Dissecting the nonlinear response of maize yield to high ...Engle, & Little, 2015; Zhu et al., 2018). Such observational informa‐ tion could be important ρinput data to drive crop

Glob Change Biol. 2019;1–15. wileyonlinelibrary.com/journal/gcb  | 1© 2019 John Wiley & Sons Ltd

Received:17October2018  |  Revised:21March2019  |  Accepted:25March2019DOI: 10.1111/gcb.14632

P R I M A R Y R E S E A R C H A R T I C L E

Dissecting the nonlinear response of maize yield to high temperature stress with model‐data integration

Peng Zhu1,2  | Qianlai Zhuang1,3 | Sotirios V. Archontoulis4 | Carl Bernacchi5,6 | Christoph Müller7

Abbreviations:AGB,abovegroundbiomass;An,anthesis;BGR,dailybiomassgrowthrate,AGBdividedbygrowingseasonlength;ET,evapotranspiration;GDD,growingdegreedays;GFP,grainfillingperiod;GSL,growingseasonlength;HDD,hightemperaturedegreedays;HDDVP,HDDAn and HDDGFP,HDDduringvegetativeperiod,anthesisandGFP;HI,harvestindex,yield/AGB;IWDRVI,integratedwidedynamicrangevegetationindex;MEM,modelensemblemean;PET,potentialevapotranspiration;SYield

T, SBGR

T, SGSL

Tand SHI

T,temperature

sensitivityofyield,BGR,GSLandHI;VP,vegetativeperiod;WDRVI,widedynamicrangevegetationindex;WS,waterstress.

1DepartmentofEarth,Atmospheric,andPlanetarySciences,PurdueUniversity,WestLafayette,Indiana2SchoolofGlobalPolicyandStrategy,UniversityofCaliforniaSanDiego,LaJolla,California3DepartmentofAgronomy,PurdueUniversity,WestLafayette,Indiana4DepartmentofAgronomy,IowaStateUniversity,Ames,Iowa5DepartmentofPlantBiology,UniversityofIllinoisatUrbana‐Champaign,Urbana,Illinois6GlobalChangeandPhotosynthesisResearchUnit,USDA‐ARS,Urbana,Illinois7PotsdamInstituteforClimateImpactResearch(PIK),Potsdam,Germany

CorrespondenceQianlaiZhuang,DepartmentofEarth,Atmospheric,andPlanetarySciences,PurdueUniversity,WestLafayette,IN.Email:[email protected]

Funding informationNationalScienceFoundation,Grant/AwardNumber:IIS‐1027955;NASA,Grant/AwardNumber:NNX09AI26G

AbstractEvidencesuggeststhatglobalmaizeyielddeclineswithawarmingclimate,particu‐larlywithextremeheatevents.However,thedegreetowhichimportantmaizepro‐cessessuchasbiomassgrowthrate,growingseasonlength(GSL)andgrainformationareimpactedbyanincreaseintemperatureisuncertain.Suchknowledgeisneces‐sary to understand yield responses anddevelop crop adaptation strategies underwarmerclimate.Herecropmodels,satelliteobservations,survey,andfielddatawereintegratedtoinvestigatehowhightemperaturestressinfluencesmaizeyieldintheU.S.Midwest.Weshowedthatbothobservationalevidenceandcropmodelensem‐blemean(MEM)suggeststhenonlinearsensitivityinyieldwasdrivenbytheintensi‐fiedsensitivityofharvestindex(HI),butMEMunderestimatedthewarmingeffectsthroughHIandoverstatedtheeffectsthroughGSL.FurtheranalysisshowedthattheintensifiedsensitivityinHImainlyresultsfromagreatersensitivityofyieldtohightemperaturestressduringthegrainfillingperiod,whichexplainedmorethanhalfoftheyieldreduction.Whenwarmingeffectsweredecomposedintodirectheatstressandindirectwaterstress(WS),observationaldatasuggestthatyieldismorereducedbydirectheatstress(−4.6±1.0%/°C)thanbyWS(−1.7±0.65%/°C),whereasMEMgivesoppositeresults.Thisdiscrepancyimpliesthatyieldreductionbyheatstressisunderestimated,whereastheyieldbenefitofincreasingatmosphericCO2 mightbeoverestimated in cropmodels, becauseelevatedCO2 bringsyieldbenefit throughwaterconservationeffectbutproduceslimitedbenefitoverheatstress.Ouranalysisthroughintegratingdataandcropmodelssuggeststhatfutureadaptationstrategiesshouldbetargetedattheheatstressduringgrainformationandchangesinagricul‐turalmanagementneedtobebetteraccountedfortoadequatelyestimatetheef‐fectsofheatstress.

K E Y W O R D S

cropmodel,cropphenologicalstages,harvestindex,hightemperaturestress,satelliteobservations,waterstress

2  |     ZHU et al.

1  | INTRODUC TION

Astheworld'slargestproducerofmaize,theUnitedStateshasseenasteadyincreaseinmaizeyieldsincetheGreenRevolution(Assefaetal.,2017),whileincreasesinconcurrentheatanddroughtacrosstheUnitedStatessincethe1950shaveposedasignificantriskformaizeproduction(MazdiyasniandAghaKouchak,2015;Schaubergeretal.,2017)andresultedinstagnatedcropproductioninmanyproducingareas(Olesenetal.,2011).Futurewarmingmightmoreseverelyde‐creasecropyieldwithfrequentextremeheatevents(Rahmstorf,&Coumou,2011;Schlenker&Roberts,2009),whichcausesoxidativedamagetochloroplasts(Crafts‐Brandner&Salvucci2002;Siebers,Yendrek,&Drag,2015),destroysreproductivestructures(Commuri&Jones,2001),andacceleratescropsenescence (Lobell,Sibley,&Ivan Ortiz‐Monasterio, 2012; Ruiz‐Vera, Siebers, Jaiswal, Ort, &Bernacchi,2018).Withwarmerclimates,currentagriculturalsystemmodelsneedtobeupgradedtobetterrepresentcropresponsestotemperature‐relatedclimateextremesand thus copewith theup‐comingchallengesofincreasingfooddemands.

In recent decades, multiple approaches have been adoptedtomaintainyield increases through improvedmanagementprac‐ticesandbreedingtechnology,likeimprovedherbicideandweedmanagement techniques, higher planting density, and new culti‐varswithlongergrainfillingperiod(GFP)(Assefaetal.,2016;Tao,Yokozawa,Xu,Hayashi,&Zhang,2006;Tollenaar&Wu,1999;Zhuetal.,2018).However,theactualeffectsoftheseintensifiedman‐agementpracticesmightbecounterproductiveduetothediverseenvironmentalconditionsandtheirinteractionwithmanagementpractices(Lobelletal.,2014).Therefore,itisnecessarytobetterunderstandtheresponseofcropyieldtoclimaticvariationinfieldconditions.

Theobservedvariationinmaizeyieldistheproductofmanyin‐teractiveprocesses thatmakeamechanisticunderstandingof thedriversofthisvariationdifficult.Throughoutthelifecycleofmaizeplants,yieldisdrivenbybiomassaccumulationandpartitioningbe‐tween organs (Lizaso et al., 2018). Biomass accumulation can beexpressedasgrowingseason length (GSL)×averagedailybiomassgrowth rate (BGR). The partitioning of biomass to grains is oftenquantified using harvest index (HI=yield/above‐ground biomassaccumulation).Thus,finalyieldistheproductofBGR,GSLandHI.WarminginfluenceonmaizeyieldcanbetherebydissectedastheinfluenceonGSL,BGRandHI.Warmer temperatureoftenmeansashorterGSLwithaccelerateddevelopmentrate(Cheikh&Jones,1994).However, the influenceofwarmingonBGRandHI ismorecomplexthanGSL.Thedirectionandmagnitudeofinfluencedependonwhetherthethresholdtemperaturehasbeenexceeded,whilethethresholdtemperatureseemstobevariableamongdifferentvariet‐iesandphenologicalstages(Rezaei,Webber,Gaiser,Naab,&Ewert,2015;Sánchez,Rasmussen,&Porter,2014).

