P-model v1.0: an optimality-based light use efﬁciency model for … · 2020. 6. 22. · with...

$: P-model v1.0: an optimality-based light use efﬁciency model for … · 2020. 6. 22. · with site-level data of the fraction of absorbed photosyn-thetically active radiation (fAPAR)$
Geosci Model Dev 13 1545ndash1581 2020httpsdoiorg105194gmd-13-1545-2020copy Author(s) 2020 This work is distributed underthe Creative Commons Attribution 40 License

P-model v10 an optimality-based light use efficiency model forsimulating ecosystem gross primary productionBenjamin D Stocker123 Han Wang4 Nicholas G Smith5 Sandy P Harrison6 Trevor F Keenan78 David Sandoval9Tyler Davis910 and I Colin Prentice9411

1CREAF Campus UAB 08193 Bellaterra Catalonia Spain2Earth System Science Stanford University Stanford CA 94305 USA3Institute of Agricultural Sciences Department of Environmental Systems Science ETH Universitaumltsstrasse 28092 Zuumlrich Switzerland4Department of Earth System Science Tsinghua University Haidian Beijing 100084 China5Department of Biological Sciences Texas Tech University Lubbock TX 79409 USA6Geography and Environmental Science Reading University Reading RG6 6AH UK7Earth and Environmental Sciences Area Lawrence Berkeley National Lab Berkeley CA 94709 USA8Department of Environmental Science Policy and Management UC Berkeley Berkeley CA 94720 USA9AXA Chair of Biosphere and Climate Impacts Department of Life Sciences Imperial College LondonSilwood Park Campus Ascot Berkshire SL5 7PY UK10Center for Geospatial Analysis The College of William amp Mary Williamsburg VA 23185 USA11Department of Biological Sciences Macquarie University North Ryde NSW 2109 Australia

Correspondence Benjamin D Stocker (bestockeethzch)

Received 23 July 2019 ndash Discussion started 5 August 2019Revised 3 February 2020 ndash Accepted 5 February 2020 ndash Published 26 March 2020

Abstract Terrestrial photosynthesis is the basis for vege-tation growth and drives the land carbon cycle Accuratelysimulating gross primary production (GPP ecosystem-levelapparent photosynthesis) is key for satellite monitoring andEarth system model predictions under climate change Whilerobust models exist for describing leaf-level photosynthe-sis predictions diverge due to uncertain photosynthetic traitsand parameters which vary on multiple spatial and temporalscales Here we describe and evaluate a GPP (photosynthesisper unit ground area) model the P-model that combines theFarquharndashvon CaemmererndashBerry model for C3 photosynthe-sis with an optimality principle for the carbon assimilationndashtranspiration trade-off and predicts a multi-day average lightuse efficiency (LUE) for any climate and C3 vegetation typeThe model builds on the theory developed in Prentice et al(2014) and Wang et al (2017a) and is extended to includelow temperature effects on the intrinsic quantum yield andan empirical soil moisture stress factor The model is forcedwith site-level data of the fraction of absorbed photosyn-thetically active radiation (fAPAR) and meteorological data

and is evaluated against GPP estimates from a globally dis-tributed network of ecosystem flux measurements Althoughthe P-model requires relatively few inputs the R2 for pre-dicted versus observed GPP based on the full model setup is075 (8 d mean 126 sites) ndash similar to comparable satellite-data-driven GPP models but without predefined vegetation-type-specific parameters The R2 is reduced to 070 when notaccounting for the reduction in quantum yield at low tem-peratures and effects of low soil moisture on LUE The R2

for the P-model-predicted LUE is 032 (means by site) and048 (means by vegetation type) Applying this model forglobal-scale simulations yields a total global GPP of 106ndash122 Pg C yrminus1 (mean of 2001ndash2011) depending on the fA-PAR forcing data The P-model provides a simple but power-ful method for predicting ndash rather than prescribing ndash light useefficiency and simulating terrestrial photosynthesis across awide range of conditions The model is available as an Rpackage (rpmodel)

Published by Copernicus Publications on behalf of the European Geosciences Union

1546 B D Stocker et al P-model v10

1 Introduction

Realistic reliable and robust estimates of terrestrial photo-synthesis are required to understand variations in the car-bon cycle monitor forest and cropland productivity and pre-dict impacts of global environmental change on ecosystemfunction (Prentice et al 2015) Understanding how photo-synthetic rates depend on temperature humidity solar ra-diation CO2 and soil moisture is at the core of this chal-lenge Process-based dynamic vegetation models (DVMs)and Earth system models (ESMs) in use today almost al-ways use some form of the Farquharndashvon CaemmererndashBerry(FvCB) model for C3 photosynthesis (Farquhar et al 1980von Caemmerer and Farquhar 1981) in combination withstomatal conductance (gs) models (Ball et al 1987 Leun-ing 1995 Medlyn et al 2011) that couple water and carbonfluxes at the leaf surface

The FvCB model describes the instantaneous saturatingrelationship between leaf-internal CO2 concentrations (ci)and assimilation (A) and how this relationship depends onabsorbed photosynthetically active radiation (APAR) It sim-ulates A as the minimum of a light-limited and a RuBisCO-limited assimilation rate AJ and AC respectively

A=min(AJAC) (1)

Although the FvCB model is standard for leaf-scale pho-tosynthesis and its environmental response on timescales ofminutes to hours DVMs and ESMs using FvCB produce di-vergent results for ecosystem-level fluxes and their responseto the environment at longer timescales (Rogers et al 2017)This is due to assumptions that have to be made about pho-tosynthetic parameters that are not predicted by the FvCBmodel stomatal conductance (gs) and the maximum ratesof RuBisCO carboxylation (Vcmax) and electron transport(Jmax) for ribulose-15-bisphosphate (RuBP) regenerationwhich together determine the relationship between ci and ACommon approaches for determining the values of Vcmax andJmax in DVMs and ESMs are to prescribe fixed values perplant functional type (PFT) and attempt to simulate the dis-tribution of PFTs in space or to use empirical relationshipsbetween leaf N and Vcmax and simulate leaf N internally orprescribe it per PFT (Smith and Dukes 2013 Rogers 2014)

While the FvCB model describes a non-linear relation-ship between instantaneous assimilation and absorbed lightecosystem production integrated over weeks to monthsscales proportionally with APAR (Monteith 1972 Medlyn1998) This observation underlies the general light use effi-ciency (LUE) model which describes ecosystem-level photo-synthesis (gross primary production GPP) as the product ofAPAR and LUE

GPP= PAR middot fAPAR middotLUE (2)

where PAR is the incident photosynthetically active radiationand fAPAR is the fraction of PAR that is absorbed by green

tissue The LUE model is the basis for observation-drivenGPP models that use fAPAR and PAR based on remote sens-ing data and combine this with different approaches for sim-ulating LUE (Running et al 2004 Zhang et al 2017 Fieldet al 1995) and for some forest growth models (Landsbergand Waring 1997) Other remote-sensing-data-based models(Jiang and Ryu 2016) apply the FvCB model in combinationwith vegetation cover and type data and prescribed Vcmax fora set of PFTs

Here we describe a model referred to as the P-model thatunifies the FvCB and LUE models following the theory de-veloped by Prentice et al (2014) and Wang et al (2017a)The model assumes an optimality principle that balances theC cost (per unit of assimilation) of maintaining transpirationand carboxylation (Vcmax) capacities It thus predicts how theratio of leaf-internal to ambient CO2 (ci ca = χ ) acclimatesto the environment given temperature (T ) water vapourpressure deficit (D) atmospheric pressure (p) and ambientCO2 concentration (ca) (Prentice et al 2014) The P-modelalso assumes that the photosynthetic machinery tends to co-ordinate Vcmax and Jmax in order to operate close to the inter-section of the light-limited and RuBisCO-limited assimila-tion rates (coordination hypothesis Chen et al 1993 Haxel-tine and Prentice 1996 Maire et al 2012) under mean day-time environmental conditions By further assuming equalityin the marginal cost and benefit of Jmax daily-to-monthlyaverage assimilation rates can then be described as fractionsof absorbed PAR ie as a LUE model (Eq 2) (Wang et al2017a)

Thus the P-model embodies an optimality-based theoryfor predicting the acclimation of leaf-level photosynthesisto its environment and for simulating LUE In combinationwith prescribed PAR and remotely sensed fAPAR it esti-mates GPP across diverse environmental conditions (Wanget al 2017a) Its prediction for acclimating photosyntheticparameters reduces the number of prescribed (and temporallyfixed) values and avoids the distinction of model parameter-isation by vegetation types or biomes (apart from a distinc-tion between the C3 and C4 photosynthetic pathways) TheP-model has a further advantage over other data-driven GPPmodels (Running et al 2004 Zhang et al 2017) and em-pirically upscaled GPP estimates (Jung et al 2011) in that itaccounts for the influence of changing CO2 and that it usesfirst principles (rather than imposed functions) to representeffects of T D and p (Sect 2) The theory underlying theP-model regarding the waterndashcarbon trade-off has been de-scribed by Prentice et al (2014) and applied by Keenan et al(2016) to simulate how changes in primary production havedriven the terrestrial C sink over past decades and by Smithet al (2019) to explain variations in observed Vcmax Wanget al (2017a) complemented the theory by including effectsof limited electron transport capacity (Jmax) and predictedvariations in observed χ across environmental gradients Toresolve model biases under conditions of low soil moisture

Geosci Model Dev 13 1545ndash1581 2020 wwwgeosci-model-devnet1315452020

B D Stocker et al P-model v10 1547

Stocker et al (2019) further applied an empirical stress func-tion to reduce LUE under dry soil conditions

The purpose of this paper is (i) to provide a full documen-tation of the model implementation and reference for open-source software (rpmodel R package available on CRAN)(ii) to provide an evaluation of model-predicted LUE andGPP against GPP derived from eddy covariance flux mea-surements (FLUXNET 2015 Tier 1 dataset) (iii) to applythis model for global-scale simulations and compare spatialpatterns and global totals of simulated GPP with other esti-mates with global coverage and (iv) to introduce a robustand pragmatic solution to resolving model bias under dryand cold conditions With (iv) we do not aim at extendingthe theoretical basis for the P-model (Prentice et al 2014Wang et al 2017a) but to include environmental controls inthe LUE model that serve to make the model applicable as aremote-sensing-data-driven GPP model for a wide range ofconditions and vegetation types The evaluation focuses ondifferent components of variability (spatial annual seasonaldaily anomalies) (Sects 46ndash42) We further address uncer-tainties associated with the fAPAR forcing (Sect 44) and theuncertainties in the evaluation data by using GPP data de-rived from different flux decomposition methods (Sect 45)The use of continuous GPP measurements rather than ex-perimentally disturbed measurements makes it challengingto assess modelled GPP under extreme environmental con-ditions We therefore make a further evaluation of simulatedGPP during the course of soil moisture drought events (fLUEdroughts Sect 43)

2 Theory

The theory underlying the P-model has been described byWang et al (2017a) and the derivation of equations is giventherein It is presented here again for completeness

21 Balancing carbon and water costs

The P-model centres around a prediction for the optimal ratioof leaf-internal to ambient CO2 concentration ci ca (termedχ ) that balances the costs associated with maintaining thetranspiration stream and the cost of maintaining a given car-boxylation capacity The optimal balance is achieved whenthe two marginal costs are equal

apart(EA)

partχ=minusb

part(VcmaxA)

partχ (3)

Here a and b are the respective unit costs b is assumed tobe constant and a to scale linearly with the temperature-dependent viscosity of water η(T ) calculated following Hu-ber et al (2009) Below we introduce β = baprime with a =ηlowastaprime and ηlowast = η(T )η(25 C) The optimal χ solves theabove equation We use Fickrsquos law (Fick 1855) to expresstranspiration and assimilation as a function of stomatal con-

ductance gs

E = 16gsD (4)

and

A= gsca(1minusχ) (5)

and use the RuBisCO-limited assimilation rate from theFvCB model

A= AC = Vcmax mC (6)

with

mC =ciminus0

lowast

ci+K (7)

where ci is given by caχ K is the effective MichaelisndashMenten coefficient for RuBisCO-limited assimilation(Sect B3) and 0lowast is the photorespiratory compensationpoint in the absence of dark respiration (Sect B1) Theoptimal χ can be derived as

χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD (8)

with

ξ =

radicβ(K +0lowast)

16ηlowast (9)

(See Appendix F1 for intermediate steps) Because bothterms in Eq (3) are divided by A the solution is indepen-dent of whether the RuBisCO-limited rate AC or the light-limited rate AJ (see below) is followed With this predictionfor χ we can use the coordination hypothesis (Chen et al1993 Haxeltine and Prentice 1996 Maire et al 2012) andthe light-limited assimilation rate from the FvCB model towrite

AJ = ϕ0 Iabs m (10)

with

m=ciminus0

lowast

ci+ 20lowast (11)

Iabs is the amount of absorbed light and ϕ0 is the intrinsicquantum yield efficiency This equation has the form of aLUE model (Eq 2) in that AJ scales linearly with Iabs UsingEqs (9) and (8) m can be expressed directly as

m=caminus0

lowast

ca+ 20lowast+ 30lowastradic

16ηlowastDβ (K+0lowast)

(12)

The unit cost ratio β has been estimated by Wang et al(2017a) to 240 based on global leaf δ13C data and a simpli-fied version of the P-model (assuming 0lowast = 0 and neglecting

wwwgeosci-model-devnet1315452020 Geosci Model Dev 13 1545ndash1581 2020


the Jmax limitation) Here we re-estimated β to 146 based onthe full version of the model using the same global leaf δ13Cdataset This is more strictly consistent with the model for-mulation implemented here Equation (12) provides the basisfor predicting CO2 assimilation rates in the form of a LUEmodel (Eq 2) where LUE is a function of T and p (bothaffecting 0lowast K and ηlowast see Sects B1 and B3) D and ca

The prediction of optimal χ has a number of corollaries(see Appendix C) An estimate for stomatal conductance (gs)and the intrinsic water use efficiency (iWUE =Ags) directlyfollow from the optimal waterndashcarbon balance (Eq 3) By as-sumingAJ = AC we can further derive Vcmax as well as darkrespiration (Rd) which is a function of Vcmax (see Sects C3and C4)

22 Introducing Jmax limitation

Equation (10) assumes that the light response of A is lin-ear up to the coordination point In reality rates saturate to-wards high light levels because the electron transport rate J necessary for the regeneration of ribulose 15-bisphosphate(RuBP) tends towards a maximum Jmax To account for thiseffect Eq (10) can be modified following the formulationby Smith (1937) using a non-rectangular hyperbola relation-ship betweenAJ and Iabs to allow for the effect of finite Jmax

AJ = ϕ0 Iabs m1radic

1+(

4 ϕ0 IabsJmax

)2

︸︷︷︸L

(13)

In this equation AJ is no longer linear with respect to Iabsand thus does not have the form of a LUE model How-ever Jmax is assumed here to acclimate on longer timescalesto Iabs so that the marginal gain in assimilation A per unitchange in Jmax is equal to the unit cost (c) of maintainingJmax

partA

partJmax= c (14)

The unit cost c is assumed to include the maintenance oflight-harvesting complexes and various proteins involved inthe electron transport chain The cost of maintaining a givenJmax is thus assumed to scale linearly with Jmax and thatthis proportionality is constant (c is constant) By taking thederivative of Eq (13) with respect to Jmax and rearrangingterms (see Appendix F2 for intermediate steps) we obtainthe Jmax limitation factor L in Eq (13) as

L=

radic1minus

(clowast

m

)23

(15)

with clowast = 4c Note that L is independent of Iabs Hence AJis again a linear function of absorbed light The cost factor clowast

is estimated from published values of Jmax Vcmax = 188 at

25 C (Kattge and Knorr 2007) and χ = 08 (Lloyd and Far-quhar 1994) at clowast = 041 (Wang et al 2017a) The revisedLUE model thus becomes

