Basic and extensible post-processing of eddy covariance flux data with REddyProc.

39 Pages·2017·2.13 MB·English

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Basic and extensible post-processing of eddy covariance flux data
with REddyProc.
ThomasWutzler1,AntjeLucas-Moffat2,3,MircoMigliavacca1,JürgenKnauer1,KerstinSickel1,Ladislav
Šigut4,OlafMenzer5,andMarkusReichstein1
1MaxPlanckInstituteforBiogeochemistry,Hans-Knöll-Straße10,07745Jena,Germany
2GermanMeteorologicalService,CentreforAgrometeorologicalResearch,Bundesallee33,38116Braunschweig,Germany
3Alsoat:ThuenenInstituteofClimate-SmartAgriculture,Bundesallee65,38116Braunschweig,Germany
4GlobalChangeResearchInstituteCAS,Beˇlidla986/4a,CZ-60300Brno,CzechRepublic
5DepartmentofGeography,UniversityofCalifornia,SantaBarbara,CA93106-4060,USA
Correspondence:ThomasWutzler
([email protected])
Abstract.
Withtheeddy-covariance(EC)technique,netfluxesofcarbondioxide(CO )andothergreenhousegasesaswellaswater
2
and energy fluxes can be measured at the ecosystem level. These flux measurements are a main source for understanding
biosphere-atmosphereinteractionsandfeedbacksbycross-siteanalysis,model-dataintegration,andup-scaling.Therawfluxes
5 measuredwiththeECtechniquerequireanextensiveandlaboriousdataprocessing.Whiletherearestandardtoolsavailable
inopensourceenvironmentforprocessinghigh-frequency(10or20Hz)dataintohalf-hourlyqualitycheckedfluxes,there
isaneedformoreusableandextensibletoolsforthesubsequentpost-processingsteps.Wetackledthisneedbydeveloping
theREddyProcpackageinthecross-platformlanguageRthatprovidesstandardCO -focusedpost-processingroutinesfor
2
reading(half-)hourlydatafromdifferentformats,estimatingtheuStarthreshold,gap-filling,flux-partitioning,andvisualizingthe
10 results.Inadditiontobasicprocessing,thefunctionsareextensibleandalloweasierintegrationinextendedanalysisthancurrent
tools.Newfeaturesincludecrossyearprocessingandabettertreatmentofuncertainties.AcomparisonofREddyProcroutines
withotherstate-ofthearttoolsresultedinnosignificantdifferencesinmonthlyandannualfluxesacrosssites.Loweruncertainty
estimatesofbothuStarandresultinggap-filledfluxeswiththepresentedtoolwasachievedbyanimprovedtreatmentofseasons
duringthebootstrapanalysis.Higherestimatesofuncertaintyinday-timepartitioningresultedfromabetteraccountingof
15 theuncertaintyinestimatesoftemperaturesensitivityofrespiration.Theprovidedroutinescanbeeasilyinstalled,configured,
used,andintegratedwithfurtheranalysis.Hencetheeddycovariancecommunitywillbenefitfromusingtheprovidedpackage,
allowingeasierintegrationofstandardpost-processingwithextendedanalysis.
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1 Introduction
Theavailabilityofecosystemlevelobservationsofnetecosystemexchange(NEE)ofcarbondioxide(CO )andothergases,
2
latentheat(LE)andsensibleheat(H)fluxesmeasuredbytheeddycovariance(EC)method(Aubinetetal.,2000)allowed
aboostinecosystemunderstandingatsitetoglobalscales(Baldocchietal.,2017).TheECmethodprovideshalf-hourlyor
5 hourlyrecordsofturbulentfluxesbetweenanentireecosystemandtheatmosphere.Thesedataarederivedfromhighfrequency
measurements (10 or 20 Hz) of wind speed and direction together with measurements of air scalar characteristics such as
CO and water vapor concentration, or temperature. Methods to compute fluxes from high frequency measurements have
2
beenconsolidatedinthelastdecades(Rebmannetal.,2012;Fokenetal.,2012;Aubinetetal.,2012).Dependingonthesite
characteristics,theNEEfluxesalsoneedtobestoragecorrected.Althoughmeasuredcontinuously,the(half)hourlyECdata
10 containgapsduetoinstrumentmalfunctionormeteorologicalconditionsunderwhichtheassumptionsoftheECtechniqueare
notmet.Suchconditionsincludeinsufficientlydevelopedturbulenceorlowsignalstability(detailsine.g.FokenandWichura,
1996;Fokenetal.,2004;Göckedeetal.,2004;Fokenetal.,2012).Dataobtainedundertheseunfavorableconditionsaresubject
toseveralconstraints,technicallycorrectbutnotrepresentativeoftheecosystem.Hence,(half-)hourlyrecordsareflaggedfor
differentqualitylevelsandneedfurtherextensivepost-processingasdescribedbyPapaleetal.(2006).
