;

sampleswereweightedtoobtainfreshweightandthenoven

driedtoconstantweightat65±5◦Ctoobtaindryweight.The

yieldwasadjustedto13%grainmoistureasusedinother

stud-ies(PopovaandPereira,2011).

(v)irrigationdepths(D,mm),observedwithraingaugesplaced

0.20mabovethecanopyandneartheprobeaccesstubes.All

fieldsweresprinklerirrigatedwithacenter-pivotinfields1

and2anda linearmoving systeminfield3,bothequipped

withoverheadrotatorsprinklers;

(vi)volumetric soilwatercontent,measuredduring2010using

previously calibrated EnviroSCAN probes (Sentek Pty. Ltd,

Stepney, South Australia) at depths of 0.10, 0.20, 0.30 and

0.50m,andduring2011and2012withaDIVINER2000probe

(Sentek Pty. Ltd, Stepney, South Australia), with

measure-mentsateach 0.10muntil 0.90mdepth.Probescalibration

followed manufacturer recommendations and procedures

Table2

SelectedsoilhydraulicpropertiesoftheSorraiaValleyexperimentalfield. Soillayer(m) FC(m3m−3) WP(m3m−3) sat(m3m−3) Ksat(cmd−1)*

0.00–0.55 0.22 0.075 0.37 445

FCisvolumetricwatercontentatfieldcapacity;WPisvolumetricwatercontent

atwiltingpoint;satisvolumetricwatercontentatsaturation;Ksatissaturated

hydraulicconductivity.

*_{Cameiraetal.(2003)}

(Sentek,2001)andthereforeacalibrationcurvewasobtained

foreachfield.Observationsweregenerallyperformedtwicea

weekat16locationsperfield.

A more detailed description of the experiments is given in

Paredesetal.(2014a).

2.1.2. Deficitirrigationtrials

Experimentswereperformedin1989attheAntónioTeixeira

ExperimentalStation,locatedintheSorraiaValley,Coruche,Central

Portugal.Thesefieldsareinsidea15,000hairrigationdistrict.The

experimentsweresetwiththeobjectiveofassessingtheimpactson

maizeyieldsatvariouslevelsofdeficitirrigationatdifferentcrop

growthstages.TheclimateissimilartothatofAlpiarc¸a,reported

above.Fig.2presentsmainclimaticdataofthemaizecrop

sea-sonincludingETocomputedwiththeFAO-PMmethod(Allenetal.,

1998).

TheexperimentswereperformedwithZ.maysL.hybridLG18

(FAO300)withaplantdensityofapproximately90,000plantsha−1.

Themaizecropwassownonthe10thMay,emergenceoccurred

on25thMay,themaximumcanopycoverwasreachedon12thto

19thJulydependingontheirrigationtreatment;thestartofcanopy

senescence,which alsodependeduponthetreatment, occurred

fromthe1sttothe28thAugust.Harvestwasperformedon5th

Septemberforalltreatments(Alvesetal.,1991).Thesoil

character-izationisgiveninTable2.Thesedatahavebeenanalyzedandused

inpreviousstudies(Rodriguesetal.,2013;Paredesetal.,2014a).

Fieldobservationsandmeasurementsrelativetoeachtreatment

included:

(i)datesofmostrelevantcropgrowthstages;

(ii)leafareaindex(LAI,m2_m−2_{),measuredatkeydatesofthe}

cropseason,usingaceptometer(LI-3000A,LI-COR,Lincoln,

Nebraska,USA).Threemeasurementswereperformedduring

(iii)finalyieldatharvesting,usingasamplingareaofabout1.6m2

pertreatment.Sampleswereseparatedintoleaves,stem,cob

andgrains;sampleswereweightedtoobtainfreshweightand

thenovendriedtoconstantweightat65±5◦Ctoobtainthe

dryweight.Yieldwasadjustedto13%grainmoisture.

(iv)irrigationdepths(D,mm)determinedusingraingaugesplaced

above the canopy and near the probe access tubes. The

irrigationtreatmentsweresetusingamodifiedsprinkler

line-sourcetechnique(Hanksetal.,1976).Irrigationwasperformed

every5daysduringthesummermonths.Infra-red

thermome-tersallowedtoconfirmthattheplantsinthewellirrigatedfield

werekeptstressfree(Jackson,1982;AlvesandPereira,2000);

(v)soilwatercontentmeasuredbeforeandaftereachirrigation

eventusinga previouslycalibratedneutronprobe (DIDCOT,

UK)atdepthsof0.10,0.15,0.20,0.30,0.40,0.50,0.60,0.80,

1.00and1.20m.CalibrationproceduresfollowedBell(1976)

andHodgnett(1986).Aspecialcalibrationoftheprobewas

performed forthe surfacelayers (0.10,0.15 and 0.20m)as

proposedbyBell(1976);

(vi)actual cropevapotranspiration (ETc adj), determined for all

periodsbetweentwosuccessiveirrigationeventsusingasoil

water balancefollowingDoorenbosandPruitt(1977).Deep

percolationwasestimatedfromsoilwatermeasurements

per-formedbelowtherootdepth(0.60to1.20m);runoffwasnull

aswellascapillaryrise.

Theirrigationtreatmentsweresetusingamodifiedsprinkler

line-sourcetechnique(Hanksetal.,1976).Thistechniqueallows

a gradual transition between treatments, the gradingof water

appliedtothecropleadalsotogradualeffectsinthecrop.

Severaldeficitand fullirrigationschedules wereestablished

considering3cropgrowthstages:vegetative,floweringtoyield

for-mation,andmaturation/ripening(Alvesetal.,1991;Paredesetal.,

2014a).Sixstrategieswithseveralreplicationswereselectedfrom theAlvesetal.(1991)datasettoperformthepresentstudy:

(A)fullirrigationinallcropgrowthstages;

(B)waterstressimposedduringthevegetativestageonly;

(C)waterstressimposedduringmaturation/ripeningonly;

(D)water stress imposed during the vegetative and flowering

stages;

(E)water stressimposed duringvegetative growthand

matura-tion/ripening;and

(F)waterstressimposedalongtheentirecropseason.

FurtherinformationisgivenbyParedesetal.(2014a).