A= ϕ0 Iabs mprime (16)

with

mprime =m

radic1minus

(clowast

m

)23

(17)

Wang et al (2017a) showed that this formulation of Jmaxcosts leads to a realistic dependence of the Jmax Vcmax ratioon growth temperature

As shown by Smith et al (2019) an alternative approachcan be used to introduce the effects of Jmax limitation re-placing Eq (13) by the more widely used one-parameterfamily of saturation curves following Farquhar and Wong(1984) This alternative is described in Appendix F3 and im-plemented as an optional method in the R package rpmodel

3 Methods

31 The light use efficiency model

A is commonly expressed in mol mminus2 sminus1 For further modeldescription and evaluation we refer to ecosystem-scalequantities in mass units of assimilated C and model GPP(g C mminus2 dminus1) following Eq (2) with

fAPAR middotPPFD = Iabs (18)LUE = ϕ0(T ) β(θ) m

prime MC (19)

Here MC is the molar mass of carbon (120107 g molminus1) toconvert from molar units to mass units and PPFD is the pho-tosynthetic photon flux density per square metre integratedover a day (mol mminus2 dminus1) fAPAR is unitless and integratesacross the canopy ie from fluxes per unit leaf area to fluxesper unit ground area LUE is in units of g C molminus1 The in-trinsic quantum yield parameter ϕ0 is modelled as temper-ature dependent and an additional (unitless) empirical soilmoisture stress factor (β(θ)) is included for modelling LUE

311 Temperature dependence of the intrinsicquantum yield of photosynthesis

The temperature dependence of the intrinsic quantum yield(ϕ0(T ) mol molminus1) is modelled following the temperaturedependence of the maximum quantum yield of photosystemII in light-adapted leaves determined by Bernacchi et al(2003) as

ϕ0(T )=aLbL

4(0352+ 0022 T minus 000034 T 2) (20)

where aL is the leaf absorptance and bL is the fraction ofabsorbed light that reaches photosystem II The factor 14



is introduced here as the equation given by Bernacchi et al(2003) applies to electron transport rather than C assim-ilation Here (aLbL4) is treated as a single calibratableparameter (see Sect 33) and is henceforth referred to ascL equiv aLbL4 (All calibratable parameters are thereafter in-dicated by a hat over the symbol) This temperature depen-dence was not accounted for in earlier P-model publications(Keenan et al 2016 Wang et al 2017a) To test the ef-fect of this temperature dependence on simulated GPP weconducted alternative simulations where a constant ϕ0 wascalibrated instead (Sect 32) Note that ϕ0 includes the fac-tor aL for incomplete leaf absorptance which is commonlyquantified separately from the quantum yield efficiency Inother vegetation models aL is commonly ascribed a valueof 072ndash088 (Rogers et al 2017) Values of ϕ0 used hereare accordingly lower than values for the intrinsic quantumyield reported from experimental studies (Long et al 1993Singsaas et al 2001) Furthermore within-canopy reflectionand reabsorption indicate that leaf-level absorptance is notequivalent to canopy-level absorptance thus ϕ0 should beregarded as canopy-scale effective value of intrinsic quan-tum yield It is treated here as a calibratable parameter whichmay vary according to the fAPAR forcing dataset used

312 Soil moisture stress

β(θ) is an empirical soil moisture stress function We useresults by Stocker et al (2018) to fit this function based ontwo general patterns First the functional form of β(θ) is ap-proximated by a quadratic expression that approaches 1 forsoil moisture at a certain threshold θlowast and held constant at 1for soil moisture values above this threshold Here θ is theplant-available soil water expressed as a fraction of availablewater holding capacity and θlowast is set to 06 The general formis

β =

q(θ minus θlowast)2+ 1 θ le θlowast

1 θ gt θlowast(21)

Second the sensitivity of β(θ) to extreme soil dryness (θrarr0) is related to the mean aridity quantified as the mean annualratio of actual over potential evapotranspiration (AET PET)(Stocker et al 2018) The decline in β(θ) with drying soilsis steep in dry climates and less steep in less dry climates InEq (21) the sensitivity parameter q is defined by the maxi-mum β reduction at low soil moisture β0 equiv β(θ = θ0) lead-ing to q = (β0minus 1)(θlowastminus θ0)

2 Note that q has a negativevalue β0 is modelled as a linear function of the mean arid-ity

β0 = aθ + bθ (AETPET) (22)

aθ and bθ are treated as calibratable parametersSoil moisture (θ ) AET and PET are simulated using the

SPLASH model (Davis et al 2017) which treats soil wa-ter storage as a single bucket and calculates potential evapo-transpiration based on Priestley and Taylor (1972) The only

difference with the model version described by Davis et al(2017) is that we account here for a variable water holdingcapacity calculated based on soil texture and depth data fromSoilGrids (Hengl et al 2014) A detailed description of theapplied empirical functions for calculating plant-availablewater holding capacity from texture data is given in Ap-pendix D

32 Simulation protocol

321 Site-scale simulations

We conducted multiple sets of site-scale simulations (Ta-ble 1) to investigate the dependence of model performanceon alternative model setups (variablefixed soil moisture andtemperature effects) alternative choices of forcing data (fA-PAR) and alternative observational target data for calibra-tion (GPP based on different flux decompositions) Param-eters (cL aθ and bθ ) were calibrated and evaluated againstthe appropriate observational data for each set of simulationsseparately

The ORG setup is the P-model in its original form as de-scribed in Wang et al (2017a) It uses a fixed quantum effi-ciency of photosynthesis (ϕ0 is calibrated instead of cL) anddoes not account for soil moisture stress (β(θ)= 1) Herethe model is forced with fAPAR data based on MODIS FPAR(MCD15A3H) linearly interpolated 4 d values to daily val-ues (see Sect 341) and is calibrated against GPP data fromFLUXNET 2015 based on the nighttime partitioning method(NT) (see Sect 351) The simulation set BRC (ldquoBernacchirdquo)is identical to ORG except that ϕ0 is allowed to vary withtemperature following Bernacchi et al (2003) and Eq (20)and cL is calibrated The full P-model setup (FULL) includesthe soil moisture stress function described above and cL aθ and bθ are calibrated simultaneously

All additional simulations account for both temperatureand soil moisture effects The simulation set FULL_FPARitpalso uses MODIS FPAR data for fAPAR but applies a splineto get daily values This is to evaluate alternative interpola-tion methods The simulation set FULL_EVI uses MODISEVI (MOD13Q1) interpolated to daily from 8 d data to as-sess to which the degree the model performance depends onthe fAPAR forcing data source See Sect 341 for more in-formation

All site-scale simulations were calibrated against GPP data(Sect 33) calculated using the nighttime flux decompo-sition method (Reichstein et al 2005) Additional simula-tion sets FULL_DT FULL_NTsub and FULL_Ty were usedto investigate the dependence of model performance on thechoice of observational data used for calibration We usedGPP data based on the nighttime decomposition method (Re-ichstein et al 2005) for FULL_NTsub the daytime decom-position method (Lasslop et al 2010) for FULL_DT and analternative decomposition method previously used in Wanget al (2017a) for FULL_Ty The Ty method estimates a con-



stant monthly background respiration rate fitted to match netecosystem exchange fluxes of CO2 from measurements as-suming a linear or saturating dependence of GPP on PPFDCalibration and evaluation of FULL_DT FULL_NTsub andFULL_Ty are done only for sites and dates where observa-tional data are available for all three datasets (DT NT andTy) hence there is the distinction between FULL_NTsuband FULL

322 Global simulations

Global simulations were conducted for the FULL setup us-ing the respectively calibrated parameters from the site-scalesimulations All vegetation is assumed to follow the C3 pho-tosynthetic pathway and we do not distinguish between crop-lands and other vegetation We conducted two simulationswith alternative fAPAR forcing data These are describedin Sect 34

33 Model calibration

Calibration was performed only for the model parameters de-termining the quantum efficiency of photosynthesis (ϕ0 orcL respectively) and the dependence of the sensitivity of thesoil moisture stress function on average aridity (parametersaθ and bθ ) Simulated GPP was calibrated to minimise theroot mean square error (RMSE) compared to observed dailyGPP (Sect 35) We used generalised simulated annealingfrom the GenSA R package (Xiang et al 2013) to calibratemodel parameters This algorithm is particularly suited tofind global minima of non-linear objective functions in situa-tions where there can be a large number of local minima Totest the robustness of the calibration and evaluation metricswe additionally performed out-of-sample calibrations for theFULL setup where the training set included data from all butone site The test dataset used to calculate R2 and RMSEcontained only data from the single left-out site

34 Forcing data

Unstressed light use efficiency mprime in Eq (19) is simulatedusing monthly mean values for daytime T and D tempo-rally constant site-specific elevation (used to calculate at-mospheric pressure scaled from sea-level standard pressureof 101 325 Pa) and annually varying observed atmosphericCO2 (MacFarling Meure et al 2006) identical across sitesThe choice of aggregating to monthly mean values is mo-tivated by the timescale of RuBisCO turnover which limitsthe rate at which photosynthetic parameters can acclimate tochanging environmental conditions (McNevin et al 2006)

Predicted monthly LUE (mprime) is multiplied by daily vary-ing Iabs and response functions ϕ0(T ) and β(θ) driven bydaily varying temperature and soil moisture This choice ismotivated by the known rapid response in stomatal conduc-tance to drying soils (represented by β(θ)) and the instanta-neous temperature response of the quantum yield efficiency

(ϕ0(T )) Simulating GPP as the product of LUE and dailyvarying PPFD would not be consistent with the non-linear in-stantaneous response ofA to light (Eq 10) given the acclima-tion timescale of photosynthesis (Suzuki et al 2001 Maireet al 2012) We therefore evaluate simulated GPP averagedover 8 d periods The choice of appropriate model predictionand evaluation timescales is further discussed in Sect 5

341 fAPAR

For site-scale simulations we used three alternative datasetsas model forcing for fAPAR (MODIS FPAR splined MODISFPAR linearly interpolated and MODIS EVI splined seeTable 1) MODIS FPAR data are from the MCD15A3H Col-lection 6 dataset (Myneni et al 2015) given at a resolutionof 500 m and 4 d The data were filtered to remove data pointswhere clouds were present values equal to 100 and out-liers (more than 3 times the interquartile range) Filtered val-ues were replaced by the mean value for the respective dayof year To obtain daily varying Iabs (Eq 18) two alterna-tives were explored For the first (used in all setups exceptFULL_FPARitp) values were derived using a cubic smooth-ing spline (function smoothspline() with parameterspar=001 in R R Core Team 2016) For the FULL_FPARitp setup daily fAPAR values were linearly interpo-lated to each day MODIS EVI data are from the MOD13Q1Collection 6 dataset (Didan 2015) given at a resolution of250 m and 8 d These data were filtered based on the sum-mary quality control flag removing ldquocloudyrdquo pixels Gapswere filled and data were splined to daily values All fAPARdata were downloaded from the Google Earth Engine usingthe google_earth_engine_subsets library (Hufkens 2017)

For global-scale simulations we used two alternativefAPAR datasets ldquoMODIS FPARrdquo is from globally grid-ded MODIS FPAR data at 05 resolution derived at theIntegrated Climate Data Center (ICDC httpsicdccenuni-hamburgde1datenlandmodis-lai-fparhtml last ac-cess 5 March 2020) based on the MOD15A2H MODISTerra leaf area indexFPAR 8 d L4 global 500 m SIN gridV006 dataset (Myneni et al 2020) For the present applica-tion 8 d data are aggregated (mean) to monthly data ldquofA-PAR3grdquo is based on Advanced Very High Resolution Ra-diometer (AVHRR) Global Inventory Modeling and Map-ping Studies (GIMMS) FPAR3g v2 data (Zhu et al 2013)15 d 112 resolution and aggregated for the present ap-plication to 05 and monthly data For all global P-modelsimulations fAPAR is held constant for each day in respec-tive months Simulations cover the years 2000ndash2016 Due tolimited temporal coverage January 2000 data are taken asFebruary 2000 for simulations driven by MODIS FPAR

342 Meteorological data

For site-scale simulations the meteorological forcing dataare derived from the FLUXNET 2015 Tier 1 dataset (daily)



Table 1 Model setups The standard fAPAR data are MODIS FPAR MCD15A3H where the original data given at 4 d intervals are splinedto daily values (ldquosplrdquo) Alternative greenness forcing data are based on MODIS EVI MOD13Q1 splined from 8 d intervals to daily andMODIS FPAR MCD15A3H linearly interpolated (ldquoitplrdquo) from 4 d intervals to daily Standard observational GPP data used for modelcalibration and evaluation are from FLUXNET 2015 based on the nighttime flux decomposition method (ldquoNTrdquo in the table variableGPP_NT_VUT_REF in FLUXNET 2015) Alternative GPP data used based on the daytime flux decomposition method (ldquoDTrdquo in the tablevariable GPP_DT_VUT_REF) and based on an alternative method (Wang et al 2017a) (ldquoTyrdquo in the table) For the ORG BRC FULLFULL_FPARitp and FULL_EVI setups data used for the model calibration are from all dates where NT data are available For FULL_DTFULL_ Ty and FULL_NTsub setups calibration data are from all dates where data are available for all three methods (DT NT and Ty)Column ϕ0(T ) specifies whether the temperature dependence of intrinsic quantum yield is included Column β(θ) specifies whether soilmoisture stress is included Columns ϕ0 cL aθ and bθ provide the calibrated parameter values in each simulation set

Setup name fAPAR data GPP Calibration set ϕ0(T ) β(θ) ϕ0 cL aθ bθ

ORG FPAR MCD15A3H spl NT NT data no no 004998 ndash ndash ndashBRC FPAR MCD15A3H spl NT NT data yes no ndash 008179 ndash ndashFULL FPAR MCD15A3H spl NT NT data yes yes ndash 008718 0 073300

NULL FPAR MCD15A3H spl NT NT data no no 02475lowast ndash ndash ndash

FULL_FPARitp FPAR MCD15A3H itpl NT NT data yes yes ndash 008486 00 074704FULL_EVI EVI MOD13Q1 spl NT NT data yes yes ndash 013136 001000 078419

FULL_DT FPAR MCD15A3H spl DT NT DT Ty yes yes ndash 008604 00 072735FULL_Ty FPAR MCD15A3H spl Ty NT DT Ty yes yes ndash 008701 010671 068802FULL_NTsub FPAR MCD15A3H spl NT NT DT Ty yes yes ndash 008719 00 073334

lowast The value represents the fitted LUE corresponding to (ϕ0mprimeMC) in Eq (19)

which provides data from measurements taken and pro-cessed along with the CO2 flux measurements The PPFD(mol mminus2 dminus1) is derived from shortwave downwelling radi-ation as PPFD= 60times60times24times10minus6 kECRSW where kEC =

204 micromol Jminus1 (Meek et al 1984) and RSW is incomingshortwave radiation from daily FLUXNET 2015 data (vari-able name SW_IN_F given in W mminus2) The factor kEC ac-counts for the energy content of RSW and the fraction ofphotosynthetically active radiation in total shortwave radia-tion Daytime vapour pressure deficit (VPD or D in Sect 2)is calculated from half-hourly FLUXNET 2015 data (vari-able name VPD_F) by averaging over time steps with posi-tive insolation (SW_IN_F) Daytime air temperature is takendirectly from the FLUXNET 2015 dataset (variable nameT_F_DAY) This is a simplification as we are not calculatingleaf temperature or VPD at the leaf surface which are moredirectly relevant for photosynthesis

