Contents lists available atScienceDirect
Agricultural
and
Forest
Meteorology
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / a g r f o r m e t
The
potential
benefit
of
using
forest
biomass
data
in
addition
to
carbon
and
water
flux
measurements
to
constrain
ecosystem
model
parameters:
Case
studies
at
two
temperate
forest
sites
T.
Thum
a,∗,
N.
MacBean
b,
P.
Peylin
b,
C.
Bacour
c,
D.
Santaren
b,
B.
Longdoz
d,
D.
Loustau
e,
P.
Ciais
baFinnishMeteorologicalInstitute,ClimateResearch,P.O.Box503,FI-00101Helsinki,Finland
bLaboratoiredesSciencesduClimatetdel’Environnement,LSCE/IPSL,CEA-CNRS-UVSQ,UniversitéParis-Saclay,F-91191Gif-sur-Yvette,France cNoveltis,153RueduLac,F-31670Labège,France
dGemblouxAgro-BioTech,UniversityofLiège,Belgium eINRA,UR1263EPHYSE,Villenaved’Ornon,France
a
r
t
i
c
l
e
i
n
f
o
Articlehistory: Received12May2015 Receivedinrevisedform 29November2016 Accepted4December2016 Keywords:
Modeldatafusion ORCHIDEE Eddycovariance
a
b
s
t
r
a
c
t
Biomassasaresource,andasavulnerablecarbonpool,isakeyvariabletodiagnosetheimpactsofglobal changesontheterrestrialbiosphere,andthereforeitsproperdescriptioninmodelsiscrucial.Model-Data
Fusion(MDF)ordataassimilationmethodsareusefultoolsinimprovingecosystemmodelsthatdescribe
interactionsbetweenvegetationandatmosphere.WeuseaMDFmethodbasedonaBayesianapproach,
inwhichdataarecombinedwithaprocessmodelinordertoprovideoptimizedestimatesofmodel
parametersandtobetterquantifymodeluncertainties,whilsttakingintoaccountpriorinformation
ontheparameters.Withthismethodweareabletousemultipledatastreams,whichallowsusto
simultaneouslyconstrainmodeledvariablesatsitelevelacrossdifferenttemporalscales.Inthisstudy
bothhighfrequencyeddycovariancefluxmeasurementsofnetCO2andevapotranspiration(ET),and
lowfrequencybiometricmeasurementsoftotalabovegroundbiomassandtheannualincrement(which
includesallcompartments),areassimilatedwiththeORCHIDEEmodelversion“AR5”atabeech(Hesse)
andamaritimepine(LeBray)forestsiteusingfourtofiveyearsoffluxdataandnineyearsofbiomassdata.
Whenassimilatingtheobservedabovegroundannualbiomassincrement(AGBinc)togetherwithnetCO2
andETflux,theRMSEofmodelledAGBincwasreducedfromtheaprioriestimatesby37%atHesseand
69%atLeBray,withoutreducingthefittothenetCO2andETthatcanbeachievedwhenassimilatingflux
dataalone.Assimilatingbiomassincrementdataalsoprovidesinsightintheperformanceoftheallocation
schemeofthemodel.Comparisonwithdetailedsite-basedmeasurementsatHesseshowedthatthe
optimizationreducedpositivebiasesinthemodel,forexampleinfinerootandleafproduction.Wealso
investigatedhowtousestand-scaletotalabovegroundbiomassinoptimization(AGBtot).However,this
studydemonstratedthatassimilatingAGBtotmeasurementsintheORCHIDEE-AR5modelleadtosome
inconsistencies,particularlyfortheannualdynamicsoftheAGBinc,partlybecausethisversionofthe modellackedarealisticrepresentationofforeststandprocessesincludingmanagementanddisturbances. ©2016ElsevierB.V.Allrightsreserved.
∗ Correspondingauthorat:FinnishMeteorologicalInstitute,ClimateResearch, P.O.Box503,FI-00101Helsinki,Finland.
E-mailaddresses:tea.thum@fmi.fi(T.Thum),
natasha.macbean@lsce.ipsl.fr(N.MacBean),philippe.peylin@lsce.ipsl.fr(P.Peylin),
cedric.bacour@lsce.ipsl.fr(C.Bacour),
diego.santaren@lsce.ipsl.fr(D.Santaren),Bernard.Longdoz@ulg.ac.be(B.Longdoz),
Denis.Loustau@bordeaux.inra.fr(D.Loustau),philippe.ciais@lsce.ipsl.fr(P.Ciais).
1. Introduction
Itis ofcritical importancetounderstandhowtheterrestrial carbon cycle will respondto changing climaticconditions and anthropogenicactivity.Theglobalterrestrialcarboncyclehasbeen intensivelystudied,butlargeuncertaintiesinthemodelpredictions ofmajorsourcesandsinksremain(Ciaisetal.,2013).The inter-modelspreadusingdifferentcoupledclimate-carboncyclemodels demonstratesthattherearestilllargeuncertaintiesincarbonflux andstockprojectionsbytheendofthiscentury(Friedlingsteinetal., http://dx.doi.org/10.1016/j.agrformet.2016.12.004
2014),withsomemodelspredictingthattheterrestrialbiosphere willbecomeasourceofcarbontotheatmosphere,whileothers predictanincreaseinthecarbonstorage(Ahlströmetal.,2012). Whilstonesourceofuncertaintyistheresultofincorrector incom-pletebiophysics,inparticularregardingthemodels’responseto elevatedCO2(Zaehleetal.,2014),anotherarisesfrompoorly cali-bratedmodelparameters(Schwalmetal.,2010).Athirdissueis relatedtodifficultyanduncertainties inaccountingforthe his-toryoflandcoverdynamicsanddisturbances(naturalandhuman induced)in themodel initialization,whichdirectlycontrolsthe vegetationandsoilstatesatthestartofasimulation(Hurttetal., 2010).
Model-DataFusion(MDF) isastatisticallyrigorousapproach thatcanbeusedtooptimizemodelparameters,givendifferent observationsandpriorinformationontheparameters.MDFhas beenappliedextensivelytooptimizeecosystemmodels,including thosewhichformthelandsurfacecomponentofglobalEarth Sys-temModels,withinsitunetCO2andevapotranspiration(ET)flux data(Braswelletal.,2005;Wangetal.,2007;Williamsetal.,2009; Carvalhaisetal.,2010;Kuppeletal.,2012;Santarenetal.,2014), aswellassatelliteNDVI/fAPARdata(Knorretal.,2010; Bacour etal.,2015;MacBeanetal.,2015)andatmosphericCO2 concen-trationdata(Kaminskietal.,2012;Peylinetal.,2016;Schürmann etal.,2016).Typicallyfluxtowerdatabring informationonthe “fast”processesthatcontrolfluxesofphotosynthesis,respiration andevapotranspirationonadiurnaltoseasonaltimescale,whereas theirpotentialforconstrainingmodelsatinter-annualtimescales is lower (Wang et al., 2012; Santaren et al., 2014).Additional measurementsofotherecosystemvariables(e.g.aboveand below-groundcarbonstocks)areoftenavailableatfluxtowerlocations (Curtisetal.,2002)andcanbeusedforoptimizingthe“slower” carbonprocessesinecosystemmodels,suchascarbonallocation, turnoverandmortality.However,longtermcarbonstockandstock incrementdatahavenotbeenusedasofteninmodel optimiza-tionstudiestodate,partlybecausetheyinvolvelongertimescales whereinitialconditions(Carvalhaisetal.,2008,2010)and distur-bancehistoryaddsuncertainties(Thorntonetal.,2002).
The useof multipledata streams in MDF hasnot yet been extensive,but somestudies haveinvestigated theadded bene-fitdifferentdatasources,includingsomethatuseground-based datathatarerelatedtocanopy-scalebiomass.Keenanetal.(2012) used18yearsofNEEfluxdatafromtheHarvardforestcombined withecologicalmeasurements,suchasphenologicalobservations ofleafbudburst,litterdata,carbonpoolsindifferentbiomass com-partmentstoconstrainthecarboncycle-relatedparametersofthe Föbaarmodel.SimilarlyWuetal.(2011)usedmicrometerological fluxdatatogetherwithbiomassdataandLAIobservations.Bacour etal. (2015)examinedthecomplementarity ofin situflux and fAPAR(fractionoftheAbsorbedPhotosyntheticallyActive Radia-tion)dataforoptimizingparametersrelatedtophotosynthesisand phenologyintheORCHIDEEmodel.Mostofthesestudiesreported that using additional information provided an extra constraint thatenabledagreaternumberofparameterstobeindependently resolvedby the optimization.The importance of differentdata streamscanbeseenintheirrelativeinfluenceonthereduction ofuncertaintiesontheoptimizedparameters(Wuetal.,2011),but thisisalsodependentontheuncertaintiesassociatedtoeachdata stream,possiblebiasesinthedataandhowmanyobservationsthey containaswellaspossiblemodel-databiasesassociatedtoeach datastream(seeMacBeanetal.,2016forareviewofthechallenges involvedwithmultipledatastreamassimilation).
MDF can also be used to study inconsistencies between data-streams, between a given model-structure and real-world observations, and also to identify processes that are not well understoodinmodelsandgiveperspective tofurther measure-mentneeds(e.g.Keenanetal.,2013).Usingseveraldifferentdata
streamshelpsinconstrainingalargerparameterspace(Kaminski etal.,2012)andenablesabetterevaluationofthemodel,possibly evenhighlightingareaswheremodelneedsimprovingandthus helpingtosetprioritiesforfuturemodeldevelopments(Rayner, 2010).Ifthemodel cannotbeoptimizedtomatchthe observa-tionswithinprescribeduncertaintiesofanunbiaseddatastream itshowsthatthemodelstructuremaybeinsufficienttodescribe theprocessesthatrepresentthevariabilityofobservedquantities, andthusrequiresfurthermodification.
In recent years large-scale maps of biomass have become available(Saatchietal.,2011;Baccinietal.,2012;Thurneretal., 2014;Santoro etal.,2015; Avitabileetal.,2016)and possessa highpotentialtodeepenourknowledgeofecosystemfunctioning (e.g.Carvalhaisetal.,2014).Inaddition,theplannedESABIOMASS satellite mission (http://www.esa.int/OurActivities/Observing theEarth/TheLivingPlanetProgramme/EarthExplorers/Future missions/Biomass) has the potential to provide us with more accurate global coverage of forest biomass and forest height estimates. These data will be very useful in constraining the slowerprocessesinlandsurfacemodels(LSMs)atregionalscales. However,integratinginsitufluxandbiomassdataintoan ecosys-temmodeltoconstrainboth“fast”and“slow”carbonprocesses imposesachallengeforaMDFapproach.Mostglobalscalemodels useasteadystateassumptionforforestgrowththatresultsinan overestimationof thesimulatedtree biomassfor youngforests (Pietschand Hasenauer,2006; Ciaiset al., 2008), as thesteady state assumption corresponds to old-growth forests that hold maximumcarbonstocks.Youngerforestsareusuallycarbonsinks becausethetreesaregrowingandstorecarbonastheyage.