2.2. TheAquaCropmodel

TheAquaCropmodel(Stedutoetal.,2012;Raesetal.,2012)isa

cropgrowthmodelwhichcombinesfoursub-models:(1)thesoil

waterbalance;(2) thecropdevelopment,growthandyield;(3)

theatmospheresub-model,handlingrainfall,evaporativedemand

(referenceevapotranspiration,ETo)andCO2concentration;(4)and

themanagementsub-model,whichincludesirrigationand

fertil-ization(Raesetal.,2012).

The model computes daily crop evapotranspiration (ETc,

mmd−1)separatingcroptranspiration(Tc,mmd−1)andsoil

evap-oration(Es,mmd−1).Tcisgivenas(Raesetal.,2012)

Tc=CC∗KcTr,xETo (1)

whereEToisreferenceevapotranspiration(mm),KcTr,xisthe

max-imumstandardcroptranspirationcoefficient(non-dimensional),

andCC*istheactualcropcanopycover (%)adjusted for

micro-advective effects. The actual (or adjusted) transpiration (Ta) is

obtainedbyadjustingTctosoilwaterstressconditionsusingthe

waterstresscoefficientKs(0−1),i.e.,Ta=KsTc.ThecoefficientKs

describesthe effects of soilwater stressonthe following crop

growthprocesses(Raesetal.,2012):(i)reductionofthecanopy

expansionrate;(ii)accelerationofsenescence;(iii)closureof

sto-mata;and(iv)changesintheharvestindex(HI)afterthestartof

thereproductivegrowth.KcTr,xisadjustedbythemodeltotakeinto

considerationageingeffectsandsenescence.

ThesoilevaporationisalsoobtainedfromCC*andEToas:

Es=Kr(1−CC∗)KexETo (2)

where Kex is the maximum soil evaporation coefficient

(non-dimensional)andKristheevaporationreductioncoefficient(0−1),

withKr<1wheninsufficientwaterisavailableinthetopsoilto

respondtotheevaporativedemandoftheatmosphere.Kexcanbe

adjustedforwitheredcanopy,formulchesandforpartialwettings

followingtheFAO56approach(Allenetal.,1998).

Theabovegrounddrybiomass(B,tha−1)isestimatedbythe

modelusingthewatertranspiredbythecropalongtheseasonand

theadjustedbiomass(water)productivity(BWP*,gm−2).BWP*

representstheabovegroundbiomassproducedperunitoflandarea

consideringboththecumulativetranspiration,afteradjustmentfor

atmosphericCO2concentration,andETo(Raesetal.,2012).A

semi-empiricapproachisusedtocomputethecropyield(Y,tha−1)from

Bas:

Y=fHIHIoB (3)

whereHIoisthereferenceharvestindex,whichindicatesthe

har-vestable proportionof biomass,and fHI is anadjustmentfactor

integratingfivewaterstressfactorsrelativetotheinhibitionofleaf

growth,inhibitionofstomata,reductioningreencanopyduration

duetosenescence,reductioninbiomassduetopre-anthesisstress,

andpollinationfailure(Raesetal.,2012).

Inthepresentstudy,HIowasobservedinallseasonsinnostress

conditionsandaveraged0.49and0.48fortheAlpiarc¸aandSorraia

Valleysites,respectively.Thisaveragingapproachfollowsthose

adoptedinotherAquaCropstudies(Arayaetal.,2010;Zelekeetal.,

2011).OurHIovaluesareintherangeofthosereportedbyDiPaolo

andRinaldi(2008)[0.36–0.53],Hengetal.(2009)andHsiaoetal. (2009)[0.48],FarréandFaci(2009)[0.16–0.51]andKaterjietal. (2013)whofoundavalueof0.46.

Themodelinputdata(Raesetal.,2012)includes:

(1)Dailyweatherdataonmaximumandminimumair

tempera-tures(◦C),precipitation,Pe(mm),referenceevapotranspiration,

ETo(mm);atmospheredatarefertoannualCO2concentration.

(2)Cropdatareferringto:(i)thedatesofemergence,when

max-imum canopy coveris reached, whenmaximum rootdepth

isattained,whencanopysenescencestarts,whenmaturityis

reached,whenfloweringstartsandends;(ii)maximumvalue

ofthetranspirationcropcoefficient(KcTr,x);(iii)minimumand

maximumrootdepthsZr(m)androotsexpansionshape

fac-tor; (iv) the initialand maximum crop canopy cover (CCo,

CCx),canopygrowthcoefficient(CGC)andthecanopydecline

coefficient(CDC);(v)adjustmentbiomass(water)

productiv-ity(BWP*);(vi)referenceharvestindex(HIo),(vii)waterstress

coefficients relative to canopy expansion, stomatal closure,

earlycanopysenescenceandaerationstressdueto

waterlog-ging.

(3)Soildataforamulti-layeredsoilincludingamaximumof5

lay-ers.Foreachlayerdatarefertolayerdepthd(m),soilwater

contentatfieldcapacity_FC(m3m−3),atthewiltingpointWP

(m3_m−3_{)andat saturationsat (m}3_m−3_{), andthesaturated}

refertothereadilyevaporablesoilwater(REW,mm)andthe

curvenumber(CN).

(4)Irrigationschedulingdata,bothdatesanddepthsofobserved

irrigation events or, when the model is used to generate

irrigationschedules,thesoilwaterthresholdsandirrigation

depthsandfrequency.

(5)Fieldmanagementpractices relativetosalinity,soilfertility,

mulchingandrunoffreductionpractices.

Thecanopycover(CC)isequivalenttothefractionofsoilcovered

bythecanopy(fc,non-dimensional)inFAO56(Allenetal.,1998);

however,themodeldoesnotallowusingobserveddatatobuildthe

CCcurvebutallowstocalibratetheCCcurves.Modelcomputations

ofCCareperformedthroughthreephases(Raesetal.,2012):the

firstoneusesanexponentialfunctionoftime,whichbeginsatcrop

emergenceandendswhenhalfofthemaximumCCisreached,with

theCCgrowthratedefinedbytheparameterCGC;thesecondphase

usesanotherexponentialfunctionuntilthemaximumCC(CCx)is

reached,withtheshapegivenbythesameCGCparameter;thelast

phasereferstothedeclineofgreencanopycoveraftersenescence

startsanditsshapeisdefinedbytheparameterCDC(Raesetal.,

2012).ToparameterizetheCCcurves(CCx,CGCandCDC)observed

LAIvaluesmaybeusedtocomputethecorrespondingCCvalues

withanexponentialtimedecayfunction(Hsiaoetal.,2009):

CC₌1_.005[1−exp(_−0.6LAI)]1.2 (4)

Furtherdescriptionsofthemodelandauxiliaryequationsare

givenbyRaesetal.(2012).