For global-scale simulations we use daily 05 mete-orological forcing from WATCH-WFDEI (Weedon et al2014) We use mean daily 2 m air temperature daily snowand rainfall shortwave downwelling radiation converted tomol photons mminus2 dminus1 by multiplication with kEC and daily2 m specific humidity (qair) converted to VPD (D) as de-scribed in Appendix E We used daily minimum and maxi-mum air temperatures for each month from Climate ResearchUnit (CRU) time series (TS) 401 data (Harris et al 2014) tocalculate a respective VPD and use their mean as input to P-model simulations in order to reduce effects of the non-lineardependence of D on T (D = (D(Tmin)+D(Tmax)2) Allprocesses that depend on atmospheric pressure use Eq (B10)

and the 05 resolution elevation map from WATCH-WFDEI(Weedon et al 2014) to calculate a temporally constant at-mospheric pressure for each grid cell

35 Calibration and evaluation data

351 Data for site-scale simulations

We used data from 59 sites for model calibration and 126sites for evaluation (Fig 1 and Table A1) The number ofvalid daily GPP data points used for the calibration set was162 158 and 241 084 for the evaluation set The calibra-tion sites were selected based on the apparent reliabilityof relationships between CO2 fluxes co-located greennessdata measured soil moisture and meteorological variablesemerging from a previous analysis (Stocker et al 2018)For the evaluation we used all sites except those classifiedas croplands or wetlands and seven sites where C4 vegeta-tion is mentioned in the site description available through theFLUXNET2015 dataset (AU-How DE-Kli FR-Gri IT-BCiUS-Ne1 US-Ne2 and US-Ne3)

GPP predictions by the P-model are compared to GPPestimates from the FLUXNET 2015 Tier 1 dataset (down-loaded on 13 November 2016) We used GPP based onthe nighttime partitioning method (Reichstein et al 2005)(GPP_NT_VUT_REF) and removed data for which morethan 50 of the half-hourly data are gap filled and forwhich the daytime and nighttime partitioning methods(GPP_DT_VUT_REF and GPP_ NT_ VUT_ REF respec-tively) are inconsistent ie the upper and lower 25 quan-



tiles of the difference between GPP values quantified by eachmethod For additional simulation sets model calibration andevaluation was performed using GPP data based on the day-time partitioning method (GPP_ DT_VUT_REF) (Lasslopet al 2010) with analogous filtering steps and GPP databased on an alternative method that fits a constant ecosystemrespiration rate as the net ecosystem exchange under con-ditions where PPFD tends to zero (FULL_Ty Wang et al2017a) For all calibration and evaluation we removed datapoints before the ldquoMODIS erardquo (before 18 February 2000)

352 Data for global-scale simulations

We compare the simulated spatial distribution of GPP fromglobal-scale simulations against seven different remote-sensing-data-driven GPP estimates with global coverageand two Sun-induced fluorescence (SiF) data products Theglobal GPP estimates are from the following models MTE(Jung et al 2011) FLUXCOM (ldquoRS+METEOrdquo setup) (Tra-montana et al 2016) MODIS GPP (MOD17A2H Collec-tions 55 and 6) (Running et al 2004 Zhao et al 2005Running et al 2015) BESS (Jiang and Ryu 2016) BEPS(He et al 2018 Chen et al 2016) and VPM (Zhang et al2017) A more detailed description of these models and ag-gregation to a common grid of 05 and monthly resolutioncan be found in Luo et al (2018) For SiF we use data fromGlobal Ozone Monitoring Experiment-2A (GOME-2A) andGOME-2B based on v2 (V27) 740 nm terrestrial chloro-phyll fluorescence data from the MetOp-A and MetOp-Bsatellites (Joiner et al 2013 2016) Data were aggregatedto monthly and 05 resolution by mean as further describedin Luo et al (2018)

36 Evaluation methods

We evaluated both simulated LUE and GPP The P-model(Sect 2) predicts variations in LUE across sites (space) andmonths (monthly LUE=mprime) while simulated GPP is af-fected by the PPFD and fAPAR data used as model forcing(Eq 19 and Sect 34) Conversely ldquoobservedrdquo LUE is cal-culated as LUEobs = GPPobs(fAPAR middotPPFD) and the eval-uation is thus also affected by the PPFD and fAPAR dataThe evaluation of LUE tests the added explanatory powerof the P-model compared to models that rely on fixed pre-scribed LUE values Evaluating GPP facilitates the compari-son of the model performance to similar models of terrestrialGPP Model performance for GPP is benchmarked against anull model (NULL) which assumes a temporally constantand spatially uniform LUE The LUE for the NULL modelis fitted to observed GPP using linearly interpolated MODISFPAR and GPP data from the NT method see Table 1 Thuswhile LUE is constant the NULL model preserves the spatialand temporal patterns in APAR (= fAPAR middotPPFD)

Figure 1 Overview of sites selected for model calibration (greendots) and evaluation (black dots) All sites and additional informa-tion are listed in Table A1 The colour key of the map representsaridity quantified as the ratio of precipitation over potential evapo-transpiration from Greve et al (2014)

361 Components of variability

For LUE we separately analysed spatial (mean annual val-ues by site) and monthly means only for the FULL setupFor GPP we analysed spatial annual seasonal (mean by dayof year) 8 d and the variability in daily anomalies from themean seasonal cycle for all setups The seasonal variabilitywas determined for different KoumlppenndashGeiger climatic zones(see Table 2) Information about the association of sites withclimatic zones was extracted from Falge et al (2017) Eval-uations were made only for climatic zones with at least threesites For each component of variability we calculated theadjusted coefficient of determination (R2

adj hereafter referredto as R2) and the RMSE Figures showing correlations be-tween simulated and observed values additionally present themean bias the slope of the linear regression model and thenumber of data points (N )

362 Drought response

The bias in GPP (modelled minus observed) was calculatedfor 20 d before and 80 d after the onset of a drought event asidentified by Stocker et al (2018) for 36 sites Drought events(fLUE droughts) are periods of consecutive days where soilmoisture separated from other drivers using neural networksreduces LUE below a given threshold The data specifyingthe timing and duration of drought events were downloadedfrom Zenodo (Stocker 2018) We then rearranged the data toalign all drought events at all sites normalised data to theirmedian value during the 10 d before the onset of droughts(normalisation by subtracting median) and computed quan-tiles per day where ldquodayrdquo is defined with respect to the onsetof each drought event



4 Results

41 Calibration results

The calibration of model parameters done with data from allcalibration sites simultaneously yielded values that closelymatched the means across parameter values derived from theout-of-sample calibrations (Fig 2) This confirms the robust-ness of the calibration and that the model is not overfittedSimilarly for the evaluation metrics the R2 and RMSE val-ues reported from evaluations against data from all evalua-tion sites pooled yielded values that closely match the meansacross the out-of-sample evaluations (each calculated withdata from the single left-out site) This analysis also showsthat the distribution of the evaluation metrics is skewed withevaluations against a few sites indicating relatively poor per-formance (R2 below 05 for ZM-Mon AR-Vir and FR-Pue)while the most frequent values indicate very good model per-formance (evaluations at 21 sites giving R2 values of above08) Because the out-of-sample calibrations are computa-tionally very expensive we performed this analysis only forone setup (FULL) and report evaluation metrics done withpooled data from all evaluation sites for the remainder of theanalysis

42 GPP variability across scales

Tables 3 and 4 provide an overview of model performance(R2 and RMSE) in simulating GPP at different scales TheORG setup captures 70 of the variance in observed GPPwith data aggregated to 8 d means (33 604 data points)Model performance both with respect to explained vari-ance (R2) and the RMSE is improved by including the ef-fects of temperature on quantum yield efficiency in the BRCmodel setup (R2

= 72 ) and by including the effects ofsoil moisture stress in the FULL model setup (R2

= 75 Fig 3) Both the BRC and FULL model setups outperformthe NULL model

421 Seasonal variations

Seasonal variations are generally reliably simulated (R2069ndash073 for P-model setups and R2 071 for the NULLmodel Fig 4) Also the NULL model captures most of theseasonal variability especially in climate zones Dfb and Dfcand Cfb and Cfa This indicates that seasonal GPP variationsare largely driven by seasonal changes in insolation (PPFD)and vegetation greenness (fAPAR) Accounting for tempera-ture effects on the quantum yield efficiency reduces the over-estimation of GPP in spring except in the case of climatezone Dfb Observed GPP increases are lagged compared tovegetation greenness with a delay of up to 2 months at somesites This lag is clearly visible at almost all sites in DfbThe early-season high bias is largely absent for sites in cli-mate zone Cfb where observed GPP starts increasing earlyand the simulations match the observations except at sites

CZ-wet DE-Hai and FR-Fon where the start of season issimulated too early

GPP is overestimated during the dry season in climatezones with a marked dry season (Aw Bsk Csa and Csb)in model setups that do not account for soil moisture stress(ORG BRC NULL) The NULL model has the largest biasHigh VPD during dry periods reduces simulated LUE andleads to lower GPP values and a smaller bias in all the P-model setups (ORG BRC FULL) The empirical soil mois-ture stress function applied in the FULL setup eliminates thedryness-related bias in zones Aw Csa and Csb and substan-tially reduces this bias for sites in zone Bsk Observationssuggest that GPP declines to values around zero during dryperiods at sites in zone Bsk (mostly savannah vegetation andgrasslands see Table A1) The remaining bias in the FULLmodel which includes the soil moisture stress function isrelated to the fact that prescribed fAPAR remains relativelyhigh and that the soil moisture stress function does not de-cline to zero

The ORG and BRC models tend to underestimate peak-season GPP more strongly compared to the FULL modelThis is a direct consequence of the calibration which bal-ances errors across all data points Across-site average peak-season maximum GPP is accurately captured by the FULLmodel in most zones (Fig 4) except for an underestimationof GPP in zones Aw Cfa and Cfb and an overestimation inzone Csa Site-level evaluations suggests no clear relation-ship between peak-season underestimation and vegetationtype in zone Cfb The overestimation of peak-season GPPin zone Csa is caused by a high bias at sites with evergreenbroadleaf vegetation (FR-Pue IT-Cp2 IT-Cpz) sites withother vegetation types show no consistent peak-season bias

422 Spatial and annual variations

The R2 for simulated GPP aggregated to annual totalsranges from 060 (ORG) to 069 (FULL) The NULL modelachieves an R2 of 058 Most of the explanatory power of thedifferent models for annual total GPP stems from their powerin predicting between-site (ldquospatialrdquo) variations (Fig 5) TheR2 for spatial variations ranges from 063 (ORG) to 069(FULL) and 065 for the NULL model In contrast interan-nual variations at a site are poorly simulated (R2 005ndash009for P-model setups and 003 for the NULL model) Inter-annual variations are generally much smaller than between-site (spatial) variations or seasonal variations Thus captur-ing them is challenging Interannual GPP variations are gen-erally better simulated at sites where the variability is highand in particular at dry sites

43 Drought response

The P-model setups that do not include the soil mois-ture stress function (ORG and BRC) systematically over-estimate GPP during droughts (Fig 6) This bias increases



Table 2 Description of KoumlppenndashGeiger climate zones and number of sites for which data are available per climate zone and hemisphereSites are classified based on Falge et al (2017) and Beck et al (2018) Only zones with data from more than three sites are shown

Code N north N south Description

Aw ndash 5 Tropical savannahBsk 5 ndash Arid steppe coldCfa 11 ndash Warm temperate fully humid with hot summerCfb 20 5 Warm temperate fully humid with warm summerCsa 12 ndash Warm temperate with dry and hot summerCsb 4 ndash Warm temperate with dry and warm summerDfb 17 ndash Cold fully humid with warm summerDfc 21 ndash Cold fully humid with cold summer

Figure 2 Out-of-sample calibration and evaluation results (andashc) Distribution of parameter values (FULL setup) from calibrations wheredata from one site were left out for each individual calibration Parameters aθ and bθ are unitless (d e) Distribution of evaluation metricscalculated on data from the left-out site based on simulations with model parameters calibrated on all other sitesrsquo data Solid vertical red linesrepresent the parameter values calibrated with data from all sites pooled These are the values reported in Tables 3 and 4 for FULL setupDashed red lines represent the mean across values from out-of-bag calibrations and evaluations

sharply at the onset of drought events and continues to in-crease throughout the drought period The bias is stronglyreduced by applying the empirical soil moisture stress func-tion (Eq 21) in the FULL model A small bias remains alsoin the FULL model This stems from overestimated values ata few sites (in particular AU-DaP US-Cop US-SRG US-SRM US-Var US-Whs US-Wkg) mostly grasslands andsites in seasonally dry climate zones (Aw Bsk and Csa seeFig 4) where flux measurements indicate an almost com-plete shutdown of photosynthetic activity during the dry sea-son In contrast the fAPAR data (MODIS FPAR) suggestvalues substantially greater than zero at these sites duringthese periods This suggests either contributions to PAR ab-sorption by photosynthetically inactive tissue underestima-tion of LUE sensitivity to dry soils at these sites or an over-

estimation of the rooting zone moisture availability by theSPLASH model

44 Uncertainty from fAPAR input data

Tests of the sensitivity of model performance to alternativefAPAR forcing datasets show that the difference betweensplined and linearly interpolated MODIS FPAR is small withslightly better performance using splined fAPAR data Modelperformance is generally better using MODIS FPAR com-pared to simulations using MODIS EVI Spatial variationsin particular are better captured using MODIS FPAR (Fig 5R2 069 for the FULL setup) compared to MODIS EVI (R2058) However the R2 of interannual variations is 015 forMODIS EVI and 009 for MODIS FPAR In terms of biasesin climate zones the overestimation of GPP during the dry



Table 3 R2 of simulated and observed GPP based on different model setups and for different components of variability

Setup 8 d Spatial Annual Seasonal Var (daily) Var (annual)

FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003

FULL_FPARitp 073 071 069 074 024 010FULL_EVI 070 058 047 071 027 015

FULL_DT 064 067 069 064 030 010FULL_NTsub 066 069 069 066 030 009FULL_Ty 068 068 049

Table 4 RMSE of simulated and observed GPP based on different model setups and for different components of variability


FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371



period in zone Bsk is larger when using MODIS EVI thanwhen using MODIS FPAR (Fig 7 right) The positive springbias in simulated GPP in zone Dfb is present irrespective ofthe source of the fAPAR forcing (Fig 7 left) as is the peak-season bias of GPP in zones Bsk Cfb and Csb (not shown)Differences between the EVI- and FPAR-forced simulationsdepend on vegetation type The EVI-forced simulation tendsto be biased low in evergreen needleleaf vegetation and hasgenerally lower values in all evergreen vegetation types com-pared to the FPAR-forced simulation However there is nogeneral difference in model bias between simulations madewith the two forcings in other vegetation types

45 GPP target data

The different flux decomposition methods make funda-mentally different assumptions regarding the sensitivity ofecosystem respiration to diurnal changes in temperatureThis should lead to systematic differences in derived obser-vational GPP values and should affect modelndashdata disagree-ment

Model predictions compare better to GPP data based onthe flux decomposition method Ty (Wang et al 2017a) thanfor GPP data based on the DT and NT methods For GPP8 d means the model achieves an R2 of 068 when com-

pared to GPP Ty (FULL_Ty model setup) as opposed to 064and 066 compared to the DT and NT methods respectively(FULL_DT and FULL_NTsub Table 3 Fig 8) Spatial andannual correlations are not evaluated for GPP Ty due to miss-ing data Evaluations presented here rely on dates for whichneither the NT DT nor Ty methods have missing values andthus contain an equal number of data points Metrics fromthe NT evaluation repeated here are not identical to the onesabove and are referred to as ldquoNTsubrdquo in Tables 3 and 4