Inordertousebiomassdatainanoptimization,realistic sim-ulationof forest growth,from planting(or last disturbance) to its current age,is required, which might imposea strong con-straintintermsofcomputingtime,especiallywhenusingMonte Carloalgorithminanoptimization.Usually,landsurfacemodels userathercomplexequations(withmanyparameters)todescribe photosynthesisandorganicmatterdecomposition,butvery sim-pleequations(withfewparameters)todescribebiomassdynamics (PurvesandPacala,2008).Inthesemodels,processessuchasstand level recruitment, competition and specific mortalityprocesses includingdisturbancesarenotrepresented,andwoodbiomassis consideredtobeawell-mixedpool(BolinandRodhe,1973)whose massbalanceresultsfromtheinputofafractionofnetprimary pro-duction(NPP)thatisallocatedtowood,andremovalassumedto beaconstantfractionofthepoolmass(Friedlingsteinetal.,1999). Inthisstudyweinvestigatedhowtouseabovegroundbiomass data,boththetotalstockandtheannualincrementforallbiomass compartments,inMDFwithaglobal-scaleprocess-basedmodel ORCHIDEE(ORganizingCarbonandHydrologyInDynamic Ecosys-tEms)(Krinneretal.,2005),versionAR5.NotethatORCHIDEE-AR5 isalsothesurfacecomponentofanEarthSystemModel(IPSL− InstitutPierreSimonLaplace)usedtomakefutureclimate predic-tions,andtheAR5versionwasusedforthelastIPCCAssessment Report (Ciaisetal.,2013).Thechallengessurroundingthe opti-mizationofaglobalLSMusingdifferenttimescalesofobservation data,asdiscussedabove,requiredspecificoptimizationstrategies tobetestedfirstatsite-level.Themainobjectivethereforeisto investigatedifferentapproachestocombinemicrometeorological insitufluxandbiomassdatawithinaMDFframework.Thestudyis conductedfortwodifferentforestsitesseparately(beechandpine forests).Inthiscontext,ourstudyaimstoinvestigatethefollowing questions:
-Q1:Whatarethechallengeslinkedtousingfluxdata,annualtotal abovegroundbiomassandabovegroundbiomassincrementdata togetherinthesameoptimizationatagivensite?
-Q2:Howdoestheassimilationofyearlybiomassincrementdata helptoconstraincarbonallocationparametersinaprocess-based modelcomparedtojustusingfluxdata?
-Q3:Whatdowegainwhenweaddoptimizationofresidencetime (turnoverrate)withtotalabovegroundbiomassdataafter opti-mizationoffastcarbonprocesseswithfluxesandaboveground biomassincrement?
Firstwestudythebenefitsofincludingabovegroundbiomass incrementintheoptimizationwiththefluxdataandthenstudy thefeasibilityofoptimizingwithtotalbiomassinasecondstep(i.e. whereeachdatastreamisassimilatedseparately).Inthisapproach thefirststepisdedicatedtooptimizingthefastprocessesthat cor-respondtoalargenumberofrelevantparameters,andthesecond steptooptimizingtheslowprocessesassociatedwithasmaller numberofparameterswhilekeepingtheparametervaluesforthe fastprocessesthatwereinferredinthefirststep.
2. Materialsandmethods
OurstudysitesincludetheHessebeechforestandtheLeBray maritimepineforest,bothofwhicharelocatedinFrance.The opti-mizationwasperformedatbothsitesseparately.Wealsocompared theoptimizedmodelresultsatHessetoanotherdatasetatthesite (Granieretal.,2008)andperformedafuturescenarioruntoassess theimpactthatoptimizedparametervalueswillhaveonthefuture deterministictrajectoryofcarbonstorageatthetwoforests(and theirassociateduncertainties).
2.1. Sitedescriptionsandmeasurements 2.1.1. Broadleafdeciduous“Hesse”
Hesseisabeech(Fagussylvatica)forestlocatedinthe temper-ateregionofnortheasternFrance(48◦40N,7◦05E,300ma.s.l.).The meanannualrainfallatthesiteis820mmandannualmean tem-peratureis9.2◦C(Granieretal.,2000).Theforestwas40yearsold (±5years)onaveragein2005(Granieretal.,2008)andthuswas plantedaround1965.TheHesseforestisayounggrowthforest, withthinningstakingplaceevery5–6years.Thinningsweredone attheendof1995,inMarch2002andattheendof2005;about 25%ofthebasalareawasremovedeachtime(Granieretal.,2008). Thevalueofleafareaindex(LAI) haschangedbetween4.6 and 7.6m2m−2,withasharpdeclineoccurringaftereachthinninghad takenplacefollowedbyarapidrecoveryinjustafewyears(Granier etal.,2008).Thesoiltypeisluvisol/stagnicluvisol(Granieretal., 2000).
Siteleveldata(finerootandleafproduction,autotrophic res-pirationandnetprimaryproduction,NPP)fromstudybyGranier etal.(2008)wasusedforcomparisonwiththeoptimizedmodel resultsfor years 1995–2005.Theobservedfineroot production wasestimatedfromallometricrelationshipsandtheleaf produc-tionfromlittertrapmeasurements.Autotrophicrespirationwas measuredusingthechambermethod.NPPisdefinedasGPPminus theautotrophicrespiration;thusit isthenetamountofcarbon assimilatedduringphotosynthesisthatisavailabletotheplants aftergrowthandmaintenancerespiration.WeusedtheNPP esti-matedbasedonmicrometeorologicalfluxmeasurementswiththe estimateforautotrophicrespirationfromchambermeasurements. 2.1.2. Needleleafevergreen“LeBray”
LeBray is a maritime pine (Pinus pinaster) forestlocated in SouthernFrance(44◦43N,0◦46W,300ma.s.l.)thatwasplantedin 1970.Theannualrainfallis972mm(Jaroszetal.,2008)andannual meantemperatureis12.9◦C(Medlynetal.,2002).Astormin1999 killedsometreesandin2005somethinningwasperformedatthe site.TheLAIrangesfrom2.6m2m−2inlatewinterto3.1m2m−2in
earlyautumn(Berbigieretal.,2001).Theclimatehasstrong intra-seasonalvariability,withhighprecipitationduringwinteranddry periodsduringsummerwhensoildroughtoftenoccurs(Ogéeetal., 2003),buttheforestisabletophotosynthesizeyearrounddueto relativelymildclimateandlackoflimitingfactors.Thesoiltypeis asandyandhydromorphicpodsol(Berbigieretal.,2001). 2.1.3. Measurementsatthesites
EcosystemscalenetCO2,waterandenergyfluxmeasurements usingtheeddycovariancetechniquestartedatbothsitesin1996. ThedataconsistofnetCO2andETfluxesandmeteorologicaldata thatareprocessedasdescribedinAubinetetal.(2000),Reichstein etal.(2005)andPapaleetal.(2006).Themeasurednetecosystem CO2flux,NetEcosystemExchange(NEE),isacombinationoftwo fluxeswithoppositesigns,thetotalecosystemrespiration(TER) andgrossprimaryproduction(GPP).Theflux-partitioningmethod ofReichsteinetal.(2005)separatesNEEusingnight-time obser-vationsand ashort-termtemperatureresponsefunctionforthe respiration,andthereforeprovidesGPPandTERfromNEE measure-ments.InthisstudyweusetheGPPandTER,andnottheNEE,data togetherwithET(andbiomass−seebelow)intheoptimization.
AtHessethestand-scalebiomasswasestimatedfrom circum-ferencemeasurementsusingallometricrelationshipsestablished atthesite(Groteetal.,2011).Biomasswasestimatedusing allomet-ricequationsandcircumferencemeasurementseachyearbetween 1995and 2005,once a year in regular years and twicea year whenthinningstookplace(Granieretal.,2008).Similarbiomass measurementsweremadeatLeBrayforeachyearfrom1996to 2007,followingtheallometricrelationshipsdevelopedforthesite (Portéetal.,2002).Theannualabovegroundbiomassincrement (AGBinc)estimateisbasedonlyonthemeasurednatural circum-ferencegrowthandnaturalmortalityoftheforestandtherefore followsapositivetrend,whereasthetotalabovegroundbiomass (AGBtot)takesthebiomassremovedfromthesiteintoaccount, andthusunderthisdefinition,thevaluesfluctuatefromyearto year(i.e.,oneyearcanbelowerthanthepreviousyear).Thereis nosignificantnaturalmortalityinthesetwoforests.
2.2. Modeldescription 2.2.1. TheORCHIDEEmodel
Weusetheecosystem modelORCHIDEE,versionAR5.Itis a process-basedmodeldescribingtheexchangeofcarbon,waterand energybetweentheatmosphereandvegetationaswellascarbon andwaterpooldynamics(Krinneretal.,2005).Themodelhas pri-marilybeendevelopedtorunatglobalscalecoupledwithaclimate model,butinthisstudyonlysitelevelrunswereperformed,with fixedvegetationandclimaticforcingmeasuredatthesite.
InORCHIDEEthevegetationisdiscretizedintoPlantFunctional Types(PFTs)sothatthebeechforestshaveparametervalues com-montothedeciduoustemperateforestPFTandthemaritimepine forestfollowsthesameequationsbutwithdifferentparameter val-uesthatapplyforthetemperateconiferousforestPFTformostofthe processes.ThetwoPFTsdifferintheirparametervaluesandthe equationsthatdefinetheirphenology.
ThefastprocessesinORCHIDEEarecalculatedatahalf-hourly timestepincludingtheassimilationandtherespirationofcarbon, thehydrologyandtheenergycycles.Thephotosynthesisisbased onthemechanicaldescriptionofFarquharetal.(1980)withthe sto-matalconductancefollowingtheBall-Woodrow-Berrymodel(Ball etal.,1987).Theautotrophicrespirationconsistsofgrowthand maintenancerespiration.Themaintenancerespirationisafunction oftemperatureandbiomass,whereasthegrowthrespirationisa prescribedfractionoftheassimilatedcarbon.Theassimilated car-bonisallocatedintodifferentbiomasscompartments(seebelow) atadailytimestep.Theheterotrophicrespirationoriginatesfrom
litterpoolslocatedabove-andbelowgroundandthreesoilcarbon pools,asisdescribedinPartonetal.(1988).Sixlitterpoolsexistin ORCHIDEE:structural,metabolicalandwoodylitter;allhaveabove andbelowgroundcompartments(ZaehleandFriend,2010).The modelequationsaredescribedinseveralpapersandforthe car-boncyclewerecommendKrinneretal.(2005),withanupdatein Santarenetal.(2014).AppendixAprovidestheequationsofthefast processesthatareoptimizedinthiswork,whilethenextsection andAppendixBgivesaspecificdescriptionofthecarbonallocation schemethatiscrucialforthisstudyinmoredetail.
