CARAIB a global model of terrestrial biological productivity

GLOBAL BIOGEOCHEMICAL CARAIB: CYCLES, VOL 8, NO 3, PAGES 255-270, SEPTEMBER 1994 A global model of terrestrial biological productivity P Warnant, L Francois,D Strivay, and J.-C G•rard Laboratoirede PhysiqueAtmosph•riqueet Plan•t•ire, Institut d'Astrophysique,Universitede Liege, Liege,Belgium Abstract CARAIB, a mechanistic modelof carbonassimilationin the biosphere estimatesthe net primaryproductivity(NPP) of the continentalvegetationon a grid of 1ø x 1ø in latitude and longitude The model considersthe annual and diurnal cycles.It is basedon the couplingof the three followingsubmodels; a leaf assimilationmodel includingestimatesof stomatal conductanceand leaf respiration,a canopymodeldescribingprincipallythe radiativetransferthrough the foliage,and a woodrespirationmodel Present-dayclimate and vegetation characteristics allow the discriminationbetweenecotypes.In particular, specific informationon vegetationdistributionand propertiesis successfully usedat four levels;the leafphysiological level,the plant level,the ecosystem level,andthe global level The productivity determinedby the CARAIB model is comparedwith local measurements and empiricalestimatesshowinga good agreementwith a global valueof 65 Gt C yr-1 Thesensitivity ofthemodelto thediurnalcycleandto the abundance of C4 species is alsotested.The productivityslightlydecreases (10%) whenthe diurnalcycleof the temperatureis neglected.By contrast,neglecting the diurnal cycleof solarirradianceproducesunrealisticallyhigh valuesof NPP Even if the importanceof this increasewouldpresumably be reducedby the coupling of CARAIB with a nutrientcyclemodel,this test emphasizes the key role of the diurnal cycle in a mechanisticmodel of the NPP Uncertaintieson the abundance and spatialdistributionof Ca plants may causeerrorsin the NPP estimates, however,as demonstrated by two sensitivitytests,theseerrorsare certainlylower than 10% at the globalscaleas shownby two tests Introduction Continental vegetationplays an important role in the climatic system Indeed, the hydrologicalcycle is modified by the extraction, transpiration, and storage of soil water in plants Moreover,photosynthesisof green plants is an important sink of carbon Atmospheric CO2 is, after water vapor, the most important greenhouse gas, and its assimilation by the biospheremodifiesthe atmosphericreservoirand therefore the heating or coolingof Earth's atmosphere In particular, globatL climate changesinducedby human activitiesmay be in- fiuencedby the coupled atmosphere-biosphere system In this scopethe study of the global carbon uptake by the biosphereis of primary importance During the last years, global models of carbon as sirnilationby the biospherebased on empirical para- These modelsestimate biosphericcarbon pool sizesand fluxes However, the parameterizations they use are calibrated with present-day CO2 levels and climatic conditionsbut may be less appropriate for future conditions On the other hand, mechanisticmodels have often been applied only at the leaf, plant, or, eventually, the canopylevel The study describedin this paper ten- tativelyusesmechanistic models[Farquharet al., 1980; Collatzet al., 1992]to predictthe net primaryproductivity (NPP) at a globalscale Even if this scaling-up method restsupon many simplifications,it is a first step toward the modeling of CO2 assimilation by continental vegetation, and it gives results as realistic as those of previous estimations Furthermore, improvementsof this model are expectedas physiologicalknowledgeand scaling-upmethodologyprogress.The sensitivity of the model to the diurnal cycle is tested It is shown that meterizations havebeendeveloped [e.g.,Esser,1991] ignoring this cycle may introduce important errors in NPP Copyright 1994 by the American Geophysical Union Paper number 94GB00850 0886-6236/94/94GB-00850510.00 estimates Model Description The C ARAIB model has been built to estimate the net primary productivity of continental vegetation at 256 WARNANT ET AL.: GLOBAL MODEL OF TERRESTRIAL BIOLOGICAL PRODUCTIVITY a global scaleusing vegetationinformationand climatic data A spatial resolution of 1ø x 1ø in latitude CARAIB intendsto be as mechanistic as possible