We found a systematic low bias of simulated GPP in thepeak-season in the climatic zone Cfb (warm temperate fullyhumid warm summer) However as shown in Fig 8 thisbias does not seem to be affected by the choice of GPP eval-uation data

46 LUE

The FULL version of the P-model captures 32 of the vari-ability in mean annual LUE across all sites and across the fullrange of observed mean annual LUE values and vegetationtypes (Fig 9) Overall 48 of the observed LUE variationwithin vegetation types is captured by the model through therelationships with climate without the need to specify pa-rameters for specific vegetation types



Figure 3 Correlation of observed and modelled GPP values of all sites pooled mean over 8 d periods for the model setups FULL (a) andNULL (b)

Figure 4 Mean seasonal cycle Observations are given by the black line and grey band representing the median and 33 66 quantiles ofall data (multiple sites and years) pooled by climate zone Coloured lines represent different model setups The annotation above each plotspecifies the climate zone (see Table 2) Only climate zones are shown here for which data from at least five sites were available



Figure 5 Correlation of modelled and observed annual GPP in simulations FULL (a) NULL (b) and FULL_EVI (c) The red lines arebased on means across years by site and represent spatial (across-site) variations Black lines and text are based on annual values with oneline for each site Lines represent linear regressions R2 and RMSE statistics for annual values are based on pooled data from all sites For aperfect fit between modelled and observed annual GPP values all black lines (representing the linear regression model of annual values fora single site) would lie on the 1 1 line and have a slope of 1 Slopes that deviate substantially from 1 or are even negative for some sitesshow poor model performance in capturing interannual variability

Overall 31 of the variability in monthly mean LUE iscaptured by the model with data from all sites and yearspooled (Fig 9) The model overestimates monthly LUE val-ues and underestimates LUE at the lowest and highest endsof the LUE range respectively The low-end overestima-tion is reflected by the overestimation of GPP in the springat winter-cold sites (Sect 421) and during soil moisturedroughts (Sect 43) The underestimation of high monthlyvalues is not clearly linked to any particular vegetation type

47 Global GPP

Simulated global total GPP is 106 Pg C yrminus1 when usingMODIS FPAR and 122 Pg C yrminus1 when using fAPAR3g forc-ing data (mean over the years 2001ndash2011 FULL setup)The spatial pattern of simulated GPP differs substantially be-tween simulations forced by MODIS FPAR and fAPAR3g(Fig 10) This is most evident in their latitudinal distribution

(Fig 11) The global spatial pattern of fAPAR3g-based GPPsimulated by the P-model generally matches the global dis-tribution of the mean across other remote-sensing-based GPPmodels and lies within the range of their estimates for thelatitudinal distribution The MODIS FPAR-forced P-modelsimulation suggests lower values in the tropics that differfrom the fAPAR3g-based estimates by a factor ofsim 2 aroundthe Equator The moderate tropical GPP of the MODISFPAR-based P-model simulation agrees well with the lati-tudinal distribution of SiF from GOME-2A and GOME-2B

5 Discussion

The performance of the P-model can be compared to re-sults obtained from other remote-sensing-driven GPP mod-els (RS models) In its FULL setup the P-model achieves anR2 of 075 and a RMSE of 196 g C mminus2 dminus1 in simulating



Figure 6 Bias in simulated GPP during the course of droughtevents Simulated GPP is from a simulation with (FULL) andwithout (BRC) accounting for soil moisture stress The timing ofdrought events is taken from Stocker et al (2018) and is identifiedby an apparent soil-moisture-related reduction of observed light useefficiency at 36 FLUXNET sites The bias is calculated as simulatedminus observed GPP Data from multiple drought events and sitesare aligned by the date of drought onset and aggregated across allsites and events (lines for medians shaded ranges from the 33 and 66 quantiles)

8 d mean GPP and evaluated against GPP data (NT method)from 126 sites This can be compared to predictions fromthe VPM model (R2 074 RMSE 208 g C mminus2 dminus1 113sites 8 d Zhang et al 2017) or BESS (R2 067 RMSE258 g C mminus2 dminus1 113 sites 8 d Jiang and Ryu 2016)The performance of the P-model in simulating annual GPPacross all 126 sites (R2 069) can be compared to resultsfrom MODIS GPP (MOD17A2 R2

= 073 12 sites Hein-sch et al 2006 and for the updated version MOD17A2HR2= 062 18 sites Wang et al 2017b) or BEPS (R2 081

RMSE 347 g C mminus2 dminus1 124 sites He et al 2018) Unfortu-nately we cannot present a direct comparison between thesemodels based on data from identical dates and sites A tar-geted model intercomparison may address this While sea-sonal and spatial variations in GPP are reliably simulated bythe P-model the modelrsquos performance in simulating inter-annual GPP variations is weaker Similar results regardingrelatively poor model performance in explaining interannualvariations have been found from previous studies in both em-pirical (Richardson et al 2007 Urbanski et al 2007b) andprocess model-based (Keenan et al 2012 Biederman et al2016) analyses This is likely due to lagged effects of climateanomalies expressed through biotic responses (Richardsonet al 2007 Keenan et al 2012)

The P-model-based estimates of global GPP(106 Pg C yrminus1 when using MODIS FPAR and 122 Pg C yrminus1

when using fAPAR3g forcing data mean over 2001ndash2011FULL setup) are within the range of other estimates ofglobal GPP (also means over 2001ndash2011) 133 Pg C yrminus1

for MTE (Jung et al 2011) 130 Pg C yrminus1 for FLUXCOM(Tramontana et al 2016) 112 Pg C yrminus1 for MODIS-55GPP and 105 Pg C yrminus1 for MODIS-6 GPP (Running et al2004 Zhao et al 2005) 133 Pg C yrminus1 for BESS (Jiangand Ryu 2016 Ryu et al 2011) 121 Pg C yrminus1 for BEPS(He et al 2018 Chen et al 2016) and 135 Pg C yrminus1 forVPM (Zhang et al 2017) The P-model results presentedhere are based on simulations that embody relatively strongsimplifying assumptions In particular we assumed allvegetation to follow the C3 photosynthetic pathway and wemade no distinction between croplands and other vegetationalthough crops are often more productive (Guanter et al2014) Due to the short period for which forcing data andoutputs from comparable models are available we did notanalyse temporal trends in global GPP here Analyses notshown here indicate that the introduction of the Jmax costfactor (not included eg in Keenan et al 2016) increasesthe sensitivity of modelled GPP to CO2 Further evaluationof model behaviour against data from CO2 manipulationexperiments will be necessary before applying the model tosimulate CO2-related trends

The large spread of tropical GPP estimates is striking Thehighest estimate among the other GPP models we used forevaluation here ndash coming from BESS ndash is more than 50 higher than MODIS GPP from Collection 6 The fAPAR3g-based P-model tropical GPP estimate falls within the rangeof other GPP models while the MODIS FPAR-based esti-mate is lower than all other models However the latterrsquoscomparably low tropical GPP agrees well with the latitudi-nal distribution of SiF (Fig 11) However large changes inleaf area index across latitudes combined with a dependencyof the SiF signal on vegetation structure (Zeng et al 2019)may undermine the validity of SiF as a benchmark for thelatitudinal GPP distribution A lack of evaluation data fromeddy covariance measurements in dense tropical forests pre-cludes us from drawing conclusions on the accurateness ofthese diverging tropical GPP estimates

With a particular focus on soil moisture effects Stockeret al (2019) presented global GPP based on the P-modelcorresponding to a setup with the soil moisture stress func-tion but without the temperature dependence of the quantumyield efficiency They also used a different parameterisationwith ϕ0 = 00579 aθ = 0107 and bθ = 0478 for their in-termediate model version Their estimate for global GPP wasaround 130 Pg C yrminus1 for recent years

The coefficients of determination (R2) of simulated versusobserved values are lower for LUE (032 for the spatial corre-lation in the FULL setup Fig 9b) than for GPP (069 for thespatial correlation in the FULL setup) This is because GPPvariations are strongly driven by variations in absorbed light(PPFDmiddotfAPAR) which are observed and used for modellingIn contrast variations in LUE cannot be observed directlyUsing remotely sensed information for estimating LUE vari-ations eg based on SiF (Frankenberg et al 2018 Li et al2018 Ryu et al 2019) or alternative reflectance indices (Ga-



Figure 7 Mean seasonal cycle for model setups with different greenness forcing data for two climate zones (Bsk and Dfb both in theNorthern Hemisphere) Observations are given by the black line and grey band representing the median and 33 66 quantiles by dayof year (DOY) of all data (multiple sites and years) pooled by climate zone Coloured lines represent model setups forced with differentgreenness data The annotation above each plot specifies the climate zone (see Table 2) Climate zones shown here are illustrative examples

Figure 8 Model performance subject to comparison with different flux decomposition methods for GPP (andashc) Mean seasonal cycle ofsimulated (red) and observed GPP (black) based on different flux decomposition methods for sites in climate zone Cfb north The grey bandrepresents the 33 66 quantiles of observed GPP by DOY (dndashf) Correlation of observed and simulated GPP values of all sites pooledmean over 8 d periods all sites pooled ldquoObserved GPPrdquo refers to the different flux decomposition methods DT for the daytime method(FULL_DT setup) NT for the nighttime method (FULL_NTsub setup) and Ty (FULL_Ty setup) for the method applied for data used inWang et al (2017b) Dotted lines in panels (dndashf) represent the 1 1 relationship red lines represent the fitted linear regressions



Figure 9 Modelled (FULL) versus observed LUE (a) Mean monthly LUE with data pooled from all sites and available years (b) Meanannual LUE by site (small dots and colour) and vegetation type (large dots and colour) Model performance metrics are given at the top withnumbers in brackets referring to the regression of data aggregated by vegetation types and non-bracketed numbers for data aggregated bysites Dotted lines represent the 1 1 relationship red lines represent the fitted linear regression to all data in panel (a) and the fitted linearregression to mean annual LUE by site in panel (b) The grey band in panel (b) represents the 95 confidence interval of the linear regressionVegetation types are closed shrubland (CSH) deciduous broadleaf forest (DBF) evergreen broadleaf forest (EBF) evergreen needleleafforest (ENF) grassland (GRA) mixed deciduous and evergreen needleleaf forest (MF) open shrubland (OSH) savanna ecosystem (SAV)woody savanna (WSA)

mon et al 1992 2016 Badgley et al 2017) is an activefield of research and the separation of remotely sensed sig-nals into contributions by LUE and absorbed light remainschallenging (Porcar-Castell et al 2014 Ryu et al 2019)Other remote-sensing-based GPP models rely on vegetation-type-specific model parameters for LUE (Zhang et al 2017Running et al 2004 Jiang and Ryu 2016) The P-modelin its FULL setup explains 48 of the variations in LUEacross sites aggregated to vegetation types without relyingon vegetation or biome-type specific parameterisations In itsORG setup it explains 12 of the variations (not shown)and 51 of the variations when excluding sites classifiedas ldquoopen shrublandsrdquo which tend have a substantially lowerLUE than simulated by the P-model (not shown) In spite ofthis substantial portion of explained variability the NULLmodel with its temporally constant and spatially uniformLUE achieves higher R2 values for GPP than the ORG P-model setup at the spatial annual and seasonal scales (Ta-ble 3) This indicates that the spatial and temporal variationsin absorbed light are the main drivers of GPP in LUE-typemodels and underlines the importance of evaluation againsta NULL model benchmark Taken together these findingsdemonstrate that the P-model offers a simple but powerfulmethod for simulating terrestrial GPP using readily avail-able input datasets and a very small number of free (calibrat-able) parameters Here three parameters are calibrated (forthe FULL setup) Other model parameters are derived fromindependent field and laboratory measurements

Accounting for the temperature dependence of the quan-tum yield efficiency (ϕ0) clearly improves model predictions

The parameter ϕ0 is commonly treated as a constant in globalvegetation models (Rogers et al 2017) Our results indicatepotential for improving such modelsrsquo photosynthesis routinesby accounting for the temperature dependence of ϕ0ϕ0 appears as a linear scalar in the LUE model How-

ever the magnitude of this scalar is uncertain and dependson whether incomplete light absorption by the leaf is in-cluded in the definition of ϕ0 or in fAPAR data We have usedMODIS FPAR and MODIS EVI data to define fAPAR in dif-ferent model setups While the two are well correlated theirabsolute values differ Hence we have calibrated an appar-ent quantum yield efficiency (ϕ0) to GPP data separately fordifferent fAPAR datasets thereby implicitly distinguishingwhat components of light absorption factors are contained inthe fAPAR data The leaf absorptance aL which is typicallytaken to be around 08 in global vegetation models (Rogerset al 2017) is similar to the ratio of fitted ϕ0 values for sim-ulation FULL and FULL_EVI here calculated as 067 (Ta-ble 1)

An improvement in model performance is obtained by ac-counting for soil moisture stress using an empirical functionHowever the use of an empirical function masks underly-ing processes Furthermore the use of an empirical functionis not consistent with the optimality approach that underliesthe P-model The bias reduction associated with using an em-pirical soil moisture stress function hints at missing factorsin the theoretical approach which rests on an assumed con-stancy of the unit costs of transpiration (a in Eq 3) Prenticeet al (2014) provide a definition of a that is explicit in termsof plant hydraulic traits and physical properties that deter-



Figure 10 Global distribution of GPP Shown are the mean annual values averaged over the years 2000 to 2016 The GPP shown as ldquomeanof other modelsrdquo is the average of MTE (Jung et al 2011) FLUXCOM (lsquoRS+METEOrsquo setup) (Tramontana et al 2016) MODIS GPP(Collections 55 and 6) (Running et al 2004 Zhao et al 2005) BESS (Jiang and Ryu 2016) BEPS (He et al 2018 Chen et al 2016) andVPM (Zhang et al 2017) P-model results are from simulations with the FULL setup and calibrated parameters as given in Table 1

Figure 11 Latitudinal distribution of GPP and SiF Values shown(GPP on the left y axis SiF on the right y axis) are grid cell area-weighted sums along 05 latitudinal bands

mine water transport along the plantndashsoilndashatmosphere con-tinuum In particular a prop (19ks)

minus1 where 19 is the max-imum daytime difference in leaf-to-soil water potential andks is the sapwood area-specific permeability However largevariations in stomatal conductance are known to occur in re-sponse to relatively fast soil dry-downs (timescale of days)(Keenan et al 2010 Egea et al 2011 Stocker et al 2018)This suggests a potential to improve the P-model by allowingthe unit cost of transpiration to be a function of rooting-zone

moisture availability and by coupling stomatal conductancewith the soil water balance

Observational uncertainty could affect both parameter cal-ibration and model evaluation Keenan et al (2019) founda systematic bias in GPP estimates based on the nighttimepartitioning method due to inhibition of leaf respiration inthe light (Kok 1949 Wehr et al 2016) which affects fluxesunevenly throughout the season and across vegetation typesHowever we found no clear difference in modelndashdata agree-ment nor in fitted parameters in comparisons of three alter-native GPP datasets that use different approaches to decom-pose net CO2 exchange fluxes from eddy covariance mea-surements into ecosystem respiration and GPP terms

We have found a consistent early-season high bias insimulated GPP for numerous sites in regions with decidu-ous broadleaved vegetation in temperate and cold climates(in particular US-MMS IT-Col US-WCr US-UMd US-UMB and US-Ha1) and also in mixed and needleleaf stands(in particular US-Syv US-NR1 FI-Hyy CA-Qfo and CA-Man) The temperature dependence of the intrinsic quan-tum yield as introduced in the BRC and FULL setups didnot resolve this bias Additional analyses (not shown) sug-gested that this bias is not related to soil temperatures TheP-model as applied here uses daily air temperature for sim-ulating temperature stress on the intrinsic quantum yieldin the BRC and FULL setups A reduction in the quan-tum yield efficiency arises from several mechanisms includ-