2.2.2. Biomasspoolsandcarbonallocation
Aschematicshowingthedifferentpoolsandtheparametersthat determinethedivisionofNPPintheORCHIDEEmodelisshown inFig.1.Thebiomassofvegetationisdividedintoeightdifferent compartmentsinORCHIDEEandtheseincludeabove-and below-groundsapwoodandheartwood(fourcompartmentsaltogether), leaves,fineroots,fruitsandcarbohydratereserve.Thefruit com-partmentincludesplantpartswithreproductivefunctions,suchas flowersandfruits.Thecarbohydratereserveenablesthe produc-tionofleavesatleafonset;thiscompartmentisonlypresentfor deciduousPFTs.Apartofthesapwoodisturnedintoheartwoodby aconstantturnoverrate.Theseparationofbiomassbetween heart-andsapwooddoesnotinfluencetheautotrophicrespirationrates. TheallocationofassimilatedcarboninORCHIDEEisbasedon Friedlingsteinetal.(1999),andassumesoptimaluseofresources dependingontheenvironmentalconditions.Carbonisallocated tosapwood,finerootsorleaves,aftermaintenancerespirationis subtractedfromGPP.Iftheplantislightlimited,itallocates car-bontosapwood.Ifthereissoilmoisturelimitation,morecarbon isallocatedtofineroots.Theequationsgoverningtheallocation areshowninAppendixB.Therearetwoparameterscontrolling theallocationtofinerootsandsapwood,r0 ands0,respectively. Thesetwoparameterswereoptimizedinthisstudy(seeSection 2.5.2).Sapwoodisfurthersplitintoaboveandbelowground com-partments,accordingtotheageoftheforest.Thisseparation is determinedbytheequation
Fabove=Sinit+0.6∗(1−exp(-Age/dalloc)) (1) whereFaboveisthepartoftheNPPallocatedtosapwoodthatwillbe locatedtoAGBcompartments,Sinitthefractionofsapwood alloca-tionabovegroundatAge=0,Ageistheageoftheforest(inyears)and dallocisatimeconstantthatdefinestheinertiaoftheage-dependent allocationofsapwoodtoAGB.TheparametersSinitanddallocwere optimized.Inadditiontothesefourallocationparameters,thejoint turnoverrateofallbiomasscompartments(i.e.theresidencetime Tres)wasalsooptimized.Tresisusedtodefinebiomasslosstolitter inORCHIDEE.TheinverseofTresdefinesaconstantmortalityrate giventhatthemodelledbiomassremovalinORCHIDEEassumesa firstorderkinetics(Krinneretal.,2005).Nodisturbancessuchas fire,drought,insectattacks,thinningthatwouldleadtoanabrupt decreaseofforestbiomass(orincreaseinmortality)aredescribed intheAR5versionofthemodel.Thefiveparametersrelatedtothe dynamicsofbiomassareshownwiththeirpriorvaluesinTable1.
2.2.2.1. New LAI scheme. In a more recent forest module of ORCHIDEE,thedevelopmentofLAIwassloweddownforyoung forests(Bellassenetal.,2010).Inspiredbythismethod,wetested adelayingofthedevelopmentofLAIinyoungforests,whichwe hereafterrefertoasthe“newLAIscheme”.Fortemperateforests thedelaywasimposedoverthefirst15years.Intheseyearsthe maximumpossibleLAI(LAImaxact)wasthedefaultmaximumLAI
(LAImax)decreasedbythesquarerootoftheage(tage)dividedby thetimeusedforthedelay(tlailimit):
LAImax act=
tage tlailimit·
LAImax (2)
Wetestedthisschemeaspartofthisstudygivenitsrelevance forsimulatingabovegroundbiomass.
2.3. Modeldatafusion(MDF)method
Weappliedastatisticaloptimization,referredtoasMDF,ofthe modelparametersusingthedatadescribedinSection2.1.3inwhich allsourcesofuncertaintiesaretakenintoaccount:measurement errors,modelstructuralerrorsandparametererrors.
TheMDFmethodusesa Bayesianformulation, whichallows priorinformationabouttheselectedparameters(seeSection2.5.1) tobeupdatedbasedonnewinformation(observations)(Tarantola, 2005).WeassumedGaussianerrorswithtruncatedPDFsforthe parametererrorsinordertoaccountforphysicalbounds(see Sec-tion2.5.1).Theoptimizationfollowstheminimizationof acost functionthatmeasuresthemisfitbetweentheobservationsandthe correspondingmodelvariablesaswellasbetweentheestimated parametersandapriorivalues:
J (x)=
i 1 2 1 Ni (Y−Mi(x))tR−1(Yi−Mi(x)) +(x−xb)tP−1b (x−xb) , (3)whereistandsfordifferentdatastreams,xistheparameter vec-tor,Yistheobservation,Niisthenumberofobservationsofeach datastream,Mi(x)isthemodeloutputandxbisthevectorwitha
prioriparametervalues.RandPbaretheerrorcovariancematrices fortheprioruncertaintiesonobservationsandparameters, respec-tively.Asinmoststudies,bothofthesematricesareassumedtobe diagonal,giventhedifficultiesinproperlydefiningcross-parameter orcross-observationerrorcovariances.Forthe micrometeorolog-icalfluxdata,dailymeanvalues wereusedintheoptimization, thuscircumventingacomplicatedtreatmentoftheuncertainties forthehalfhourlydata,whichstudieshaveshownhavea Lapla-ciandistribution(Hollinger andRichardson,2005;Lasslopetal., 2008).ThisapproachfollowsRichardsonetal.(2010),whoassumed that random errors in half-hourly eddy covariance data would beapproximatelynormalwhenintegratedoveraday.Dailyflux observationswereused,withafurthersmoothing(15-day run-ningaverage)applied.Thisallowsustofocustheoptimizationon timescalesrangingfromapproximatelybi-weeklytoseasonaland inter-annualvariability.
FollowingthestudyofSantarenetal.(2014)(whoalsousedthe ORCHIDEEmodel),weusedanimplementationofthegenetic algo-rithm(GA)(Goldberg,1989),whichisa“globalsearch”method,to performtheinversions.ThisMonteCarlotypeofapproachproved tobemoreefficientthanagradientbasedmethodtofindtheglobal minimumofJandlesspronetogettingtrappedinlocalminima(see Santarenetal.,2014formoredetails).TheGAusestheprinciples ofthegeneticsandnaturalselectiontoperformastochasticsearch overthewholeparameterspace(Goldberg,1989;HauptandHaupt, 2004),andfollowingGaussiantruncatedPDFs.Inourset-upa pop-ulationof30chromosomeswasusedwith40–100iterations,andat eachiteration80%ofthenewchromosomeswerecreatedby “mat-ing”,therestby“mutations”.Thisset-upwasdeterminedinthe Santarenetal.(2014)studywhichtestedmultipleconfigurations anddecidedonthebestbasedontheconvergenceofthesystem (i.e.thepointafterwhichcostfunctiondoesnotchangeandthe minimumhasbeenreached).Theconvergenceofthecostfunction wasvisuallycheckedandconfirmedwithinthe40–100iterations.
Fig.1. DistributionofNPPintothedifferentbiomasspoolsofORCHIDEE.NexttothearrowitiswrittenwhichparametersinfluencetheamountofNPPtransportedtothe respectivepool.Thegrayboxindottedlinesurroundsthebiomasspoolsthatareaffectedbytheresidencetime.
Table1
Optimizedparameters.ThepriorvalueisgivenfirstforHesseandthentoLeBray,ifthevalueisdifferent.
Parameter Description Units Priorvalue Parameterset
Photosynthesis
Vc(max) Maximumcarboxylationrate molm−2s−1 55.0/35.0 P1
GS,slope Slopeinthestomatalconductanceequation(Ball-Berry) – 9.0 P1
cT,opt Offsetforoptimalphotosynthesistemperaturerelationship ◦C 26.0/25.0 P1
cT,min Offsetforminimalphotosynthesistemperaturerelationship ◦C −2.0/−4.0 P1
cT,max Offsetformaximumphotosynthesistemperaturerelationship ◦C 38.0 P1
SLA Specificleafarea(LAIperdrymattercontent) gm−2 0.026/0.00926 P1
LAIMAX MaximumLAI m2m−2 5.0 P1
Klai,happy LAIthresholdtostopusingcarbohydrates – 0.5 P1
Fstress Limittophotosynthesisfromsoilwaterstress – 6.0 P1
Phenology
Kpheno,crit Multiplicativefactorforgrowingseasonstartthreshold – 1.0 P1
cT,senescence Offsetfortemperaturethresholdforsenescence ◦C 12.0 P1
Lage,crit Averagecriticalageforleaves days 180/910 P1
leafinit Timetoattaintheinitialfoliageusingcarbohydratereserve days 10 P1
Soilwateravailability
Humcste Rootprofile – 0.8/1.0 P1
Respiration
Q10 Temperaturedependenceofheterotrophicrespiration – 1.99 P1
KsoilC Multiplicativefactorofinitialcarbonpools – 1.0 P1
HRH,a First-degreecoefficientofthemoisturecontrolofheterotrophicrespiration – −1.1 P1
HRH,b First-degreecoefficientofthemoisturecontrolofheterotrophicrespiration – 2.4 P1
HRH,c Offsetofthefunctionformoisturecontrolfactorofheterotrophicrespiration – −0.29 P1
HRH,min Minimumvalueofthefunctionformoisturecontrolfactorofheterotrophic
respiration
– 0.25 P1
MRa Slopeoftherelationshipbetweentemperatureandautotrophicrespiration – 0.16 P1
MRb Offsetoftherelationshipbetweentemperatureandautotrophicrespiration – 1.0 P1
GRfrac Fractionofbiomassavailableforgrowthrespiration – 0.28 P1
Zdecomp Scalingdepthdeterminingeffectofsoilwateronlitterdecomposition – 0.2 P1
Hcritlitter Scalingdepthdeterminingthelitterhumidity – 0.08 P1
Energybalance
Z0overheight Roughnesslength m 0.0625 P1
Kalbedo,veg Multiplyingfactorforsurfacealbedo – 1.0 P1
Allocation
r0 Controllingallocationtofinerootswithlightandbelowgroundlimitations(Eq.
