FieldCropsResearch143(2013)56–64
ContentslistsavailableatSciVerseScienceDirect
Field
Crops
Research
j o ur n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / f c r
The
use
of
satellite
data
for
crop
yield
gap
analysis
David
B.
Lobell
DepartmentofEnvironmentalEarthSystemScienceandCenteronFoodSecurityandtheEnvironment,StanfordUniversity,Stanford,CA94305,UnitedStates
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t
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f
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Articlehistory:
Received19February2012 Receivedinrevisedform18July2012 Accepted8August2012 Keywords: Remotesensing GIS Agronomy
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Fieldexperimentsandsimulationmodelsareusefultoolsforunderstandingcropyieldgaps,butscaling uptheseapproachestounderstandentireregionsovertimehasremainedaconsiderablechallenge. Satellitedatahaverepeatedlybeenshowntoprovideinformationthat,bythemselvesorincombination withotherdataandmodels,canaccuratelymeasurecropyieldsinfarmers’fields.Theresultingyield mapsprovideauniqueopportunitytoovercomebothspatialandtemporalscalingchallengesandthus improveunderstandingofcropyieldgaps.Thisreviewdiscussestheuseofremotesensingtomeasure themagnitudeandcausesofyieldgaps.Examplesfrompreviousworkdemonstratetheutilityofremote sensing,butmanyareasofpossibleapplicationremainunexplored.Twosimpleyetusefulapproaches arepresentedthatmeasurethepersistenceofyielddifferencesbetweenfields,whichincombination withmapsofaverageyieldscanbeusedtodirectfurtherstudyofspecificfactors.Whereastheuseof remotesensingmayhavehistoricallybeenrestrictedbythecostandavailabilityoffineresolutiondata, thisimpedimentisrapidlyreceding.
©2012ElsevierB.V.
1. Introduction
Twogoalsunderliemostdiscussionsofcropyieldgaps(Van
Ittersumetal.,2013).Thefirstistomeasurethesizeoftheyieldgap,
definedasthedifferencebetweenyieldpotential(Yp)andaverage
yields,inordertoidentifythepotentialscopeforraisingaverage
yieldsviamanagementchanges.Thesecondistoidentifythekey
causesoftheyieldgap,inordertoprioritizeeffortsinextension,
research,andpolicytoraiselandandlaborproductivity.
Afundamentalchallengeinpursuitofeitherofthesegoalsis
theconsiderablespatial and temporal heterogeneityof
agricul-turallandscapes.Inthemeasurementofyieldgaps,forexample,
actualyieldsareoftenreportedforadministrativeunitsthatspan
hundredsorthousandsoffields.Yieldpotential,meanwhile,ismost
readilyestimatedforindividualfields,usingeitheragronomic
tri-alsorwell-testedcropsimulationmodels(Lobelletal.,2009).How
shouldthemeasurementsatthesetwodifferentspatialscalesbe
comparedwhencomputingayieldgap?Somestudiesignorethe
scalemismatch,implicitlyassumingthatpoint-levelestimatesof
YpareagoodproxyforaverageYpacrossthespatialdomainof
thereportedaverageyield.OtherstudiesattempttoestimateYp
atmultiplepointswithinthedomainandthentakeanaverage,a
sensibleapproachprovidedthatdataofsufficientqualityexistto
estimateYpatmultiplepoints.
Similarly, studies to understand causes of the yield gap
mayreasonably startby evaluatingyield responsestodifferent
E-mailaddress:[email protected]
managementchangesinanexperimentalstation,oronfarmers’
fields.However,thefieldsanalyzedmaynotberepresentativeof
theentireregion,ortheyear(s)inwhichthestudywasdonemay
notberepresentativeofthefullrangeofconditionsthatfarmers
face.
Agronomistshavelongappreciatedthechallengeof
generaliz-ingresultsfromasmallhandfulofsitesandyearstothebroader
scales relevant to regional measures of performance. Over the
pasttwo decades,remotesensing hasemerged asa usefultool
fordealingwithheterogeneity,tocomplement moretraditional
approachessuchasfieldtrialsorsimulation models.In
particu-lar,remotesensingfromairplane-orsatellite-mountedsensorscan
potentiallyprovideobservationsforeverysinglefieldinaregion
foreverysinglegrowingseason.Althoughremotesensing-based
estimatesofquantitiessuchascropyieldareoftenlessaccurate
thanfield-basedmeasures,theunprecedentedspatialand
tempo-ralcoverageofremotesensingcanoftenoutweighthenegatives
formanyapplications.
Thegoalofthispaperis tospecificallyaddressthepotential
valueofsatellite-basedremotesensingforeffortstomeasureand
explaincropyieldgaps.Thepremiseofthepaperisthataseffortsto
understandyieldgapsintensify,newapproachesthatcan
comple-mentthetraditionaltoolboxofagronomistshavegreatpotential
value,andremotesensingmaybeonesuchtool.
The promise of satellite data is enhanced by at least two
recentdevelopments.Oneisthedecisionin2008bytheUnited
States Geological Survey to make the entire archive of
Land-satdataavailableatnocharge(http://landsat.usgs.gov/products
data atnocharge.php).Thischange,coupledwithimprovements
0378-4290 ©2012ElsevierB.V. http://dx.doi.org/10.1016/j.fcr.2012.08.008
Open access under CC BY-NC-ND license.