Figure 12 Distribution of anomalies from the mean seasonal cycle evaluated for daily values (a) and 8 d means (b)

ing increased non-photochemical quenching a reduction inchlorophyll and absorption by screening pigments (Huneret al 1993 Oquist and Huner 2003 Ensminger et al2004 Adams et al 2004 Verhoeven 2014) These adapta-tions serve to limit oxidative damage under high light andlow temperature conditions where an imbalance betweenelectron supply and demand exists arising from an imbal-ance between temperature-insensitive photochemical ratesand temperature-sensitive biochemical rates The reversionof these adaptations and resumption of the intrinsic quan-tum yield efficiency and photosynthesis requires sustainedtemperatures above a certain critical threshold (Tanja et al2003) and exhibits a delay with respect to instantaneous airtemperatures (Pelkonen and Hari 1980 Maumlkelauml et al 2004)Approaches accounting for a delayed resumption of photo-synthesis after cold periods offer scope for further improve-ment of the P-model and may be included in global vegeta-tion and Earth system models where this effect is currentlynot accounted for (Tanja et al 2003 Rogers et al 2017)

There is a positive bias in simulated GPP during the dryseason at a number of sites where the vegetation phenologyis influenced by drought The positive bias is related to thecombination of using prescribed fAPAR data which showssubstantial absorption by non-green vegetation and insuffi-cient sensitivity of simulated LUE to soil drying HoweverGPP is accurately simulated at other sites affected by season-ally recurring water stress The modelled sensitivity to drysoils is determined by the soil moisture stress function whichdepends on the mean aridity of the site as estimated using afixed depth soil moisture ldquobucketrdquo Accounting for variabil-ity in rooting zone depth which may also be influenced bylocal topographical factors and access to groundwater (Fanet al 2013 2017) may help to minimise model biases indrought-prone areas

The current implementation of the P-model involves somesimplifications in terms of climate drivers by using averagedaily meteorological conditions measured above the canopyas input Optimality in balancing carbon and water costs foraverage daily conditions is not necessarily equivalent to op-timality in balancing integrated water and carbon costs overthe diurnal cycle Large variations in ambient conditions overa diurnal cycle combined with a non-linear dependence ofcosts on these conditions suggest that the approach of tak-ing average daily conditions may be an oversimplificationNevertheless prior evaluations have shown robust and ac-curate predictions of optimal χ across a range conditions(Wang et al 2017a) Using above-canopy VPD values in-stead of VPD at the leaf surface for scaling water lossesimplicitly assumes a perfectly coupled atmospheric bound-ary layer Using above-canopy air temperature instead of leaftemperatures introduces a bias when the two become decou-pled (Michaletz et al 2015) The impact of these simplifica-tions may be minor but should be evaluated

A further simplification is that investment in electrontransport capacity (expressed by Jmax) and investments in thecarboxylation capacity (expressed by Vcmax) are coordinatedso that for conditions with which the model is forced (heremonthly means of daily averages) photosynthesis operates atthe co-limitation point of the light- and RuBisCO-limited as-similation rates and an effective linear relationship betweenabsorbed light and mean assimilation emerges This assump-tion follows from the coordination hypothesis which itselfcan be understood as an optimality principle (Haxeltine andPrentice 1996 Maire et al 2012) and is well supported byobservations (Maire et al 2012) However this coordinationis contingent on the timescale at which photosynthetic ac-climation occurs which is not known precisely (Smith andDukes 2013 Way and Yamori 2014) By simulating χ us-ing monthly mean meteorological variables we assume a



monthly timescale of acclimation This is probably a conser-vative estimate (Smith and Dukes 2017 Veres and WilliamsIII 1984) Considering the concave relationship of assimi-lation rates and absorbed light that follows from the FvCBmodel for a given Jmax linearly scaling a given monthly LUEterm with daily varying absorbed light levels should lead toan overestimation of assimilation rates at high light levelsThis overestimation should disappear as the timescale overwhich light levels are averaged is increased However ourresults do not confirm these expectations (Fig 12) The factthat the model did not exhibit a systematic error in simulatingGPP variations when applied at the daily timescale is prob-ably due to the fact that day-to-day variability in light levelsis relatively small compared to the within-day variability andthe non-linearity between A and daily varying light levelsdoes not play an important role

6 Conclusions

The P-model provides a simple parameter-sparse but pow-erful method to predict photosynthetic capacity and lightuse efficiency across a wide range of climatic conditionsand vegetation types It provides a basis for a terrestriallight use efficiency model driven by remotely sensed vege-tation greenness Using optimality principles for the formu-lation of the P-model reduces its dependence on uncertain orvegetation-type-specific parameters and enables robust pre-dictions of GPP and its variations through the seasons be-tween years and across space Further work is required todevelop a distinct treatment of C4 vegetation for global appli-cations and additional evaluations are needed to examine theP-modelrsquos sensitivity to increasing CO2 We have shown thataccounting for the effects of low soil moisture and the reduc-tion in the quantum yield efficiency under low temperaturesimproves model performance There is potential to includebelow-ground water limitation effects in the mechanistic op-timality framework of the P-model

Code and data availability The P-model is implemented as anR package (rpmodel) and available through CRAN and Zenodo(Stocker 2019a) Results shown here correspond to rpmodel ver-sion v104 A documentation of the R package is available un-der httpsstinebgithubiorpmodel (last access 5 February 2020)Both site-scale and global simulations shown here are done with theFortran implementation of the P-model within the SOFUN mod-elling framework (version v120) available on Zenodo (Stocker2019b) Site-scale forcing data ingest and filtering model calibra-tion and evaluation were done using the R package rsofun (versionv10wrap_sofun) available on Zenodo (Stocker 2020b) Scriptsthat implement the workflow (repository eval_pmodel version v2)are available on Zenodo (Stocker 2020a) Model outputs are avail-able on Zenodo (Stocker 2019c)



Appendix A Site information

Table A1 provides metadata information and references foreach site from the FLUXNET2015 Tier 1 dataset used formodel calibration and evaluation in the present study

Table A1 Sites used for evaluation Long is longitude negative values indicate west longitude Lat is latitude positive values indicate northlatitude Veg is vegetation type deciduous broadleaf forest (DBF) evergreen broadleaf forest (EBF) evergreen needleleaf forest (ENF)grassland (GRA) mixed deciduous and evergreen needleleaf forest (MF) savanna ecosystem (SAV) shrub ecosystem (SHR) wetland(WET) References not available in the metadata provided with the FLUXNET2015 dataset are listed as NA (not available)

Site Long Lat Period Veg Clim N Calib Reference

AR-SLu minus6646 minus3346 2009ndash2011 MF Bwk 448 Ulke et al (2015)AR-Vir minus5619 minus2824 2009ndash2012 ENF Csb 747 Y Posse et al (2016)AT-Neu 1132 4712 2002ndash2012 GRA Dfc 3709 Wohlfahrt et al (2008)AU-Ade 13112 minus1308 2007ndash2009 WSA Aw 532 Y Beringer et al (2011a)AU-ASM 13325 minus2228 2010ndash2013 ENF Bsh 953 Y Cleverly et al (2013)AU-Cpr 14059 minus3400 2010ndash2014 SAV Bsk 1412 Meyer et al (2015)AU-Cum 15072 minus3361 2012ndash2014 EBF Cfa 744 Beringer et al (2016)AU-DaP 13132 minus1406 2007ndash2013 GRA Aw 1820 Y Beringer et al (2011b)AU-DaS 13139 minus1416 2008ndash2014 SAV Aw 2230 Y Hutley et al (2011)AU-Dry 13237 minus1526 2008ndash2014 SAV Aw 1600 Y Cernusak et al (2011)AU-Emr 14847 minus2386 2011ndash2013 GRA Bwk 812 Schroder et al (2014)AU-Gin 11571 minus3138 2011ndash2014 WSA Csa 942 Y Beringer et al (2016)AU-GWW 12065 minus3019 2013ndash2014 SAV Bwk 664 Prober et al (2012)AU-Lox 14066 minus3447 2008ndash2009 DBF Bsh 273 Stevens et al (2011)AU-RDF 13248 minus1456 2011ndash2013 WSA Bwh 571 Bristow et al (2016)AU-Rig 14558 minus3665 2011ndash2014 GRA Cfb 1130 Beringer et al (2016)AU-Rob 14563 minus1712 2014ndash2014 EBF Csb 337 Beringer et al (2016)AU-Stp 13335 minus1715 2008ndash2014 GRA Bsh 1951 Y Beringer et al (2011c)AU-TTE 13364 minus2229 2012ndash2013 OSH Bwh 475 Cleverly et al (2016)AU-Tum 14815 minus3566 2001ndash2014 EBF Cfb 4346 Leuning et al (2005)AU-Wac 14519 minus3743 2005ndash2008 EBF Cfb 976 Kilinc et al (2013)AU-Whr 14503 minus3667 2011ndash2014 EBF Cfb 1064 Y McHugh et al (2017)AU-Wom 14409 minus3742 2010ndash2012 EBF Cfb 935 Y Hinko-Najera et al (2017)AU-Ync 14629 minus3499 2012ndash2014 GRA Bsk 475 Yee et al (2015)BE-Vie 600 5031 1996ndash2014 MF Cfb 4910 Y Aubinet et al (2001)BR-Sa3 minus5497 minus302 2000ndash2004 EBF Am 1192 Wick et al (2005)CA-Man minus9848 5588 1994ndash2008 ENF Dfc 1910 Dunn et al (2007)CA-NS1 minus9848 5588 2001ndash2005 ENF Dfc 1067 NACA-NS2 minus9852 5591 2001ndash2005 ENF Dfc 1123 NACA-NS3 minus9838 5591 2001ndash2005 ENF Dfc 1395 NACA-NS4 minus9838 5591 2002ndash2005 ENF Dfc 756 NACA-NS5 minus9848 5586 2001ndash2005 ENF Dfc 1245 NACA-NS6 minus9896 5592 2001ndash2005 OSH Dfc 1190 NACA-NS7 minus9995 5664 2002ndash2005 OSH Dfc 929 NACA-Qfo minus7434 4969 2003ndash2010 ENF Dfc 2416 Bergeron et al (2007)CA-SF1 minus10582 5448 2003ndash2006 ENF Dfc 526 NACA-SF2 minus10588 5425 2001ndash2005 ENF Dfc 676 NACA-SF3 minus10601 5409 2001ndash2006 OSH Dfc 660 NACH-Cha 841 4721 2005ndash2014 GRA Cfb 2944 Merbold et al (2014)CH-Dav 986 4682 1997ndash2014 ENF ET 4973 Zielis et al (2014)CH-Fru 854 4712 2005ndash2014 GRA Cfb 2861 Y Imer et al (2013)CH-Lae 837 4748 2004ndash2014 MF Cfb 3551 Y Etzold et al (2011)CH-Oe1 773 4729 2002ndash2008 GRA Cfb 2184 Y Ammann et al (2009)CN-Cha 12810 4240 2003ndash2005 MF Dwb 1019 Guan et al (2006)



Table A1 Continued


CN-Cng 12351 4459 2007ndash2010 GRA Bsh 1071 Y NACN-Dan 9107 3050 2004ndash2005 GRA ET 680 Shi et al (2006)CN-Din 11254 2317 2003ndash2005 EBF Cfa 921 Yan et al (2013)CN-Du2 11628 4205 2006ndash2008 GRA Dwb 595 Chen et al (2009)CN-HaM 10118 3737 2002ndash2004 GRA 949 Kato et al (2006)CN-Qia 11506 2674 2003ndash2005 ENF Cfa 995 Y Wen et al (2010)CN-Sw2 11190 4179 2010ndash2012 GRA Bsh 382 Shao et al (2017)CZ-BK1 1854 4950 2004ndash2008 ENF Dfb 1185 Acosta et al (2013)CZ-BK2 1854 4949 2004ndash2006 GRA Dfb 163 NADE-Gri 1351 5095 2004ndash2014 GRA Cfb 3642 Y Prescher et al (2010)DE-Hai 1045 5108 2000ndash2012 DBF Cfb 4247 Y Knohl et al (2003)DE-Lkb 1330 4910 2009ndash2013 ENF Cfb 1214 Lindauer et al (2014)DE-Obe 1372 5078 2008ndash2014 ENF Cfb 2260 Y NADE-RuR 630 5062 2011ndash2014 GRA Cfb 1227 Y Post et al (2015)DE-Tha 1357 5096 1996ndash2014 ENF Cfb 5141 Y Gruumlnwald and Bernhofer (2007)DK-Sor 1164 5549 1996ndash2014 DBF Cfb 4936 Y Pilegaard et al (2011)ES-LgS minus297 3710 2007ndash2009 OSH Csa 833 Reverter et al (2010)ES-Ln2 minus348 3697 2009ndash2009 OSH Csa 182 Serrano-Ortiz et al (2011)FI-Hyy 2430 6185 1996ndash2014 ENF Dfc 4857 Y Suni et al (2003)FR-Fon 278 4848 2005ndash2014 DBF Cfb 3262 Y Delpierre et al (2015)FR-LBr minus077 4472 1996ndash2008 ENF Cfb 2814 Y Berbigier et al (2001)FR-Pue 360 4374 2000ndash2014 EBF Csa 4722 Y Rambal et al (2004)GF-Guy minus5292 528 2004ndash2014 EBF Af 3609 Bonal et al (2008)IT-CA1 1203 4238 2011ndash2014 DBF Csa 1036 Sabbatini et al (2016)IT-CA3 1202 4238 2011ndash2014 DBF Csa 913 Sabbatini et al (2016)IT-Col 1359 4185 1996ndash2014 DBF Cfa 3350 Y Valentini et al (1996)IT-Cp2 1236 4170 2012ndash2014 EBF Csa 764 Y Fares et al (2014)IT-Isp 863 4581 2013ndash2014 DBF Cfb 641 Y Ferreacutea et al (2012)IT-La2 1129 4595 2000ndash2002 ENF Cfb 513 Marcolla et al (2003a)IT-Lav 1128 4596 2003ndash2014 ENF Cfb 3947 Y Marcolla et al (2003b)IT-MBo 1105 4601 2003ndash2013 GRA Dfb 3682 Y Marcolla et al (2011)IT-Noe 815 4061 2004ndash2014 CSH Cwb 3070 Y Papale et al (2014)IT-PT1 906 4520 2002ndash2004 DBF Cfa 891 Y Migliavacca et al (2009)IT-Ren 1143 4659 1998ndash2013 ENF Dfc 3405 Y Montagnani et al (2009)IT-Ro2 1192 4239 2002ndash2012 DBF Csa 3113 Tedeschi et al (2006)IT-SR2 1029 4373 2013ndash2014 ENF Csa 675 Y Hoshika et al (2017)IT-SRo 1028 4373 1999ndash2012 ENF Csa 3797 Y Chiesi et al (2005)IT-Tor 758 4584 2008ndash2014 GRA Dfc 2172 Y Galvagno et al (2013)JP-MBF 14232 4439 2003ndash2005 DBF Dfb 471 Matsumoto et al (2008)JP-SMF 13708 3526 2002ndash2006 MF Cfa 1288 Y Matsumoto et al (2008)NL-Hor 507 5224 2004ndash2011 GRA Cfb 2188 Y Jacobs et al (2007)NL-Loo 574 5217 1996ndash2013 ENF Cfb 4671 Y Moors (2012)RU-Fyo 3292 5646 1998ndash2014 ENF Dfb 4635 Y Kurbatova et al (2008)RU-Ha1 9000 5473 2002ndash2004 GRA Dfc 567 Belelli Marchesini et al (2007)SD-Dem 3048 1328 2005ndash2009 SAV Bwh 770 Y Ardo et al (2008)SN-Dhr minus1543 1540 2010ndash2013 SAV Bwh 688 Y Tagesson et al (2014)US-AR1 minus9942 3643 2009ndash2012 GRA Cfa 1060 NAUS-AR2 minus9960 3664 2009ndash2012 GRA Cfa 981 NAUS-ARb minus9804 3555 2005ndash2006 GRA Cfa 542 NAUS-ARc minus9804 3555 2005ndash2006 GRA Cfa 582 NA