As aC4 plant,maize often has a higher optimal temperaturefor photosynthesis than C3 plants, thus warmer leaf tempera‐tures in early vegetative growth can potentially lead to either

no impacts or a positive impact onmaize photosynthetic activ‐ity (Crafts‐Brandner & Salvucci, 2002; Parent & Tardieu, 2012).However,maizeyieldbecomesincreasinglysensitivetohightem‐peratureduringreproductivedevelopment(Cheikh&Jones,1994;Siebersetal.,2017).Thus,thesamelevelofwarmingtreatmentindifferent stagesmight result indifferentor evenopposite influ‐enceonmaizeyield(Siebersetal.,2017).Inparticular,identifyingcroppingsystemvulnerabilitiesanddevisingtargetedadaptationstrategiestodealwithfuturewarmingshouldbeonthepremiseofaclearunderstandingofhowcropyieldsrespondtowarmingduringdifferentdevelopmentstages.Duetolimitedknowledgeofcropstages(Butler&Huybers,2015),analysesonthesensitivityofcropyieldstotemperaturetypicallyignorethattheresponsetotemperatureisstagedependent(Cheikh&Jones,1994;Siebersetal.,2017).Thismightleadtoconsiderableuncertaintywhenpro‐jectingcropyieldunderfuturewarmerclimate.

Field warming experiments have been devised to explorethe effects of warming in different growth stages on crop yield(Hatfield & Prueger, 2015; Ruiz‐Vera et al., 2018; Siebers et al.,2017).Ithasbeensuggestedthatmaizegrainyieldissignificantlyreduced under heat stress through pollen viability that in turndetermines kernel number and HI, which explained most of thevariation inmaize yield (Edreira&Otegui, 2012, 2013; Lizaso etal.,2018). In termsof the timingofheating treatment, itappearsthatkernelnumberperplantwasmorereducedbyheatingduringsilkingthanbeforeanthesis(Edreira&Otegui,2012).Influenceofheatingonphenological development is alsoevident.Grain yieldwassignificantlyreducedduetoshorteningofGFPwhentempera‐tures were increased from 25°C to 31°C, despite the enhancedgrain filling rate (Dias& Lidon, 2009).Heating during pre‐silkingcausedalargerdelayinsilkingdatethaninanthesisdate,leadingtoalengthenedanthesis‐silkinginterval(Cicchino,RattalinoEdreira,Uribelarrea,&Otegui,2010),whichisagoodindicatorofthefinalmaizeyield (Bolanos&Edmeades,1996).However, theseexperi‐mentsareoftenlimitedtosmallscalesandcouldnotrepresentthecomplexanddiversecropsystems,makingtheconclusionhardtobeextrapolatedtootherregions.

Cropmodelshaveshownthepotential tosimulateandrepro‐ducethelarge‐scalespatiotemporalvariabilityofcropyield(Elliottetal.,2015;Mülleretal.,2017).Generally,cropmodelsrepresentourunderstandingofresponseofcropplantstoclimaticvariation,soil nutrient status, hydrological conditions, andagronomicman‐agementpractices.Theyarenormallyabletoadequatelysimulateaverageconditionsbutfailtohandleclimateextremes(Eitzingeretal.,2013;Lobelletal.,2012;Sánchezetal.,2014).Suchlimitationiscriticaltoevaluatecropresponseunderongoingclimaticchange,whichisexpectedtobringmoreextremeweatherfortheagricul‐tural sector across theworld. In addition, somebasic knowledgemighthavenotbeenupdatedfordecades.Forexample,thedefaultparametersrelatedtothephysiologicalpropertyofcropvarietiesmightbeunabletoreflecttherecentprogressincultivarsthroughbreedingtechniques.Thus,itmightbringsubstantialuncertainties

     |  3ZHU et al.

whenusing thesemodels to reproducehistoric or project futurecropyield.Recently,anensembleofmulti‐modeloutputhasbeenwidelyusedasan improvedwayofevaluatingandprojectingcli‐matechangeandmanagementeffectsoncropproductionwithre‐duceduncertainty (Assenget al., 2014;Rötter,Carter,Olesen,&Porter,2011).

Newtechniquesemployingsatellitedatahavebeenincreasinglyused in theagricultural sector tomapcrop types,delineate irriga‐tion/non‐irrigation boundary, derive crop phenology information,and project field crop yield (Azzari, Jain, & Lobell, 2017; Deines,Kendall,&Hyndman,2017;Guanetal.,2017;Lobell,Thau,Seifert,Engle,&Little,2015;Zhuetal.,2018).Suchobservationalinforma‐tioncouldbeimportantinputdatatodrivecropmodelsorcalibratemodelparameters.Thederivedcropphenologyinformationislikelytoprovideobservationalevidencetocharacterizetheregional‐scalespatiotemporalpatternsoffieldcropgrowthstatus(Zhuetal.,2018)andthusassist theunderstandingof responseofcropyield tocli‐maticvariationduringdifferentgrowthstages.

Here we integrated satellite‐derived crop stage information,regionalcropmodeloutput,surveyedyielddatafromtheUnitedStates Department of Agriculture (USDA) and site‐level experi‐mentdatatodissecthowhightemperaturesinfluencemaizeyieldthrough different physiological processes. Surveyed yield data,togetherwithsatellite‐basedcropstageinformationandmodeledmaize aboveground biomass (AGB) calibrated against site‐mea‐suredAGB,enabledus to retrievecounty‐levelGSL,BGR (AGB/GSL) andHI (Yield/AGB). Thiswas used to decompose the tem‐perature sensitivity of yield (SYield

T) into the temperature sensitiv‐

ities ofBGR (SBGRT),GSL (SGSL

T), andHI (SHI

T),whichwere estimated

withapanelmodel(Schaubergeretal.,2017;Schlenker&Roberts,2009;Tack,Barkley,&Nalley,2015).Eachcomponentcharacter‐izesthetemperatureresponseofnetassimilationratedeterminedby photosynthesis and respiration (SBGR

T), plant development rate

(SGSLT),andreproductivegrowthdeterminedbygrainsizeandgrain

weight (SHIT), respectively. In addition,SYield

T, SBGR

T, SGSL

T, and SHI

T based

onmultiplecropmodeloutputswerealsoanalyzedtocomplementthe survey and satellite data. The relative contribution of directheatstressandindirectwaterstress (WS)toyieldreductionwasfurtherestimatedusingstatisticalmodelandcropmodel simula‐tionto investigatetheunderlyingdriverofmaizeyieldreductionwithclimaticwarming.Inthisstudy,wefocusedonthreeMidweststatesdominatedbyrainfedmaize—Indiana,Illinois,andIowa—thataccount forapproximately40%ofU.S.maizeproduction (USDA,2015). Thus, the conclusions drawn from this study are likely toprovideinsightforunderstandingthetemperatureresponseofthewholeU.S.rainfedmaizeproduction.

2  | MATERIAL S AND METHODS

2.1 | Satellite data derived crop stage information

In this study,8‐day timeseriesof250mdaily surface reflectanceMODISdatasetsonboardEarthObservingSystem(EOS)Terraand

Aqua satellite platforms:MOD09Q1 (2000–2015) andMYD09Q1(2002–2015)Collection6,wereused.Hereascaledwidedynamicrangevegetation index (WDRVI)wasusedtomonitorthegrowingstatusofmaizeplants(Gitelson,2004),becauseWDRVIhasahighersensitivitytochangesatmoderatetohighbiomassthanthenormal‐izeddifferencevegetationindex(NDVI).ThescaledWDRVIiscalcu‐latedwiththefollowingequation:

whereρred and ρNIRaretheMODISsurfacereflectanceintheredandNIRbands,respectively.Thescalingfactorαisintroducedtodegradethe fractionof theNIRreflectanceatmoderate‐to‐highgreenvegetation(Guindin‐Garcia,Gitelson,Arkebauer,Shanahan,&Weiss, 2012). Hereα was set as 0.1 as a comparison ofmul‐tiplevegetation indexes indicatesWDRVIwithα=0.1showedastrong linear correlationwith corn green LAI (Guindin‐Garcia etal., 2012). BeforeWDRVI calculation, the reflectancedatawerequality‐filteredusingthequalitycontrolflags.Onlythedatapass‐ingthehighestqualitycontroltestareretained.Ahybridmethodcombiningshapemodelfitting(SMF)andthreshold‐basedanalysiswasimplementedtoderivemaizephenologyusingMODISWDRVIdata at 250×250m spatial resolution from 2000 to 2015 (Zhuet al., 2018). Shape model was obtained by averaging multipleyearsWDRVIobservationstocharacterizetheclimatologyofcorngrowthcycle (Zhuetal.,2018).Theshapemodelwas thengeo‐metricallyscaledtofiteachWDRVItimeseries,sothepredefinedphenologicaldatesontheshapemodelcanbescaledlikewisetoestimatephenologicaldatesforeachpixel.Wehavederivedfourkeymaizegrowthstagesofemergence(lateMay),silking(MiddleJuly),dent(lateAugust),andmaturity(lateSeptember)acrossthefour states: Indiana, Illinois, Iowa, andNebraska. Verification atthe state level showed a good agreement betweenMODIS‐de‐rived maize phenology and the National Agricultural StatisticsService (NASS)–reported statemean phenological dates (Zhu etal., 2018). In this study,we focusedon the three rainfed states:Iowa,Illinois,andIndiana.