2.3. Modelparameterization,calibrationandvalidation

TheAquaCropmodelusesalargenumberofparameters

includ-ingseveralconservativeonesthatareexpectedtochangelittlewith

time,managementor location,andaredescribed andtabledby

Raesetal.(2012).Thesetabledvalueswereusedtogetherwith

otherconservativeparametersobtainedformaizebasedonfield

experimentsreportedbyHsiaoetal.(2009)andHengetal.(2009).

Themodelwasfirst parameterizedforappropriatelydescribing

theCC curvegivenitsgreat importancetomodel both

transpi-rationandsoilevaporation(Eqs.(1)and(2)).Thus,thetrialand

errorprocedurefocused firstontheparametersthatdetermine

theCCcurve,i.e.,CCx,CGCandCDC.Specificparametersvalues

weresearchedforeachyearandtreatment.Subsequently,thetrial

anderrorprocedurefocusedonadjustingtheKcTr,x,aswellasREW

andCN,bycomparingsimulatedandobservedfielddataof

avail-ablesoilwater(ASW)or/andET.Inthisapplication,theREWand

CNforAlpiarc¸awerethoseobtainedinapreviousstudywiththe

SIMDualKcmodel(Paredesetal.,2014a).BWP*forAlpiarc¸a and

SorraiaValleycasestudieswere33.7and32.3gm−2,respectively,

inagreementwiththevaluesproposedbyHsiaoetal.(2009).The

modelwascalibratedwiththeAlpiarc¸adataof2011andwastested

withdatacollectedin2010and2012anddataofalltheSorraia

treatments.

Toassessthe“goodness-of-fit”ofthemodel,variousstatistical

approacheswereused,asinpreviousstudies(Rosaetal.,2012;

Paredesetal.,2014a).Thefirstapproachreferstothelinear

regres-sionforced through theorigin relating observed and predicted

values;therespectiveregression anddetermination coefficients

areusedasindicators.Aregressioncoefficient(b)closeto1.0

indi-catesthatthepredictedvaluesarestatisticallyclosetotheobserved

ones;a determinationcoefficient(R2_{)closeto1.0indicatesthat}

mostofthevarianceoftheobservedvaluesisexplainedbythe

model.

Asetofindicatorsofresidualestimationerrorswasalsoused

(Moriasietal.,2007):therootmeansquareerror(RMSE),which

expressesthevarianceoferrors,and theaverageabsoluteerror

(AAE),thatexpressestheaveragesizeoftheestimateerrors.These

indicatorsarecomputedfromthepairsofobservedandpredicted

valuesOiandPi(i=1,2,...,n)whosemeansare,respectively,O

andP,thus: RMSE=











Totest thequality of themodellingapproach the Nashand

Sutcliffe(1970) modellingefficiency (EF,non-dimensional) was

used.Itisanormalizedstatisticthatdeterminestherelative

mag-nitudeof theresidualvariancecompared tothemeasureddata

variance(Moriasietal.,2007)andisdefinedas:

EF=1.0−





EFapproaches1.0whentheresidualvarianceismuchsmaller

thanthemeasureddatavariance,whilenegativeEFvaluesindicate

thatthemeanisabetterestimatorthanthemodel(Moriasietal.,

2007).

3. Resultsanddiscussion

3.1. Modelperformancewhenappliedtorealfarmingmaize

production

3.1.1. Canopycovercurve

Theobservedmaizedataoncropgrowthstages,rootsdepths

andLAIwerepresentedbyParedesetal.(2014a).Aspreviously

explained,model calibrationwasperformed byminimizingthe

differencesbetweenobservedandsimulatedavailablesoilwater

(ASW,mm),biomassandyieldrelativeusingdataoffield1in2011.

Thatcalibrationwasperformedafterappropriate

parameteriza-tionoftheCCcurve.Allcalibratedvalues(CCx,CGC,CDC,KcTr,x,

BWP*,HIo)andconservativeones(i.e.,relativetoparametersthat

changelittlewithmanagementorlocation,Raesetal.,2012)are

presentedinTable3;thedefaultvaluesusedtoinitiatethemodel

applicationarealsoincluded.ThecalibratedKcTr,x=1.18(Table3),

whichcorrespondstothebasalcropcoefficientforthemid

sea-son(Kcbmid)(Allenetal.,1998),issimilartotheoneobtainedby Abedinpouretal.(2012),KcTr,x=1.15,butishigherthantheone

reportedbyHsiaoetal.(2009)andHengetal.(2009),KcTr,x=1.05.

ThecalibratedKcTr,xissimilartotheKcbmid=1.15proposedbyAllen

etal.(1998),whichwasalsoobtainedbyParedesetal.(2014a)

forthesamedataset,andinthestudiesbyZhangetal.(2013).

ThecalibratedKcTr,xalsocompareswellwiththesinglecrop

coef-ficient values reported by Piccinni et al. (2009) and Gao et al.

(2009).

Asreferredbefore,anappropriateparameterizationoftheCC

curveisamajorrequisiteforthemodeltoproducegoodestimates

ofsoilevaporation,croptranspirationandbiomass(Eqs.(1)–(3))

and,hence,goodyieldpredictions.However,thisrequirementis

notproperlyidentifiedbythemodeldevelopers(e.g.,Hsiaoetal.,

2009;Hengetal.,2009;Raesetal.,2012)orotherauthors.As

pre-viouslyreferred,observedLAIvalueswereusedtocomputethe

CCvalues(Eq.(4))thatwereusedforthatparameterization.

Spe-cificCCx,CGCandCDCwereobtainedforeachtreatment(Table3).

ResultsofthefittedCCcurvesareshowninFig.3for2011and2012.

The “goodness-of-fit” indicators relative to the CC curves

when usingdefault and calibratedparameters arepresented in

Table3

ConservativeandcalibratedcropparametersofAquaCropmodel.