Table A1 Continued


US-Blo minus12063 3890 1997ndash2007 ENF Csb 1859 Goldstein et al (2000)US-Cop minus10939 3809 2001ndash2007 GRA Bsk 1186 Bowling et al (2010)US-GBT minus10624 4137 1999ndash2006 ENF Dfc 615 Zeller and Nikolov (2000)US-GLE minus10624 4137 2004ndash2014 ENF Dfb 3134 Y Frank et al (2014)US-Ha1 minus7217 4254 1991ndash2012 DBF Dfb 3932 Y Urbanski et al (2007a)US-KS2 minus8067 2861 2003ndash2006 CSH Cfa 1254 Powell et al (2006)US-Me1 minus12150 4458 2004ndash2005 ENF Csb 284 Irvine et al (2007)US-Me2 minus12156 4445 2002ndash2014 ENF Csb 3581 Y Irvine et al (2008)US-Me6 minus12161 4432 2010ndash2014 ENF Csb 1298 Ruehr et al (2012)US-MMS minus8641 3932 1999ndash2014 DBF Cfa 4865 Y Dragoni et al (2011)US-NR1 minus10555 4003 1998ndash2014 ENF Dfc 5115 Monson et al (2002)US-PFa minus9027 4595 1995ndash2014 MF Dfb 4749 Desai et al (2015)US-Prr minus14749 6512 2010ndash2013 ENF Dfc 811 Nakai et al (2013)US-SRG minus11083 3179 2008ndash2014 GRA Bsk 2117 Y Scott et al (2015a)US-SRM minus11087 3182 2004ndash2014 WSA Bsk 3354 Y Scott et al (2009)US-Syv minus8935 4624 2001ndash2014 MF Dfb 2365 Y Desai et al (2005)US-Ton minus12097 3843 2001ndash2014 WSA Csa 4336 Y Baldocchi et al (2010)US-UMB minus8471 4556 2000ndash2014 DBF Dfb 4015 Y Gough et al (2013)US-UMd minus8470 4556 2007ndash2014 DBF Dfb 2050 Y Gough et al (2013)US-Var minus12095 3841 2000ndash2014 GRA Csa 4356 Y Ma et al (2007)US-WCr minus9008 4581 1999ndash2014 DBF Dfb 3425 Y Cook et al (2004)US-Whs minus11005 3174 2007ndash2014 OSH Bsk 2233 Scott et al (2015b)US-Wi0 minus9108 4662 2002ndash2002 ENF Dfb 228 Noormets et al (2007)US-Wi3 minus9110 4663 2002ndash2004 DBF Dfb 415 Noormets et al (2007)US-Wi4 minus9117 4674 2002ndash2005 ENF Dfb 712 Y Noormets et al (2007)US-Wi6 minus9130 4662 2002ndash2003 OSH Dfb 351 Noormets et al (2007)US-Wi9 minus9108 4662 2004ndash2005 ENF Dfb 302 Noormets et al (2007)US-Wkg minus10994 3174 2004ndash2014 GRA Bsk 3198 Scott et al (2010)ZA-Kru 3150 minus2502 2000ndash2010 SAV Bsh 2439 Archibald et al (2009)ZM-Mon 2325 minus1544 2000ndash2009 DBF Aw 645 Y Merbold et al (2009)

Table A2 Fixed parameters ldquoSCrdquo stands for ldquoat standard conditionsrdquo (25 C 101 325 Pa) ldquoMM coefrdquo refers to ldquoMichaelisndashMenten coeffi-cientrdquo

Symbol Value Units Description Reference

β 1460 1 Unit cost ratio Eq (3) This study0lowast25p0

4332 Pa Photorespiratory compensation point SC Bernacchi et al (2001)Kc25 3997 Pa MM coef for CO2 SC Bernacchi et al (2001)Ko25 27 480 Pa MM coef for O2 SC Bernacchi et al (2001)1H0lowast 37 830 J molminus1 Activation energy for 0lowast Bernacchi et al (2001)1HKc 79 430 J molminus1 Activation energy for Kc Bernacchi et al (2001)1HKo 36 380 J molminus1 Activation energy for Ko Bernacchi et al (2001)HV 71 513 J molminus1 Activation energy for Vcmax Kattge and Knorr (2007)Hd 200 000 J molminus1 Deactivation energy for Vcmax Kattge and Knorr (2007)p0 101 325 Pa Standard atmosphere ndashg 980665 m sminus2 Gravitation constant ndashL 00065 K mminus2 Adiabatic lapse rate ndashR 83145 J molminus1 Kminus1 Universal gas constant ndashMa 28963 g molminus1 Molecular mass of dry air ndashMC 120107 g molminus1 Molecular mass of carbon ndashaS 66839 J molminus1 Kminus1 Intercept for entropy term in Eq (C6) Kattge and Knorr (2007)bS 107 J molminus1 Kminus2 Slope for entropy term in Eq (C6) Kattge and Knorr (2007)



Table A3 Variables returned by the function rpmodel() Variable names correspond to the named elements of the list returned by therpmodel() function call Symbols correspond to their use in this paper

Variable name Symbol Description Units Reference

ca ca Ambient CO2 partial pressure Pa Sect 21gammastar 0lowast Photorespiratory compensation point Pa Sect B1kmm K MichaelisndashMenten coefficient for photosynthesis Pa Sect B3ns_star ηlowast Change in the viscosity of water relative to its value at 25 C unitless Huber et al (2009)chi χ Ratio of leaf-internal to ambient CO2 unitless Sect 21ci ci Leaf-internal CO2 partial pressure Pa Eq (F8)lue LUE Light use efficiency g C molminus1 Eq (19)mj m CO2 limitation factor for light-limited assimilation unitless Eq (11)mc mC CO2 limitation factor for RuBisCO-limited assimilation unitless Eq (7)gpp GPP Gross primary production g C mminus2 dminus1 Eqs (2) and (19)iwue iWUE Intrinsic water use efficiency Pa Eq (C2)gs gs Stomatal conductance mol C mminus2 dminus1 Paminus1 Sect C1vcmax Vcmax Maximum rate of carboxylation mol C mminus2 dminus1 Eq (C4)vcmax25 Vcmax25 Maximum rate of carboxylation normalised to 25 C mol C mminus2 dminus1 Eq (C5)rd Rd Dark respiration mol C mminus2 dminus1 Eq (C11)



Appendix B Temperature and pressure dependence ofphotosynthesis parameters

B1 Photorespiratory compensation point 0lowast

The temperature- and pressure-dependent photorespiratorycompensation point in absence of dark respiration 0lowast(T p)is calculated from its value at standard temperature (T0 =

25 C) and atmospheric pressure (p0 = 101 325 Pa) re-ferred to as 0lowast25p0

It is modified by temperature fol-lowing an Arrhenius-type temperature response functionfArrh(TK1H0lowast) with activation energy 1H0lowast and is cor-rected for atmospheric pressure p(z) at elevation z

0lowast(TKz)= 0lowast

25p0fArrh(TK1H0lowast)

p(z)

p0(B1)

Values of 1H0lowast and 0lowast25p0are taken from Bernac-

chi et al (2001) The latter is converted to Pa andstandardised to p0 by multiplication with p0 (0lowast25p0

=

4275 micromol molminus1times 10minus6

times 101 325 Pa= 4332 Pa) 1H0lowastis 37 830 J molminus1 All parameter values are summarised inTable A2 The function p(z) is defined in Sect B4 Note thatTK indicates that the respective temperature value is given inKelvin and TK0 = 29815 K

To correct for effects by temperature following the Arrhe-nius equation with its form x(TK)= exp(cminus1Ha(TKR))the temperature-correction function fArrh(TK1Ha) used inEq (B1) and further equations below is given by

fArrh(TK)= x(TK)x(TK0)= exp(1H(TKminus TK0)

TK0 R TK

) (B2)

where 1H is the respective activation energy (eg1H0lowast in Eq B1) and R is the universal gas constant(83145 J molminus1 Kminus1)

B2 Deriving 0lowast

The temperature and pressure dependency of 0lowast followsfrom the temperature dependencies of Kc Ko Vcmax andVomax and the pressure dependency of pO2(p)

0lowast(TKp)=pO2(p) Kc(TK) Vomax(TK)

2 Ko(TK) Vcmax(TK) (B3)

pO2(p) is the partial pressure of atmospheric oxygen (Pa)and scales linearly with p(z) Kc is the MichaelisndashMentenconstant for carboxylation (Pa) Ko is the MichaelisndashMentenconstant for oxygenation (Pa) Vcmax is maximum rateof carboxylation (micromol mminus2 sminus1) and Vomax is the maxi-mum rate of oxygenation (micromol mminus2 sminus1) The temperature-dependency equations for these four terms are given in Ta-ble 1 of Bernacchi et al (2001) with respective scaling con-

stants c and activation energies 1Ha as

Kc(TK)= exp(3805minus 7943(TKR)) (B4a)Ko(TK)= 1000times exp(2030minus 3638(TKR)) (B4b)Vomax(TK)= exp(2298minus 6011(TKR)) (B4c)Vcmax(TK)= exp(2635minus 6533(TKR)) (B4d)

By substituting the temperature-dependency equations foreach term in Eq (B3) and rearranging terms 0lowast can be writ-ten as

0lowast(TKz)= pO2(z) exp(6779minus 3783(TKR)) (B5)

With pO2(p) at standard atmospheric pressure (101 325 Pa)taken to be 21 000 Pa and assuming a constant mixing ratioacross the troposphere its pressure dependence can be ex-pressed as

pO2(p)= 02095 middotp(z) (B6)

hence

0lowast(TKp)= p(z)exp(5205minus 3783(TKR)) (B7)

We can use this to calculate 0lowast at standard tempera-ture (TK = 29815 K) and pressure (p(z)= 101 325 Pa) as0lowast25p0

= 4332 PaNote that to convert Eq (B5) to the form corresponding

to the one given by Bernacchi et al (2001) the partial pres-sure of oxygen (pO2) has to be assumed at standard condi-tions pO2 is approximately 21 000 Pa and with the standardatmospheric pressure of 101 325 Pa pO2 can be convertedfrom Pascals to parts per million (ppm) as 21000101325times106= 207254 ppm = exp(1224) ppm This can be combined

with the exponent in Eq (B5) to exp(1224) middot exp(6779)=exp(1902) This corresponds to the parameter values deter-mining the temperature dependence of 0lowast given by Bernac-chi et al (2001) as 0lowast = exp(1902minus 3783(TKR))

B3 MichaelisndashMenten coefficient of photosynthesis

The effective MichaelisndashMenten coefficient K (Pa) ofRuBisCO-limited photosynthesis (Eq 6) is determined bythe MichaelisndashMenten constants for the carboxylation andoxygenation reactions (Farquhar et al 1980)

K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)

where Kc is the MichaelisndashMenten constant for CO2 (Pa)Ko is the MichaelisndashMenten constant for the carboxylationand oxygenation reaction respectively and pO2 is the partialpressure of oxygen (Pa) Kc and Ko follow a temperaturedependence given by the Arrhenius equation analogously tothe temperature dependence of 0lowast (Eq B1)

Kc(TK)=Kc25 fArrh(TK1HKc) (B9a)Ko(TK)=Ko25 fArrh(TK1HKo) (B9b)

Values 1HKc = 79 430 J molminus1 1HKo = 36 380 J molminus1Kc25 = 3997 Pa and Ko25 = 27 480 Pa are taken from



Bernacchi et al (2001) (see also Table A2) The latter twohave been converted from micromol molminus1 in Bernacchi et al(2001) to units of Pa by multiplication with the standard at-mosphere (101 325 Pa) Note thatKc25 andKo25 are rate con-stants and are independent of atmospheric pressure Pressuredependence of K is solely in pO2(p) (see Eq B6)

B4 Atmospheric pressure

The elevation dependence of atmospheric pressure is com-puted by assuming a linear decrease in temperature with el-evation and a mean adiabatic lapse rate (Berberan-Santoset al 1997)

p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)

where z is the elevation above mean sea level (m) g is thegravitational constant (980665 m sminus2) p0 is the standard at-mospheric pressure at 0 m asl (101 325 Pa) L is the meanadiabatic lapse rate (00065 K mminus2) Ma is the molecularweight for dry air (0028963 kg molminus1) and R is the uni-versal gas constant (83145 J molminus1 Kminus1) All parameter val-ues that are held fixed in the model (not calibrated) are sum-marised in Table A2

Appendix C Corollary of the χ prediction

C1 Stomatal conductance

Stomatal conductance gs (mol C Paminus1) follows from the pre-diction of χ given by Eq (8) and gs = A(ca (1minusχ)) (fromEq 5) Stomatal conductance can thus be written as

gs =

(1+

ξradicD

)A

caminus0lowast (C1)

This has a similar form as the solution for gs derived from adifferent optimality principle by Medlyn et al (2011) (theirEq 11) Differences are that an additional term g0 is miss-ing here and that 0lowast does not appear in Medlyn et al (2011)The theory presented by Prentice et al (2014) provides a the-oretical interpretation for the parameter g1 in Medlyn et al(2011) it is given by ξ (Eq 9) and can thus be predicted fromthe environment However it is notable that the underlyingoptimality criterion used by Medlyn et al (2011) as pro-posed by Cowan and Farquhar (1977) is one that maintainsa constant marginal water cost of carbon gain λ= partEpartA Itthus describes an instantaneous gs adjustment eg to diurnalvariations in D and has been adopted into DVMs and ESMsfor respective predictions (with a given Vcmax ) In contrastthe theory presented here and underlying the P-model pre-dicts χ which is jointly controlled by gs and Vcmax In otherwords it predicts a gs that is coordinated with Vcmax and thusacclimates at a similar timescale (which is on the order ofdays to weeks) This χ can be understood as a ldquoset pointrdquo

for an average χ with actual χ varying around it at a daily tosubdaily timescale

C2 Intrinsic water use efficiency

The intrinsic water use efficiency (iWUE in Pa) has been de-fined as the ratio of assimilation over stomatal conductance(to water) (Beer et al 2009) as iWUE= A(16gs) The fac-tor 16 accounts for the difference in diffusivity between CO2and H2O Using Fickrsquos law (Eq 5) this is simply

iWUE=ca(1minusχ)

16 (C2)

or using the prediction of optimal χ given by Eq (8) thiscan be expressed as

iWUE=1

16(

1+ ξradicD

) (caminus0lowast) (C3)

C3 Maximum carboxylation capacity

With AJ = AC Vcmax can directly be derived as

Vcmax = ϕ0 Iabsci+K

ci+ 20lowast= ϕ0 Iabs

mprime

mC (C4)

ci is given by caχ The second part of the equation followsfrom the definitions ofm (Eq 11) andmC (Eq 7) Normalis-ing Vcmax to standard temperature (25 C) following a mod-ified Arrhenius function based on Kattge and Knorr (2007)gives Vcmax25 as

Vcmax25 = VcmaxfV(TKTK0) (C5)

fV(TKTK0)= fArrh(TK1HV)

middot1+ exp((TK01SminusHd)(TK0R))

1+ exp((TK1SminusHd)(TKR)) (C6)

whereHV is the activation energy (71 513 J molminus1)Hd is thedeactivation energy (200 000 J molminus1) and 1S is an entropyterm (J molminus1 Kminus1) calculated using a linear relationshipwith T from Kattge and Knorr (2007) with a slope of bS =