(B1))
– 0.3 P2
s0 Controllingallocationtosapwoodwithlightandbelowgroundlimitations(Eq. (B2))
– 0.3 P2
Sinit InitialallocationofsapwoodabovegroundatAge=0(Eq.(1)) – 0.2 P2
dalloc Timeconstantforabovegroundsapwoodallocationdefiningtheinertiaof
age-dependentallocationofsapwoodtoabovegroundbiomass(Eq.(1))
year 5 P2
Afterreachingtheminimumofthecostfunction,afirstorder measureoftheparameteruncertaintiesanderrorcorrelationscan besimplyderivedbyassuminglinearityofthemodelaroundthe estimated parameters and Gaussian errors. The posterior error covariancematrixPa iscalculatedfromthepriorerrormatrices andtheJacobianofthemodel(i.e.,H∞,thederivativeofallmodel outputswithrespecttoparametersattheminimumofthecost function)(Tarantola,2005),asinthefollowingequation:
Pa=
Ht∞R−1H∞+P−1b
−1. (4) ValuableinformationcanbederivedfromPa,suchashowmuch constraintcanbebroughtbythedataoneachparameter (diago-nalofPa),andthelevelofaposterioricorrelationsbetweenthe parameters(non-diagonaltermsthatappearaftertheoptimization, indicating forinstanceequifinalityof parameters).TheJacobian (H∞)is calculated withthe finite differencemethod.However, giventhattheparameterpriorerrorsarenotGaussianbut trun-catedGaussianPDFs,theposteriorPDFsarealsotruncatedandthe estimateduncertainties(i.e.,the1-sigmainterval)willrepresenta largerintervalthatthestandardGaussian68.27%.Theyshouldbe usedasafirstorderapproximationtoevaluatetherelative con-straintbroughtbytheobservationsonthedifferentparameters.Theobservationerrorthatshouldaccountforbothmodeland measurementerrorswasdefinedastheRMSEbetweenthe obser-vationsand themodel simulationsusingtheaprioriparameter values(Kuppeletal.,2012).Thisshouldincludeforexamplethe uncertaintiesrelatedtopartitioningthenetCO2fluxintoits compo-nentfluxes(GPPandTER).Micrometeorologicalfluxmeasurements includebothrandom(e.g.turbulencesamplingerrorand instru-menterror)andsystematicerrors(e.g.instrumentcalibrationand designanddataprocessing)(Lasslopetal.,2010;Richardsonetal., 2012).Estimationofbiomassatstandlevelissubjecttoerrorsfrom samplingand measurementaggregationfromindividuals tothe standscale(Wutzleretal.,2008)aswellaserrors inallometric equations.
Forthebiomassobservationsonlyannualvalueswereavailable. Thereforethereisanimbalanceinthenumberofobservationsthat wereavailableforthedifferentdatastreams.Aproper account-ingofallerrorcorrelationsinRwouldbethemostrigorousway toaddressthisissue.Giventhatwewerenotabletocharacterize theseoffdiagonalterms,theimbalancewaspartlycompensated forbydividingeachtermofthecostfunctionbythenumberof observations(divisionbyNiinEq.(3))toavoidasituationwhere theoptimizationsolutionisdominatedbytheassimilationof data-streamswithdensersampling.Thisweightingapproachremoves possiblealiasingofbiasesinrichdatastreams ontoparameters relatedtosparsedatastreams(WutzlerandCarvalhais,2014),and thuslikelydecreasestheoverallimpactofmodelandobservation biases.However,sincetheweightingisremovingsomeofthe cer-taintywehaveintherichdatastreams,theposteriorerroronthe parametersconstrainedbytherichdatastreamsislikely overesti-mated(WutzlerandCarvalhais,2014).
2.4. Optimizationprotocol 2.4.1. Optimizedparameters
Weselectedparametersbasedonapreliminarysensitivity anal-ysisandexpertevaluationofthephysicalequationscontrollingthe uptake,allocationandreleaseofcarboninORCHIDEE(seeKuppel etal.,2012).SinceLeBrayisaconiferousforestafewparameters related toonlydeciduousleafphenology wereleftout. In con-trasttopreviousstudiesdedicatedtotheoptimizationofORCHIDEE parameters(seethelistofstudiesunder:https://orchidas.lsce.ipsl. fr/results.php),weincludedfiveadditionalparametersrelatedto theallocationofcarboninthedifferentreservoirsbecauseinthis
studyweareassimilatingbiomassdata,asdescribedabove.The apriorirangeofallparameterswasbasedonexpertknowledge and thea prioriuncertainty foreach parameterwassetto40% ofthatrange withfurtherconstraintprovidedbydefined phys-icalboundaries (shownintheSupplementary materialin Table A1).TheparametersandtheirapriorivaluesareshowninTable1 andtheequationsusingtheseparametersaregiveninAppendixA. ParametersetP1inTable1consistsofparametersrelatedtocarbon andenergyfluxesandparametersetP2includesthefour param-etersrelatedtoallocation.ParametersetP3consistsofonlyone parameter,thelivingbiomasscarbonresidencetime.
2.4.2. Simulationsandoptimizationsperformed
Weadoptedthefollowingapproachforthemodelsimulations andoptimizations,inordertoinvestigatethedifferentobjectives ofourstudy:
2.4.2.1. Forwardsimulations. Threedifferentprotocolswereused for theforward simulationsin order toexamine thedifference betweenforestinsteadystateoraforestgrowntobeitsrealistic age.
a.“SS”:Spin-upofdifferentcarbonpoolsizesfollowedbya tran-sientsimulationoverperiods2001–2004(Hesse)and2001–2005 (LeBray)withtheforestat“equilibrium”(i.e.,aforestinsteady statewhoseagedoesnotmatchthatofthesite)
b.“RA”:Spin-upofthedifferentcarbonpoolsizesfollowedbya clear-cutoftheforestandasimilartransientsimulationtomatch therealageoftheforestduringtheperiodofmeasurements. c.“RALAI”:Similarto“RA”withLAIdescribedasafunctionofage
(Eq.(2))−i.e.thenewLAIscheme.
Thespin-upisperformedbycyclingofthepresentdayclimateto accumulateenoughsoilcarbonsothatthenet(decadal-scale) car-bonfluxbetweenecosystemandtheatmosphereisclosetozero.In ordertosimulatetherealageoftheforest,biomasspoolswereall resettozero,i.e.thebiomasswasremovedfromthesystem,after thespin-upandpartlytransferredtothewoodylitterpool, follow-ingtheproceduredevelopedbyBellassenetal.(2010).Theforest wasthenallowedtogrowtoitstrueagedrivenbythe meteorolog-icalforcingavailableateachsite.Thedifferentmodelsimulations performedinthisstudyaresummarizedinTable2.
2.4.2.2. Optimizationscenarios. Intheoptimizations,however,only theforestwiththerealisticagewasused.Giventhelackof repre-sentationofforestmanagement andnaturaldisturbancesinthe modelitwasachallengetouseAGBtotdirectlyinthe optimiza-tions.Intermsofbiomass-relatedobservations,measurementsof AGBincmorecloselymatchwhatORCHIDEEcurrentlysimulates andthereforeweusedthesedataasastartingpointinour opti-mization.However,thisisonlyafirststepandourfinalaimistobe abletoassimilatethetotalbiomassstockandnottheincrement.
Wedecidedtosplittheoptimizationprocessintotwosteps,the firststepusingthestandarddatastreamset(fluxdataandAGBinc, theannualincrementofabovegroundbiomass)tooptimizethefast processesandallocationinthemodel(“Step1”).Thetwoforests are mono-aged standswithoutnatural regeneration by recruit-ment.Theslowprocessofmortalityisthenoptimizedinasecond step(“Step2”)byadjustingtheresidencetimeparameterTres.In ordertooptimizeTresthesimulationperiodneedstocorrespondto theactualforestagesinceplantingaftertheclearcut,asopposed tojustthemeasurementtimeperiod,sothatthemeasuredtotal biomassvaluecanbecomparedtothemodeledone.Thisincreases thecomputing timeof theoptimizationproceduresignificantly (i.e.byseveraldays),whichhamperstheuseofasimultaneous approachwithallparametersoptimizedatonceincludingalldata
Table2
Theshortnamesanddescriptionsofthedifferentsimulationrunsandoptimizations.
Nameoftherun Description
Initializations
SS Forestisinsteadystate.
RA Clearcutissimulatedfortheforestaftersteadystateandthenitissimulatedtobeinitsrealage.
RALAI LikeRAwiththenewLAIscheme(Eq.(2))included.
Optimizations
REFprior Thereferencerunbeforeoptimization.
REFpost ThereferencerunwithdatastreamsGPP,TER,ETandAGBinc,afteroptimizationusingparametersetsP1andP2. T1 1 Optimizationdonewithpartitionedfluxes,GPP,TERandETandparametersetP1.
T1 2 OptimizationdonewithAGBinc,usingparametersetP2.
T2 OptimizationdonewithAGBtot,usingparametersetP3.
streams.Theadvantageofsuchastepwiseapproachisthatwecan useashortsimulationperiodfortheStep1optimizationinorder tooptimizemany(over20)parametersforthe“fast”processesand allocation,andthentherequiredlongersimulationtooptimizejust Tresinstep2.OptimizingwiththetotalbiomassinStep2willlikely nothaveastrongfeedbackonthe“fastparameter”values (hav-ingonlyinfluenceonthemagnitudeoftheautotrophicrespiration whichdependsonbiomass)andthereforethereisnostrongneed tofurtheriterateafterStep2.
InStep1wealsoperformeddifferenttestcasesbychanging thenumberofdatastreamsassimilated,aswellasthenumberof parameters.Thisprovidedinsightabouttheimportanceandrole ofthedifferentdatastreams/parametersinordertoanswerthe questionsposedin theintroductionsection,e.g.how muchthe informationcontentofbiomassdataaddstotheoptimization(see Tables2and3).Aftereachoptimizationwecomparethepriorand optimizedmodelperformanceandevaluatetheimpactofthe dif-ferentdatastreamsontheposteriorparameters.
ThedifferentoptimizationsperformedinStep1andStep2are summarizedinTable3.Additionallywemadefutureclimate simu-lationswiththeoriginalparametersetandtheonesobtainedfrom theoptimization.Thesesimulationsandtheirresultsaredescribed inSupplementaryMaterial,sectionB.