Description Unitsorsymbolmeaning Value

Conservativeparameters Default* _Adopted

Basetemperature ◦C 8 8

Cut-offtemperature ◦_{C 30 30}

Canopycoverat90%emergence(CCo) cm2perplant 6.5 4.1

Soilwaterdepletionthresholdforcanopyexpansion Upperthreshold 0.14 0.14 Soilwaterdepletionthresholdforcanopyexpansion Lowerthreshold 0.72 0.72 Shapefactorforwaterstresscoefficientforcanopyexpansion Curveshapemoderatelyconvexcurve 2.9 2.9 Soilwaterdepletionthresholdforstomatalcontrol FractionofTAWatwhichstomatastart

toclose

0.69 0.69

Shapefactorforwaterstresscoefficientforstomatalcontrol Highlyconvexcurve 6.0 6.0 Soilwaterdepletionthresholdforfailureofpollination FractionofTAWatwhichpollination

startstofail

0.80 0.80

Calibratedparameters Default Calibrated

CropcoefficientfortranspirationatCCx Basalcropcoefficient(KcTr,x) 1.05 1.18

BWP* Biomass(water)productivityadjusted

forEToandCO2(gm−2)

33.7 33.7

HIo Referenceharvestindex(%) 0.50 0.49

Canopycovercurveparameters Default 2010 2011 2012

Maximumcanopycover,CCx, % 97 96 96 96

Canopygrowthcoefficient,CGC %GDD−1 _{1.30 1.49 1.49 1.56}

Canopydeclinecoefficient,CDC %GDD−1 _{1.06 0.40 0.35 0.43}

*_{DefaultparametersaretabledbyRaesetal.(2012)}

tendencyfor under-estimationof theobserved CC values, with

theregression coefficient b<0.95 for allcases, high estimation

errors(RMSE>16.6%andAAE>10.5%)andlowtomediummodel

efficiency(EFranging0.18to0.71).Differently,whenaproper

cal-ibrationoftheCCcurveparameters(CCo,CCx,CGCandCDC)was

performed,resultsdonotshowanytendencytooveror

under-estimation(b rangingfrom0.97 to1.03)andthedetermination

coefficientsarehigher(R2_{>0.96),thusindicatingthattheCCmodel}

highly explainsthe variance of observed CC values. Estimation

errors are then small,withRMSE ranging 4.6 to7.9% and AAE

varyingbetween3.1and5.3%.TheseRMSEvaluesobtainedwith

calibrationareintherangeorsmallerthanthosereportedbyHsiao

etal.(2009),withRMSErangingfrom4.8to13.6%.García-Vilaand Fereres(2012)reportedalargerRMSEofapproximately13%and

highervalueswerereportedbyHengetal.(2009)forrainfedmaize

(7.2to34.5%).HighEFvalues werealsoobtained(>0.94)which

indicatethattheresidualvariancewasmuchsmallerthanthe

mea-sureddatavariance.Theseresults(Table4)clearlyshowtheneed

foracarefulcalibrationoftheCCcurvewhensearchingforaccurate

results.

Table4

“Goodness-of-fit”indicatorsrelativetocanopycoverusingdefaultandcalibratedparameters,Alpiarc¸acasestudy. Fieldandyear Goodnessoffitindicators

b R2 _{RMSE(%) AAE(%) EF}

Usingdefaultparameters Field1,2011 0.75 0.52 35.7 18.7 0.18

Field2,2012 0.95 0.77 18.0 10.5 0.68

Field3,2012 0.93 0.87 16.6 11.0 0.71

Alldata 0.88 0.69 24.5 13.2 0.49

Usingcalibratedparameters Field1,2011 0.97 0.99 4.6 3.1 0.99

Field2,2012 1.01 0.96 7.2 4.5 0.95

Field3,2012 1.03 0.96 7.4 5.1 0.94

Alldata 1.01 0.97 6.6 4.3 0.96

3.1.2. Simulationoftheavailablesoilwater

Resultsofmodelsimulationoftheavailablesoilwater(ASW) throughoutallcropseasonsarepresentedinFig.4whenusing

cali-brated,notdefaultparameters.Observationsshowthatstressonly

occurredduringthe2010season,withtheobservedASWfalling

belowthereadilyavailablesoilwater(RAW)thresholdduring

mid-season(Fig.4bandc).Despiteadoptingacarefulparameterization

(Section2.3),themodeldidnotproperlysimulateASW.Resultsin

Fig.4ashowatrendforoverestimation,whichismoreimportant

forthelowervaluesofASW.Thesametrendforoverestimationof

lowerASWvaluesisobservedfortheothersimulationresults.

Con-trarily,whenASWareclosertofieldcapacitynotrendisobserved.

Theseresultsaresomewhatdifferentfromthose obtainedwith

SIMDualKcmodelforthesamedatasets,whicharereportedby

Paredeset al. (2014a) and showa betterfit without bias.This

indicatesthattheAquaCropmodeldoesnotsimulateproperly,in

particularwhensoilwaterdeficitsoccur.

The“goodness-of-fit”indicatorsrelative tothesimulation of

ASWusingthecalibratedparameters(Table3)andrepresented

inFig.4aregiveninTable5.Resultsshowregressioncoefficients

rangingfrom0.96to1.09anddeterminationcoefficientsranging

from0.59to0.88,withR2_{=0.88forthecalibration(field1,2011).}

Theseresultsindicatethat a biasof estimationoccurredfor all

experiments.Differently,SIMDualKcresults(Table5)haveshown

bvaluesrangingfrom0.98to1.01andR2_{rangingfrom0.79to0.94.}

EstimationerrorswithAquaCrop arerelatively low,withRMSE

rangingfrom8.4to11.7mm,whichcorrespondtoavariationof

5.1to13.5%ofthetotalavailablesoilwater(TAW),andtheAAE

valuesarealsosmall,lessthan8.8mm.However,smallererrors

wereobtainedwithSIMDualKc,withRMSEfrom4.0to6.5mm.The

modellingefficiencywithAquaCropisgenerallyacceptable,withEF

from0.57to0.72,exceptforfield2in2012whereEF=0.03.This

valueindicatesthattheresidualsvarianceisclosetothemeasured

datavariance;contrarily,resultsfortheotherdatasetsindicate

thattheresidualsvarianceislowerthanthemeasureddata

vari-ance.However,theindicatorsof“goodness-of-fit”failedthelimits

forR2_{andEF,respectively,0.80and0.70,proposedbyMaetal.}

(2011)forcropmodels.UsingSIMDualKc(Table5),EFvariedfrom

0.74to0.92,thusabovethelimitssuggestedbyMaetal.(2011).