15 NEEfromperiodswithlowfrictionvelocity(uStar)(Aubinetetal.,2012)needtobedetectedandfilteredouttoavoidsystematic
biasesinnighttimeNEE(Papaleetal.,2006).Thescreenedfluxtimeserieswithgapsneedtobefilled(Reichsteinetal.,2005a)
using the available flux data and auxiliary micrometeorological measurements. An additional information can be obtained
fromNEEthankstofluxpartitioningmethods,thatprovidemodelestimatesofgrossprimaryproduction(GPP)andecosystem
respiration(R )(Reichsteinetal.,2005a).Thesegrossfluxesareimportanttounderstandland-atmosphereinteractions.
eco
20 All these post-processing steps need to be performed routinely for EC data. Hence, it is desirable to have automated and
reproduciblepost-processingtoolsavailablethatcanbeeasilyused,extended,andintegratedintoresearcher’sownworkflow.
ForthispurposewecompiledallroutinesfortheimportantCO -focusedpost-processingstepsintheREddyProcpackagefor
2
thecross-platform,freeRlanguage.TheREddyProcpackageloadstimeseriesofqualitycheckedandstoragecorrectedfluxes
andthebasicsetofmeteorologicalvariablesandprovidesasoftwareenvironmenttoperformuStarthresholddetectionand
25 filtering,gapfillingandpartitioning.Furthermore,aseriesofotherfunctionalitieslikedataimportroutinesanddatavisualization
areprovided.
The objectives of the paper are to 1) provide a reference that describes the methodology of the processing used in the
REddyProcpackage,and2)showthattheobtainedresultsdonotdiffersystematicallyfromresultsobtainedwithstandard
post-processingimplementedintheFLUXNETcommunity(basedonPapaleetal.,2006;Reichsteinetal.,2005a;Lasslopetal.,
30 2010;Pastorelloetal.,2017).
Table1explainsusedabbreviations.Thefirstpartofthepaper(section2)describesthepost-processingmethods.Thesecond
part (Section 3) presents the benchmarks the REddyProc implementation with standard post-processing tools. It details
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differencesintheimplementationsandpossibleconsequencesinobtainedresultsandaggregatedfluxes.Anappendixgivesan
overviewofthepackagewithgeneraldesign,anexampleofthepost-processing,andlinkstohelpandresourcessothatreaders
cangetstartedpost-processingtheirowndata.
Table1.Abbreviationsusedrepeatedlyinthepaper.
Symbol Description
EC eddy-covariance
CO2 carbondioxide
NEE netecosystemexchangetowardstheatmospherein
µmolCO2m−2s−1(aggregatedingCm−2yr−1)
GPP grossprimaryproductivity(sameunitsasNEE)
R ecosystemrespiration(sameunitsasNEE)
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H,LE sensibleandlatentheatinWm−2
uStar frictionvelocityinms−1
Rg shortwaveincomingglobalradiationinWm−2
Tair airtemperaturein°C
VPD vaporpressuredeficitinhPa
MDS marginaldistributionsampling(section2.2)
LUT look-uptable(section2.2.1)
MDC meandiurnalcourse(section2.2.2)
E0 temperaturesensitivityparameterineq.1
R respirationatreferencetemperatureparametereq.1
Ref
DP06 C-implementationoftheuStarthresholdestimation
byDarioPapale(section3)
LRC lightresponsecurve(section2.3.2)
2 MethodsofPost-processing
5 Thepost-processingreliesonhalf-hourlyorhourlymeasurementsofNEEandancillarymeteorologicaldataofuStar,Rg,Tair
orsoiltemperature,andVPD.Thefluxesshouldbequalitycheckedand,ifapplicable,storagecorrectedbeforetheiruseinthe
package.