3. Resultsanddiscussion
3.1. Steadystateversusrealageforestbiomassinforward simulations
Abovegroundbiomass(AGBtot)simulatedwiththesteadystate assumption(SS)(Section2.5.2.1a)washighlyoverestimatedfor bothHesseandLeBray,whichwere36and31yearsoldin2001, respectively(seeFig.2).TheORCHIDEEsimulationswiththe stan-dardparametersoverestimatedAGBtotatHesseby223.6%andby 136.1%atLeBrayovertheperiod1997–2005.Whensimulatingthe realforestage(RA)(Section2.5.21b)thesimulatedbiomasswas significantlylower,andtheagreementwithdatawasimproved. AfterthischangetheAGBtotremainedoverestimatedby65.0%at Hessehoweverandunderestimatedby11.9%atLeBray.
TheoverestimationofsimulatedabovegroundbiomassatHesse was caused by several factors. Disturbances that resulted in decreasesinthebiomass,suchasthinnings(whichtookplaceat Hessein1999and2005,Fig.2a)havenotbeentakenintoaccount inthecurrentversionofthemodel.
Asecondfactorcontributingtothelargediscrepancyinthe mod-elledbiomasswasrelatedtothefactthattheORCHIDEEAR5model doesnotdescribetheearlystagesoftheforestgrowthin realis-ticway.WhenthenewLAIschemewasused(“RALAI”run)the positivebiasofAGBtotwasreducedtoonly11.3%fortheHesse forest.However,forLeBraythefittotheAGBtotobservationwas degradedwiththe“RALAI”simulation,increasingthe underesti-mationofAGBtotto24.8%,whichindicatedthatthecarboninput totheabovegroundwoodybiomassistoolow.Followingthisinitial evaluationwedecidedtousethenewLAIschemeforHesseonly.
ThesuccessofthenewLAIschemeatHessebutnotatLeBray bringsoutanotherissuerelatedtolarge-scalemodelling.Thenew LAIschemehasbeenparameterizedusingpermanentmonitoring plots,yieldtablesandFrenchinventorydata,buteventhoughitis verysuccessfulforsomeforestecosystemsinFrance,thebiomass isunderestimatedforconiferousforestsin southwesternFrance withoutoptimization(Bellassenetal.,2011).Themaritimepineat LeBrayisafastgrowingspeciesandtheproposedgeneric depen-denceofmaximumLAIonforestage(Eq.(2))isprobablynotwell adapted.Toovercometheseissues,wecouldincreasethenumber ofspeciesinthemodelwithspecificLAIdependenceequations, insteadofrelyingongenericPFTclassifications,ormovetoward theuseofamoregenericcarbonallocationschemethatdoesnot requiretheprescriptionofamaximumLAI(ORCHIDEE-CANrecent versiondescribedinNaudtsetal.,2015).
3.2. Optimizationwitheddycovariancefluxesandbiomass increment
3.2.1. ResultsfromtheoptimizationofGPP,TER,ETandAGBinc (REF)
3.2.1.1. Hesse. DailyGPP,TERand ET measurementswereused in the REF optimization, the Step 1 optimization, simultane-ouslywithannualabovegroundbiomassincrementatHessefor years 2001–2004.Theresultsare shown in Fig.3.There wasa Table3
Theabbreviationsfordifferenttestrunswithuseddatastreams,optimizedparametersetsandmotivationforeachtest.
Test Useddatastreams Optimizedparameters Motivation
REF GPP,TER,ET,AGBinc P1,P2 Thereferenceoptimizationwithpartitionedfluxesandbiomassincrement.Theinversion
makesuseofmaximumavailableinformationondailytointer-annualtime-scaleprocesses.
T11 GPP,TER,ET P1 ToassesstheroleoftheAGBincbycomparingtoREF.P2parameterswerenotincludedas
theirinfluenceonthethreefluxesisratherweak.
T12 AGBinc P2 Toassesshowwellthebiomassdataalonecanconstraintheallocationrelatedparameters.
T2 AGBtot P3 Optimizationinasecondstepusingtheoptimizedparametersfromthe“REF”optimization.
TheaimistodemonstratehowtobestusetheAGBtotdataintheoptimizationin combinationwithotherdata.
Fig.2. ThemeasuredabovegroundbiomassatHesseandLeBrayin1997–2005displayedinblackbars,thesimulatedabovegroundbiomassatsteadystate(SS)inblueand thesimulatedabovegroundbiomassinrealisticage(RA)inred.IncyanisshownthesimulatedabovegroundbiomassusingthenewLAIscheme(RALAI).
Fig.3.Themicrometeorologicalfluxes(GPP,TERandET)andannualabovegroundbiomassincrementsatHessein2001–2004.The15-dayrunningaveragesofthefluxdaily valuesareshown.Themeasurementsareshowninblack,apriorisimulationresultasblueandaposterioriinred.TheRMSEvaluebetweensimulationandobservationis showninparenthesis.
Table4
RMSEvaluesandbiases(inparenthesis)fordifferentobservationsbetweenvariousoptimizationsatHesseandLeBray.
GPP[gCm−2day−1] TER[gCm−2day−1] ET[Wm−2] AGBinc[gCm−2]
Hesse Prior 2.74(1.0) 2.51(1.7) 31.40(17) 171.3(−149) REFpost 1.64(−0.28) 1.08(0.13) 16.53(7.7) 108.2(−44) T11 1.76(−0.49) 1.03(0.07) 12.76(2.8) 193.7(−172) T12 2.64(0.90) 2.18(1.40) 30.59(16.7) 87.1(15) LeBray Prior 1.72(−0.31) 1.47(1.01) 19.10(−4.4) 51.3(−49) REF post 1.65(0.08) 1.01(−0.02) 15.72(−2.1) 15.8(6) T1 1 1.63(−0.03) 1.04(0.04) 15.83(−1.3) 73.7(71) T12 1.77(−0.44) 1.31(0.80) 19.43(−4.9) 11.9(−5)
RMSEvaluesbetweenobservationsandmodelestimatesbetweenyears2001–2004atHesse,2001–2005atLeBray.Thetimeperiod2001–2004wasusedintheoptimizations atHesse,and2001–2005atLeBray.ThepriorvaluesarethedefaultvaluesinORCHIDEbeforeoptimization.Thereferenceoptimizationreferstooptimizationusing simultaneouslyGPP,TER,ETandAGB inc.ThelasttwolinesrefertooptimizationswhereonlyGPP+TER+ET,orAGBincwereused,respectively(seeTable3).Theunitsfor eachvariableareshowninbrackets.
considerablereductionintheRMSEbetweenthemodelandthe observationsforallfourdatastreamsaftertheoptimization(see Table4,columns‘REFprior’and‘REFpost’).
AtHessetherewasadroughtduringspringandsummer2003 andspring2004(124and100dayswithsoilwaterdeficit, respec-tively;Granieretal.,2008)comparedto2001and2002(23and zerodayswithsoilwaterdeficit),whichwereconsidered“normal” years.Thisinter-annualvariabilityaffectedtheobservedcarbon andwaterexchangesbetweenthevegetationandatmosphereat thesite (Granieretal.,2008),withGPPandTERbeingstrongly correlatedwithsoilwater contentandeven prematureleaffall reportedin2003(Brédaetal.,2006).TheapriorisimulatedGPP didnotreplicatetheobserveddecreaseinuptakebythevegetation duringthetwodryyears,andtheannualmeanGPPwas overes-timatedby41.9%insteadofby6.6%onlyin2001–2002(Fig.3a). TheaposteriorisimulatedGPPwasabletocapturethedecreased uptakecausedbydrought,yetwitharesidualoverestimationof theannualmeanoptimizedGPPof14.3%and10.2%for2003and 2004,respectively.However,aftertheoptimizationcarbonuptake inyear2002becameunderestimated(by23.3%),whereas thea prioricarbonuptakewasaccurate(i.e.,1.7%fromobserved).The MDFdidnotalter theseasonal dynamicsof thesimulatedGPP greatly,butdiminishedtheCO2 uptakein autumn,anyhownot leadingtounderestimatesintheposterioriresults.Thesimulated GPPalsoshowedaslightlymoreabrupt increasethanobserved duringspring.Forbeechforests,aftertheleafexpansion,thereisa gradualincreaseofphotosyntheticcapacityintheleaves,andthis isnotincludedinthemodel.
TheapriorisimulatedannualmeanTERwasoverestimatedby 54.5%(Fig.3b).AlthoughthesimulatedTERreachedtheobserved magnitudeafteroptimization(within0.2%forallfouryears),the optimizedmodelresultsdidnotfullyreplicatethemagnitudeof theobserveddecline in respirationcaused bythedrought.Yet, theoverestimationofTERfor 2003–2004was92.6%beforethe optimizationandwasreduced to23.4%afteroptimization.This moderateinabilityofthemodeltocaptureTERreductionindry periods,evenafteroptimization,mayindicatelimitsofthe formu-lationofdroughtresponseofthedecompositionprocessesinthe soilinORCHIDEE,orlimitsofthelineardependenceofautotrophic respirationtoGPP.However,thereisuncertaintyintheTER esti-mateinthefluxseparation(Rajetal.,2016),anditisnotknown howwelltheseparationmethodworksduringdroughtconditions, andthereforetheperformanceoftheoptimizedmodelmightbe moresatisfactorythanrevealedinFig.3b.
Theapriorisimulatedevapotranspirationwasoverestimatedin allcases,withthesummertime(June-August)averageET over-estimated by 52.5% and a RMSE of 31.4Wm−2 (Fig. 3c). After optimization,thisoverestimateandtheRMSEdroppedto19.6%and
16.5Wm−2,respectively,thusimprovingthemagnitudeoftheET. ThedeclineintheobservedETmagnitudeduringthedrysummers wasreproducedintheMDFresults,butthetemporaldynamicsof thedroughtresponsewerenotwellcaptured.Thisislikely con-nectedtothefactthatthemodelismissingaprocessrepresenting increasedsoil–rootresistancetowaterflowwhensoilwater poten-tialisveryloworamismatchbetweensimulatedandrealsoilwater contents.AnewerversionofORCHIDEEhasincludedafully mech-anisticschemefortheplanthydraulicarchitecture(Naudtsetal., 2015),thusissuessuchasthiswillbeinvestigatedagaininfuture studiesusingthisversionofthemodel.