107 J molminus1 Kminus2 and intercept of aS = 66839 J molminus1 Kminus1

1S = aSminus bST (C7)

Note that T is in units of C in the above equation Equa-tion (C6) describes the instantaneous response to tempera-ture and is not the same as the optimality-driven acclimationto temperature predicted by the P-model

C4 Dark respiration Rd

Dark respiration at standard temperature Rd25 is calculatedas being proportional to Vcmax25

Rd25 = b0 Vcmax25 (C8)



where b0 = 0015 (Atkin et al 2015) Dark respiration fol-lows a slightly different instantaneous temperature sensitivitythan Vcmax following Heskel et al (2016)

Rd = Rd25 fR (C9)

fR = exp(

01012(TK0minus TK)minus 00005(T 2K0minus T

2K))

(C10)

By combining Eqs (C6) (C8) and (C9) Rd at growth tem-perature T can directly be calculated from Vcmax as

Rd = b0fR

fVVcmax (C11)

Appendix D Soil water holding capacity

The soil water balance is solved following the SPLASHmodel but with the total soil water holding capacity perunit ground area (θWHC in mm) calculated as a functionof the soil texture Precipitation in the form of rain (Prain)and snow (Psnow) are taken from WATCH-WFDEI (Weedonet al 2014) and are summed and converted from kg mminus2 sminus1

to mm dminus1 by multiplication of (60times 60times 24) s dminus1 To ob-tain θWHC we use soil depth to bedrock and texture datafrom SoilGrids (Hengl et al 2014) extracted around theFLUXNET sites We assumed that the plant-available WHCis determined by the WHC down to a maximum depth of 2 mand is limited by the depth to bedrock The water holding ca-pacity (wWHC in mm) was defined as the difference in volu-metric soil water storage at field capacity (WFC in m3 mminus3)and the permanent wilting point (WPWP in m3 mminus3)

θWHC = (WFCminusWPWP) (1minus fgravel)

middotmin(zbedrockzmax) (D1)

fgravel is the gravel fraction zbedrock is the depth to bedrock(in mm) and zmax is 2000 mm The volumetric soil waterstorage at field capacity and wilting point were derived fromtexture and organic matter content data through pedotransferfunctions as described by Saxton and Rawls (2006) WFC iscalculated as

WFC = kFC+ (1283 middot k2FCminus 0374 middot kFCminus 0015) (D2)

where

kFC =minus0251 middot fsand+ 0195 middot fclay+ 0011 middot fOM (D3)+ 0006 middot (fsandfOM) (D4)minus 0027 middot (fclayfOM) (D5)+ 0452 middot (fsandfclay) (D6)+ 0299 (D7)

fsand fclay fOM are the sand clay and organic matter con-tents in percent by weight WPWP is calculated as

WPWP = kPWP+ (014 middot kPWPminus 002) (D8)

where

kPWP =minus0024 middot fsand+ 0487 middot fclay+ 0006 middot fOM (D9)+ 0005 middot (fsandfOM) (D10)minus 0013 middot (fclayfOM) (D11)+ 0068 middot (fsandfclay) (D12)+ 0031 (D13)

Appendix E Vapour pressure deficit

Vapour pressure deficit (D) is calculated from specific hu-midity (qair) as

D = esatminus eact (E1)

with

esat = 6110 middot exp(

1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)

p(z) is atmospheric pressure taken here as a constant func-tion of elevation z (Sect B4) wair is the mass mixing ratio ofwater vapour to dry air (dimensionless) and derived from spe-cific humidity aswair = qair(1minusqair)Rd andRv are the spe-cific gas constants of dry air and water vapour respectivelyand are given by RMd and RMv respectively where Ris the universal gas constant (8314 J molminus1 Kminus1) and Md(28963 g molminus1) and Mv (1802 g molminus1) are the molecularmass of dry air of water vapour respectively T is air temper-ature in C

Appendix F Extended theory

F1 Deriving χ

Using Eqs (4) and (5) the term on the left-hand side ofEq (3) can thus be written as

part(EA)

partχ=

16 Dca (1minusχ)2

(F1)

Using Eq (6) and the simplification 0lowast = 0 the derivativeterm on the right-hand side of Eq (3) can be written as

part(VcmaxA)

partχ=minus

K

ca χ2 (F2)

Equation (3) can thus be written as

a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)

where ba = βηlowast The exact solution without the simplifi-cation 0lowast = 0 and following analogous steps is

χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)

This can also be written as

ci =0lowastradicD+ ξ ca

ξ +radicD

(F8)

F2 Deriving the Jmax limitation factor

By taking the derivative of AJ with respect to Jmax Eq (14)can be expressed as

c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)

This can be rearranged to(4cm

)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)

For simplification we can substitute

k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)

With this we can write

11+ kminus2 = u (F13)

This can be rearranged to

(1minus u)12 =1

radic1+ k2

(F14)

The right-hand term now corresponds to the Jmax limitationfactor L in Eq (13) and we get Eq (15)

To sum up the P-model calculates GPP as

GPP= Iabs ϕ0(T ) β(θ) mprime MC (F15)

where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)

Iabs is the absorbed light (taken as fAPARtimesPPFD mol mminus2)ϕ0(T ) is the temperature-dependent intrinsic quantum yieldβ(θ) is the soil moisture stress factor and MC is the molarmass of carbon (g molminus1)

F3 An alternative method for introducing the Jmaxlimitation

Section 22 introduced the effect of a finite Jmax leading to asaturating relationship between absorbed light and the light-limited assimilation rate AJ An alternative method was pre-sented by Smith et al (2019) and is implemented in rp-model as an optional method (argument method_jmaxlim= ldquosmith19rdquo) Following their approach the light-limitedassimilation rate is described as

AJ =

(J

4

)m (F18)

m is the CO2 limitation factor (Eq 11) and J is a saturatingfunction of absorbed light approaching Jmax for high lightlevels following Farquhar et al (1980)

θJ 2minus (ϕ0Iabs + Jmax)J +ϕ0IabsJmax = 0 (F19)

θ is a unitless parameter determining the curvature of the re-sponse of J to Iabs here taken as 085 based on Smith et al(2019) and references therein Equation (F19) can be substi-tuted into Eq (F18) to yield

AJ =(m

4

)ϕ0Iabs+ Jmaxplusmn

radic(ϕ0Iabs+ Jmax)

2minus 4θϕ0IabsJmax

2θ (F20)

from which the smaller root is used to derive AJ Similar asin the method used by Wang et al (2017a) and outlined inSect 22 a proportionality between AJ and Jmax is assumed(partApartJmax = c Eq 14) Taking the derivative of Eq (F20)with respect to Jmax and setting equal to c leads to

Jmax = ϕ0 Iabs ω (F21)



with

ω =minus(1minus 2θ )+

radicradicradicradicradic(1minus θ) 1

4cm

(1minus θ 4c

m

) minus 4θ

(F22)

Using thisAJ can be written analogously to Eq (16) but with

mprime =mωlowast

8θ (F23)

and

ωlowast = 1+ωminusradic(1+ω)2minus 4θω (F24)

The cost parameter c was assumed to be non-varying Understandard conditions of 25 C 101 325 Pa atmospheric pres-sure 1000 Pa vapour pressure deficit and 360 ppm CO2 atwhich the ratio of Jmax to Vcmax was assumed to be 207(Smith and Dukes 2017) c was derived as 0053 (Smithet al 2019)

Using the definition of Vcmax from Eq (C4) m can be re-placed by mprime from Eq (F23) to calculate an ldquointermediaterate of Vcmaxrdquo (Smith et al 2019) as

Vcmax = ϕ0 Iabsmprime

mC (F25)

Appendix G The rpmodel() function of the rpmodelR package

The rpmodel R package provides an implementation of the P-model as described here The main function is rpmodel()which returns a list of variables that are mutually consistentwithin the theory of the P-model (Sect 2) and based on cal-culations defined in this paper References for the returnedlist of variables are given in Table A3



Author contributions BDS designed the study wrote the modelcode conducted the analysis and wrote the paper HW developedthe model and wrote the initial version of the model descriptionNGS developed the model and implemented model code SPH con-tributed to designing the study and writing the manuscript TK con-tributed to the study design model implementation and manuscriptwriting DS implemented the water holding capacity model TDwrote an initial version of the model code and model documen-tation ICP developed the model and contributed to designing thestudy

Competing interests The authors declare that they have no conflictof interest

Acknowledgements This work contributes to the AXA Chair Pro-gramme in Biosphere and Climate Impacts and the Imperial Collegeinitiative on Grand Challenges in Ecosystems and the Environment

Financial support This research has been supported by the H2020Marie Skłodowska-Curie Actions (FIBER grant no 701329) theSwiss National Science Foundation (grant no PCEFP2_181115)the Texas Tech University the Laboratory Directed Research andDevelopment (LDRD) fund under the auspices of DOE (DOEgrant) BER Office of Science at Lawrence Berkeley National Lab-oratory and the NASA Terrestrial Ecology Program IDS award(award no NNH17AE86I) the ERC-funded project GC 20 (grantno 694481) and the ERC under the European Unionrsquos Hori-zon 2020 research and innovation programme (grant agreementno 787203 REALM)

Review statement This paper was edited by Jatin Kala and re-viewed by two anonymous referees

References

Acosta M Pavelka M Montagnani L Kutsch W Lin-droth A Juszczak R and Janouš D Soil surface CO2efflux measurements in Norway spruce forests Com-parison between four different sites across Europe ndashfrom boreal to alpine forest Geoderma 192 295ndash303httpsdoiorg101016jgeoderma201208027 2013

Adams W W Zarter C R Ebbert V and Demmig-Adams BPhotoprotective Strategies of Overwintering Evergreens Biosci54 41ndash49 2004

Ammann C Spirig C Leifeld J and Neftel A Assess-ment of the nitrogen and carbon budget of two managed tem-perate grassland fields Agr Ecosyst Environ 133 150ndash162httpsdoiorg101016jagee200905006 2009

Archibald S A Kirton A van der Merwe M R ScholesR J Williams C A and Hanan N Drivers of inter-annual variability in Net Ecosystem Exchange in a semi-arid savanna ecosystem South Africa Biogeosci 6 251ndash266httpsdoiorg105194bg-6-251-2009 2009

Ardo J Molder M El-Tahir B A and Elkhidir H A M Sea-sonal variation of carbon fluxes in a sparse savanna in semi aridSudan Carb Bal Manage 3 7 httpsdoiorg1011861750-0680-3-7 2008

Atkin O K Bloomfield K J Reich P B Tjoelker M G As-ner G P Bonal D Boumlnisch G Bradford M G CernusakL A Cosio E G Creek D Crous K Y Domingues T FDukes J S Egerton J J G Evans J R Farquhar G D Fyl-las N M Gauthier P P G Gloor E Gimeno T E Grif-fin K L Guerrieri R Heskel M A Huntingford C IshidaF Y Kattge J Lambers H Liddell M J Lloyd J LuskC H Martin R E Maksimov A P Maximov T C MalhiY Medlyn B E Meir P Mercado L M Mirotchnick NNg D Niinemets U OrsquoSullivan O S Phillips O L PoorterL Poot P Prentice I C Salinas N Rowland L M RyanM G Sitch S Slot M Smith N G Turnbull M H Vander-Wel M C Valladares F Veneklaas E J Weerasinghe L KWirth C Wright I J Wythers K R Xiang J Xiang S andZaragoza-Castells J Global variability in leaf respiration in re-lation to climate plant functional types and leaf traits New Phy-tol 206 614ndash636 httpsdoiorg101111nph13253 2015

Aubinet M Chermanne B Vandenhaute M Longdoz BYernaux M and Laitat E Long term carbon dioxide ex-change above a mixed forest in the Belgian Ardennes AgrForest Meteorol 108 293ndash315 httpsdoiorg101016s0168-1923(01)00244-1 2001

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Baldocchi D Chen Q Chen X Ma S Miller G Ryu Y XiaoJ Wenk R and Battles J The Dynamics of Energy Waterand Carbon Fluxes in a Blue Oak (Quercus douglasii) Savanna inCalifornia in Ecosystem Function in Savannas 135ndash151 CRCPress httpsdoiorg101201b10275-10 2010

Ball J T Timothy Ball J Woodrow I E and Berry J AA Model Predicting Stomatal Conductance and its Contributionto the Control of Photosynthesis under Different EnvironmentalConditions in Progress in Photosynthesis Research 221ndash2241987

Beck H E Zimmermann N E McVicar T R Vergopolan NBerg A and Wood E F Present and future Koumlppen-Geiger cli-mate classification maps at 1-km resolution Sci Data 5 180214httpsdoiorg101038sdata2018214 2018

Beer C Ciais P Reichstein M Baldocchi D Law B E Pa-pale D Soussana J-F Ammann C Buchmann N FrankD Gianelle D Janssens I A Knohl A Koumlstner B MoorsE Roupsard O Verbeeck H Vesala T Williams C A andWohlfahrt G Temporal and among-site variability of inherentwater use efficiency at the ecosystem level Global BiogeochemCy 23 GB2018 httpsdoiorg1010292008GB003233 2009

Belelli Marchesini L Papale D Reichstein M Vuichard NTchebakova N and Valentini R Carbon balance assessmentof a natural steppe of southern Siberia by multiple constraint ap-proach Biogeosciences 4 581ndash595 httpsdoiorg105194bg-4-581-2007 2007

Berberan-Santos M N Bodunov E N and Pogliani L On thebarometric formula Am J Phys 65 404ndash412 1997

Berbigier P Bonnefond J-M and Mellmann P CO2 and wa-ter vapour fluxes for 2 years above Euroflux forest site Agr



Forest Meteorol 108 183ndash197 httpsdoiorg101016s0168-1923(01)00240-4 2001

Bergeron O Margolis H A Black T A Coursolle C DunnA L Barr A G and Wofsy S C Comparison of carbondioxide fluxes over three boreal black spruce forests in CanadaGlobal Change Biol 13 89ndash107 httpsdoiorg101111j1365-2486200601281x 2007

Beringer J Hacker J Hutley L B Leuning R ArndtS K Amiri R Bannehr L Cernusak L A Grover SHensley C Hocking D Isaac P Jamali H Kanniah KLivesley S Neininger B U K T P Sea W StratenD Tapper N Weinmann R Wood S and Zegelin SSPECIALndashSavanna Patterns of Energy and Carbon Integratedacross the Landscape B Am Meteorol Soc 92 1467ndash1485httpsdoiorg1011752011bams29481 2011a

Beringer J Hutley L B Hacker J M Neininger B andU K T P Patterns and processes of carbon water andenergy cycles across northern Australian landscapes Frompoint to region Agr Forest Meteorol 151 1409ndash1416httpsdoiorg101016jagrformet201105003 2011b

Beringer J Hutley L B Hacker J M Neininger B andU K T P Patterns and processes of carbon water andenergy cycles across northern Australian landscapes Frompoint to region Agr Forest Meteorol 151 1409ndash1416httpsdoiorg101016jagrformet201105003 2011c

Beringer J Hutley L B McHugh I Arndt S K CampbellD Cleugh H A Cleverly J Resco de Dios V Eamus DEvans B Ewenz C Grace P Griebel A Haverd V Hinko-Najera N Huete A Isaac P Kanniah K Leuning R Lid-dell M J Macfarlane C Meyer W Moore C Pendall EPhillips A Phillips R L Prober S M Restrepo-Coupe NRutledge S Schroder I Silberstein R Southall P Yee MS Tapper N J van Gorsel E Vote C Walker J and Ward-law T An introduction to the Australian and New Zealandflux tower network ndash OzFlux Biogeosciences 13 5895ndash5916httpsdoiorg105194bg-13-5895-2016 2016