2.2 | Derivation of county‐level maize yield, AGB, GSL, and HI

Theobservedvariationinmaizeyieldistheendresultofintegra‐tionofmanyprocesseswithdifferentsensitivitiestohightemper‐aturestress.Tothisend,wedecomposethetotalyieldvariationintothreecomponents:BGR,GSL,andHI.County‐levelcorngrainyielddatasetfrom2000to2015coveringthethreestates(Illinois,Indiana, Iowa)was retrieved from theQuick Stats 2.0 database.The unit system formaize yield is bushel per acre (bu/ac). Thisdatasetwasusedtogetherwithremotesensingmodeledcounty‐levelAGBtoestimateHI (Yield/AGB).HIgenerallycharacterizesdrymatterpartitioningbetweensourceorganandsinkorganand

(1)NDVI=(�NIR−�red

)/(�NIR+�red

)

(2)WDRVI=100×

[(�−1

)+

(�+1

)×NDVI

][(�+1

)+

(�−1

)×NDVI

]

4  |     ZHU et al.

is mainly related to processes determining grain size and grainweight.

Thirty‐two site‐year maize AGB data measured at the end ofgrowing season across theU.S.Midwestwere collected (details ongeolocationandyearinformationcanbefoundinTableS1).Thisfieldexperimentmeasurementwasusedtoconstructa regressionmodelbetweenWDRVI andAGB. To this end,WDRVI in 3×3 pixelwin‐dowscenteredonthesitemeasuredAGBwasobtainedandaqualitycontrolprocedurewasappliedtotheWDRVItimeseriestoremovelow‐quality, cloud/aerosol‐contaminated observations. Pearson cor‐relationwasthenestimatedbetweentheWDRVItimeseriescenteredonthesiteandthesurroundingeightpixels.ThreeWDRVItimese‐riesscoringthehighestcorrelationandthecenteronewereaveragedforconstructingtheregressionmodel.Previousstudieshaveshowedtheintegratedenhancedvegetationindex(EVI)overthegrowingsea‐sonisagoodproxyofvegetationAGB(Ponce‐Camposetal.,2013).Similarly,we integratedWDRVI (IWDRVI)by summingWDRVIoverthegrowingseason,whichwasbasedonthepreviousstudy‐retrievedphenologydates(Zhuetal.,2018).Alinearregressionmodelwascon‐structedbetweeninsitumeasuredAGBandprocessedIWDRVIwiththeabovemethod.ThemodelshowsIWDRVIhasagoodexplainingpower(R2=0.75,p<0.0001)withtheequation:AGB=(16.4 ± 2.5)∗

IWDRVI(0.8±0.08)(±SE)(Figure1).WealsoappliedthesameproceduretoNDVIandenhancedvegetationindex2(EVI2),whicharealsocom‐monlyusedvegetationindexesfortemporalmonitoringofvegetationgreennessandproductivity,buttheR2ofNDVI(R2=0.68)andEVI2(R2=0.64)islowerthantheoneusingWDRVIasthepredictor.Withthis regressionmodel,AGBwasspatiallyestimatedwithsatellite‐re‐trievedIWDRVI.Finally,the16yearsofsatellitedataderivedGSLandAGBwereintegratedtocountyleveltoestimateHI(Yield/AGB)anddailyBGR(AGB/GSL)foreachcounty.

2.3 | Statistical analysis of temperature sensitivity across different growth stages

Temperaturesensitivityofmaizeyield(SYieldT

)wasestimatedusingapanel datamodel (Equation3)with growing seasonmean surfaceair temperature (Tsa) and precipitation (Prcp) as the explanatoryvariables:

�1tcapturestheyieldincreasingtrendinrecentyears.Countyi cor‐respondstofixedeffectsofcountyiandaccountsfortime‐invariantcountydifferences, like the soilquality. t stands foreachyear.εi,t standsfortheerrortermforcountyiatyeart.�2 or � ln (Yield)

�Tsadefines

thetemperaturesensitivityofyield.ThetemperaturesensitivityofBGR(SBGR

T),HI(SHI

T),andGSL(SGSL

T)canbeestimatedwithEquation(3)

inasimilarway.Here,thedependentvariableYield(BGR,GSLandHI)waslogged,sotheestimatedtemperaturesensitivityrepresentsthepercentagechangeinYield(BGR,GSLandHI)with1°Ctempera‐tureincrease.

TheclimatedatausedherewereobtainedfromtheUniversityofIdahoGriddedSurfaceMeteorologicalData(http://metdata.north‐westknowledge.net/)withaspatialresolutionof4km(Abatzoglou,2013). It is a gridded product covering continental United Statesfrom1979to2016.Thisdatasetiscreatedbycombiningtheattri‐butesoftwodatasets:temporallyrichdatafromtheNorthAmericanLandDataAssimilationSystemPhase2(Mitchell,2004)andspatiallyrichdatafromtheParameter‐elevationRegressionsonIndependentSlopesModel(PRISM)(Dalyetal.,2008).AftervalidationusinganextensivenetworkofweatherstationsacrosstheUnitedStates,thisdataset proved to be suitable for application in a landscape‐scaleecologicalmodel.ThengrowingseasonmeanTsaandPrcpwerees‐timatedby integratingdaily climatevariable according toMODIS‐derivedgrowingseasonstartingandendingdate.

AsYield=HI ⋅BGR ⋅GSL,SYieldTcanbewrittenasfollows:

Theseequationsindicatethatthepercentagechangeinyieldwith1°CwarmingcanbedissectedintopercentagechangesinBGR,GSL,andHI,whichcorrespondstophysiologicalprocessesofcarbonassim‐ilationratethroughphotosynthesis,cropdevelopmentrate,andmaizereproductive growth determining biomass partitioning, respectively.We furtherdivided thedatasetofyield,BGR,GSL,andHI into fivegroupsaccordingtothequintileofmeangrowingseasontemperature.Thisseparationhelpsustounderstandhowmaizephysiologicalpro‐cessesrespondtowarmingastemperatureincreases.

Althoughthecoefficientinalinearmodeliseasytointerpret,theactualresponseofcropyieldandassociatedphysiologicalprocesses

(3)log(Yieldi,t

)= �1t+�2Tsai,t+�3Prcpi,t+Countyi+�i,t

(4)� ln (Yield)

�Tsa=� ln (HI)

�Tsa+� ln (BGR)

�Tsa+� ln (GSL)

�Tsa

(5)�Yield

Yield ⋅�Tsa=

�HI

HI ⋅�Tsa+

�BGR

BGR ⋅�Tsa+

�GSL

GSL ⋅�Tsa

F I G U R E 1   Theregressionmodelusedtorelatetheintegratedwidedynamicrangevegetationindex(IWDRVI)withabovegroundbiomass(AGB).Eachpointcorrespondstoasite‐measuredAGBandMODIS‐derivedIWDRVI.Theshadedareaindicatesthe95%confidenceinterval

8.6 8.8 9 9.2

Log(IWDRVI)

9.6

9.8

10

10.2

Log(

AG

B)

AGB = 16.4IWDRVI0.8

R = 0.752

     |  5ZHU et al.

toclimatevariablesismorelikelytobenonlinear(Rezaeietal.,2015;Schlenker&Roberts,2009).Therefore,analternativemodel(6)wasusedbyaddingaquadraticfunctionofTsaandPrcptocapturethenonlinearclimaticresponseofyieldformation:

ThesensitivityofHI,GSL,andBGRcanbemodeledsimilarlybyreplacingYieldwiththecorrespondingvariables.