andis basedon the coupling of the threefollowing submodels: a leafassimilation modelincluding estimatesof stomatalconductance andleafrespiration, a and longitudehasbeenchosen because it permitsthe descriptionof relativelyfine spatial variationsof the NPP, while stayingcomputationally manageable.At canopymodeldescribing principallythe radiativetransthisresolution the continents cover15,347gridpoints ferthroughthe foliage,anda woodrespiration model The NPP is calculatedindependently at eachof these Photosynthesis is the majorcarbonfluxdetermining grid points The functioningof the modelis outlined plantgrowth.In thisstudytheemphasis isthusputon in Figure 1, which the diagramillustratesthe various theestimation ofgross primary productivity (GPP).By submodels coupled in CARAIB withtheprocesses they contrast, respiration of leaves and wood is not known consider,the input data they require,andthe timescale accurately Only a roughestimateof respiration rates (dayor season) to whichtheyapply.In thelowerright willthusbeperformed here,mainlyto provide thevalue ofnetprimaryproductivity andto enable thecomparitext (sections 2.3 and 3.2) for the areaand carbonal- sonofmodel results within situmeasurements (existing of Figure I is a summaryof the symbolsusedin the locationfractionsof the differentvegetationcoversof a for NPP but not for GPP) gridpoint CARAIB considers the maintwosolarcycles,thediurnalandannualcycles.Because ofthelarge Leaf Assimilation Submodel variationof the photosynthetic rateduringthe day,the Theleafgross assimilation rateA (/zmolm-2 s-1) CO2uptakeiscalculated onanhourlybasis.Thehourly isdescribed bytwoquadratic equations [Collatz et al., values aresubsequently summed upto provide thedaily 1991]' assimilation.However,sincea monthlymeanclimatic data set is used,randomday-to-dayvariationsof wea- therconditions cannotbetakenintoaccount Thedaily NPP is thusestimatedfor a midmonthdayandmultipliedby the monthlengthto obtainthemonthlyvalue LEAF LEVEL OAp • - Ap(A1 + A•)+ A1A•= (1) /SA • - A(Ap + Aa)+ A;,Aa =0 (2) CANOPY LEVEL PLANT LEVEL Trendat Wood J Mainten Respiration Construction , I I SOIL HYDROLOGY Wood Biotaare VEGETATION AREA FRACTION ALLOCATION , Airhumicity • water BARE SOIL GROUND Bucket , I -f o C, VEGETATION C4 fo • ( I - f •,) f0• fo, • , TREE LEAVES h o ( 1- { fo ( 1- { ) WOOD (1- h0 )( 1- CARbonAssimilation In the Biosphere ( CARAIB) Figure1 A schematic diagram showing thestructure ofthecarbon assimilation inthebiosphere (CARAIB) model Theparameters defining theareaandcarbon allocation fractions (see text) ofthedifferent vegetation covers ofa gridpointaresummarized at lowerright WARNANT ET AL.: GLOBAL MODEL OF TERRESTRIAL where and /• are parameters; A1, A2 and As are functionsdescribinglimitations of the assimilationrate BIOLOGICAL PRODUCTIVITY 257 Finally,the leafnet assimilation rateAn (/zmolm-2 s-1) is givenby (•umol m-2 s-i); andApistheassimilation rateresul& = A- ting fromthe couplingof the firsttwo limitations(/zmol m-2 s-l) These two equations indicate that the assimilation rate is limited by three processes,with a coupling between them representedby the parameters and For Ca species, A1 is the ribulos-biphosphatecar- boxylaseoxygenase(Rubisco)limited rate, mudA2 is the electrontransportlimitedor light-limitedrate [Farquharet al., 1980].They are givenby A1 = Vcmax Pi - F + + (9) where Rd, the dark respiration rate, is assumedto be proportional to Vcmax The proportionality constant usedis 0.015for Ca plants[Sellerset al.,1992]and0.020 for C4 plants(estimatedfrom Gollatzet al.'s [1992]value of the dark respirationrate at 25øC) The CO2 pressurein interee!!ularspacesis related to the atmospheric CO•.pressure, p•tm (Pa), by a diffusion equation Pi Patm = P P (3) (10) g where Vcma•is the maximum catalytic capacity of Ru- to bisco(/zmolm-2 s-1); Pi istheintercellular CO2pres- whereg, thetotal conductance is given by sure(10-6 Pa);O2istheintercellular O2pressure (Pa); I I F is the CO2 compensationpoint in the absenceof - = ] (11) g gst darkrespiration (10-6 Pa);KcistheMichaelis-Menten constant for CO2(10-6 Pa); andKois the Michaelis- where gst is the stomatal conductance;and gbl is the leaf boundary layer conductmace The stomatal conductance to CO• is estimated fol- Mentenconstantfor O2 (Pa) pi - F A2= J4(pi +2r.) (4) lowingBall et al., [1987]' whereJ is the potentialrate of electrontransport(/zEq m-2 s-1) V•m•, F., Kc,andKoarefunctions oftemperature, while J is a function of temperature and of the absorbed irradiance J saturates at a level Jmax at high irradiance As is the rate limited by the capacityfor the export or A,•hsP gst •.