Thus,resultsindicatethatAquaCropdoesnotaccuratelysimulate

ASW.

WhenusingthedefaultparametersgivenbyRaesetal.(2012)

andtheCCcurveisalsosimulatedwithdefaultparameters,the

“goodness-of-fit”indicators(Table5)showacleartrendfor

over-estimationofASW(1.10<b<1.30)andtheestimationerrorsare

high,withRMSErangingfrom11.6to25.7%ofTAW.EFisthen

gen-erallynegative,whichindicatesthatthemeanisabetterpredictor

thanthesimulatedvalues.Itcanbeconcludedthatacareful

param-eterizationoftheCCcurveisdefinitelyrequiredwhensoilwateris

simulated,andthatitisadvisabletoparameterizethemodelusing

accuratesoilwaterobservationsthroughoutthecropseason.

Thepoorfittingoftheobserved ASWwhenusingAquaCrop

aftermodelcalibrationislikelyrelatedtothelessgoodestimations

oftranspiration(Eq.(1))andsoilevaporation(Eq.(2)).Fig.5

com-paresTaandEssimulatedbyAquaCropandtheSIMDualKcmodel

(Paredesetal.,2014a)alongthecropseasonsof2010,2011and

2012usingthesamedatasets.ResultsshowthatAquaCroptends

toover-estimateTaandtounder-estimateEs,thusresultingina

biasofestimatesofASWasindicatedbythelessgoodEFvaluesin

Table5.Over-estimationofTaisgreaterwhenwaterstressoccurs

asevidencedwhencomparingFig.5aandb.Similardifferences

werealsoobserved anddiscussed for AquaCropapplicationsto

maize byKaterji et al. (2013),peas (Paredeset al., 2014b)and

barley(Paredesetal.,2014c).Theover-estimationsofTaaredue

toproblemsinestimatingtheadjustedbasalcropcoefficientsin

Tacomputations(Eq.(1)).Toverifythisassumption,theseasonal

variationoftheadjustedKcbcalculatedwithAquaCropand

SIMD-ualKcarecomparedinFig.6togetherwiththecanopycovercurve

simulatedbyAquaCrop.ItcanbeobservedthatwhileKcbadj

esti-matedwithSIMDualKcfollowstheclassicalcropcoefficientscurve

(Allenetal.,1998,2005;Rosaetal.,2012),theKcTrcomputedwith

AquaCropfollowtheCCcurve(Raesetal.,2012),thusbecoming

differentthanthecommoncropcoefficientcurves(Fig.6).

There-fore,sincethetwomodelsfollowdifferentconceptualapproaches,

theadjustedKcbcurves aredifferent,resultingintheAquaCrop

KcTrnot beingimpactedbywaterstressiftheCCcurveitselfis

notaffectedbywaterstress.ThisiswellevidentinFig.6bwhere

Kcbadjishighlyimpactedbywaterstressearlyinmidseasonbut

KcbTrisnot.Differencesamongbothmodels,orbetweenAquaCrop

andtheFAO56approach,alsoexistinsoilevaporationestimation:

whileinFAO56andSIMDualKcEsisdailyestimatedwithawater

balanceof theevaporative layer(Allen etal., 1998,2005;Rosa

etal., 2012), in AquaCropEs varieswiththeCCcurve(Eq.(2)).

ThisapproachjustifieswhyEsisunderestimatedwhenthecanopy

coverishigh,i.e.,duringmid-andlateseason.Itisalsolikelya

reasonforoverestimationoflowASWvaluesasreferredabove.

ProblemsreportedforTa andEsestimationarelikelytoexplain

theless good“goodnessof fit”indicators inTable5.Therefore,

the KcTr and CC curve proportionality should be revised since

thelatter is not sensitivetodaily water stressthroughout the

seasonbutonlytowater stressduringthevegetativestage.An

approachsimilartothatadoptedinFAO56(Allenetal.,1998,2005)

couldbeconsideredforestimationofbothtranspirationandsoil

evaporation.

3.2. Modelperformancefordeficitirrigationexperiments

TheparameterizationoftheCCcurvewasthefirstfocusofthe

calibrationprocedureusingLAIobservationstogetobservedCC

valuesusingEq.(4).TheCCovalueusedinthesimulationwashigher

(0.045)thanfortheAlpiarc¸astudies(Section3.1)becausetheplant

densitywashigherintheseexperiments(seeSection2.1.2).TheCCx

wassetasthemaximumobservedforthefullirrigationtreatment

(0.97);CGCandCDCweresetas2.53%GDD−1and0.72%GDD−1,

respectively.TheCGCvalueishigherthanthatusedforAlpiarc¸a

Fig.4. Observed( )andsimulated( )availablesoilwater(ASW)fortheAlpiarc¸amaizefields:(a)field1in2011(calibration),(b)field1in2010,(c)field2in2010;(d) field2in2012;and(e)field3in2012.

thehybridPR33Y74,ofFAO600typeusedatAlpiarc¸a,i.e.,requiring

200GDDless,approximately.

Fig.7presentsexamplesofCCcurvessimulatedbyAquaCrop

relativetoeachtreatment.Theseresultsclearlyshowsome

dis-crepanciesbetweensimulatedandobservedCCvaluesduringthe

vegetativedevelopmentand themid-seasonstages, particularly

whenwaterstresswasimposedduringthevegetativestage,i.e.,

treatmentsB,D,EandF.

Table6presentsthe“goodness-of-fit”indicatorsrelativetothe

adjustmentofCCcurveforeverytreatmentwhenusingbothdefault

andcalibratedparameters.Themodelperformanceisgoodwhen

usingthecalibratedCCparameters,withbrangingfrom0.96to

1.03andR2_{rangingfrom0.80to0.96.Theestimationerrorsare}

small, withRMSE<7% and AAE<6%. EF are high, rangingfrom

0.75to0.96,henceindicatingthattheresidualsvarianceismuch

smallerthanthemeasureddatavariance.Contrarily,whenusing

thedefaultparameters,resultsshowapoormodelperformance,

withb<0.86andR2_{<0.78.Highestimationerrorswerefound,with}

RMSEranging23.9to40.7%andAAErangingfrom15.3to32.2%.