The total temperaturesensitivityofyieldestimatedabovecanbe regarded as the integrated effects of high temperature stressandthermaltimeaccumulationduringdifferentphenologicalstages.Followingpreviousstudies(Schlenker&Roberts,2009;Tacketal.,2015),yieldsensitivitywasexpressedas:

Herehigh temperature stress isquantifiedwithhigh tempera‐turedegreedays (HDD),whichcharacterizesthehigher‐than‐opti‐malthermaltimeaccumulation.Growingdegreedays(GDD)drivescropdevelopmentandcharacterizesthethermaltimeaccumulationintheabsenceofextremeconditions.sstandsforthethreegrowthstagesVP,An,andGFP.BasedonEquation(7),warmingeffectsonyieldthroughHDDinGFPcanbeestimatedas �Yield

�HDDGFP

�HDDGFP

�Tsa.

When daily maximum temperatures exceed 30 degree, maizekernelsetwasshowntobereducedby1.7%perdegreedayunderrainfedconditionsinAfrica(Lobell,Bänziger,Magorokosho,&Vivek,2011).Herewe alsoused30degree as the threshold to estimateHDDtocharacterizehightemperaturestress.GDDandHDDwereestimated with the following equations using hourly temperaturevalues,whichwereobtainedbyfittingasinefunctiontointerpolatedailymaximumTsaandminimumTsa.

where t represents thehourly timestep,N is the totalnumberofhours ineachgrowingperiod,andDD isdegreedays. Ithasbeenprovedthatinterpolatingdailytemperaturetohourlyvalueisbetterincapturingsub‐dailyheatstress(Tacketal.,2015).

Theselectedthreeperiodsaregenerallydistinguishedbytheirmainrolesindeterminingthefinalyield:vegetativeperiodisrelatedtoleafdevelopmentandexpansion,anthesisisrelatedtopollinationanddeterminesgrainnumber,andGFPisrelatedtophotosynthatetranslocationtokernelsanddeterminesgrainweight.Maizegrowth

stageinformationisretrievedfromthepreviousstudy(Zhuetal.,2018). VP is defined as the duration from emergence to 10daysaheadofsilking.GFPisdefinedasthedurationfrom10daysaftersilking tomaturity. Althoughwe did not exactly extract anthesistimingfromtheremotesensingdata,apreviousstudysuggeststhattheanthesisisaround1weekbeforesilking(Bolanos&Edmeades,1996).Hence,inthisstudy,weuse10daysbeforeandaftersilkingdateasaconservativeestimationofanthesis.

ToobtainthesensitivityofmaizeyieldtoGDDandHDDindif‐ferentgrowthstages,thefollowingpanelmodelwasusedfollow‐ingpreviousstudies(Schlenker&Roberts,2009;Tacketal.,2015):

where�0tcapturestheyieldincreasingtrend,Countyicorrespondstothecountyfixedeffects,and�1−�6definesthesensitivityofyieldtoGDDandHDDinthethreegrowthstages.Thus,yieldsensitivitytoHDDcanbeestimatedwiththefirst‐orderdifference:

IntermsofthesensitivityofHDDtowarminginVP(

�HDDVP

�Tsa

),an‐

thesis(

�HDDAn

�Tsa

),andGFP

(�HDDGFP

�Tsa

),dailytemperaturewasuniformlyin‐

creasedby1°Cor2°CforeachstageandthenthedifferencebetweenHDDunderwarmingscenarioandtheoriginalHDDwasusedasthesensitivity of HDD to warming. Finally, warming effects on yieldthrough high temperature stress (HDD) in different growth stagescanbeestimatedwiththecorrespondingtermsinEquation(7).

2.4 | Relative contribution of heat and water stress to yield decline

Warming trendsnot only increase the frequencyof extremeheateventsbutalsoWSbyregulatingbothwaterdemandandwatersup‐ply(Lobelletal.,2013).Thusthewarminginfluenceonyieldcanbeinterpretedasthejointeffectofhightemperaturestress(HDD)andWSwiththefollowingequation:

HDD, GDD, andWSwere integrated over thewhole growingseason.

SensitivityofHDD,GDD,andWStotemperature(

�HDD

�Tsa,�GDD

�Tsa,�WS

�Tsa

)

wasestimatedwithsimplelinearmodelthroughregressingcounty‐levelHDD(GDD,WS)overtemperature.

ToestimatetheyieldsensitivitytoHDD,GDD,andWS,wecon‐structapanelmodeltoregressyieldoverHDD,GDDandWS:

where�0tcaptures the linear increasingtrendofyieldandCountyi correspondstothecountyfixedeffects.Then,

(6)log

(Yieldi,t

)= �1t+�2Tsai,t+�3Tsa

2i,t+�4Prcpi,t

+�5Prcp2i,t+Countyi+�i,t

(7)�Yield

�Tsa=

�Yield

�HDD

�HDD

�Tsa+

�Yield

�GDD

�GDD

�Tsa

=

3∑s=1

�Yield

�HDDs

�HDDs

�Tsa+

�Yield

�GDDs

�GDDs

�Tsa

(8)GDD308

=

N�t=1

DDt,DDt=

⎧⎪⎪⎨⎪⎪⎩

0,when Tsa<8

Tsa−8,when 8≤Tsa<30

22,when Tsa≥30

⎫⎪⎪⎬⎪⎪⎭

(9)HDD∞

30=

N�t=1

DDt,DDt=

⎧⎪⎨⎪⎩

0,when Tsa<30

Tsa−30,when Tsa≥30

⎫⎪⎬⎪⎭

(10)Yieldi,t= �0t+�1GDD

VPi,t

+�2HDDVPi,t

+�3GDDAni,t+�4HDD

Ani,t

+ �5GDDGFPi,t

+�6HDDGFPi,t

+�7Prcpi,t+Countyi+�i,t

(11)�2=�Yield

�HDDVP; �4=

�Yield

�HDDAn; �6=

�Yield

�HDDGFP

(12)�Yield

�Tsa=�Yield

�HDD

�HDD

�Tsa+�Yield

�GDD

�GDD

�Tsa+�Yield

�WS

�WS

�Tsa

(13)Yieldi,t=�0t+�1GDDi,t+�2HDDi,t

+�3WSi,t+Countyi+�i,t

6  |     ZHU et al.

WarmingeffectsonyieldthroughhightemperaturestressandWScanbethusseparatelyestimatedas�2

�HDD

�Tsa and �3

�WS

�Tsa.

Here,WSwas characterized by the ratio of potential evapo‐transpiration (PET) to evapotranspiration (ET). ET and PET from2001 to 2015 based onMODIS ET product (MOD16) were em‐ployed. This product has a spatial resolution of 1kmwith 8‐daytemporalresolution.ETandPETinMOD16wereestimatedusingtheimprovedETalgorithmbasedonthePenman–Monteithequa‐tion with MODIS‐derived land surface temperature, vegetationcover, andglobalmeteorologydata (Mu,Zhao,&Running,2011).AlthoughvariousmetricshavebeenproposedtomeasureWS(Jinetal.,2016),thereisnoconsensusonwhichoneisthebest.Sofar,thisobservationaldata‐generatedETproductistheonlyonewithfinespatialandtemporalresolution.MODIS‐basedgrowingseasonPET/ETwascalculatedforpixelswith70%areacoveredbymaizecroplandandthenaveragedtocounty level tobeconsistentwiththeothervariables.

2.5 | Uncertainty quantification

Our sensitivity analysis depends on yield statistical data, satel‐lite‐derivedphenologicaldate,andvegetationindexes.Allofthesevariablesaresubjecttouncertainties:(1)uncertaintiesinthecountyyieldstatisticaldataandsatellite‐derivedGSL, IWDRVI; (2)uncer‐taintiesofparametersintheregressionmodelconvertingIWDRVItoAGB.Herewequantifiedtheuncertaintiesrootedinthesedatasetsthroughrunningthepanelmodelforthousandstimeswiththesam‐plesgeneratedfromagivenparameter'sconfidenceinterval.

We estimated each county's yield uncertainty based on fieldlevelyielddatapublished inapreviousstudy (Lobelletal.,2014),whereeachcountyincludes100samplesofyieldreports.Thisdata‐setenablesustouse1,000timesbootstraptoestimatethestan‐darderror(SE)ofyieldineachcounty.ThenormalizedSE(SE/mean)isshowninFigureS1.Asthefielddataendin2012andwefound92%normalizedSEduring2000–2012weresmallerthan10%,weset the normalizedSE during 2013–2015 as 10%,whichwill be aconservativeestimationofyieldassociateduncertainty.As to theuncertainty related toGSL,we similarly estimated its SE through1,000 timesbootstrapbasedonMODIS‐derivedpixel levelmaizeGSL informationwithin each county (Figure S2). In terms ofBGRandHI,weusedthefollowingequationstoestimatetheassociateduncertainty.