-.• (g0 q-glPatm-••) (12) where h8 is the air relative humidity at the leaf surface; andF is the compensation point(10-6 Pa) The factor 1.6 accounts for the ratio of the diffusi- vitiesof CO2 and H20 vaporin the stomates[Collatz the utilizationof the productsof photosynthesis [Collatz et al., 1992];go = 0.01(mol•_om-2 s-1) andgl= 9.2 et al., 1991]' for Cs species[Leuning,1990];mudgo= 0.08 (moln2o &= Ycmax m-2 s-1) and gl= 3.0 for C4 species [Collatzet al., (s) 1992] For low air relativehumidity (hs _• 0.46), gl is decreasedlinearly with the available soil water frac- Similar equationsdescribethe C4 speciesbehavior tion (wn•_o - wp)/(fc - wp) = (hs- 0.1)/0.9 (seesec[Collatzet al., 1992].In this case,A1 and A2 areinde- tion 3.1) This linear decreasetends to simulatethe pendentof p•, and As is a CO2-1imitedrate proportional to Pi observed behavior of the stomatal conductance at low water availability[Mc Mutttie et al., 1992] This forA1 = V•max Aa = a I As= k pi (6) (7) mulation of the stomatal conductanceinvolves the hypothesisthat the stomates open and closeto optimize the uptake of CO2, while limiting the H20 losses In the presentversionof the model a constantvalue g• = 0.0714molco•_ m-2 s-1 isusedasa firstapproximation (8) where V•m• is a "Q10function"(Q10 is the factor by which the rate, i.e Vcmax,is multiplied for each 10øC increase in +•empera•ure• + of temperasure •orrec•ed to limit the assimilationrate at low or high temperature; a is the slope of the photosyntheticresponseto light for the leaf boundary layer conductmace Equations(1), (2), and (9)-(12) haveto be solvedsimultaneouslyto calculatethe leaf net assimilationrate An Since A1, A2, and As are not identical functions of pi for Cs and C4 specie, the mathematical •!ution of these equationswill also differ For Cs, speciesequa- tions (10)-(12) are combinedto give the intercellular pressureof CO2, pi, as a function of the assimilation (molco•_/mO]photon); I is the irradiance absorbed by the leaf (•molphoton m- s- ; k is the initial slopeof pho- rate, An This functionis then introducedin (3) (retosynthetic C02 response (mo]m-2 s-1) andis a spectively(4)), assumingthat A1 (respectively A2) is functionof temperature; and P is the atmosphericpres- the only limiting rate This procedure leads to two cu- sure(Pa) bic equations,the solutionsof which yield A1 and A2 258 WARNANT ET AL.: GLOBAL MODEL OF TERRESTRIAL Finally,(1) and (2) are solvedto provideAp, and A, andthusAN by makinguseof (9) SinceAx and A2 are not functionsof pi for Ca species,(1), (2), (6)-(8), and (10)-(12) can be combinedinto a cubicequationdirectly providingthe leafgrossassimilationrate, A (Collatz et al., 1992) A• is then calculatedfrom (9) BIOLOGICAL PRODUCTIVITY canopy,LAIc (assuming,as mentionedabove,that the layerthicknessin LAI is 0.2) To obtain the net primary productivity of the grid point (per unit areaof groundsurface),the respiration rate R•, of the woody parts of the vegetation must be substracted from the total Canopy Submodel leaf net assimilation NPP - LNA- R• rate (16) The CO2 uptake by the green vegetationis directly Consequently,an estimate of the woody respiration related to the net assimilationof a singleleaf, assuming rate is needed before the net primary productivity of that physiologicalparameters are constant throughout the vegetation can be calculated Woody respirationis the canopy The canopy is divided into layers of equal very poorly known quantitatively, and a very crude esthickness in leaf areaindex(LAI) The assimilation rate timate is made here only for completenessof the model of each layer is determined as describedin section 2.1., The approach adopted here is similar to that used by and layer values are added to provide the canopy assiRaichet al., [1991]and McGuireet al., [1992]in their milation In order to perform this integrationeasily,the calculation