Moreover,EFisnegativeforalltreatments,whichindicatesthat

theresidualsvarianceislargerthanthemeasureddatavariance

and the modelledvalues arenot appropriate estimators.

Over-allresultsshow thatthe modelappropriately simulatestheCC

curvewhentheparametersareproperlycalibratedandthat,

con-trarily,thesimulationsareveryinaccuratewhenusingthedefault

parameters.

TheAquaCropwastestedforseasonalevapotranspiration

Table5

“Goodness-of-fit”indicatorsrelativetosimulationsofASW(mm)whenusingAquaCropwithdefaultandcalibratedparameters,andSIMDualKcmodelforallAlpiarc¸afields andyears.

Model Year Field Goodnessoffitindicators

b R2 _{RMSE(mm) RMSE/TAW(%) AAE(mm) EF}

AquaCrop Usingdefaultparameters 2010 Field1 1.20 0.78 16.6 17.8 14.7 0.00

Field2 1.26 0.71 16.3 22.6 13.7 −0.36

2011 Field1 1.10 0.53 17.9 11.6 13.0 −0.26

2012 Field2 1.30 0.03 34.5 25.7 29.9 −8.40

Field3 1.22 0.37 36.3 19.6 33.1 −5.30

Alldata 1.21 0.89 22.3 18.0 0.59

Usingcalibratedparameters 2010 Field1 1.00 0.71 9.5 10.2 8.1 0.66

Field2 1.09 0.80 9.1 12.6 7.4 0.58

2011 Field1 0.96 0.88 8.4 5.5 6.7 0.72

2012 Field2 0.96 0.59 11.7 8.7 8.8 0.03

Field3 1.04 0.79 9.5 5.1 7.1 0.57

Alldata 1.02 0.93 9.5 7.7 0.93

SIMDualKc(Paredesetal.,2014a) 2010 Field1 1.01 0.92 4.8 3.1 3.9 0.91

Field2 1.00 0.94 4.0 3.1 3.2 0.92 2011 Field1 0.99 0.85 6.3 4.1 5.5 0.84 2012 Field2 0.98 0.79 5.7 4.3 4.7 0.74 Field3 0.99 0.85 6.5 3.5 5.7 0.80 Alldata 1.00 0.98 5.0 4.1 0.98 Table6

“Goodness-of-fit”indicatorsrelativetoAquaCropadjustmentofCCcurveforalltreatmentswhenusingthedefaultandcalibratedparameters,SorraiaValley. Treatment Goodnessoffitindicators

b R2 _{RMSE(%) AAE(%) EF}

Usingdefaultparameters A 0.86 0.75 27.1 16.2 −2.1

B 0.82 0.78 26.7 18.9 −2.2 C 0.79 0.63 30.4 20.6 −2.3 D 0.61 0.71 38.8 31.9 −7.4 E 0.64 0.47 40.7 32.2 −5.8 F 0.84 0.73 23.9 15.3 −0.4 Alldata 0.81 0.71 28.9 19.4 −1.7

Usingcalibratedparameters A 1.00 0.96 3.1 2.0 0.96

B 0.99 0.88 5.3 3.8 0.87 C 1.00 0.95 3.6 2.4 0.95 D 1.03 0.80 6.7 5.9 0.75 E 0.99 0.86 5.9 4.3 0.86 F 0.96 0.91 6.6 5.0 0.90 Alldata 0.99 0.92 5.1 3.6 0.91 Table7

“Goodness-of-fit”indicatorsrelativetoETsimulationsforalltreatmentswhenusingdefaultandcalibratedparameters,SorraiaValleyexperiments.

Treatment Goodnessoffitindicators

b R2 _{RMSE(mm) AAE(mm) EF}

Usingdefaultparameters A 0.91 0.89 5.0 4.0 0.87

B 0.93 0.75 6.6 5.0 0.72 C 0.91 0.87 5.7 4.9 0.85 D 0.87 0.59 9.7 7.8 0.47 E 0.88 0.60 8.6 6.4 0.49 F 0.97 0.71 6.9 5.2 0.67 Alltreatments 0.92 0.77 6.6 5.0 0.74

Usingcalibratedparameters A 1.02 0.88 5.1 4.0 0.86

B 1.02 0.83 5.4 3.9 0.82 C 1.02 0.89 5.2 4.4 0.87 D 0.98 0.76 6.7 5.3 0.75 E 1.00 0.74 6.4 4.9 0.72 F 1.01 0.74 6.5 4.9 0.70 Alltreatments 1.02 0.81 5.7 4.3 0.81

Fig.5. Seasonalvariationoftheactualtranspiration(Ta, )andsoilevaporation(Es,–)infield2in2010((a)and(b)),field1in2011((c)and(d)),andfield3in2012 ((e)and(f)):onleftwhenusingAquaCropand,onright,withtheSIMDualKcmodel.

ET(mm)withmodelsimulationsforalltreatments.Fig.8shows

thatcomparisonforselectedexamplesoffullirrigation(treatment

A),milddeficitirrigation(treatmentB)andheavydeficitirrigation

(treatmentF).Results(Fig.8andTable7)showthattheheavystress

treatmentspresenthigherRMSE(6.5mmvs.5.1mm)butnotrends

ofover-orunderestimationofETweredetected(brangingfrom

0.98to1.02).Contrarily,thereisatrendofunderestimationofET

whendefaultparametersareused(bfrom0.87to0.97).EFvalues

areacceptable,ranging0.70to0.87whencalibratedparametersare

used.EFvaluesforthecaseofstressedexperimentsDtoFhighly

decreasewhendefaultparametersareused(Table7).

Fig.9showsexamplesofthedifferentresponsesoftheadjusted

cropcoefficient–KcTrincaseofAquaCropandKcbadjincaseof

SIM-DualKc–towaterstress,thusidentifyingamuchlargerdependency

incaseofKcbadjthanforKcTrbecausethelatterisverymuchtiedto

theCCcurve.ResultsshowthatinAquaCroptheimpactsofwater

stressontranspirationareminimizedduetothedependencyof

KcTrandTauponCC,asdiscussedbefore.Contrarily,when

adopt-ingtheapproachbyFAO56thatisconsideredinSIMDualKc(Allen

etal.,1998,2005;Rosaetal.,2012),Kcbadjissensitivetowater

stress.FollowingdiscussionsinSection3.1,itcanalsobeconcluded

thattheKcTrandCCcurveproportionalityshouldberevisedandan

approachsimilartothatadoptedinFAO56couldbeconsidered.