Theapriorisimulationsunderestimatedthemagnitudeofthe AGBincby 148.8gCm−2 (Fig.3d). The a priorisimulation also hadamuchlowerannualAGBincvariabilitythanobserved,with astandarddeviationof19.5gCm−2 comparedto95.1gCm−2 in theobservations.AfterMDF,theoptimizedmeanAGBincwasin betteragreementwiththeobservation, witha negative biasof 44.3gCm−2;however,wedidnotimprovethecorrelationofthe interannualvariation betweentheobservations and themodel, even thoughthestandard deviation becamecomparable tothe observations.ThemeasuredAGBincwasthehighestin2002and droppedin2003and2004,butthisbehaviorwasnotseeninthe modeledvalues.
3.2.1.2. LeBray. SimilartoHesse,theoptimizationimprovedthe modelperformancefor thefourvariables atLeBray(Fig.4and Table4).Overall,theprior modeldatafitwasbetterat LeBray thanatHesseandtheperformanceoftheoptimizedmodelinterms ofRMSEwasrelativelysimilarbetweenthetwosites.Themodel wasnotabletocapturetheinterannualdynamicsofGPPevenafter theoptimizationandthesummertimemagnitudeofGPPremained lowerthanthatoftheobservationsinyears2001,2003and2004 (Fig.4a).Beforeoptimizationthemodeloverestimatedthe aver-ageannualGPPby9.2%,whichwasreducedbytheoptimizationto 5.2%.AfterMDFthesummertimeTERlevelsmatchedthe observa-tionsbetter(theaverageannualoverestimationbeing18.5%before optimization,andonly3.5%after),butwintertimerespiration dur-ingthelasttwoyearswasstilloverestimatedbythemodel(Fig.4b). MDFdidnotchangetheETmuch(Fig.4c),withthesummertime ETbeing underestimatedbeforetheoptimization by11.5% and afterby9.7%.ThesimulatedannualAGBincatLeBraywascloser totheobservationsafterMDF;thesimulatedaveragevaluewas 49.5gCm−2higherthantheobservationsbeforetheoptimization, butthispositivebiaswasreducedtoonly6.3gCm−2 after opti-mization.However,evenaftertheoptimization,theyear-to-year variationsdidnotmatchthatoftheobservations(Fig.4d)likefor theHessesite,althoughthemagnitudeofinter-annualvariation wasclosertothatoftheobservations.Thestandarddeviationofthe
Fig.4.Themicrometeorologicalfluxes(GPP,TERandET)andannualabovegroundbiomassincrementsatLeBrayin2001–2006.The15-dayrunningaveragesoftheflux dailyvaluesareshown.Themeasurementsareshowninblack,apriorisimulationresultasblueandaposterioriinred.
observationswas21.4gCm−2.Bycomparisonthemodelsimulated anaprioristandarddeviationofonly9.0gCm−2,whichincreased to18.6gCm−2aftertheoptimization.
Theoptimizationconvergedafter40iterationsatHesseandafter 100iterationsatLeBrayofthegeneticalgorithm,implyingthatthe MDFmethodhadmoredifficultiesinfindingtheglobalminimumat LeBray.Thecostfunctionvaluesbeforeandaftertheoptimization aswellasthereduced2valuesareshowninTableC1inthe Supple-mentarymaterial.Thecostfunctionvaluesdifferbetweenthecases duetodifferentdatastreamsassimilatedanddifferentparameters optimized.Thelowerreduced2values(afteroptimization)forthe fluxdataatHessefortheREFandT11optimizationsindicatebetter modelperformancesatthissitecomparedtoLeBray(smaller mis-fit).Reversely,thesignificantlylowervaluesfortheaboveground biomassincrementsatLeBrayfortheREFandT12casesindicate thatthecarbonallocationschemebettercapturesthedynamicsof theabovegroundgrowthofthepineforestsite.
3.2.2. Trade-offsandco-benefitsofassimilatingeachdatastream 3.2.2.1. GPP+TER−+ET(“T11”). Inthistest(T11)weomittedthe AGBincfromthereferencecaseandonlyincludedtheeddy covari-ancefluxesintheoptimization,toinvestigate,bycomparisonwith thereferenceoptimization,thebenefitofassimilatingaboveground biomassincrementinadditiontothefluxesandtoseeifit modi-fiestheresultantgrosscarbonfluxes.Notsurprisingly,thelargest differencewasseenintheestimationofAGBinc,whichwasworse atbothsiteswhenthisvariablewasnotassimilatedandonlythe fastparametersareoptimized(Table4).InfactthefittoAGBinc dataafteroptimizationoffluxesresultedinanevenlargerRMSE thantheapriorivalue(Table4),thusthefluxesdegradedthefitto thedataforAGBinc.Otherwise,therewerenomajorchangesin theoptimizationperformancecomparedtotheREFcaseregarding thematchto15-dayaverageeddycovariancefluxes,exceptthea posterioriRMSEforGPPwasslightlyworsethaninthereference
caseatHesse,thereforetheadditionofAGBinc(andtheparameter setP2)alsoimprovedthefluxoptimizationinthereferencecase. 3.2.2.2. AGBinc(“T12”). Theobjectiveofthistestwastoassess thepotentialofusingonlyAGBinc,obviouslya“weak”constraint onallthe“fast”modelparameters.OptimizationofAGBincbrings informationaboutsapwoodallocation,becausealthoughAGBincis determinedbybothGPPandTERprocesses,itiscalculatedroughly asafractionofGPPminustheautotrophicrespirationandallocation tootherbiomasscompartments.Therefore,assimilatingAGBinc couldpotentiallyreinforcetheconstraintsonGPPandTER.
Asexpected,theoptimizedAGBincwasimprovedatbothsites butthetrade-offwasthatfittotheeddycovariancefluxes(that werenotincludedintheoptimization)deteriorated(Table4).With respecttomatchingobservedfluxes,thistestwasthusworsethan theT11caseortheaprioriresults.Thiswasnotsurprisingasthe AGBincdataaremoredirectlyrelatedtoprocessesthatare act-ingonanannualtimestep,andthereforedonotcontainenough informationtoconstrainthe“fast”surfacefluxesoperatingata half-hourlytoseasonaltimescales.Additionally,onlyarestrictedsetof parameterswasusedthatarecontrollingonlythecarbon alloca-tion.However,thereferencecasegavegoodRMSEforalsoAGBinc, eventhoughnotasgoodaswiththistest;itisthusbettertoinclude thefluxeswithAGBincandobtainthebestfitalsoforGPP. 3.3. Optimizationusingtotalabovegroundbiomassinasecond step(“T2”)
AsdescribedinSection2.5.2weonlyoptimizeTresusingtotal aboveground biomass in the second step. Fig. 5 compares the observed total abovegroundbiomass togetherwiththea priori simulatedbiomassandthesimulatedbiomassafterStep1(results describedinSection3.2.1)andafterStep2.Thesimulatedbiomass from the REF inversion at both sites (Step 1) showed a large
Fig.5.TheabovegroundbiomassatHesse(a)andLeBray(b).Theobservedabovegroundbiomassisshowninblack,thepriormodelestimateinblue(REFprior),themodel estimatein“Step1”(REFpost)inredandthemodelestimatein“Step2”(T2)incyan.TheRMSEvaluesbetweentheobservationandmodelestimatesareshowninparenthesis inunitskgCm−2.
discrepancywithobservedAGBtot,since theuseof AGBinc in Step1ledtoanincreaseintheannualbiomassproductionfromthe prioratbothsites.Thiswasbecausethetotalbiomassobservations showedadecreaseinsomeyearsduetodisturbanceor manage-mentwhichwasnotaccountedforinthebiomassincrement.
AfteroptimizationoftheresidencetimeinStep 2the simu-latedAGBtotwasfoundtobemuchclosertotheobservationsat Hesse,withanRMSEof0.52kgCm−2andoverestimationofjust 1.7%.Thiswasachievedasaresultofalargedecreaseinthe res-idencetimefromitsdefaultvalueof40yearsdownto16.8years (i.e.factoroftwoincreaseinmortality).Thisisaquitelow resi-dencetimeforwoodymatter,likelyexplainedbythefactthatinour set-up,theadjustmentofTresimplicitlyaccountsfornon-modelled biomasscarbonremovalbydisturbances(mainlythinningevents, plusadditionalmortalityrelatedtoclimateextremessuchasthe 2003drought)thataretakenintoaccountintheobservations(as mentionedabove).
Whenasimulationwasperformedwithbothoptimized resi-dencetimeandoptimizedparametersfromtheREFpost,thenew valueofTresdidnothaveastrongimpactontheGPP,TERandETflux simulationsexceptforasmalldeclineinthemagnitudeofTER.This wasduetoalowerautotrophicrespirationbecauseofthesmaller amountofbiomass.However,thenewresidencetimehadastrong impactontheAGBinc,resultinginlowervaluesforthisvariable duetothefasterturnoverratecausingmorebiomasstogotothe litterpool.TheannualincrementwithoptimizedTres becameso smallthatit actuallywasnegativein 2004(seeSupplementary Material,sectionD),whentheGPPwasthelowestforthewhole period.Therefore,theshortresidencetimeobtainedbyoptimizing themodeltofitthetotalAGBtotbecomesunrealistic(when inter-pretedasaconstantmeanmortality)anditfalsifiedonecomponent ofthemodel(AGBinc).
TheoptimizedresidencetimeatLeBraywas31years,which wasagainlowerthantheapriorivalueof40years.However,the posteriorRMSEvalueforAGBtotatLeBrayinStep2wasslightly higher(1.134kgCm−2)thantheapriori RMSE(1.105kgCm−2). Thisresultmightbesurprising,butitjustrevealsthatchanging the“fast”parametersinStep1(P1andP2sets)doesnotallowtofit theAGBtotaswellaswiththepriorvaluesandalsotheinclusionof AGBincchangesallocationparameterswithouttakingintoaccount thatthetotalbiomassmightalsodecrease.Notethatthe simu-latedbiomasslinearlyincreasedovertimewhiletheobservations showedamorestableevolutionwithlargechangesin1999–2000 and2004–2005.SimilarlytoHesse,thenewoptimizedresidence timedidnotinfluencethemodelperformanceforthefluxes,but itdiddegradetheAGBincestimateaswasseenattheHessesite, eventhoughitwasnotnegativeinanyyearlikeatHesse.