Fig.1. Examplesoftheeffectofimageresolutionontheabilityofremotesensingtomonitorindividualfields.Thetoprowdisplaysa2.5km×2.5kmsectionofaRapidEye 5m×5mresolutionimageof(left)Xinjiang,China,(middle)KingsCounty,UnitedStates,and(right)Bahia,Brazil.Lowerrowsshowimagesresampledtorepresentthe coarserresolutionsofsomeothercommonsensors:ASTER(15m,secondrow),Landsat(30m,thirdrow),andMODIS(250m,bottomrow).
inpreprocessingalgorithmstogeographicallyregistertheimages,
havevastlyreducedtheexpenseandtimerequiredtoobtainimages
atrelativelyfinespatialresolution(30m×30m)fortheperiodof
1982topresent.Thisresolutionissufficienttodelineateindividual
fieldsthatareroughly1hainsizeorgreater,whichincludesmany
regionsoftheworld(seeFig.1).Second,newcommercialsystems
aredeliveringevenhigherspatialresolution(5m×5morfiner)at
coststhatareapproaching1USD$perkm2(or$0.01perha).Inthe
nextdecade,itshouldbeincreasinglyfeasibletoobtainmultiple
yearsofdataforregionswherefieldsizeshavebeentoosmallto
distinguishwithtraditionalsensorslikeLandsat.
Thenextsectionbrieflysummarizesthecapabilitiesand
limi-tationsofremotesensingformeasuringcropyields.Thefollowing
twosectionsdiscussexamplesandpotentialusesofremotesensing
forthetwomaingoalsofcropyieldanalysis:measurementand
explanation.Finally,someconclusionsandrecommendationsfor
futureworkarepresented.
2. Remotesensingofcropyield
2.1. Approaches
Numerous approaches exist for estimating crop yields with
remotesensing.Severalreviewsonthistopicareavailable(Moulin
et al., 1998; Gallego et al., 2010), and so only a brief
58 D.B.Lobell/FieldCropsResearch143(2013)56–64
vegetationindices(VIs)computedfromremotesensing
measure-mentsoflightatredandnear-infrared(NIR)wavelengths.Crop
plants,likeallvegetation,areveryreflectiveintheNIRand
absorp-tiveatredwavelengths,andthereforesomecombinationofthe
twoareagoodmeasureofvegetationvigor(Tucker,1979;Sellers,
1987).Measuresatthesetwowavelengthsremainthemainstay
ofnearlyallapproachestocropyieldestimation,althoughother
partsofthespectrumarecommonlyutilizedinmoresophisticated
approaches(e.g.,Gitelsonetal.,2003).
Thesimplestapproach toestimatingcropyieldsisto
estab-lishempiricalrelationshipsbetweenground-basedyieldmeasures
andVIsmeasuredonasingledateorintegratedoverthe
grow-ingseason.Earlyapplicationswithwheatandmaizeindicatedthat
variationsinVIcanexplainover80%oftheobservedvariationin
cropyieldswithinindividualfields(Tuckeretal.,1980;Wiegand
andRichardson,1990;Shanahanetal.,2001).However,aswithany
purelyempiricalapproach,extrapolationofequationstonew
loca-tionsoryearscanbeproblematic,andforthisreasonmanyefforts
havebeenmadetowardmoregeneraltechniques.
Oneclassofmodelsreliesonthelight-useefficiencyapproach
pioneeredby Monteith (1977), which states that total biomass
productionisdirectlyproportionaltototal absorptionof
photo-syntheticallyactiveradiation(PAR)overthecourseofthegrowing
season.TheratioofbiomasstoPAR,knownasradiationuse
effi-ciency(RUE),isrelativelyconstantbecauseplantsadjusttotalleaf
area,andthuscaptureofsunlight,inresponsetoothergrowth
con-straintssuchasnutrientortemperaturestress(Bloometal.,1985).
Numerousstudieshaveconfirmedtheutilityofthisconceptfor
predictingbiomassindifferentcrops,althoughvariationsinRUEdo
occurinsomesettings,particularlywhenplantsexperienceacute
moisturestress(Steinmetzetal.,1990;SinclairandMuchow,1999).
ModelsthatrelyontheRUEconcepttopredictyieldhaveat
leastfourrequiredinputs,asindicatedinEq.(1):
Yield=
n t=1 PARt·fPARt ·RUE·HI (1)wherethesummationindicatesasumoverthegrowingseason,
oftenusingadailytimestep,fPARtisthefractionofPARabsorbed
bythecropcanopyattimet,andHIistheharvestindex,orthe
ratioofyieldtototalbiomass.ThefirstinputisPARthroughoutthe
growingseason,whichistypicallyobtainedfromlocal
meteoro-logicalstationdataorsatellite-basedestimates.Second,estimates
offPARthroughoutthegrowingseasonarerequired.Forremote
sensing-basedstudies,estimatesoffPARaremostoftenderived
fromestablishedrelationshipswithVIs.However,becauseremote
sensingdataarenotavailableonadailybasis,someinterpolation
isneededtoestimatedailyfPAR.