of total plant respiration Maintenance and LAI is reducedto the nearestmultiple of the layer thickconstructionrespirationrates are calculatedseparately, ness,taken as 0.2 in this study The temperature, relasincethe former is proportional to the biomassand the tive humidity, and CO2 pressureof the air are supposed latter to the net carbon assimilation Thus R,, can be to be constantthroughoutthe canopy,while light is ab- written as sorbedwithin the canopy An exponentialattenuation R• = R• + R•, (17) of the solar flux Ir within the foliageis implemented whereR• is proportionalto woodybiomass,and R•, [Sellers,1985] It = Io exp(-kLL) (13) is proportionalto the part of net assimilationallocated to wood growth FollowingMcGuireet al., [1992],the increase of/• whereIo is the irradianceat the top of the canopy;L is with temperature is representedby a "Qm relationthe cumulative LAI; and kr.is the extinction coefficient ship," in which Q•o is, itself, temperature dependent As leavesare assumedto be sphericallydistributed, and is calculated from a third-order polynomial fit to kLis given by observations kr = (1 - •)o.• (14) 2p where p is the cosineof the zenith angle of the solar So we have 10 [j•o Tln(Q•o) T] (18) R• m= KrBwexp where B•ois the woody phytomassin standingvegetation; Kr is the respirationrate per unit massof woody Net Primary Productivity of a Grid Point material at 0øC; and T is temperature in øC Sinceonly the living part of the woodyphytomassrespires,K• Usingthe leaf and canopysubmodelspresentedabove, must be substantiallylower than the valueslisted by the total leaf net assimilation(LNA) rate per unit area McGuire et al., [1992]for averagevegetation(leaves of ground surface at a model grid point is calculated pluswood)in differentecotypes.In the absence of prefrom the relationship cise measurements,the K• value has been chosenhere in sucha way that the globaland annual averageof the LNA= fo , • A•(C4) (15) respirationrate is comparableto the valuereportedby beam;and •v is the scatteringcoefficient(0.175) [f•Lc Harvey[1989] The woodyphytomass B•ois not cal- L=I + (1- fc,) L=I ] culated explicitly in the model Rather, it is estimated from a simpleparameterizationlinking the annualmean NPP andthe phytomass [Esser,1984,1991] B•o= 0.59181NPP•, •%o.7v2•6 (19) where thesummation extends overcanopy layers, A,r (C4 andA•(C3) arethe net assimilation of layerL for C4 where •"o is the mean stand age of woody material, and C3 species calculatedfrom (9) with solarirradiance and NPP,, is the annual mean NPP allocated to wood derivedfrom (13); fc4 is the fractionof vegetationus- growth This annual mean value of B•o is used to ing the C4 photosynthetic pathway at the grid point calculateR•, assumingthat B•o is roughly constant considered;fo is the fraction of the soil surface cove- throughoutthe year The value of •% dependson the red by vegetation; and Lc, the number of layers in the ecotype.Note that sincethe annualmeannet primary canopy,is determined from the leaf area index of the productivity of the wood NPP,, is not known until the WARNANT ET AL.: GLOBAL MODEL OF TERI•STRIAL calculationis performedoverthe wholeyear, it will be necessaryto use an initial guessof Bw while starting an iterativeprocedure(seebelow) The NPP allocated to woodgrowthis relatedto total NPP by the simple relationship NPP• = (1 - H) Nee (20) where the herbaceous factor H is also a characteristic of BIOLOGICAL PRODUCTIVITY 259 adoptedbecauseit avoidsan explicitcalculationof the biomass from mass conservationequations This sim- plifiedmethodneglectsthe seasonality of carbonallocation (parameters H and h0) associated with the phenologicalchanges,but it, nevertheless, allowsa correction of the net assimilationfor wood respiration, so that the model NPP can be compared with average measurements in the major ecotypesof the world the ecotypeand is calculatedhere from the fraction• of the vegetatedsurfacecoveredby groundvegetation Input Data (asopposedto trees)as follows: Z = •+(1-•)ho (21) where h0 is the Ëaction of tree NPP allocated to leaf growth Usinga similarapproach to that of Raichet a/.,[1991], we assumethat the rate of constructionrespiration/• is given by R• = 0.2NA,, NA,, >0 R•,=0 NA,, _0 R• = (LNA- R•) _