TheseresultsindicatethatmodelcomputationsoftheactualETare

lesssensitivetotheCCcurvethansoilwatercomputationsbecause

theover-estimationsofTapartlycompensatesforthe

underestima-tionofEs,thusresultinginsmalldifferencesbetweenestimatedand

Fig.6.SeasonalvariationoftheadjustedbasalcropcoefficientwhenusingSIMDualKc,Kcbadj( ),andusingAquaCrop,KcTr( ),comparedwiththecanopycover

curves(···)relativetoAlpiarc¸afields:(a)field2in2010,field1in2011(b),andfield3in2012(c). Table8

Sowingandharvestingdates,dryfinalabovegroundbiomass,yieldandharvestindexforallmaizeseasonsandfieldsinAlpiarc¸a.

Field,year Cropseasondates Harvesteddrytotalabovegroundbiomass(tha−1_{) Drytotalyield(tha}−1₎ Harvestindex()

Sowing Harvest Field1,2010 25/05 13/10 41.86(±8.37) 20.62(±4.14) 0.49(±0.04) Field2,2010 25/05 13/10 26.27(±5.25) 12.78(±2.56) 0.49(±0.03) Field1,2011 20/04 20/09 40.02(±5.86) 19.46(±2.97) 0.49(±0.01) Field2,2012 16/04 20/09 38.70(±7.09) 19.32(±2.63) 0.50(±0.05) Field3,2012 30/05 12/10 33.62(±7.64) 16.53(±3.72) 0.49(±0.04)

Standarddeviationofobservationsbetweenbrackets

3.3. Evapotranspiration-yieldrelations,andbiomassandyield predictions

Theobserved finalharvested biomass, yieldand theharvest indexfortheAlpiarc¸acasestudyarepresentedinTable8;thesedata

wasusedtotestAquaCroppredictions.Higheryieldswereobtained

infield1in2010and2011.Thelowestyieldswereobtainedin

field2in2010due topoorirrigationmanagementthatdidnot

avoidstressduringflowering.Thevariationofyieldsobservedwas

discussedby Paredeset al. (2014a) aimingat developing more

appropriatemanagementscenarios.

Theobservedaveragefinal harvestedbiomass andyield and

theharvestindexforalltreatmentsintheSorraiaValleyare

pre-sentedinTable9.Resultsshowthathigherbiomassandyieldwas

attainedforthefullirrigationtreatment(A)followedbythe

treat-mentwherestresswasimposedlaterintheseason(C).Treatment

F,wherestresswasimposedalongthecropseason,producedthe

lowesttotalbiomassandyield.

Alinearrelationshipbetweenyield(Tables8and9)andETcadj

andwithTawasobserved.Fig.10presentstheserelationshipsusing

allexperimentaldatarelativetobothmaizehybridsLG18(FAO300)

andPR33Y74(FAO600).Theapproachadoptedhereinofusingfield

Table9

Dryfinalabovegroundbiomass,yieldandharvestindexforallmaizetreatments (Alvesetal.,1991).

Treatment Drytotalabove groundbiomass (tha−1₎

Drytotalyield (tha−1₎ Harvestindex() A 26.57(±3.42) 12.15(±1.20) 0.48(±0.02) B 21.61(±2.19) 10.03(±1.27) 0.46(±0.05) C 25.02(±0.96) 12.23(±0.40) 0.45(±0.08) D 17.59(±0.88) 6.65(±0.26) 0.38(±0.01) E 19.06(±0.27) 7.11(±1.13) 0.38(±0.07) F 14.02(±0.39) 6.66(±0.98) 0.47(±0.06)

Fig.7. Selectedexamplesofmaizecanopycover(CC)simulated( )andobserved(䊉)forSorraiaValleyexperiments,treatments(A)–(F).

Table10

“Goodness-of-fit”indicatorsrelativetomodelpredictionofbiomassalongthecropseason,andyieldusingdatafrombothcasestudies,whenusingdefaultandcalibrated parameters.

Goodnessoffitindicators

b R2 _RMSE(tha−1_{) AAE(tha}−1_{) EF}

Biomassalongcropseason Default 0.75 0.91 7.21 5.71 0.70

Calibrated 0.97 0.92 3.83 2.83 0.92

Finaldrybiomass Default 0.84 0.77 6.14 4.71 0.41

Calibrated 1.01 0.82 3.49 2.93 0.81

Finalyield Default 0.84 0.82 2.51 1.77 0.63

Fig.8.Selectedexamplesoffieldestimatedvs.AquaCropsimulatedcropevapotranspiration(ETcadj)forselectedSorraiaValleytreatments:(a)fullirrigation(treatmentA);

(b)milddeficitirrigation(treatment(B));and(c)heavydeficitirrigation(treatment(F)).

Fig.9.SeasonalvariationoftheadjustedbasalcropcoefficientwhenusingSIMDualKc,Kcbadj( ),andAquaCrop,KcTr( )comparedwiththecanopycovercurve(···)

relativetoselectedexamplesof(B)and(F)treatments.

observationsrelative todifferenthybridsand observationyears foryieldpredictionswasalsoadoptedbyothers,e.g.,Rettaand Hanks(1980),Livermanetal.(1986)andParedesetal.(2014a).

Resultsin Fig.10indicatea similarbehaviourof thesehybrids.