Threegeneralapproachesareusedtoaddresstheinterpolation
issue.Inthecaseofregularlyspacedsatellite-basedmeasures,such
astheeight-daycompositesoffPARfromtheModerate
Resolu-tionImagingSpectroradiometer(MODIS)(Mynenietal.,2002),the
timestepinEq.(1)cansimplybecoarsenedtomatchthesatellite
data.Asecondapproachistointerpolatebasedonsomestatistical
function,suchaslocallinearinterpolationorfittingdoublelogistic
curves(Nightingaleetal.,2009).Thesetwoapproachescanalsobe
combined,forinstancewhentryingtoaccountformissingor
low-qualitydatapointswithinaneight-dayproduct(Zhaoetal.,2005;
Nightingaleetal.,2009).
Third,interpolationcanbeachievedbyusingacropmodelto
simulatethedailyevolutionoffPARbetweenavailable
observa-tions.Thiscanbeachieved,forexample,bycalibratingparameters
ofasimplecropgrowthmodeluntilthesimulatedfPARvaluesmost
closelymatchtheremotesensingestimates(Lobelletal.,2003).
Thisapproachhasthebenefitofallowingflexibilityinthetiming
ofremotesensingdata,andbeingabletoprovideestimateseven
whenonlytwoorthreeimagesareavailableduringthegrowing
season,asisoftenthecasewhenusinghigherresolutionimagery.
Anotherfeatureistheabilityofthecropmodeltoaccountforeffects
oftemperaturesoncropdevelopmentrates.
ThefinaltwofactorsinEq.(1)areestimatesofRUEandHI.Both
ofthesearetypicallyassumedconstant,andderivedfromfielddata
orcalibrationtoreportedstatistics.Incomparisontosimple
empir-icalrelationships,RUEmodelscancapturevariationsinyielddue
tochangesinPAR,andinterpolationoffPARallowsmore
flexibil-ityinthetimingofimagesrelativetocropgrowthstage(whereas
empiricalmethodsaretypicallyspecifictoanarrowrangeof
tim-ing).
BeyondsimpleRUEmodels,manyapproachesattempttomore
fullyintegratecropsimulationmodelswithremotesensingdata.
Forexample,Doraiswamyetal.(2004,2005)adjustedparameters
inasimpleclimate-basedcropmodeltomatchMODISestimates
ofleafareaindex(LAI)overmaizeandsoybeanfieldsintheUnited
States.Severalstudieshaveuseddifferentsensors,spatialscales,
andcropmodels(Weissetal.,2001;Prévotetal.,2003;Launayand
Guerif,2005;Denteetal.,2008),butallwiththesameprinciple
ofadjustingcropmodel parametersonapixel-by-pixelbasisto
matchremotesensingestimatesofsomecropattribute,oftenLAI.
Thesimulatedyieldbythecropmodelthenprovidesanestimateof
yieldforeachpixel.(Notethecontrastwiththeuseofcropmodels
onlytointerpolatefPAR(e.g.,Lobelletal.,2003),withyieldthen
calculatedfromEq.(1).)
The useof crop simulation modelsallows the possibility of
accountingfor factorssuchas acutemoisturestress,whichcan
resultinvariationsinRUEandHIthatconfoundestimatesusingEq.
(1).However,thisaddedcomplexitycomesatacostofrequiring
moremodelinputs,suchassoilproperties,andgreater
computa-tiontime.
2.2. Accuraciesandlimitations
Overall,thereisclearevidencethatcropyieldestimationis
pos-siblewithremotesensing,withgoodaccuraciesinsomecases.Most
evaluationsofremotesensingareatscalesbroaderthan
individ-ualfields,forexamplebycomparingreportedyieldsforcountiesor
cropreportingdistrictswiththeaverageofremotelysensedyields
overthisdomain(Doraiswamyetal.,2005;Becker-Reshefetal.,
2010;Lobelletal.,2010).Suchcomparisonswilltypicallypresent
overlyoptimisticviewsofthefield-scaleaccuraciesthataremost
relevanttoyieldgapassessments.Asanexampleofthe
deterio-rationofaccuracyatfinerscales,Reevesetal.(2005)used1km
MODISdatatoestimatewheatyieldsinNorthDakotaand
Mon-tana,andfoundaccuraciestowithin5%forstatelevelestimates
butmuchloweraccuraciesatthecountylevel.
Nonetheless,field levelaccuraciesaresometimesquitehigh,
withrootmeansquareerrorsoflessthan10%forpredicting
farmer-reportedyieldsfor individual commercialfields(Clevers,1997;
Lobelletal.,2005,2007b).Inmostsituations,non-negligibleerrors
existinthefarmer-reporteddata,suggestingthatthetrue
accu-raciesofremotesensingdatacanbeevenhigher.However,the
conditionsnecessaryforaccurateyieldestimationarenotalways
met,andmanystepsintheprocessofyieldestimationintroduce
errors.Evenatcoarsespatialscales,accuraciescanbetoolowto
provideusefulresults.Itistelling,forexample,thatboththeUnited
States’andEuropeanagenciesinchargeofforecastingdomesticand
internationalcropproductioncurrentlyuseremotesensingonlyin
aqualitativefashion(Allenetal.,2002;Baruthetal.,2008).