ThenormalizedSE(SE/mean)forBGRandHIisshowninFiguresS9andS10.

WiththeestimatedSEforeachvariablecorrespondingtoeachcounty‐year,1,000randomsamplesweregeneratedwithinits95%confidenceinterval(mean ± 1.96∗SE).Therefore,werunthepanelmodel(Equations3,10,and13)1,000timeswitheachsampleset.Themean of panelmodel‐reported temperature sensitivity confi‐denceintervalwasusedtoquantifytheuncertaintyrelatedtothedatasource.

2.6 | Crop model output

Here,nineglobalgriddedcropmodelsimulationsat0.5°×0.5°reso‐lutionwereselectedbasedonwhethermaizeyield, totalbiomass,andgrowingseasondurationweresubmitted.Thesesimulationsre‐sultedfromthejointeffortoftheAgriculturalModelIntercomparisonand Improvement Project (AgMIP) (Rosenzweig et al., 2013) andInter‐Sectoral Impact Model Intercomparison Project 1 (ISIMIP1)(Warszawskietal.,2014)forassessingtheimpactofclimatechangeandmanagementpracticesonglobalstaplecropproduction.Wese‐lectedrainfedmaizesimulationforcedbyWFDEI.CRU,asthisforc‐ingdatacoveredthelongestsimulationuntil2012.Intermsofthemanagementscenario,“harmnon”wasselected,meaningthesimu‐lationusingharmonizedfertilizerinputsandassumptionsongrow‐ingseasons.MoredetailsonthesimulationprotocolcouldbefoundinElliottetal. (2015)and thedataset isdescribed.Then thedailyclimate data (temperature and precipitation)were integrated overthegrowingseasontoestimatethetemperaturesensitivityofyield,BGR,HI,andGSLwithmodeloutputs.

The nine crop models used here can be basically divided intotwogroups: (a)designedsolely foragricultural systems, likepAPSIM,pDSSAT,pDSSAT‐pt(pDSSAT‐ptispDSSATmodelwiththePriestley–TaylormethodestimatingpotentialET),GEPIC,PEGASUS,andCGMS‐WOFOST(b)evolvingfromtheterrestrialecosystemmodelandcoveringboth natural and agro ecosystems, like CLM‐Crop, LPJ‐GUESS, andLPJmL.Modelsinthefirstgroupoftenhaveamoredetailedrepresenta‐tionofcropdevelopmentprocessesandhaveadifferentparameteriza‐tionofhightemperaturestressovercropvegetativeandreproductivestages.MoredetailsonhowtemperaturestresswasimplementedintheninecropmodelscanbefoundinTableS2.

We then applied the abovementioned statistical models to0.5×0.5 gridded AgMIP outputs to investigate (a) howwarmerclimatesinfluencemaizeyieldthroughdifferentprocessesrelatedtoBGR,GSL,andHI;and(b)therelativecontributionofhightem‐peraturestress(characterizedwithHDD)andWStomaizeyieldincropmodels.WeemployedmodeloutputET,yield,andestimatedPETusingthePenman–MonteithequationforcedbyWFDEI.CRUaswell.

(14)�1=�Yield

�GDD, �2=

�Yield

�HDD, �3=

�Yield

�WS

(15)BGR=AGB

GSL=�IWDRVI�

GSL

(16)HI=Yield

AGB=

Yield

�IWDRVI�

(17)Var(BGR)=

(�BGR

��

)2

Var(�)+

(�BGR

��

)2

Var(�)

+

(�BGR

�IWDRVI

)2

Var(IWDRVI)+

(�BGR

�GSL

)2

Var(GSL)

(18)Var(HI)=

(�HI

��

)2

Var(�)+

(�HI

��

)2

Var(�)

+

(�HI

�IWDRVI

)2

Var(IWDRVI)+

(�HI

�Yield

)2

Var(Yield)

     |  7ZHU et al.

2.7 | APSIM model experiment

TheAPSIMmodelisaprocess‐basedcropmodelthatexplicitlyac‐countsforthehightemperaturestressandWSduringdifferentcropgrowthstages,whichisalsoincludedinISIMIP1(pAPSIM,thepar‐allelversionAPSIM). Itsimulatesanumberofcropsundervariousclimaticandmanagementconditions,andhenceisusedworldwideto address various research questions related to agricultural sys‐tems(Holzworthetal.,2014).TheAPSIM‐MaizemoduleisinheritedfromtheCERESMaize,withmodificationsonstressrepresentation,biomass growth rate, and phenological development. This flexibleprocess‐basedmodelallowsustoinvestigatethedifferentrolesofhigh temperature stress across stages in determining maize yieldvariation.

WaterstressinAPSIMiscalculatedastheratioofwatersupplytowaterdemand.Waterdemandisdrivenbythepotentialbiomassgrowthrateandtranspirationefficiency that isadjusted forvaporpressuredeficit(VPD).Watersupplyiscalculatedastheamountofwaterabovethecrop'swiltingpointinsoil layerscontainingroots.ThisamountismultipliedbyaKLfactorthataccountsfortheabilityofrootstoextractwaterfromasoil layer.Astemperaturerises, itwillincreasewaterdemandthroughVPDandwillreducethesupplyofsoilwaterthroughelevatedET.

Here,wedesignedtwogrid‐basedsimulationexperiments tofurtherinvestigatehowWSandhightemperaturestressinfluencemaizeyieldwithincreasingtemperature:sim1isacontrolsimula‐tionusingdefaulttemperaturestressandWS;sim2isasimulationwith temperature stress blocked. More details on model setupcan be found in the Supplementary Information. Here we onlyblock high temperature stress, becauseWS ismore complex tomanipulate.Sim1 includesbothhigh temperature stressandWSduring photosynthesis, anthesis, and grain filling, whereas sim2onlyincludesWS.Thus,hightemperaturestresscanbeseparatelyestimatedbycomparingthetwosimulationoutputs.Thesimula‐tion isrunforthethreestatesover2000−2015andforcedwithUniversityofIdahoGriddedSurfaceMeteorologicalDataaswell.Soilparameters,suchassoilhydraulicpropertiesandsoilorganicmatter fractions,wereextracted fromtheStateSoilGeographic(STATSGO) database, as collected by the National CooperativeSoilSurveyoverthecourseofacentury.Foreachsimulationgrid,the soil information was obtained through the R package “soilDB” (http://ncss‐tech.github.io/AQP/). Management informationlikeplantingdensityand fertilizer applicationamountwas takenfromtheUSDANASSsurveyreportatthestatelevel.CropsowingdatewasderivedfromtheCropCalendarDataset(Sacks,Deryng,Foley,&Ramankutty, 2010). The genericmaizehybrid (“B_110”)included inAPSIMversion7.7wasusedand itreferstoahybridwitha110‐dayrelativematurity.Thephenology‐relatedparame‐ters characterizingGFP thermal time requirementwere spatiallyparameterized based onMODIS‐derived crop stage information(Zhuetal.,2018).Spatiallyexplicitparametersareexpectedtoim‐provemodelsimulationwithabettermatchwiththeactualmaizephenologicaldevelopment.

3  | RESULTS

Accordingtotheregressionmodel(Figure1),spatiallyexplicitAGBwas estimated with MODIS‐derived IWDRVI. BGR, GSL, and HIat county levelwerealso retrieved.Theirmulti‐yearmean revealsthereisaclearvariationinthespatialpatternofBGR,HI,andyield,and lower values are often identified in those southern counties(Figure2).However,GSLisrelativelyhomogeneousacrossthecoun‐ties,implyingvarietieswithdifferentmaturitygroupswereselectedtoadapt to the local thermal timeenvironment.Thus thecorrela‐tionbetweenGSLandyieldisquitelow(R2=0.004),butthisdoesnotcontradict the fact that longerGSL leads tohigheryield foragivensite.Thespatialvariationofyield ismorecorrelatedwithHI(R2=0.88)andBGR(R2=0.74),implyingthedominantroleofdailybiomassaccumulationandpartitioningtograin indrivingtheyieldvariationspatially.