Thepost-processingfollowsaspecificworkflow:
1. determinationandfilteringofperiodswithlowturbulentmixing(uStar-filtering),
10 2. replacingmissingdatainthehalf-hourly/hourlyrecords(gap-filling),and
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Import half-hourly data
NEE
+ Meteo
Estimate quantiles of uStar threshold distribution
Filter u* > 0.28 u* > 0.35 u* > 0.41
Fill gaps
NEE_U05_f NEE_U50_f NEE_U95_f
Partition fluxes
GPP_U50_f GPP_U95_f
GPP_U05_f Reco_U05_f Reco_U50_f Reco_U95_f
Export results
Figure1.Theworkflowstartswithimportingthehalf-hourly(orhourly)data,heretheyear1998ofsiteDE-Thaisplottedasanexample.
Next,aprobabilitydistributionofuStarthresholdisestimatedforeachseason.Gap-fillingandflux-partitioningisperformedforseveral
quantilesofthisdistributionforanestimateofuncertainty.Finallytheresultsareexported.
3. partitioningNEEintothegrossfluxesGPPandR (flux-partitioning).
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UsageoftheREddyProcpackagefollowsthisdatapost-processingworkflow(Fig.1).Thefollowingsectionsexplainthesteps
inmoredetail.
2.1 uStar-filtering
5 Determining periods with low turbulent mixing is a critical step in the EC data post-processing. Standard steady state and
integralturbulencecharacteristicstestsintheinitialprocessingexcludethemostproblematicrecordsofsensible(H),latent(LE)
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8 1998006 (01.06.98−31.08.98)
(9.3−10.8°C)
)
1
−yr 6 uStarThr=0.42 + + + + +
−2 m 4 +++++ + + + + +
C + +
g
( 2 +
E
E
N
0
−2
0.2 0.4 0.6 0.8
uStar (m s−1)
Figure2.ConceptoftheuStar-filter:NEEatlowuStarfrictionvelocitiesbelowathreshold,i.ewithlowturbulence,isbiasedlowcompared
higheruStarwithotherwisesimilarenvironmentalconditions.TheuStarthreshold(dashedline)isestimatedbyamovingpointmethodon
uStarbins(crosses)acrosshalf-hourlyrecords(circles)hereforaseason-temperaturesubsetofdatafromDE-Tha.
heatandCO fluxes(FokenandWichura,1996).However,itiswellknown(summarizedinAubinetetal.,2012,chapter5),that
2
suchaqualitycheckingstrategyisnotsufficient,especiallyinthecaseofCO .Stablestratificationthatispresentoftenduring
2
thenight-timedampensturbulenceandleadstoanunderestimationofthenight-timeNEE,i.e.theecosystemrespiration(Gorsel
etal.,2007).MassmanandLee(2002)proposedthatunfavorableconditionscouldbedetectedbyinspectingtherelationship
5 ofnight-timeNEEversusuStar.Withinsimilartimeperiodandsimilarenvironmentalconditionsrespirationshouldnotbe
dependentontheuStar.AtlowuStarvalues,anegativelybiasedrespirationismeasured.Aheuristicclassofmethods,whichis
widelyaccepted,assumesthatathresholdofuStarcanbeestablishedabovethatnighttimefluxesareconsideredvalid.Hence,
theuStarthresholdistheminimumuStarabovewhichrespirationreachesaplateau(Fig.2).Thisthresholdisspecificforeach
seasonofasiteyear.UncertaintiesintheuStarthresholdestimaterepresentoneofthelargestuncertaintycomponentsinthe
10 post-processingofNEE.
ThereareatleasttwomethodsofestimatingtheuStarthreshold:themovingpointmethod(Reichsteinetal.,2005c;Papale
etal.,2006),whichiscurrentlymoreroutinelyused,andthebreak-pointdetectionmethod(Barretal.,2013).
2.1.1 MovingpointmethodforuStar
Themethodof(Papaleetal.,2006) detectsaplateauintherelationshipofnight-timeNEEversusuStaramongallrecords
15 withintemperaturesubsetbyamovingpointtestofrecordsbinnedintodifferentuStarbins.
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Thenighttimedata(default:Rg<10 Wm 2)issplitintodifferenttimesofyear,herecalledseasons,toaccountfordiffering
−
surfaceroughness.Thenthedataofeachseasonissplitintodefaultsixtemperaturesubsetsofequalsize(accordingtoquantiles).
Withineachtemperaturesubsetdataissplitinto20aboutequallysizeduStarbins.Thedefaultmovingpointmethod,called
Forward2,determinesthethresholdbasedontheseuStarbins.ItchecksforeachbinifthemeanNEEishigherthan0.95
5 timesthemeanofthefollowing10bins.Ifthisholdstruealsoforthenextbin,themeanuStarofthebinisreportedasthreshold.