Sourcesoferrorinyieldestimationincludepotential
misclas-sificationof which cropsaregrowingin whichpixels,errors in
estimatingfPAR withreflectancedata,difficulties in
interpolat-ingvaluesbetweenavailableobservations,imperfectrelationships
inpredictingvariationsinHI.Thefirstoftheseissues,
misclassi-ficationof croptype, is particularlyproblematic inregions that
growmultiplecropswithverysimilarphenologies,orinregions
withintercroppedfields.Intheformercase,cropscansometimes
bedistinguishedbasedonspectraldifferences,butaccuraciesare
generallylowrelativetocasesthatseparatecropsbasedonclearly
distinctphenologies(Thenkabail,2001).Inthelattercase,suchas
mixed-croppingsystemsfoundthroughoutAfrica,bothcroptype
andyield estimationare extremelydifficultand totheauthor’s
knowledgetherearenogoodexamplesofreliableyieldestimates
inthesesituations.
Othersourcesoferrorreflectthedifficultyofpredictingaspects
ofcropgrowthwhicharenotrelatedtoabsorptionofPAR,such
asRUEandHI.Recentstudieshaveindicatedthatremotesensing
basedindicators ofchlorophyllcontent arerelated toRUE,and
thus incorporation of wavelengths associated with chlorophyll
canimproveestimatesofinstantaneouscarbonuptake(Pengand
Gitelson, 2011).However, these approaches have not yet been
demonstratedtoimproveyieldestimates.Harvestindexvariations
areparticularlyhardtopredictfromremotesensing,andthemain
approachremainseitherassumingaconstantHIorusingcrop
mod-elsthatpredictchangesinHI.Althoughirrigatedcerealcropstend
tohavestableHI,rainfedandnon-cerealcropscanexhibitverylow
valuesofHIwhenexposedtostress(Hay,1995).Forexample,past
effortsbytheauthortoestimatesaffloweryieldswerehampered
bylargevariationsinHI.
Furthersourcesoferrorstemfrominherenttradeoffsbetween
acquiringdatawithsufficientlyhighspatialresolutiontodelineate
individualfields,anddatawithsufficientlyhightemporal
resolu-tiontoobtainmultiplecloud-freeobservationsduringthegrowing
season.Historically,Landsat(orsimilarsensorssuchasSPOT)has
beenthemainsourceofdatawithsufficientspatialresolutionin
mostagriculturalareas,butwitha16-daygapbetweensuccessive
images,andfrequentcloudcoverinmostcroppingregions(with
theexceptionofdry,irrigatedareas),itcanbedifficulttoobtain
morethanoneortwoclearimageswithinagrowingseason.The
mainsourceoffinetemporalresolutiondatahasbeenMODIS,but
with250mspatialresolutionitisextremelydifficulttoidentify
individualfieldsinmostregions(Fig.1).Thetradeoffbetween
spa-tialandtemporalresolutionismostextremeinregionswithsmall
fieldsizes,forwhichevenLandsatcannotresolveindividualfields.
Movingforward,thelowercostandincreasednumberoffine
spatialresolutionsensorsshouldhelptopartlymitigatethe
inher-ent tradeoff betweenspatial and temporal resolution. Another
promisingdevelopmenthasbeenrecentprogressindatafusion
methodsthatcombineobservationsfromdifferentsensors.One
approach,termedthespatialand temporal adaptivereflectance
fusionmodel(STARFM)usesapairoffineandcoarseresolution
images(e.g.,LandsatandMODIS)acquiredonthesameday,along
withcoarseimagesacquiredonotherdates,togeneratehigh
tem-poralresolutiondataatthefinerspatialscale(Gaoetal.,2006).
Animportantstepinthisapproachistoidentify,foreachpixel,
spectrallysimilarpixelswithina neighborhood,which arethen
assumed to change similarly over time. An enhanced STARFM
(ESTARFM)wasalsointroducedrecently(Zhuetal.,2010),which
reliesona pairof fineresolutionimagestodefinesimilarity.A
thirdapproach tofusingfine andcoarseresolution imageswas
introducedbyZurita-Millaetal.(2009),whichreliesonmodeling
eachpixel’sreflectanceasthelinearsumofreflectancefrom
indi-viduallandcovertypeswithinthepixel.Thecriticalassumptions
inthismethodarethatareliablemapoflandcovertypesatfine
resolutioncanbeobtainedandthatallpixelsofthesamelandcover
typebehaveidenticallywithinawindowaroundthecentralpixel.
Theseapproacheshavebeentestedinafewcaseswith
promis-ingresults(Gaoetal.,2006;Hilkeretal.,2009),buthaveyettobe
rigorouslyevaluatedinagriculturalsettings.Allthreeapproaches
assume that nearby pixelsthat appear similarat a singledate
behavesimilarlythereafter.Thisassumptionisproblematicin
agri-culturalsettings,whereforexamplefieldsaresownatdifferent
timesandthereforemayappearsimilaratonedatebutvery
dif-ferent in another. Nonetheless, data fusion methods are likely
toimproveoverthenextfewyears, andofferopportunitiesfor
improvingyieldestimationatfieldscales.