SYieldT was estimated and then decomposed into three compo‐

nents: SBGRT

, SHIT, and SGSL

T with Equation (5). Each component rep‐

resents different physiological controls of temperature on maizeyield through reproductive growth during anthesis and GFP (SHI

T),

photosynthesisdominatedcarbonassimilation(SBGRT),andplantde‐

velopmentrate(SGSLT).AlthoughSYield

Tvariesconsiderablyamongindi‐

vidualcropmodels,asimilarestimationofSYieldTisidentifiedbetween

themodelensemblemean(MEM,−7.1±3.1%per°C)andobserva‐tions(−7.2±0.9%per°C)(Figure3).Whenwelookedintoeachcom‐ponent,MEMoverestimatedSGSL

TwhileunderestimatedSHI

Tcompared

withthecorrespondingestimationbasedonobservationalevidence.Asmodelparametersarenormallybasedontheknowledgeofcropdevelopmentandgrowthprocesseslate20thcentury,thisdiscrep‐ancyprobablysuggeststhatthedevelopmentrateofnewlyadoptedmaizecultivarmighthavebetteradapted towarmerclimatewhilelittleprogresshasbeenachievedfordealingwithwarmingeffectsduringmaize reproductivegrowth. Instead,managementpracticesintendedtoimproveyield,suchashigherapplicationofnitrogenfer‐tilizer,mightleadtohighersensitivityofheatstressduringgrainfor‐mationprocesses (Ordóñez,Savin,Cossani,&Slafer,2015;Wahid,Gelani,Ashraf,&Foolad,2007).IntermsofthesensitivityofBGR,bothMEManddatashowaweakresponse,consistentwiththefactthatmaizephotosynthesishasarelativelyhighoptimaltemperature(Dekov,Tsonev,&Yordanov,2000).Somemodels,likeLPJ‐GUESS,overestimated thewarming influenceonBGRbutunderestimatedtheinfluenceonHI,whichsuggeststhatinthesemodels,excessivetemperaturestressisimposedonprocessesrelatedtophotosynthe‐siswhilethestressduringgrainformationisoverlooked.

Thetemperaturesensitivityanalysiswasfurtherdividedintofivegroupsbasedon thequintileofgrowingseasonmean temperature,which provides an insight into how temperature sensitivity evolvesas the mean temperature increases in the future. Generally, SYield

T

estimated with observational evidence is significantly enhanced inwarmerdivisions,whichchangesfrom0.3±1.1%perdegreeCelsiusto−16.6±4.3%perdegreeCelsius fromthe lowest tohighest tem‐perature quintile (Figure4a). It is noted that the increase inSYield

T is

mainly driven by SHIT,whichvariesfrom1.5±1.4%perdegreeCelsisu

8  |     ZHU et al.

to −12.6 ±3.8%perdegreeCelsius,correspondingly.Thisresultcon‐firmstheconclusionbasedonfieldexperimentsthatwarmingduringgrain formation ismore influential (Edreira&Otegui, 2012; Siebers

etal.,2017).Despiteincreasingbackgroundtemperature,SGSLTkeeps

a relatively stable valueof approximately−2.6%perdegreeCelsiusand SBGR

T shows a small enhancement. Therefore, it can be inferred

F I G U R E 2   Spatialpatternofmulti‐yearmeanbiomassgrowthrate(BGR),growingseasonlength(GSL),harvestindex(HI),andYieldatcountylevelover2000–2015acrossthethreeMidweststates(a–d).Correlationbetweenyieldandmulti‐yearmeanBGR,GSL,andHIwitheachpointrepresentingacounty(e–g).ThecorrelationanalysissuggeststhatyieldvariationisspatiallycorrelatedwithHIandBGRbutnotGSL

38

40

42

44

−96 −93 −90 −87 −84

Longitude

Latit

ude

170

160

150

140

130

120

Mean yield over 2000−2015

38

40

42

44

−96 −93 −90 −87 −84

Longitude

Latit

ude

0.50.480.460.440.420.4

Mean harvest index over 2000−2015

38

40

42

44

−96 −93 −90 −87 −84Longitude

Latit

ude

1716.51615.515gC per m /day

Mean biomass growth rate over 2000−2015

38

40

42

44

−96 −93 −90 −87 −84Longitude

Latit

ude

135

130

125

120

days

Mean grow season length over 2000−2015

2

100 120 140 160 180

0.35

0.4

0.45

0.5

0.55

Har

vest

inde

x

Yield (bu/ac)

100 120 140 160 18015

15.5

16

16.5

17

17.5

18

Bio

mas

s gr

owth

rat

e (g

C/m

2 /day

)

Yield (bu/ac)

100 120 140 160 180115

120

125

130

135

140

Gro

win

g se

ason

leng

th (

days

)

Yield (bu/ac)

bu/ac

R = 0.74 R = 0.88R = 0.004 222

(a) (b)

(c) (d)

(e) (f) (g)

     |  9ZHU et al.

that warming‐induced yield decline is mainly driven by GSL in thethreelowertemperaturedivisions,whereastheeffectsofwarmingonHIbecomemoredominant in the twohigher temperaturedivisions(Figure4a).

Whenmodeloutputwassimilarlydividedbasedonthequintileofgrowingseasonmeantemperature,MEMofSYield

T, SBGR

T, SGSL

T, and SHI

T

wasusedtogaininsightintohowwarmingeffectswererepresentedin crop models. The individual model performance is shown inFigureS6.Comparedwiththeestimationswithobservationaldata,

MEM reproduces the patterns ofSYieldT

, SBGRT

, SGSLT

, and SHIT across the

temperature gradient (Figure 4b). Changes in MEM SHIT drive the

increasing SYieldT (Figure 4b), but SHI

T is underestimated relative to

observationaldata. In termsofSGSLT, it isoverestimated forall five

temperaturequintiles(approximately−5.4%perdegreeCelsiusrel‐ative to −2.6%perdegreeCelsiusinobservationaldataestimation).ThestableSGSL

Testimatedwithbothcropmodelsandobservational

datasuggeststhatmaizeplantdevelopmentisquasi‐linearlydrivenbytemperature(Edreira&Otegui,2012;Hatfield&Prueger,2015)

F I G U R E 3   Temperaturesensitivityofyield,harvestindex(HI),biomassgrowthrate(BGR),andgrowingseasonlength(GSL)basedonsatellitedataandNationalAgriculturalStatisticsService‐reportedyield(greyverticalline)andcropmodels,wherethehorizontalcolorlineswithintheshadedareaindicatesensitivityestimationineachmodelandverticalpurplelinesindicatemodelensembleestimation.Theerrorbarsrepresentthe95%confidenceintervalofestimatedsensitivity.Theobservationaldata‐basedtemperaturesensitivityuncertaintieswereestimatedthroughresampling.ThemeansensitivityandconfidenceintervalforMEMandobservationaldataarealsoreportedin TableS3.ThisfiguresuggeststhatyieldsensitivityismainlydrivenbyHI,butmodelensembleoverestimatedeffectsthroughGSL

Yield HI BGR GSL−12

−10

−8

−6

−4

−2

0

2

4

Tem

pera

ture

sen

sitiv

ity (

% p

er °

C)

ObsModel ensemblepAPSIMCLM-CroppDSSATpDSSAT−ptGEPICLPJ−GUESSLPJmLPEGASUSCGMS-WOFOST

F I G U R E 4   Temperaturesensitivityofyield,harvestindex(HI),biomassgrowthrate(BGR),andgrowingseasonlength(GSL)whenyield,HI,BGR,andGSLweredividedbythequintileofgrowingseasonmeantemperaturebasedonsatellitedataandNationalAgriculturalStatisticsServiceyield(a)andbasedoncropmodels(b).Theerrorbarsin(a)representthe95%confidenceintervalofestimatedsensitivity.Boxplotsin(b)indicatethemedian(horizontalline),25th–75thpercentile(graybox),and5th–95thpercentile(whiskers)ofcropmodel‐estimatedtemperaturesensitivity.ThisfiguresuggeststhatthenonlinearresponseofyieldsensitivityismainlydrivenbyHI.Althoughthemodelensembleshowsasimilarpattern,itoverestimatedeffectsthroughGSL

(a) (b)

10  |     ZHU et al.

and is relativelymore heat tolerant comparedwithwheat plants,whichshowanacceleratedsenescencewhenexposedtoheatstress(Lobelletal.,2012).ThesmallenhancementinSBGR

Testimatedwith

bothcropmodelandobservationaldatasuggeststhatphotosynthe‐sis‐dominatedBGR is likely to be slightly influenced under futurewarmer climate, whichmight result from the higher optimal tem‐peratureofC4photosynthesis.