TheinformationcontainedinAGBtotrelatestoprocessesthat operateduringthewholelife-timeoftheforestpriorto observa-tion.AGBtotassimilationhasanegligibleinfluenceonCO2fluxes inthe modelassuch(onlya weakeffectthrough maintenance respiration), but a larger effecton carbon storage,so this type ofmeasurementscanthusbeusedtoconstrainlongerterm pro-cessessuchasmortalityandmanagement(ifnotexplicitlytaken intoaccountinthemodel).Largedatasetsexistforbiomass,e.g. fromremotesensingandforestinventories,thathavemuch bet-terspatialcoveragethansparsenetworkoffluxmeasurements. Howeverthesedatasetsdonotprovidetheageoftheforest,which thusfurthercomplicatestheassimilationoftheseobservations. Nevertheless in upscalingstudies thefast parameters couldbe constrainedwithafewfluxtowersandmorenumerousbiomass observations could be used to constrain the slow parameters, thoughasmentionedweneedancillaryinformationoftheforest age.
3.4. Evaluationoftheoptimizedmodel
3.4.1. Optimizedparametersanderrorestimation
Theerrorsoftheparametersweregreatlyreducedfromtheir priorvaluesafteroptimizationatbothsites,andforallthe differ-enttestcasesthatwereperformedwithdifferentdatastreams(i.e. REFcomparedtoT11andT12Table5).Inadditiontothe opti-mizedparametervalueanduncertainties, thecross-correlations betweenthedifferentparametersrevealimportantinformation.If theparametersdrifttothemarginsoftheirpriorrange,thiswould indicateproblemswithsub-modelstructures.However,this did notoccurateithersite.
AtHesse,fluxrelatedparameters(P1)differedbetweeneachtest anditisnotstraightforwardtoevaluatethedifferencesbetween each case due to parameter correlations. The Vcmax parameter decreased in the reference case and increased in thetest case T11 when AGB data were not used (Table 5), likely showing thatoptimizingallocation-relatedparametershasaninfluenceon parameterscontrollingphotosynthesis.Leaflevelobservationsof Vcmaxshowalargespreadofvalues(Montpiedetal.,2009)andthe valuesfromtheoptimizationsarewithinthisrange.Observations atanotherbeechforest(Epronetal.,1999)andamodelinversion study(Verbeecketal.,2008)suggestsmallervaluesofVcmax(than thedefaultvalueofORCHIDEE)aremoreappropriatefortemperate deciduousforests,implicatingthattheREFcasegavethemost rea-sonableresultinthisrespect.TheLAIMAXparameter,whichdefines apeakLAIvaluethatcannotbesurpassedinthemodel,decreased toomuch(4.3m2m−2)whencomparedtotheobservedmaximum LAIreachedinthepeakgrowingseason(7.6m2m−2).
Theallocation-relatedparameterr0,whichcontrolsthe alloca-tiontofineroots(Eq.(B1)),decreasedintheREFandT12cases inwhichitwasoptimized,whereastheparameters0controlling allocationtosapwood(Eq.(B2)),increasedinbothoptimizations. dalloc(Eq.(1)),whichisthetimeconstantfortheaboveground sap-woodallocation,alsomovedinthesamedirection(decreased)in bothcases.However,theSinit parameter(Eq.(1)),whichdefines the initial allocation of sapwood derived from NPP to above-groundcompartment,decreasedstronglyinthereferencecasebut increasedintheT12test.ThedifferencesbetweentheREFand T12caseswerecausedbythefactthatintheREFcasethefluxes andAGBincwereconstrainingotherparametersthatexertedan influenceover Sinit. IntheT12case (AGBinc only)many large correlationsbetweentheallocationrelatedparametersexist,the largestbeingpositivecorrelationbetweenr0andSinit(0.43).This nicelyshowsthattheeddycovariancefluxesintheREFcasebring extrainformationthatfurtherresolvestheparameterspace com-paredtoanoptimizationwithbiomassdataalone.
AtLeBray,weobtainedsimilarparametererrorcorrelationsand similarcomplexpatternsbetweentheREF,T11andT12cases.The optimizedVcmaxincreasedinbothcases(REFand TP11),which isinlinewithobservations(Medlynetal.,2002)andthe previ-ousMDFstudy(Santarenetal.,2007).AtLeBraytheLAIMAXvalue increasedinbothcases,whichwasintheoppositedirectiontothe observedLAI.Theallocationparametersr0ands0increasedinboth thereferenceandT12cases.
3.4.2. Evaluationagainstotherinsitudata
Theresultsfromthesimulationsusingtheoptimized parame-tersetfromtheREFinversionatHessewerecomparedtoadata setfromGranieretal.(2008)havingdifferentmeasurementsat thesite. We first consideredthefine rootproduction as calcu-latedfromtheturnoverrate,asonlythefinerootproductionwas observedbyGranieretal.(2008)andnotthemaximumsizeoffine rootcarbonpool.Thefinerootproductionoftheapriorimodel wasmuchhigherthantheobservations,withanannualaverage of218.4gCm−2(standarddeviationof/±7.0gCm−2)comparedto
theobservedvalueof68.2gCm−2(±9.7gCm−2).Thispositivebias wasreducedaftertheoptimization,withanoptimizedannual aver-ageof41.7gCm−2(±29.1gCm−2).Thisresultisconsistentwith theadjustmentofparameterr0,whichcontrolsallocationtofine roots,andwasreducedafteroptimization(0.165insteadofthea priorivalueof0.300;seeTable4).
Theapriorimodelalsooverestimatedleafproductionwithan annualaverageof214.1gCm−2 (±7.0gCm−2), comparedtothe observedvalueof157.8gCm−2(±22.8gCm−2).Theaposteriori simulation resulted in a lower annual average of 126.2gCm−2 (±3.2gCm−2)thatisclosertotheobservations.Aswiththefine rootproduction,theleafproductionhasbeencalculatedfromthe turnoverrateinordertocomparethemodeloutputwiththe mea-surements.Insummary,theallocationtobothfinerootsandleaves wasreducedaftertheoptimization.Thisisconsistentwiththefact thatmorebiomasswasallocatedtosapwoodafteroptimization,as seeninFig.4d,andalsointheincreaseofparameters0(from0.30 to0.42),whichcontrolstheallocationofassimilatedcarbonto sap-wood.Thattheallocationintheoptimizedmodelisthereforemore consistentwiththeobservationsafterMDF,highlightstheadded benefitofusingannualabovegroundbiomassincrementdatain theoptimizations.However,simulationswithoptimized parame-terswerestillnotabletocapturetheinter-annualvariationseen intheobservationsoffinerootandleafproduction.
The observed autotrophic respiration (maintenance plus growth) wasestimated tobe72.2% ofthe totalecosystem res-piration,basedonGranieretal.(2000).Theobservedvaluehas significantuncertaintyduetothepartitioningand thepresence of nighttimeadvection at thesite (Aubinet et al.,2005).The a priorimodeloverestimatedautotrophicrespiration−theannual averagewas974.2gCm−2year−1(±44.6gCm−2year−1),whilethe observed value was 736.2gCm−2year−1 (±97.7gCm−2year−1). After optimization, the simulated annual average for the autotrophic respiration was reduced to 528.3gCm−2year−1 (±19.3gCm−2year−1).TheratioofautotrophicrespirationtoTER was52.5%beforetheoptimizationand37.7%after,muchlowerthan inGranieretal.(2008),demonstratingthatalthoughthedecrease inTERafteroptimizationresultedinabetterfittothedata over-all,theautotrophicrespirationwasreducedtoomuchcomparedto heterotrophicrespiration.
TheobservedannualaverageofNPPwas690.6gCm−2year−1 (±147.9gCm−2year−1) (Granier et al., 2008). Both the a priori and a posteriori model results overestimated NPP by almost a factor of two, with an a priori value of 1167.5gCm−2year−1 (±50.7gCm−2year−1) and an a posteri-orivalue of 1148.2gCm−2year−1 (±89.3gCm−2year−1)− thus almostnochangeaftertheoptimization.Thiswaspartlydueto thefactthateven thoughtheoptimizations resultedinalower GPP,theautotrophicrespirationwasalsodecreased,andtherefore theNPPremainedtoohigh.Theoptimizedsimulationswerealso notabletocapturethestronginter-annualvariabilityseeninthe observationsof NPPand autotrophicrespiration,asfor thefine rootandleafproduction.
4. Perspectivesonassimilatingbiomassdataintoglobal terrestrialecosystemmodels
IncludingAGBinc in anoptimization togetherwiththeflux dataenabledtheoptimizationof theallocation-related parame-terswithoutanydeteriorationcomparedtoonlyusingfluxdata intheoptimization.However,althoughthenewLAIschemedid help to improve the simulated a priori AGBtot with respect to the observations at Hesse, we faced some challenges when assimilatingbothabovegroundincrementandtotalaboveground biomasswithintheORCHIDEEmodelstructureandthereforeuseda
Table5
Theparametervaluesandtheiruncertainties(inparenthesis).