There are often subsets of data, where no clear threshold can be detected. Hence, there are quality criteria on whether the
estimateofagivensubsetisusedinsubsequentaggregation.OnequalitycriterionspecifiesthattemperatureanduStarshould
notbecorrelatedwithinthetemperaturesubset,anotherrequiresaminimumnumberofvalidrecordswithinasubset.Next,the
uStarestimatesfordifferenttemperatureclassesandperiodsareaggregatedtoderivearobustuStarestimate.Withinoneseason,
10 themedianistakenacrosstheestimatesofdifferenttemperaturesubsets.Withinoneyear,themaximumistakenacrossthe
associatedseasons.
Records during night-time with uStar smaller than the estimated threshold are flagged as invalid and are replaced in the
subsequentgap-fillingprocessingstep.
2.1.2 BreakpointdetectionmethodforuStar
15 Alternatively,abreakpoint-detectioncanbeappliedtotheunbinneddata,thatavoidsthesensitivityoftheMovingpointmethod
tothespecificsofthebinningschemes(Barretal.,2013).REddyProc providesthismethodbyestimatingthebreakpoint
basedonunbinnedrecordswithintheseasons/temperaturesubsetsusingthesegmentedR-package(Muggeo,2003,2008).
However, REddyProc differs from (Barr et al., 2013) by keeping the same aggregating scheme of seasonal/temperature
estimatestoannualthresholdsaswiththeMovingpointmethod.
20 2.1.3 BootstrappinguncertaintyoftheuStarthreshold
EstimatesoftheuStarthresholdareoftensensitivetothespecificsofthecombinationofmethodsandthedata,e.g.thebinning,
minimumnumberofrecordswithinaseasonortemperaturesubset,criteriainaggregation,etc.Therefore,bootstrap(re-sampling
withreplacement)isappliedtogenerate200artificialreplicatesofthedatasetandforeachreplicatethethresholdisestimated
(EfronandTibshirani,1986;DavisonandHinkley,1997).The5%,50%and95%oftheestimatesarereportedasarangeof
25 thresholdestimates.Thesubsequentpost-processingstepsofgap-fillingandpartitioningarethenrepeatedusingthosedifferent
thresholdstopropagatetheuncertaintyofuStarthresholdestimationtoderivedquantitiessuchasannualNEE,GPPandR
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2.2 Gap-fillingmethods
Fillingofgapsinhalf-hourlyNEEdataisnecessarytoobtaincompletetimeseriesforthecalculationofdailyaveragesor
balancessuchasmonthlyorseasonalsums.
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Thedatasetofhalf-hourlyfluxesafterqualitychecksanduStar-filteringmaycontainupto50percentgaps,sometimeseven
higher,dependingonthesiteconditions.Forthesite-yeardatasetsusedinthismanuscriptasabenchmark,thepercentageof
gapsrangedfromonaverageof32%beforeuStar-filteringto60%or48%aftergap-fillingforupperorloweruStarthreshold
estimaterespectively.
5 Thegap-fillingmethodimplementedinREddyProc istheso-calledmarginaldistributionsampling(MDS)by(Reichstein
etal.,2005b).Inacomparisonwithgap-fillingmethodsfornetcarbonfluxesby(Moffatetal.,2007),thismethodperformed
wellforthedifferentartificialgapscenariosrangingfromsinglehalf-hourstoseveraldays.Duetoitsflexibilityindealingwith
missingmeteorologicalinputdataanditsfastandhighlyautomatedroutinesavailableasBGConlinetool,theMDSgap-filling
methodhasbeenwidelyused.Thealgorithmexploitsthecovariationofthefluxeswiththemeteorologicalvariablesandthe
10 temporalautocorrelationofthefluxesbasedontwobasicmethods,the(moving)look-uptableapproach(LUT)andthemean
diurnalcourse(MDC),whicharedescribednext.
2.2.1 Look-up-tableforgap-filling
Inthelook-uptable(LUT)approach,thefluxesarebinnedbythemeteorologicalconditionswithinacertaintimewindow.The
missingvalueofthefluxisthencalculatedastheaveragevalueofthebinnedrecordsanditsuncertaintyestimatedfromtheir
15 standarddeviation.