3. Measurementofyieldgaps
Yield gapestimation requires two quantities: Yp and actual
yields.Given thatremote sensing canonlyassess actualyields,
additionalinformationor assumptionsaboutYparerequiredto
estimateyieldgaps.Onesimpleapproachwouldbetopair
indepen-dentestimatesofYp(forexamplebasedonmethodsusedinvarious
papersinthisspecialissue)withremotesensing-basedestimates
ofactualyieldsforthecorrespondingsitesandlocations.No
exam-plesofthisexist,totheauthor’sknowledge,presumablybecause
averageyieldsarealreadyknownincaseswhereYpestimatesare
available.
Analternativeistousethemaximumyieldwithintheremote
sensingestimatesasaproxyforYp,whichassumesthatsome
farm-ersinagivenyearachieveYp.Thisassumptionhasbeentestedin
somecases(Lobelletal.,2009),butingeneralismadewithout
inde-pendentdatatotestitsvalidity(ifsuchdataexisted,theassumption
wouldnotbenecessary).Earlyexamplesofthisapproachinclude
a studyof various crops in Pakistan using 1.1km AVHRR data
(BastiaanssenandAli,2003),andastudyofwheatinMexicousing
Landsat(Lobelletal.,2002).Inbothcases,theauthorsdidnotuse
thesinglemaximumvalueofyieldsintheregion,butinsteaddefine
thegapusingahigh(e.g.,95th)percentileoftheyielddistribution.
Inbothcases,itwasalsoassumedthatasinglevalueofYpwas
applicabletotheentirestudyregion.Thisassumptionislikelya
goodapproximationforrelativelysmallstudyregions,but
other-wisecouldintroducesignificanterrorsintotheanalysis.Thereisno
inherentreason,however,whyasinglevalueofYpmustbeused
fortheentirestudyregion.Forexample,onecouldcomputeYp
foreachpixelbasedonthemaximumor95thpercentileofyield
observedinasmallsurroundingregion(e.g.,a5km2areacentered
onthepixel).
Such an approach, though, would still rely onthe
assump-tionthatthehighestyieldingfieldsareapproachingYp.Ahybrid
approachcoulduseindependentestimatesofYpforspecificpoints
withinthestudyregion,obtainedforinstanceusingcropsimulation
models.TheremotesensingestimatesofYp,obtainedbythe
mov-ingwindowapproachdescribedabove,couldthenbecomparedto
thesepointestimatesandaregressionequationdefinedtoadjust
remotesensingestimatestomatchthepointestimates.Thus,one
couldleveragetheabilityofremotesensingtodetectspatial
gradi-entsinYpwithoutrelyingexclusivelyontheassumptionthatsome
farmersachieveyieldsclosetoYp.
Ingeneral,verylittleefforthasbeendevotedtousingremote
sensingtomeasurethemagnitudeofyieldgaps.Therearesome
reasonstobelievesatellitedatacancomplementpoint-level
esti-matesofYpfromothermethods,oreveninsomecasescircumvent
theneedforothermethodsaltogether.However,muchmorework
is neededtoestablishthetrueutilityofremote sensingin this
application.
4. Analysisofyieldgapcauses
Muchmorecommonthanworkfocusedexplicitlyonthesize
ofyieldgapshasbeensatellitebasedstudiesofspatialvariationin
observedyields.Asubstantialamountofworkhasbeendevoted
60 D.B.Lobell/FieldCropsResearch143(2013)56–64
inordertoinformprecisionagricultureapplications(Yangetal.,
2001;Zarco-Tejadaetal.,2005).Ofmorerelevancehere,however,
arestudiesthatspanalargenumberoffieldswithinaregion.
Worktounderstandcausesofspatialyield variationshasan
obviousbutpotentiallylimitedrelevancetothequestionofwhat
causesyieldgaps.Inparticular,ifallfieldsinaregionarewellbelow
Yp,thenexplainingvariationsbetweenthefieldswillnot
necessar-ilyhelptoexplainhowtoraiseaverageyieldsclosetoYp.Insuch
cases,however,itisverylikelythatatleastthemainproximate
causesoftheyieldgaparealreadyknown,suchasthecaseof
insuf-ficientfertilizerinputsandsoilfertilitythroughoutmuchofAfrica.
Intheseinstancesitisalsolikelythatvariationsbetweenfieldswill
bedominatedbythesameconstraintthatissobindingtooverall
productivity(Tittonelletal.,2008).
Ingeneral,twotypesofapproaches havecharacterized
stud-iesoflandscapeyieldheterogeneity.First,mapsofyieldsderived
fromremote sensing can becompared toancillary datasetson
factorsthoughttocontrolyields,suchassoilpropertiesor
man-agementpractices.Statisticalanalysescanthenbeusedtoevaluate
therelative importanceofeach factorin drivingobservedyield
variations.Animportantstepinsuchstudiesisaccountingfor
spa-tialcorrelationofmodelerrors:giventhehighspatialdensityof
remotesensingmeasurements,itisrelativelyeasyto
underesti-matestandarderrorsifspatialcorrelationisignored.