Theyalsoindicatethatusingtheyield-Ta relationshipis

prefer-abletotheonebetweenyieldandETcadj.NotonlyR2ishigherbut,

asobservedbyotherauthors(Stewartetal.,1977;Payeroetal.,

2006;Raesetal.,2012;Paredesetal.,2014a),usingtheyield-Ta

relationshipavoidsthevariabilityduetothesoilevaporation

com-ponent,whichdependsuponcropandirrigationmanagement,and

refersonlytotranspirationthatisdirectlyresponsibleforyield.All

datarelativetobiomassandyieldfromalltheabovedescribedcase

Fig.10.Relationshipbetweenmaizeseasonalevapotranspiration(ETcadj)andyield(onleft),andbetweentranspiration(Ta)andyield(onright)usingobservedyieldusing

Fig.11.Maizeactualandsimulatedfinalbiomass(tha−1_{),onleft,andyield(tha}−1_{),onright,usingdatafromallfieldsofAlpiarc¸a()andfromallexperimentsofSorraia}

Valley().

studies(Tables8and9)wereusedtoassessthemodelaccuracy

inpredictingmaizebiomassandyield(Fig.11).Whencalibrated

parameters were used,there wasno trend in biomass

estima-tion(Fig.11a)butjustaslighttrendforover-estimationofyield

(Table10).Thebvalueiscloseto1.0forbiomasspredictionsand

b=1.05 forfinalyieldestimation.Ifdefaultparametersareused

thenunder-estimationsoccur,withb≤0.84and RMSEdoubling

thoseobservedwhencalibratedparametersareused.Withdefault

parameters,EFisrelativelylow(<0.70)butishigherwhenusing

calibratedparameters(EF≥0.81),thusindicatingthatthe

resid-ualsvariance is much smallerthantheobserved datavariance.

Resultsforbiomassandyieldpredictionsthereforeevidencethe

advantageinusingappropriatelycalibratedparameters.Theyield

over-estimationbyAquaCropislikelyrelatedtotheabovereferred

insufficienciesinthepartitionofETcadjintoEsandTa,thelatter

beingover-estimated.

Hsiaoetal.(2009),Hengetal.(2009)andGarcía-VilaandFereres (2012)usedAquaCropforpredictingmaizefinaldrybiomassand

reportedRMSEvaluessimilartothebulkvaluegiveninTable10.

However, the RMSE reported by Heng et al. (2009) for deficit

irrigationarelarger.Applicationsofdifferentmodelsledto

com-parableresults,e.g.,López-Cedrónetal.(2005)usingCERES-Maize,

and Ma et al.(2006) withDSAAT-Ceres and RZWQ-CERES. The

RMSEresultsforyieldprediction(Table10)arealsocomparable

withotherAquaCropmaizeapplications,e.g.,Hengetal.(2009)

andGarcía-VilaandFereres(2012),aswellaswithRMSEobtained

withdifferentmodelssuchasMaetal.(2006)withthe

DSAAT-Ceresand RZWQ-CERESmodels,López-Cedrónet al.(2005),Liu

etal.(2011)andDeJongeetal.(2012)withCERES-Maize,Monzon etal.(2012)withCropSystandCERES-Maize,Caveroetal.(2000)

withtheEPICmodel.Inapreviousstudy,usingthesamecase

stud-iesdata,Paredesetal.(2014a)combinedthesoilwaterbalance

modelSIMDualKcwithboththeglobalandmulti-phasicStewarts’

modelsand obtainedRMSEof1.80and1.21tha−1,respectively,

i.e.,achievedbetterresultswiththatsimplifiedapproachthanwith

AquaCrop.

4. Conclusions

TheAquaCropmodelwastestedusingasetofcalibrated

param-eters describing the canopy cover, ET, soil water content, and

biomassandyieldobservedinlargefarmfieldsatAlpiarc¸aandin

experimentalfieldsattheSorraiaValley.Itwasfurthertestedfor

thesamelocationsusingthedefaultparametersprovidedbyRaes

etal.(2012).Resultsshowedthatacorrectcalibrationofthecanopy

covercurveparametershighlyimprovedthemodels’performance

becausetheCCcurveisusedbythemodelfordailycomputations

ofcroptranspirationandsoilevaporation.Naturally,iftheCCcurve

adherestofieldcanopydataitislikelythattheresulting

transpi-rationandevaporationestimatesarebetterthanthoseobtained

usingdefaultparameters.

Resultsshowedaninsufficientaccuracyofthemodelin

simulat-ingthesoilwatercontentdynamicsalongacropseasonparticularly

ifdefaultparametersareused.Therefore,AquaCropisnotsuitable

forirrigationschedulingpurposes.Problemswerealsoidentified

relative to daily ET calculation and its partition. The adjusted

basal crop coefficient is extremely tied to the CC curve, thus

lessinfluencedbywaterstressandleadingtoover-estimationof

planttranspiration.Similarly,soilevaporationisunderestimated

becauseitisalsomadedependentontheCCcurve.Nevertheless,

thecumulativeETthroughouttheseasoncouldbesimulatedquite

wellsincetheover-estimationofTaiscompensatedbythe

under-estimationofEs.ItisthereforeadvisabletorevisetheETpartition,

usingtheapproachesproposedinFAO56.

Good predictionresultswereobtainedfor biomassand crop

yieldwhenusingproperlycalibratedparameters.Resultsshowed

a slightunder-estimationof biomassalong thecropseasonbut

relativelysmallerrorsofestimateswereobtainedforthefinal

har-vestedbiomass.Differently,theestimationsofthefinalyieldhave

shownatendencyforover-estimation(b=1.05)butwithlow

esti-mationerrors.Thereferredover-estimationsarelikelyrelatedto

themodeltrendofoverestimatingtranspiration,whichisthemain

drivingvariableusedforyieldestimation.Whendefaultparameters

areused,finalbiomassandyieldestimationhavealargererror,

nev-erthelessacceptableformostapplicationswhenfielddataarenot

available.Summarizing,overallresultsshowadequacyofAquaCrop

forestimatingbiomassandyield.

Resultsevidencethatwhenusingthemodelforresearch

pur-poses,thuswhenhighaccuracyisdesired,itisrequiredtocalibrate

thecanopycovercurveusingfielddata.Ifthemodelistobeusedfor

managementpurposes,itisalsonecessarytocalibratethemodel

for soil water or ETsimulation. Calibration/parameterizationis

alsoadvisablewhenaccuracyinbiomassandyieldpredictionsare

theestimationsrelativetothecomponentsofthewaterbalance,

mainlyaimingatimprovingtheestimationoftranspiration,which

hasmajorinfluenceonyieldestimation.

Acknowledgements

The support, during the experimental seasons of 2010–12,

providedbyEngs.ManuelCampilho,Diogo CampilhoandAbílio

PereiraofQuintadaLagoalvadeCimaareherebyacknowledged.

ThanksareduetothecolleaguesJulianoMartins,ErlánFariaFilho

and Diogo Martins for the help during field work. The

schol-arship SFRH/BD/62339/2009 provided by FCT to P. Paredes is

acknowledged.ThestudywaspartiallyfundedbytheFCTproject

PTDC/GEO-MET/3476/2012.

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