TheoriginalLUTconsistedoffixedperiodsoverayear(Falgeetal.,2001),whileintheMDSalgorithm,themeteorological
conditionsaresampledwithamovingwindowaroundthegaptobefilled.Withinthechosentimewindowandrespectivebin,
eachmeteorologicalvariableshouldnotdeviatemorethanafixedmargintoensuresimilarmeteorologicalconditions.The
defaultmeteorologicalvariablesareRg,Tair,andVPDwithdefaultmarginsof50Wm 2,2.5°C,and5.0hPa,respectively.
−
20 2.2.2 Meandiurnalcourseforgap-filling
TheNEEfluxeshaveameandiurnalcourse(MDC)thatfollowsthecourseofthesunwithonlyrespiration(releaseofCO )
2
duringnighttimeandacombinationofrespirationandphotosynthesisduringdaytime.Thisautocorrelationofthefluxesis
exploitedbytakingtheaveragevalueatthesametimeofdaywithinamovingtimewindowofadjacentdays(Falgeetal.,2001).
ThoughtheMDCmethodonlyshowedamediumperformanceinthegapfillingcomparisonby(Moffatetal.,2007),ithasthe
25 advantagethatthisapproachcanbeusedevenifnometeorologicalinformationisavailable.
IntheMDCalgorithm,thesametimeofdayincludesalsothefluxesoftheadjacenthour(±1hour).Thenumberofadjacent
daysneedtobespecified.
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sMDSGapFilling()
Don‘t fill:
Yes
NEE present ? Filled only for uncertainty estimate
No
Fill with average of available values:
Yes
Rg, T, VPD available with |dt| ≤ 7 days fFillLUT(7, Rg,T,VPD)
No
Yes
Rg, T, VPD available with |dt| ≤ 14 days fFillLUT(14, Rg,T,VPD)
No
Yes
Rg available with |dt| ≤ 7 days fFillLUT(7, Rg)
No
Yes
|dt| ≤ 1 hour on same day fFillMDC(0)
No
Yes
|dt| ≤ 1 hour on ≤ 1, 2 days fFillMDC(1), fFillMDC(2)
No
Yes
Rg, T, VPD available with |dt| ≤ 21, 28, ..., 70 days fFillLUT(seq(21,70,7), Rg,T,VPD)
No
Yes
Rg available with |dt| ≤ 14, 21, ..., 70 days fFillLUT(seq(21,70,7), Rg)
No
Yes
|dt| ≤ 1 hour on ≤ 7, 14, ..., 210 days fFillMDC(seq(7,140,7))
Figure3.FlowdiagramoftheMDSgap-fillingalgorithmasimplementedinREddyProc.Seetable1forabbreviations.
2.2.3 Marginaldistributionsamplingforgap-filling
ThemarginaldistributionsamplingcombinestheLUTandMDCmethodsdependingontheavailabilityofthemeteorological
data.Threedifferentconditionsareidentifiedforeachhalf-hourlyNEEflux:
1. Thedataofallthreemeteorologicalvariables(Rg,Tair,andVPD)areavailable.
5 2. TairorVPDaremissing,butRgisavailable.
3. AlsoRgismissing.
Case1):ThemissingvalueisreplacedbytheaveragevalueundersimilarmeteorologicalconditionsinaLUTapproach.Similar
meteorologicalconditionsbasedonRg,TairandVPD.Ifnosimilarmeteorologicalconditions(minimumoftwohalf-hourly
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fluxes)arepresentwithinthestartingtimewindowof7days,thewindowssizeisincreasedto14days.
Case2):ThesameLUTapproachistaken,butsimilarmeteorologicalconditionscanonlybedefinedviaRgwithinatime
windowof7days.
5
Case3):Themissingvalueisreplacedwiththemeandiurnalcourse(MDC).Thenumberofdaysstartwithoneday,thus
alinearinterpolationofavailabledataatadjacenthours(±1hour)atthesameday.Thenumberisthenincreasedto±1and±2days.
IfafterthesestepstheNEEvaluescouldnotbefilled,theprocedureisrepeatedwithincreasedwindowsizesuntilthevaluecan
10 befilled,seeflowdiagraminFigure3.