Wealsousedanalternativepanelmodel(Equation6)byaddingquadraticfunctionofTsaandPrcptocapturethenonlinearresponseofyield,HI,BGR,andGSLtoclimatevariation.Thetemperaturere‐sponseofyield,HI,BGR,andGSLwasexpressedasthenormalizedquadraticfunctionoftemperature.Thisalternativeanalysisdemon‐stratedthatastemperaturerises,thenonlinearresponseofyieldismainlydrivenbyHIwhileyielddeclinethroughGSLislinear,whichisinlinewiththestatisticalanalysisusinggroupedtemperaturegra‐dient(Figure5).ThetemperatureresponsecurvesalsoconfirmthattheoptimaltemperatureofBGRishigherthanthatofHIandyield(Edreira&Otegui,2012).

AsthenonlinearreductionofyieldandHIbywarmingremainsunclear, apaneldatamodelwasused to investigate thedifferent

sensitivity of yield to HDD during vegetative period(

�Yield

�HDDVP

),

anthesis(

�Yield

�HDDAn

), and GFP

(�Yield

�HDDGFP

). The analysis suggests that

yieldisthemostsensitivetoHDDduringGFP(−0.46 ±0.07%perdegreedays)(Figure6a),whichisinlinewithfieldheatingexperi‐ments (Edreira, Mayer, & Otegui, 2014; Ruiz‐Vera et al., 2018;Siebersetal.,2017).TheyieldsensitivitytoHDDduringanthesis(−0.33 ±0.11%perdegreedays)isslightlyhigherthanHDDduringVP(−0.30 ±0.12%perdegreedays)(Figure6a).TheyieldsensitivitytoGDDissmallinallthreeperiodsandevenshowsapositiveresponseforGDDinVPandGFP(Figure6a).Meanwhile,theincreaseinHDDduringGFPisthelargestofthethreestages,probablyduetothehigh background temperature (Figure 6b). According to Equation(7),whenauniform1°Cand2°Cwarmingisappliedtowholegrow‐ing season temperature, yield is reduced by 5.9% and 21.7%, re‐spectively.When1°C(2°C)warmingwasseparatelyappliedtoHDDduring “VP,” “Anthesis,”and “GFP,”maizeyieldwillbe reducedby1.8%(6.9%),1.3%(5.2%),and3.3%(13.1%),respectively(Figure6c).This nonuniform response suggests that the warming‐inducedhigherHDDduringGFPexclusivelyaccountedformorethanhalfofyieldreductionandwasthemaindriverofyielddecline.

Inadditiontodirectheatstress,itwaspreviouslysuggestedthatanextremeheateventmightthreatenmaizeyieldindirectlythrough

F I G U R E 5   ResponseofYield(a),biomassgrowthrate(BGR)(b),growingseasonlength(GSL)(c),andharvestindex(HI)(d)togrowingseasonmeantemperature.TheverticaldashedlinesindicatetheoptimalmeantemperatureofYield,HI,orBGRderivedfromobservationalevidence.Theresponsefunctionisnormalizedbythemaximumvalueineachresponse.TheX‐axisrangeisdeterminedbytheminimumandmaximummeangrowingseasontemperatureacrosstheU.S.Midwestduring2000–2015.TheconfidenceintervaloftemperatureresponsecurveforeachmodelresultsisalsoreportedinFigureS8

Nor

mal

ized

BG

R r

espo

nse

pAPSIMCLM-CroppDSSATpDSSAT−ptGEPICLPJ−GUESSLPJmLPEGASUSCGMS-WOFOST

pAPSIMCLM-CroppDSSATpDSSAT−ptGEPICLPJ−GUESSLPJmLPEGASUSCGMS-WOFOST

(a) (b)

(c) (d)

     |  11ZHU et al.

WS (Lobell et al., 2013).Abetter discernmentof theeffect ofWSandheatstresswouldhelpfarmerstomakeproperdecisionstobet‐teradapttofuturewarmingchallenges.ApanelmodelanalysiswasusedheretoestimatetherelativecontributionofWS(PET/ET)andhigh temperaturestress (HDD)onyield.Themodel result suggeststhat1°Cwarmingwill increaseGDD,HDD,andWSby50±3.3 de‐gree days, 17±1.2 degree days, and 0.011±8 × 10

−4, respectively(Figure7a).However,aunit increase inGDD,HDD,andWScausesyielddeclineof−0.0054±0.001%,−0.27 ±0.04%,and−1.54 ±0.48%,respectively(Figure7a).Takentogether,theregressionmodelshowsthat1°Cwarmingwillreduceyieldby0.27± 0.15%,4.6±1.0%,and1.7 ±0.65% through GDD, HDD, andWS, respectively (Figure 7a),suggestingthatthewarmertemperaturereducesmaizeyieldmainlythroughdirecthightemperaturestress.Themeansensitivityandcon‐fidenceintervalisalsoreportedinTableS4.

When the samepanelmodelwas applied to cropmodel outputfromAgMIP, themodel results generally showed smallwarming ef‐fectsthroughGDDbutvariedsubstantially intermsofthewarmingeffectsthroughWSandHDD.Comparedwiththeobservationalev‐idence,MEMunderestimated thedirect high temperature influencethroughHDDbutoverestimated the indirect influence throughWS(Figure 7b). As suggested in a field CO2 enrichment experiment onmaize,water conservation effects of increasingCO2might result inmoreyieldbenefitunderWSconditions(Hussainetal.,2013;Jinetal.,2017)but itsyieldbenefitunderheatstressmaybe limited(Siebersetal.,2015).This impliesthat incurrentcropmodelsthedirecthightemperaturestressonyieldisunderestimated,whereastheyieldben‐efitofelevatedatmosphericCO2 isoverestimated.ThisdiscrepancycouldbiastheprojectionofmaizeyieldvariationgivenfuturehigheratmosphericCO2 andmorefrequentheatwaves.

F I G U R E 6   SensitivityofmaizeyieldbasedonNationalAgriculturalStatisticsServicereporttogrowingdegreedays(GDD)andhightemperaturedegreedays(HDD)indifferentgrowingstages:vegetativeperiod(VP),anthesis,andgrainfillingperiod(GFP)(a).BoxplotofHDDincreaseinresponseto1°Cand2°Cwarming(b).Boxplotsindicatethemedian,25–75thpercentile,and5th–95thpercentileofHDDincreaseacrossallcountiesduring2000–2015.Estimationofyieldreductionisbasedontotheregressionmodel(Equation7).Yieldreductionof“Allseason”indicatesthetemperaturewasincreaseduniformlyacrossthewholegrowingseason,whereas“VP,”“Anthesis,”and“GFP”meanstemperaturewasincreasedexclusivelyforHDDduring“VP,”“Anthesis,”and“GFP.”Theyieldreductionherecharacterizestherelativecontributionofhightemperaturestressduringaspecificmaizestage.Errorbarsin(a)and(c)representthe95%confidenceintervalofestimatedsensitivitythroughresampling,whicharealsoreportedinTablesS4andS5

VP Flowering GFP−0.6

−0.4

−0.2

0

0.2

Yie

ld s

ensi

tivity

(%

/deg

ree

days

)

GDDHDD

0

20

40

60

80

100

HD

D in

crea

se (

degr

ee d

ays)

VPAnthesisGFP

1°C warmer 2°C warmer

(a) (b) (c)

1°C warmer 2 °C warmer−25

−20

−15

−10

−5

0

Yie

ld r

educ

tion

thro

ugh

HD

D (

%)

TotalVPAnthesisGFP

F I G U R E 7   Theeffectofwarming‐induceddirectheat(HDD)andindirectwaterstress(WS)onmaizeyieldbasedonNationalAgriculturalStatisticsServiceyieldreport,MODIS‐derivedcropstagesinformation,andMODISPET/ETproduct(MOD16)(a).Thenumbersmarkedonthearrowsindicatetheeffectsof1°Cwarmingonyieldthroughgrowingdegreedays(GDD),hightemperaturedegreedays(HDD),andwaterstress(WS),correspondingtothecoefficientsinEquation(12).ComparisonofwarmingeffectsonmaizeyieldthroughGDD,HDD,andWS(potentialevapotranspiration[PET]/evapotranspiration[ET])estimatedfromobservationalevidenceandcropmodels(b).Errorbarsforobservationaldatarepresentthe95%confidenceintervalthroughsampling(detailsinTableS6)anderrorbarsinmodelensemblerepresentthestanddeviationofmulti‐modelestimatedyieldresponses(b)

pAPSIMCLM-CroppDSSATpDSSAT−ptGEPICLPJ−GUESSLPJmLPEGASUSCGMS-WOFOST

Model ensemble

(a) (b)

War

min

g ef

fect

s on

yie

ld (

% p

er °

C)

PET/ET

50 ± 3.3

17 ± 1.2

0.011 ± 0.0008

–0.000054 ± 0.00001

–0.0027 ± 0.0004

–1.54 ± 0.48

GDD HDD

12  |     ZHU et al.