Hesse Prior REFpost T11 T12
P1parameters Vc(max) 55.0(22.4) 51.7(4.64) 67.2(2.93) – GS,slope 9.00(2.40) 6.67(0.407) 6.55(0.566) – cT,opt 26.0(6.40) 18.3(1.88) 19.5(0.832) – cT,min −2.00(4.00) 0.871(0.524) −2.37(0.218) – cT,max 38.0(16.0) 54.8(8.89) 22.9(0.348) – SLA 0.0260(0.0148) 0.0388(0.00549) 0.0412(0.00155) – LAIMAX 5.00(2.00) 4.28(0.237) 3.40(0.116) – Klai,happy 0.500(0.140) 0.540(0.0192) 0.500(0.0264) – Fstress 6.00(3.68) 2.64(0.751) 2.21(0.411) – Kpheno,crit 1.00(0.480) 1.04(0.0158) 1.00(0.480) – cT,senescence 12.0(8.00) 13.5(0.112) 12.0(0.144) – Lage,crit 180(48.0) 165(7.27) 172(7.54) – leafinit 10.0(10.0) 12.0(3.05) 10.0(3.16) – Humcste 0.800(1.12) 2.91(0.498) 1.77(0.608) – Q10 1.99(0.600) 1.77(0.153) 1.39(0.157) – KsoilC 1.00(1.50) 0.287(0.231) 0.358(0.434) – HRH,a −1.10(0.800) −1.72(0.800) −1.53(0.800) – HRH,b 2.40(1.68) 5.27(1.67) 1.89(1.68) – HRH,c −0.290(0.600) −0.388(0.590) −0.257(0.600) – HRH,min 0.250(0.200) 0.553(0.200) 0.410(0.162) – MRa 0.160(0.0640) 0.101(0.0362) 0.0938(0.0296) – MRb 1.00(0.760) 0.763(0.576) 0.814(0.366) – GRfrac 0.280(0.0640) 0.201(0.0255) 0.280(0.0259) – Zdecomp 0.200(1.98) 3.19(1.97) 2.48(1.97) – Hcritlitter 0.0800(0.196) 0.215(0.180) 0.377(0.196) – Z0overheight 0.0625(0.0320) 0.0382(0.00820) 0.0625(0.00714) – Kalbedo,veg 1.00(0.160) 1.13(0.120) 0.988(0.158) – P2parameters r0 0.300(0.240) 0.165(0.0880) – 0.232(0.107) s0 0.300(0.240) 0.420(0.0242) – 0.461(0.0659) Sinit 0.200(0.160) 0.113(0.0942) – 0.223(0.150) dalloc 5.00(7.60) 2.36(7.52) – 3.80(7.39) P3parameter Tres 40(35) 16.8(1.08) – –
LeBray Prior REFpost P1 P2
P1parameters Vc(max) 35.0(12.0) 45.6(3.26) 45.3(1.17) – GS,slope 9.00(2.40) 9.40(0.248) 10.4(0.307) – cT,opt 25.0(6.40) 24.6(0.992) 23.8(0.426) – cT,min −4.00(4.00) −2.86(0.599) −2.93(0.110) – cT,max 38.0(16.0) 24.9(0.204) 25.2(0.228) –
SLA 0.00926(6.4e−3) 0.0199(1.93e−3) 0.0199(3.72e−3) –
LAIMAX 5.00(1.60) 5.97(0.358) 5.31(0.0140) – Fstress 6.00(3.68) 7.95(2.78) 7.94(2.15) – Lage,crit 910.(160.) 749.(29.6) 713.(27.4) – Humcste 1.00(1.50) 2.68(0.616) 2.58(0.498) – Q10 1.99(0.600) 2.10(0.158) 2.49(0.225) – KsoilC 1.00(1.50) 1.98(0.220) 0.961(0.275) – HRH,a −1.10(0.800) −0.151(0.796) −0.820(0.788) – HRH,b 2.40(1.68) 4.21(1.42) 2.80(1.28) – HRH,c −0.290(0.600) −0.692(0.515) −0.311(0.527) – HRH,min 0.250(0.200) 0.250(0.164) 0.291(0.174) – MRa 0.160(0.0640) 0.0924(0.0379) 0.0818(0.0333) – MRb 1.00(0.760) 0.188(0.545) 0.580(0.118) – GRfrac 0.280(0.0640) 0.233(0.0329) 0.288(0.0212) – Zdecomp 0.200(1.98) 0.190(0.121) 0.503(0.415) – Hcritlitter 0.0800(0.196) 0.0288(0.0150) 0.0610(0.0730) – Z0overheight 0.0625(0.0320) 0.0997(0.00238) 0.0994(0.00181) – Kalbedo,veg 1.00(0.160) 0.812(0.137) 0.860(0.154) – P2parameters r0 0.300(0.240) 0.488(0.240) – 0.319(0.206) s0 0.300(0.240) 0.490(0.0315) – 0.346(0.0108) Sinit 0.200(0.160) 0.00447(0.0778) – 0.200(0.103) dalloc 5.00(7.60) 18.5(6.73) – 2.90(6.73) P3parameter Tres 40(35) 31.2(5.05) – –
stepwiseapproachtodealwiththis.Thedifferencebetweenthese
twosetsofobservationsandthemodelisimportanttokeepinmind
formodelevaluationandoptimization.IntheORCHIDEE“AR5”
ver-sionusedinthisstudy,inwhichmortalityisaconstantfractionof
biomass,thechangeofAGBtotandAGBincarealwayspositive
inayounggrowingforestnot atequilibrium.InrealityAGBtot
datamight decline during a highmortalityyear due to
distur-banceorforestmanagement.Thereforethereisaninconsistency
betweenthesetwoobservationsandhowthemodelis
simulat-ingtheforeststanddynamics.Processesrelatingtodisturbance
andmanagement (e.g.episodic canopythinning)arenot
repre-sentedinthisversionoftheORCHIDEEmodel,andthereforeusing
AGBtottooptimizethelong-termmeanresidencetimeresulted
inanunrealisticallylowvalue.Asaresultthemodelsimulateda
negativeabovegroundbiomassincrementwasmodelledforone
year,whichwasthereforeoppositetothepositivevaluesseenin
theobservations.Theseresultsthereforeimplythatlong-term
res-idencetimeorturnoverrateparameterscannotbeoptimizedusing
totalabovegroundbiomassdataunlessthehistoryofdisturbance
andmanagementareaccountedforinthemodel.
AnewversionofORCHIDEEthatincludesprocesseslinkedto
standgrowthand mortality,aswellas management (including
thinning;Naudtsetal.,2015,basedonBellassenetal.,2010),will
bea moreappropriatemodelintermsofusingbiomassdatain anassimilationframework.However, thisversion stilldoesnot describemortalitypeaksduetonaturaldisturbanceandmaystill notcaptureyeartoyearvariationofAGBtot.Ifthemodeldidhave anadequaterepresentationoflong-termforestdynamics,AGBinc observationscouldbeusedtoconstrainmodelledwoodybiomass incrementofsurvivingtrees,i.e.theannualNPPincrement,inorder tocalibrateparametersrelatingtothenaturalfluxesand alloca-tion.TheAGBtotmeasurementscouldthenbeusedtooptimize thetrajectoryofthetotalabovegroundbiomass,including param-etersrelatedtodisturbanceandhuman-relatedmanagementas discussedabove.Whetherornotthesetwodata-streamswereused insimultaneousorstep-wiseapproachwouldthenonlydepend oncomputationaltime constraints.Note that using a two step approachcanbeapracticalsolutionwhenonesteprequireslonger simulationsinordertooptimizeoneortwo“slow”process param-eters.Thisstudydoesnotyetprovideanswersforhowtodealwith theseissuesglobally,butitisaninitialstudyonhowtousebiomass datainMDFwhileanticipatingtheavailabilityofglobaldatasets, e.g.fromESABIOMASSmission.
Theoptimization helpedtogreatly decrease theuncertainty (reductionof 63%at Hesse and 78%at LeBray) intotal above-groundbiomassprojectionsinafutureclimatesimulationatboth sites(derivedfromtheparameteruncertainties;see Supplemen-taryMaterial,SectionB).However,itonlyresultedinpronounced differencesinthemeanvalueatLeBray(25kgm−2in2100after theoptimizationinsteadof15kgm−2 before).Thiswasduetoa largerNPPproductionaftertheoptimizationduetodecreasesin autotrophicrespirationandincreaseinsapwoodallocation.These resultsthereforedemonstratetheimportanceofhavingagoodNPP estimateinordertohavereliableestimatesoftheAGBtotandits temporalevolution. UseofNPP intheoptimizationis challeng-inghowever,asitcannotbemeasureddirectlyandthereforeis derivedfromotherobservations.Thereisthusaneedforreliable estimatesforautotrophicrespiration,ashasalsobeenstatedin otherstudies(Richardsonetal.,2010),inordertoderivethenet carbonassimilatedintotheplantandsoil.
ManyofthelargescaleLSMsperformpoorlywhensimulating abovegroundbiomass(Wolfetal.,2011).Wehaveshownthatusing abovegroundbiomass incrementdatacanhelp toconstrainthe allocation-relatedparameters,whichthereforehelpedtoimprove themodel-datafitandhelpedtoreduceuncertaintyinfuture pro-jections.However,itisalsopossiblethattoosimplisticallocation
schemeiscontributingtoLSMpoorperformance(DeKauweetal., 2014).Atlargescales,theuseofsimplifiedschemescanbejustified; however,theallocationbetweenabovegroundandbelowground componentsisquiteimportantasthedecayprocessesforthe cor-respondingbiomassstoresareverydifferent(Repoetal.,2011). Somelargescalemodelsdonotevenseparatebetweenthe above-groundandbelowgroundwoodbiomassstores(Wolfetal.,2011), asthishasnotbeenessentialintheirdevelopmentalneeds.We sug-gestthatitisimportanttodifferentiatebetweenthesetwostores andtotrytoconstraintheallocationrelatedparametersinorder toachieverealisticsimulationsofbiomass.Finally,ourstudyalso bringsforththeimportanceoftakingtheforestageintoaccount whenstudyingbiomassstocksintothefuturewhichmanyglobal LSMsdonotdo.
5. Conclusions
Inthisstudyweincludedabovegroundforestbiomassdatain theoptimizationofthedetailedandcomplexORCHIDEE process-based model for the first time. Joint assimilation of annual abovegroundincrementdatainadditiontothe micrometeorologi-calfluxdataprovedtobefeasible(andbeneficial)attwodifferent forestsites,allowingthefurtherconstraintofallocation parame-tersinadditiontoparametersrelatedtothe“fast”processesinthe model(photosynthesis,respirationandphenology).Addingtotal standbiomassrevealed inconsistenciesbetweenthese observa-tionsandthestructureofthisversionofORCHIDEEduetomissing processesinthemodel.The“AR5”versionofORCHIDEEusedin ourstudydoesnotincludeadescriptionofage-dependentgrowth rates,competition,andmortalityprocessesthatarecrucialto sim-ulatestandbiomass.AnewversionofORCHIDEEbyNaudtsetal. (2015)includessomeof thesemissingprocesses, andtherefore opens interesting avenues for the assimilation of aboveground biomassdatainthefuture.
Aside from the model developments described above, our resultshighlighttheneedtohavebetterdifferentiationbetween totalecosystemrespirationandautotrophicrespirationandtohave amodelthatisconsistentwithdifferenttypesofbiomass observa-tions.Havingreliableobservation-basedNPPestimatewouldalso beveryusefulforfutureMDFapplications.Theoptimizationwe didinthisworkgreatlyhelpedtoreduceuncertaintiesinthefuture climatescenariosfortheabovegroundbiomass(shownin Supple-mentB).
Finally,weexpectthathavingagreaternumberofobservations ontheparameterswouldhelpprovidefurtherinformationtothe optimizationbyrestrictingtheirbounds.Clearlythisisnota triv-ialtask,asmanydirectobservationsofmanyparametersdonot exist.However,wehopethatclosercommunicationbetween mod-ellersandexperimentaliststakingsite-basedmeasurementswould contributetomakingthismorefeasibletask.
Acknowledgements
ThisworkispartoftheEU-fundedprojectCarbo-Extreme(FP7, GA 226701). TT would like to acknowledge the funding from theFinnishAcademy(grantnumber 266803).We wouldliketo acknowledgeEuropeanCommissionFP7EMBRACEproject,under GrantAgreementnumber282672.Wethankthetwoanonymous reviewersfortheircommentsthatgreatlyhelpedtoimprovethis manuscript.