AseriesofstudiesconductedintheYaquiValleybytheauthor
andcolleaguesprovideseveralexamplesofthis approach,with
comparisonsofsatellite-derivedyielddatatomanagementsurveys
(Lobelletal.,2005),sowingdateandweedmaps(Ortiz-Monasterio andLobell,2007),anddatasetsonirrigationdeliveries(Lobelland Ortiz-Monasterio,2008).Studiesinotherregionsincludeeffectsof
positionalongirrigationcanalsforriceinMali(ZwartandLeclert,
2010), effectsofdistancetomainirrigationcanalsandroadson
wheatyieldsinPunjab,India(Lobelletal.,2010),andeffectsofsoil
sodicityonwheatyieldsinMexicali,Mexico(Seifertetal.,2011).
Inalloftheabovecases,statisticallysignificantyieldeffectsof
thevariablesinquestionweredetected.Moreover,becauseofthe
largesamplesizesaffordedbyremotesensing,itispossibleto
iden-tifyimportantinteractions,nonlinearities,orthresholdsthatare
notuncoveredwithtraditionallinearregressiontechniquesapplied
tosmallerdatasets.Forexample,Seifertetal.(2011)detecteda
yielddeclinebeginningatvaluesofsoilexchangeablesodium
per-centage(ESP)valuesof6,whereasthecommondefinitionofsodic
soilsisforESPabove15.
Asecondapproachtostudyingyieldgapswithremotesensing
reliesexclusivelyonspatialandtemporalpatternsintheyieldmaps
themselves. Although these approaches cannot provide insight
intospecificyieldcontrols,andarethusnotsufficientby
them-selves,theyprovidearelativelyrapidassessmentofwhattypesof
factorsdeservefurtherscrutiny.Thatis,differentspatialand
tem-poralpatternsinthedatawillsuggestdifferenttypesofpotential
yieldcontrols.Forexample,iffarmercharacteristicsliketechnical
knowledgeoraccesstocreditcanexplainmuchoftheyield
vari-ation,thenonewouldexpecttoseeyieldsconsistentlyhighyear
afteryearinfieldswherefarmershavethefavorabletraits.
Simi-larly,ifsoilqualityanddegradationpresentmajorobstaclestoyield
improvement,andthesesoilpropertiesarenotthemselvesdriven
bymanagement (Tittonelletal.,2008),onemightexpecttosee
yieldpatternsthatreflectrelativelysmoothvariationofsoil
prop-erties,asopposedtotheabrupttransitionsinmanagementacross
fieldboundaries(LobellandOrtiz-Monasterio,2006).Incontrast,
iftheyieldresponsestomanagementorsoilpropertiesdepend
stronglyonweatherconditions,onewouldexpectamorevariable
spatialpatternofyieldsfromyeartoyear.
One simple way togain insight into yield gap causes is to
examinethespatialdistributionofaverageyields,withthe
aver-agecalculatedovervaryinglengthsoftime.Ingeneral,averages
calculatedoverlongerperiodsoftimewillshowlessspatial
vari-ation thanaverages over shorter periods,since factorsthat are
idiosyncraticwilltendtocanceloutacrossyears.Anexamplein
Fig.2forwheatyieldsintheYaquiValley,Mexicoillustratesthis
effect.Forasingleyear,arelativelywide(andasymmetric)
distri-butionofyieldsisobservedwithmanylocations(i.e.,30m×30m
pixels)achievingbothcomparativelyhigh(e.g.,20%aboveaverage)
andlow(e.g.,20%belowaverage)yields.Theaverageyieldsover
eightseasons(shownonlyforfieldsthathadwheatinatleastfive
oftheseseasons),displaysamuchnarrowerdistribution,with
vir-tuallynolocationsachieving20%abovetheregionalaverageand
muchfewerlaggardsat20%belowaverage.
Thisvisualimpressioncanbeformalizedbyextractingsomekey
statisticsoftheyielddistribution,suchasthedifferencebetween
themaximumyields(or95thpercentile)andaverageyields.Wecan
refertothisquantityasYGML,whereYGMreferstoyieldgap
rel-ativetomaximumyieldsandthesubscriptLreferencesthelength
oftherecord(in#ofseasons)usedtocomputetheaverageyields
foreachpixel.ValuesofYGMLforLvaryingfromonetothelength
oftherecordcanthenbeplottedona“yieldgapcurve,”as
out-linedFig.3.Thesteepnessofthiscurvethenprovidesinsightinto
howpersistentspatialyielddifferencesarethroughoutthestudy
period,andthushowimportantpersistentfactorslikesoilquality
orfarmerskillareinexplainingtheoverallyieldgap.
Fig.4presentsyieldgapcurvescomputedforthreedifferent
regionswhereatleastsixseasonsofwheatyieldestimateshave
beengeneratedbasedonLandsat(datatakenfromLobelletal.,
2007a,2010).Forreference,eachplotalsoincludesagrayline
indi-catingtheshapeofthecurveexpectedifonerandomlyscrambles
yieldsacrossspaceforeachimage.Thisgraylinethusrepresents
thenulldistributionifyieldpatternswereentirelyinconsistent(i.e.,
random)fromyeartoyear,andthedistancebetweenthetwolines
providesanindicationoftheoverallpersistenceinspatialyield
patterns.
EvidentinFig.4areimportantdifferencesbetweenthethree
locations,withtheYaquiValleypossessingthesteepestcurvethat
closelyresemblesthenullcurve.Sangrur,Indiashowsashallower
curveandBhatinda,Indiaisshallowerstill.Bythemselves,these
curvessuggestthatthereareveryfewpersistentfactorsexplaining
theyieldgapinYaquiValley,incontrasttotheIndiansiteswhere
atleastsomepersistenceisevident.