2.3 Flux-partitioningmethods
ThegrossfluxesofGPPintothelandsystemandR outofthelandsystemarethetwoopposingpartsofNEE:NEE=R -
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GPP.AvailabilityofGPPandR ispivotalastheyarethetwobiggesttermsofthecarboncycle(e.g.Chapinetal.,2006;Jung
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etal.,2011).Moreover,understandingtheirsensitivitytoenvironmentaldrivers(e.g.,radiation,temperature,andsoilmoisture)
15 isimportanttointerpretland-atmosphereinteractionsandtoimproveearthsystemsmodels(Reichsteinetal.,2012).Therefore
severalmethodsweredevelopedtopartitionNEEintothesetwocomponents(Reichsteinetal.,2005c;Lasslopetal.,2010;
Moffat,2012;WehrandSaleska,2015;Desaietal.,2008;Stoyetal.,2006).
Thetwomostwidelyusedmethodsaretheso-callednight-timepartitioningandday-timepartitioning(Reichsteinetal.,2012).
The night-time partitioning (Reichstein et al., 2005c) relies on the temperature response function of nighttime NEE fluxes
20 that are representative of Reco. It assumes that this relationship is applicable also to daytime data. The relationship is then
usedtopredictR frommeasuredtemperatureandGPPiscomputedasadifferencebetweenR andNEE.Thismethodis
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currentlythemostwidelyusedapproach.Alternatively,theday-timepartitioning(Lasslopetal.,2010)fitsaLRCtodaytime
NEEobservations,accountingfortheeffectsofradiationandVPDonGPPaswellastheeffectsoftemperatureonR .
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2.3.1 Nighttimeflux-partitioning
25 Themethodof(Reichsteinetal.,2005c)estimatesatemporallyvaryingrespiration-temperaturerelationshipfromnighttime
data.Firstnight-timedataisselectedbyathresholdofRg<10Wm 2,whichiscongruentwiththeBGConlinetoolbutdiffers
−
fromthe20Wm 2reportedin(Reichsteinetal.,2005c).
−
Next,temperaturesensitivity,E oftheLloydandTaylor(1994)relationship(1)isestimatedbyfittingthemodeltosuccessive
0
15dayperiodsofnight-timedata,andtheresultingE seriesisaggregatedtoanannualestimate.
0
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1 1
R (T)=R exp E , (1)
eco Ref 0
T T −T T
(cid:20) (cid:18) Ref− 0 − 0(cid:19)(cid:21)
where T is kept constant at -46.02°C Lloyd and Taylor (1994) and where reference temperature T is 15°C, which is
0 Ref
congruentwiththeBGConlinetoolbutdiffersfromthe10°Creportedin(Reichsteinetal.,2005c).Forrobustnesseachfitis
repeatedonatrimmeddatasetexcludingrecordswithresidualsoutsidethe5%-95%residualdistribution.Theannualaggregate
5 isthemeanacrossthe3validestimateshavingthelowestuncertaintyinthefit.SingleestimatesofE0areconsideredvalid,if
therewereminimumof6records,temperaturerangedacrossatleast5°C,andestimateswereinsidetherangeof30to450K.
Subsequently, the respiration at reference temperature, R , is re-estimated from night-time data using the annual E
Ref 0
temperaturesensitivityestimatefor7-daywindowsshiftedconsecutivelyfor4days.Theestimatedvalueisthenassignedtothe
centraltime-pointofthe4dayperiodandlinearlyinterpolatedbetweenperiods.Hence,theobtainedrespiration-temperature
10 relationshipvariesacrosstime.
Finally,R isestimatedforbothday-andnight-timefromthetemporarilyvaryingR temperaturerelationshipanddaytime
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GPPiscomputedasR -NEE.
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2.3.2 Daytimeflux-partitioning
Themethodof(Lasslopetal.,2010)modelsNEEusingthecommonrectangularhyperboliclight-responsecurve(LRC)(Falge
15 etal.,2001):
αβR
g
NEE= +γ, (2)
αR +β
g
whereα(µmolCO J 1)isthecanopylightutilizationefficiencyandrepresentstheinitialslopeofthelight-responsecurve,
2 −
β (µmolCO m 2s 1)isthemaximumCO uptakerateofthecanopyatinfiniteRg,associatedwithlightsaturation,andγ
2 − − 2
(µmolCO m 2s 1)isatermaccountingforecosystemrespiration.Thehyperboliclight-responsecurveismodifiedtoaccount
2 − −
20 forthetemperaturedependencyofrespirationafterGilmanovetal.(2003)bysettingrespirationγ totheLloydandTaylor
respirationmodel(LloydandTaylor,1994)(1).Further,theLRCsettingparameterβin(2)toanexponentialdecreasingfunction
(Körner,1995)athigherVPDvalues(3).
β exp[ k(VPD VPD )]
0 0
β= − − , (3)

β0

10