AlthoughtheMEMsuggestsa lower influenceof temperaturethroughHDD,thereareindividualmodelswithcloseestimationtoobservationaldata.Forexample, theAPSIMcropmodel suggestsahigher influenceoftemperaturethroughHDDthanthroughWS(Figure7b).WealsoappliedtheAPSIMmodeldefaultWSmetric,theratioofwatersupplytowaterdemand,astheWStermtocon‐structanalternativepanelmodeltotestwhethertheresultsarero‐busttotheselectionofWSmetric.ThisalternativemetricproducedasimilarestimationofwarmingeffectsonyieldthroughGDD,HDD,andWSastheoneusingPET/ETastheWSmetric(FigureS4).

AmodelexperimentwasdesignedtobetterunderstandhowWSandheatstressinfluencemaizeyieldthroughdifferentphysiologicalprocesses.Inthisexperiment,sim1isthecontrolrunwithbothhightemperaturestressandWS,whereassim2blockedthehightempera‐turestress.Theresultsshowthatastemperatureincreases,thereisnosignificantchangeinSBGR

T and SGSL

Tbetweensim1andsim2butSHI

Tissig‐

nificantlyenhancedinsim2(Figure8).AsGSLismainlydrivenbyther‐maltimeaccumulation,SGSL

Tshowsasimilarresponsewithincreasing

backgroundtemperatureinbothsim1andsim2.Thus,theothertwocomponentsSBGR

T and SHI

Trepresentthemaineffectsofhightempera‐

turestressonyield.Thecomparisonbetweensim1andsim2suggeststhat,astemperaturerises,hightemperaturestressreducesmaizeyieldprimarilythroughprocessrelatedtograinformation,whereasthehightemperature‐inducedWS influencesyieldmainly throughprocessesrelatedtoBGR,suchasphotosynthesisorrespiration(Figure8).

4  | DISCUSSION

By integrating satellite observations, cropmodel simulations, sur‐veys, and experimental data,we examined the response ofmaizeyieldanditsconstituentprocessestohightemperaturestressinananalyticalway.The results suggest that thenonlinear responseof

yield (SYieldT

) can be decomposed into small effects on SBGR

T, linear

(SGSLT

), andnon‐linear

(SHIT

) processes, and thatheat stressduring

GFPposesastrikingthreatformaizeyielddecline.Photosynthesis‐dominatedBGRisonlymarginallyinfluencedbytemperaturestress,whichis likelytoresultfromthehigheroptimaltemperatureofC4 photosynthesis. With the advancement in computing power and

finer spatial and spectral information brought with new satellitedata,themethodologyherecanbereadilyextrapolatedtootherre‐gions and further improve our understanding of maize and othercropyieldperformanceunderextremeconditions.

Our analysis also pinpoints both strengths andweaknesses ofcropmodelsincharacteringhightemperaturestressonmaizeyieldandprovidesanimportantfeedbackforthecropmodelingcommu‐nity.MostmodelsunderestimatedthewarmingeffectsthroughHIwhileoverstatedthetemperaturesensitivityofGSL.Meanwhile,theindirectWSeffectwasoverestimated inmostcropmodels,whichmight bring substantial uncertainties when projectingmaize yieldunderfuturehotterconditions.Oneexplanationforthediscrepancybetween estimations based on model and observational datasetsis possibly the issue of different scales, since crop models oper‐ated at 0.5◦

× 0.5◦gridsandobservationaldatasetswereanalyzedatthecountylevel.However, it ismorelikelyduetothelimitationofmodels inaccuratelyrepresentingheatstress influence,suchasslowupdatesofkeyparametersrelatedtoheatanddroughtresis‐tanceandlackofexplicitlyaccountingforheatstresseffectduringthedevelopmentstagesofdifferentmaizecultivars.Rezaei,Siebert,Hüging,andEwert(2018)alsofoundthatignoringcultivarchangesinanalysesofhistoricchangesinphenologyleadstoanoverestimateofthetemperaturesensitivityofthephenologyofwinterwheatinGermany.A similarmodel parametrization biasmay exist in othercrops,e.g.maizeintheUnitedStates.

Inaddition,mostevaluatedmodels,exceptCLM‐Crop, lackacanopyenergybalanceschemetosimulate leaftemperatureandthereforeuseair temperature insteadof leaftemperaturetopa‐rameterize effects of heat stress.However, air temperature candeviate significantly from leaf temperature, especiallyunderdryconditionsorelevatedCO2wherecanopiescanbeseveraldegreeshotter than theairdue to reduced transpiration.Thus, improve‐mentincanopyenergybalanceamongallmodelsisnecessaryforbetterrepresentingtheheatstresseffectsoncropyield(Webberetal.,2017).

The selected metric here to quantify heat stress andWS isalso importantforevaluatingtheirrelativecontributionstoyielddecline. Threshold‐based thermal time accumulation has beenwidelyusedtocharacterizeheatstress(Deryng,Sacks,Barford,&Ramankutty,2011;Lobelletal.,2012;Schlenker&Roberts,2009).

F I G U R E 8   Temperaturesensitivityofyield,harvestindex(HI),growingseasonlength(GSL),anddailybiomassgrowthrate(BGR)dividedbyquintileofgrowingseasonmeantemperatureintwoAPSIMsimulationresults.sim1(circle)isthesimulationwithbothwaterandhightemperaturestressandsim2(triangle)isthesimulationwithonlywaterstress

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IntermsofWS,severalmetricshavebeenproposed,suchasVPD,PET/ET, soil moisture content, and the ratio of water supply towater demand (Jin et al., 2016; Lobell et al., 2014).HigherVPDmeansanincreaseinatmosphericwaterdemandandcandecreasephotosynthetic activity through reducing stomatal conductance.Soilwatercontentregulatestransportofwaterinthesoil–plant–atmospherecontinuumanddeterminestheamountofextractablewater by crop plants. PET/ET and the ratio of water supply towaterdemandaccountsforbothatmosphericwaterdemandandsoilwateravailability.These twometricsalsogiveasimilaresti‐mateofWSeffectsonmaizeyield(FigureS4).DuetothedifferentrolesofVPDandsoilwatercontentindeterminingtheplantphys‐iologicalprocesses, itmightbeuseful todisentangle thetwoef‐fects.However,therearelimitedcontrolledexperimentsdesignedtoaddressthedifferentresponsesofcropplantstoatmosphericwaterdemand(VPD)andsoilwaterdryness,partlybecauseVPDisoftenhardtobecontrolled inthefieldconditions (Grayetal.,2016). In this context, more field experiments are necessary tomechanisticallyunderstandthe relativecontributionofdifferentsourcesofWSoncropyield.

Overall, our analysis through model‐data integration suggeststhat warming‐induced decline in maize yield is mainly driven bydirectheatstress imposedonreproductiveprocesses,whereasin‐directWSonlycontributesasmallfraction.Therefore,futureadap‐tationstrategiesshouldbetargetedattheheatstressduringgrainformation.Asmodelparameterizationusedhereoftenrepresentsastaticmanagementsystemfromaroundtheyear2000(Elliottetal.,2015), the discrepancy in temperature sensitivity between cropmodelsimulationsandobservationaldatasuggeststhatchangesinmanagement systems need to be better accounted for to achieveprogressinheatstressestimates(Glotter&Elliott,2016).

ACKNOWLEDG EMENTS

We thank three anonymous reviewers whose comments signifi‐cantlyimprovedthisstudy.ThisresearchwassupportedbyanNSFproject (IIS‐1027955) and a NASA LCLUC project (NNX09AI26G)toQ.Z.WeacknowledgetheRosenHighPerformanceComputingCenteratPurdueforcomputingsupport.

ORCID

Peng Zhu https://orcid.org/0000‐0001‐7835‐3971

Christoph Müller https://orcid.org/0000‐0002‐9491‐3550

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How to cite this article:ZhuP,ZhuangQ,ArchontoulisSV,BernacchiC,MüllerC.Dissectingthenonlinearresponseofmaizeyieldtohightemperaturestresswithmodel‐dataintegration. Glob Change Biol. 2019;00:1–15. https://doi.org/10.1111/gcb.14632