Theseimpressionsaresupportedbymoredetailedanalysesin
eachregion.InYaquiValley,farmersarerelativelyadvancedintheir
understandingofcropmanagementandhavefairlyreliableaccess
toirrigationandchemicalinputs.Comparisonswithfieldsurveys
intwoyearsindicatedthatdifferentmanagementfactorsbecome
importantindifferentyears,namelytimingofirrigationinoneyear
andamountoffertilizerinputsinanother(Lobelletal.,2005).Of
course,alackofpersistenceinyieldpatternsdoesnotsuggestthat
farmerskilloraccessisnotimportant,butthatvariationsinthese
factorsarenotsufficienttoexplainyielddifferences,presumably
becauseofuniformlyhighlevelsoffamerskillandaccess.
In Sangrur, India, comparisons with ancillary datasets on
irrigationindicatethatfarmersatthetailendofirrigationcanals
haveconsistentlyloweryields(Lobelletal.,2010).Althoughthere
areseveralpossibleexplanationsforthistrend,themostlikelyis
lessreliableaccesstosurfacewater.Asimilarexplanationappliesto
Bhatinda,exceptthemagnitudeofthiseffectisgreaterbecausethat
districtismuchmorereliantonsurfacecanalsrelativeto
ground-waterthanSangrur(Lobelletal.,2010).Moreover,asubstantial
fraction of land in southwestern Bhatinda is routinelyplanted
latebecauseofcottoncultivationinthesummerthatdelaysthe
wheatseason.Thus,persistentvariationsinbothsowingdateand
positionalongirrigationcanalscontributetotheshallowerslope
of theyield gap curvein Bhatinda compared to theother two
Fig.2. Theeffectofmulti-yearaveragingonspatialyieldpatternsinpartoftheYaquiValley,Mexico.(a)Mapand(b)histogramofLandsat-basedyieldestimatesforwheat forthe2007–2008growingseason.Valuesareexpressedasapercentageofthemeanyieldestimatefortheentireregion(meanyield=100).(c)Mapand(d)histogramof theaverageyieldestimatesforeightgrowingseasonsbetween1999and2008,forthesamelocations.Onlyfieldswithwheatinatleastfivegrowingseasonsareincluded. Thedistributionofyieldstendstonarrowasoneaveragesyieldsoverlongertimeperiods,becausesomeofthefactorsdrivingspatialdifferencesinanysingleyeararenot persistent.
Fig.3.Summaryofproceduretocomputeyieldgapprofiles.Imagesfrommultipleyearsareaveragedtocreatemapsofaverageyieldsforvaryingperiodsoftime.Themaps arethenusedtocomputethedifferencebetweenmaximumandaverageyieldingfields,andthisdifferenceisplottedversusthenumberofyearsusedintheaverage.
62 D.B.Lobell/FieldCropsResearch143(2013)56–64
Fig.4. Yieldgapprofilesforwheatindifferentregions.(a)YaquiValleyDistrict,Mexico,(b)SangrurDistrict,India,(c)BhatindaDistrict,India.Eachpointshowsthedifference betweenmaximumyieldandaverageyieldwithinthedistrict,whereyieldsarecalculatedastheaverageover1–6years.Differencesdiminishintimebecauseofalackof persistenceinspatialpatterns.Thegraylinerepresentstheexpectedchangeinyieldgapwithincreasingyearsifyieldpatternswereentirelyrandominspace(computedby randomlyre-orderingthespatialdistributionofyieldsineachyear).
TheyieldgapcurvesinFig.4arejustonewaytosummarizethe
persistenceofyielddifferences.Anothersimplesummaryisshown
inFig.5,whichsplitsfieldsinto10groupsaccordingtotheyield
deciles(0–10%,10–20%,etc.)forthemostrecentyieldimage.The
figuresummarizestheyielddistributionforeachofthesegroups
acrossallyearsexcepttheyearusedtodefinethegroups.Theboxes
showtheinterquartilerangeofthedata(25thand75thpercentile),
thehorizontallineindicatesthemedian,andthewhiskersshow
the10thand90thpercentilesofthedata.Thesignificantoverlap
betweenthedistributionsindicatesagainthelackofstrong
persis-tenceinyieldpatterns;fieldswithverydifferentyieldsinasingle
yearhaverelativelysimilaryielddistributionsinotheryears.The
degreeofoverlapisgreatestinthecaseoftheYaquiValley,which
similartoFig.4indicatestheleastpersistenceinthisregion
rela-tivetotheIndiansites.Atthesametime,allthreesitesexhibita
positiveslopeinFig.5,whichindicatesatendencyforhighyielding
fieldstoremaininthehighyieldingcategory,andforfieldsinthe
lowestdecileofyieldstoremainrelativelylowyielding.
Animportantissuewhenanalyzingspatialyielddistributions
issettingtheextentoftheanalysis.Intheaboveexamples,the
boundariesofthecropdistrictswereusedtodefinetheextent.If
theextenthadbeenlarger,suchasananalysisfortheentirestate,
theamountofpersistentyielddifferenceswouldlikelyincreaseas
soil,climate,andmanagementconditionsatoppositeendsofthe
extentwouldlikelygrow.Foryieldgapanalysis,itseemspreferable
tokeeptheextentsmallenoughsuchthatvariationsinclimate,and
thusyieldpotential,acrossthedomainaresmall,butlargeenough
suchthatalargenumberoffieldsareincludedinthesample.
How-ever,thesensitivityofresultstochoosingdifferentspatialextents
hasnotbeenconsideredinpaststudies,andisatopicworthyof
moreresearch.
Thedatarequired toassembleFigs. 4and 5 aresubstantial:
sixyearsofLandsatdata,with2–3imagesperyearforeach
fig-urepanel.However,themethodstoprocesssuchdata,including
radiometricandgeometriccorrectionoftheremotesensingdata
andincorporationoftemperatureandradiationdatatoestimate
yields,canbeincreasinglyautomated.Inpractice,themain
obsta-cleistypicallyperformingimageclassificationsforeachseasonto
identifywhichpixelsaresowntothecropofinterest–ataskthat
canbemadedifficultifmultiplecropswithsimilarphenologiesare
growninthesameregion.
Thetwoapproachesforanalyzingyieldgapcauseswithremote
sensing–thosewithandwithoutexplicituseofancillarydatasets
–canobviouslybeusedascomplementstoeachother.Inaregion
wheremultipleseasonsofcloud-freeimagesareavailable,auseful
startingpointistoconstructyieldgapcurves(e.g.,Fig.4)toidentify
thepersistenceofyield-limitingfactors.Ifpersistenceisfoundto
occur,themapsofaverageyieldsover5ormoreyearscanbeusedto
Fig.5.Asummaryofwheatyieldpersistencein(a)YaquiValleyDistrict,Mexico,(b)SangrurDistrict,India,(c)BhatindaDistrict,India.Eachplotshowsyielddistributionsfor 10groupsoffields,wherethegroupsaredefinebytheyielddecilesinasingleyear(inthiscase,thelastyearofthestudyperiod).Theyielddistributionsarecalculatedfrom yieldsonthesefieldsfromsevenyearspriortotheyearusedtodefinethegroups.Distributionsarerepresentedbythemedian(horizontalline),25thand75thpercentiles (box),and10thand90thpercentiles(whiskers).Thesignificantoverlapbetweenthedistributionsindicatesthattherelativerankingofyieldsacrossfieldstendstovarya lotfromoneyeartothenext(i.e.,alackofstrongpersistence).However,thepositivetrendinallthreeregionsindicatessomelevelofpersistence,withhigh(low)yielding fieldsinoneyearmorelikelythanaveragetobehigh(low)inotheryears.
generatehypothesesaboutthespecificcausesofyieldvariationand
thetypesofancillarydatasetsthatwarrantefforttoobtain.Maps
ofpersistentyielddifferencescanalsobeusedtotargetground
effortsatmanagementorsoildatacollection.Conversely,inregions
wherefeweryears ofimageryare currentlyavailable,orwhere
ancillarydatasetsarealreadyinpossession,thendetailedanalyses
ofanindividualyearortwowouldbeausefulstartingpoint.
Sub-sequentstudiesofmultipleyearscanthenbeusedtotestwhether
thefactorsidentifiedinthesingleyeararepersistent.
5. Conclusions
Todate, satellitedata have played a relativelysmall role in
understandingthemagnitudeand causesof yieldgaps inmost
regions.However,thefewexamplesthatexistindicatethatremote
sensingcanhelp toovercomesomeoftheinherent spatialand
temporal scalingissues associated withfield-basedapproaches.
Althoughthecostoravailabilityofsatellitedatawithsufficient
spa-tialresolutiontodiscriminateagriculturalfieldswasanobstaclein
thepast,thisbarrierisrapidlydiminishing.Improvedalgorithms
topre-processremotesensingdataandestimateyields,andthe
increasedavailability ofnew,largegeospatial datasets onsoils,
management,andweathershouldalsobenefitfutureeffortsinthis
area.
Thus,remotesensingispoisedtobecomearegulartoolinthe
analyst’stoolboxforassessingthemagnitudeandcausesofyield
gaps.Thescopeforapplicationsinthenear-futurewilllikelybe
limitedtoregionswithoutextensiveintercroppingwithinfields,
givendifficultiesofassessingyieldswithremotesensingin
mixed-croppingsystems. Importantdirections for future workinclude
furtherdevelopmentandtestingofalgorithmstoestimateyields
(particularlyforrainfedandnon-cerealcrops),andcomparisonand
integrationofremotesensingwithstudiesofyieldgapsbasedon
simulationandexperimentalapproaches.Asdescribedthroughout
thisspecialissue,improvedknowledgeofyieldgapswillplaya
criticalroleinmeetingfuturecropdemandsataffordableprices
andwithminimalenvironmentalimpacts.Theuseofsatellitedata
canacceleratethepaceofdiscovery,andassuchitrepresentsan
importantareaforfuturework.
Acknowledgements
ThisworkwassupportedbyNASANewInvestigatorgrantno.
NNX08AV25GtoD.B.L.Ithanktwoanonymousreviewersforvery
helpfulcommentsonthemanuscript.
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