Bernacchi C J Singsaas E L Pimentel C Portis A R J andLong S P Improved temperature response functions for modelsof Rubisco-limited photosynthesis Plant Cell Environ 24 253ndash259 2001

Bernacchi C J Pimentel C and Long S P In vivo tem-perature response functions of parameters required to modelRuBP-limited photosynthesis Plant Cell Environ 26 1419ndash1430 2003

Biederman J A Scott R L Goulden M L Vargas RLitvak M E Kolb T E Yepez E A Oechel W CBlanken P D Bell T W Garatuza-Payan J Maurer G EDore S and Burns S P Terrestrial carbon balance in adrier world the effects of water availability in southwest-ern North America Global Change Biol 22 1867ndash1879httpsdoiorg101111gcb13222 2016

Bonal D Bosc A Ponton S Goret J-Y Burban B GrossP Bonnefond J-M Elbers J Longdoz B Epron DGuehl J-M and Granier A Impact of severe dry sea-son on net ecosystem exchange in the Neotropical rainfor-est of French Guiana Global Change Biol 14 1917ndash1933httpsdoiorg101111j1365-2486200801610x 2008

Bowling D R Bethers-Marchetti S Lunch C K Grote E Eand Belnap J Carbon water and energy fluxes in a semiarid

cold desert grassland during and following multiyear drought JGeophys Res 115 G4 httpsdoiorg1010292010jg0013222010

Bristow M Hutley L B Beringer J Livesley S J EdwardsA C and Arndt S K Quantifying the relative importance ofgreenhouse gas emissions from current and future savanna landuse change across northern Australia Biogeosciences 13 6285ndash6303 httpsdoiorg105194bg-13-6285-2016 2016

Cernusak L A Hutley L B Beringer J Holtum J Aand Turner B L Photosynthetic physiology of euca-lypts along a sub-continental rainfall gradient in north-ern Australia Agr Forest Meteorol 151 1462ndash1470httpsdoiorg101016jagrformet201101006 2011

Chen B Liu J Chen J M Croft H Gonsamo A He L andLuo X Assessment of foliage clumping effects on evapotran-spiration estimates in forested ecosystems Agr Forest Meteorol216 82ndash92 httpsdoiorg101016jagrformet2015090172016

Chen J-L Reynolds J F Harley P C and Tenhunen J D Co-ordination theory of leaf nitrogen distribution in a canopy Oe-cologia 93 63ndash69 1993

Chen S Chen J Lin G Zhang W Miao H WeiL Huang J and Han X Energy balance and parti-tion in Inner Mongolia steppe ecosystems with differentland use types Agr Forest Meteorol 149 1800ndash1809httpsdoiorg101016jagrformet200906009 2009

Chiesi M Maselli F Bindi M Fibbi L Cherubini P Ar-lotta E Tirone G Matteucci G and Seufert G Modellingcarbon budget of Mediterranean forests using ground and re-mote sensing measurements Agr Forest Meteorol 135 22ndash34httpsdoiorg101016jagrformet200509011 2005

Cleverly J Boulain N Villalobos-Vega R Grant N Faux RWood C Cook P G Yu Q Leigh A and Eamus D Dynam-ics of component carbon fluxes in a semi-arid Acacia woodlandcentral Australia J Geophys Res-Biogeosci 118 1168ndash1185httpsdoiorg101002jgrg20101 2013

Cleverly J Eamus D Van Gorsel E Chen C Rumman RLuo Q Coupe N R Li L Kljun N Faux R Yu Qand Huete A Productivity and evapotranspiration of two con-trasting semiarid ecosystems following the 2011 global car-bon land sink anomaly Agr Forest Meteorol 220 151ndash159httpsdoiorg101016jagrformet201601086 2016

Cook B D Davis K J Wang W Desai A BergerB W Teclaw R M Martin J G Bolstad P V Bak-win P S Yi C and Heilman W Carbon exchange andventing anomalies in an upland deciduous forest in north-ern Wisconsin USA Agr Forest Meteorol 126 271ndash295httpsdoiorg101016jagrformet200406008 2004

Cowan I R and Farquhar G D Stomatal function in relation toleaf metabolism and environment Symp Soc Exp Biol 31471ndash505 1977

Davis T W Prentice I C Stocker B D Thomas R T Whit-ley R J Wang H Evans B J Gallego-Sala A V Sykes MT and Cramer W Simple process-led algorithms for simulatinghabitats (SPLASH v10) robust indices of radiation evapotran-spiration and plant-available moisture Geosci Model Dev 10689ndash708 httpsdoiorg105194gmd-10-689-2017 2017

Delpierre N Berveiller D Granda E and Dufrecircne E Woodphenology not carbon input controls the interannual variabil-



ity of wood growth in a temperate oak forest New Phytol 210459ndash470 httpsdoiorg101111nph13771 2015

Desai A R Bolstad P V Cook B D Davis K J andCarey E V Comparing net ecosystem exchange of car-bon dioxide between an old-growth and mature forest in theupper Midwest USA Agr Forest Meteorol 128 33ndash55httpsdoiorg101016jagrformet200409005 2005

Desai A R Xu K Tian H Weishampel P Thom J Bau-mann D Andrews A E Cook B D King J Y andKolka R Landscape-level terrestrial methane flux observedfrom a very tall tower Agr Forest Meteorol 201 61ndash75httpsdoiorg101016jagrformet201410017 2015

Didan K MOD13Q1 MODISTerra Vegetation In-dices 16-Day L3 Global 250 m SIN Grid V006httpsdoiorg105067MODISMOD13Q1006 2015

Dragoni D Schmid H P Wayson C A Potter H Grim-mond C S B and Randolph J C Evidence of increased netecosystem productivity associated with a longer vegetated sea-son in a deciduous forest in south-central Indiana USA GlobalChange Biol 17 886ndash897 httpsdoiorg101111j1365-2486201002281x 2011

Dunn A L Barford C C Wofsy S C Goulden M L andDaube B C A long-term record of carbon exchange in a bo-real black spruce forest means responses to interannual vari-ability and decadal trends Global Change Biol 13 577ndash590httpsdoiorg101111j1365-2486200601221x 2007

Egea G Verhoef A and Vidale P L Towards an improvedand more flexible representation of water stress in coupledphotosynthesisndashstomatal conductance models Agr Forest Me-teorol 151 1370ndash1384 2011

Ensminger I Sveshnikov D Campbell D A Funk C Jans-son S Lloyd J Shibistova O and Oumlquist G Intermittentlow temperatures constrain spring recovery of photosynthesis inboreal Scots pine forests Global Change Biol 10 995ndash1008httpsdoiorg101111j1365-2486200400781x 2004

Etzold S Ruehr N K Zweifel R Dobbertin M Zingg APluess P Haumlsler R Eugster W and Buchmann N The Car-bon Balance of Two Contrasting Mountain Forest Ecosystems inSwitzerland Similar Annual Trends but Seasonal DifferencesEcosystems 14 1289ndash1309 httpsdoiorg101007s10021-011-9481-3 2011

Falge E Aubinet M Bakwin P S Baldocchi D BerbigierP Bernhofer C Black T A Ceulemans R Davis K JDolman A J Goldstein A Goulden M L Granier AHollinger D Y Jarvis P G Jensen N Pilegaard KKatul G Kyaw Tha Paw P Law B E Lindroth ALoustau D Mahli Y Monson R Moncrieff P MoorsE Munger J W Meyers T Oechel W Schulze E dThorgeirsson H Tenhunen J Valentini R Verma S BVesala T and Wofsy S C FLUXNET Research NetworkSite Characteristics Investigators and Bibliography 2016httpsdoiorg103334ornldaac1530 2017

Fan Y Li H and Miguez-Macho G Global Patternsof Groundwater Table Depth Science 339 940ndash943httpsdoiorg101126science1229881 2013

Fan Y Miguez-Macho G Jobbaacutegy E G Jackson R Band Otero-Casal C Hydrologic regulation of plant root-ing depth P Natl Acad Sci USA 114 10572ndash10577httpsdoiorg101073pnas1712381114 2017

Fares S Savi F Muller J Matteucci G and Paoletti E Simul-taneous measurements of above and below canopy ozone fluxeshelp partitioning ozone deposition between its various sinks in aMediterranean Oak Forest Agr Forest Meteorol 198-199 181ndash191 httpsdoiorg101016jagrformet201408014 2014

Farquhar G D and Wong S C An Empirical Modelof Stomatal Conductance Funct Plant Biol 11 191ndash210httpsdoiorg101071PP9840191 1984

Farquhar G D von Caemmerer S and Berry J A A biochem-ical model of photosynthetic CO2 assimilation in leaves of C3species Planta 149 78ndash90 1980

Ferreacutea C Zenone T Comolli R and Seufert G Estimat-ing heterotrophic and autotrophic soil respiration in a semi-natural forest of Lombardy Italy Pedobiologia 55 285ndash294httpsdoiorg101016jpedobi201205001 2012

Fick A Ueber Diffusion Ann Phys 170 59ndash86httpsdoiorg101002andp18551700105 1855

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Frank J M Massman W J Ewers B E Huckaby L S andNegroacuten J F Ecosystem CO2H2O fluxes are explained byhydraulically limited gas exchange during tree mortality fromspruce bark beetles J Geophys Res-Biogeosci 119 1195ndash1215 httpsdoiorg1010022013jg002597 2014

Frankenberg C Koumlhler P Magney T S Geier S Lawson PSchwochert M McDuffie J Drewry D T Pavlick R andKuhnert A The Chlorophyll Fluorescence Imaging Spectrom-eter (CFIS) mapping far red fluorescence from aircraft RemoteSens Environ 217 523ndash536 2018

Galvagno M Wohlfahrt G Cremonese E Rossini MColombo R Filippa G Julitta T Manca G Siniscalco Cdi Cella U M and Migliavacca M Phenology and carbondioxide sourcesink strength of a subalpine grassland in responseto an exceptionally short snow season Environ Res Lett 8025008 httpsdoiorg1010881748-932682025008 2013

Gamon J Pentildeuelas J and Field C A narrow-waveband spec-tral index that tracks diurnal changes in photosynthetic efficiencyRemote Sens Environ 41 35ndash44 httpsdoiorg1010160034-4257(92)90059-S 1992

Gamon J A Huemmrich K F Wong C Y S Ensminger IGarrity S Hollinger D Y Noormets A and Pentildeuelas J Aremotely sensed pigment index reveals photosynthetic phenol-ogy in evergreen conifers P Natl Acad Sci USA 113 13087ndash13092 httpsdoiorg101073pnas1606162113 2016

Goldstein A Hultman N Fracheboud J Bauer M PanekJ Xu M Qi Y Guenther A and Baugh W Effectsof climate variability on the carbon dioxide water and sen-sible heat fluxes above a ponderosa pine plantation in theSierra Nevada (CA) Agr Forest Meteorol 101 113ndash129httpsdoiorg101016s0168-1923(99)00168-9 2000

Gough C M Hardiman B S Nave L E Bohrer G Mau-rer K D Vogel C S Nadelhoffer K J and Curtis P SSustained carbon uptake and storage following moderate dis-turbance in a Great Lakes forest Ecol Appl 23 1202ndash1215httpsdoiorg10189012-15541 2013

Greve P Orlowsky B Mueller B Sheffield J ReichsteinM and Seneviratne S I Global assessment of trends in



wetting and drying over land Nat Geosci 7 716ndash721httpsdoiorg101038ngeo2247 2014

Gruumlnwald T and Bernhofer C A decade of carbon wa-ter and energy flux measurements of an old spruce for-est at the Anchor Station Tharandt Tellus B 59 387ndash396httpsdoiorg103402tellusbv59i317000 2007

Guan D-X Wu J-B Zhao X-S Han S-J Yu G-R SunX-M and Jin C-J CO2 fluxes over an old temperate mixedforest in northeastern China Agr Forest Meteorol 137 138ndash149 httpsdoiorg101016jagrformet200602003 2006

Guanter L Zhang Y Jung M Joiner J Voigt M Berry J AFrankenberg C Huete A R Zarco-Tejada P Lee J-E Su-san Moran M Ponce-Campos G Beer C Camps-Valls GBuchmann N Gianelle D Klumpp K Cescatti A BakerJ M and Griffis T J Global and time-resolved monitoring ofcrop photosynthesis with chlorophyll fluorescence P Natl AcadSci USA 111 E1327ndashE1333 2014

Harris I Jones P Osborn T and Lister D Updatedhigh-resolution grids of monthly climatic observations ndashthe CRU TS310 Dataset Int J Climatol 34 623ndash642httpsdoiorg101002joc3711 2014

Haxeltine A and Prentice I C A General Model for the Light-Use Efficiency of Primary Production Funct Ecol 10 551ndash5611996

He L Chen J M Gonsamo A Luo X Wang R LiuY and Liu R Changes in the Shadow The Shifting Roleof Shaded Leaves in Global Carbon and Water Cycles Un-der Climate Change Geophys Res Lett 45 5052ndash5061httpsdoiorg1010292018GL077560 2018

Heinsch F A Running S W Kimball J S Nemani R RDavis K J Bolstad P V Cook B D Desai A R RicciutoD M Law B E Oechel W C Wofsy S C Dunn A LMunger J W Baldocchi D D Hollinger D Y RichardsonA D Stoy P C Siqueira M B S Monson R K Burns S Pand Flanagan L B Evaluation of remote sensing based terres-trial productivity from MODIS using regional tower eddy fluxnetwork observations IEEE Trans Geosci Remote Sens 441908ndash1925 httpsdoiorg101109TGRS2005853936 2006

Hengl T de Jesus J M MacMillan R A Batjes N HHeuvelink G B M Ribeiro E Samuel-Rosa AKempen B Leenaars J G B Walsh M G andGonzalez M R SoilGrids1kmndashglobal soil informationbased on automated mapping PLoS One 9 e105992httpsdoiorg101371journalpone0105992 2014

Heskel M OrsquoSullivan O Reich P Tjoelker M Weeras-inghe L Penillard A Egerton J Creek D BloomfieldK Xiang J Sinca F Stangl Z Martinez-De La TorreA Griffin K Huntingford C Hurry V Meir P Turn-bull M and Atkin O Convergence in the temperature re-sponse of leaf respiration across biomes and plant func-tional types P Natl Acad Sci USA 113 3832ndash3837httpsdoiorg101073pnas1520282113 2016

Hinko-Najera N Isaac P Beringer J van Gorsel E Ewenz CMcHugh I Exbrayat J-F Livesley S J and Arndt S K Netecosystem carbon exchange of a dry temperate eucalypt forestBiogeosciences 14 3781ndash3800 httpsdoiorg105194bg-14-3781-2017 2017

Hoshika Y Fares S Savi F Gruening C Goded I De MarcoA Sicard P and Paoletti E Stomatal conductance mod-

els for ozone risk assessment at canopy level in two Mediter-ranean evergreen forests Agr Forest Meteorol 234-235 212ndash221 httpsdoiorg101016jagrformet201701005 2017

Huber M L Perkins R A Laesecke A Friend D G SengersJ V Assael M J Metaxa I N Vogel E Mares R andMiyagawa K New international formulation for the viscosityof H2O J Phys Chem Ref Data 38 101ndash125 2009

Hufkens K khufkensgee_subset Google Earth Engine subsetscript and library httpsdoiorg105281zenodo833789 2017

Huner N P Oquist G Hurry V M Krol M Falk S and Grif-fith M Photosynthesis photoinhibition and low temperature ac-climation in cold tolerant plants Photosynth Res 37 19ndash391993

Hutley L B Beringer J Isaac P R Hacker J M and Cer-nusak L A A sub-continental scale living laboratory Spa-tial patterns of savanna vegetation over a rainfall gradient innorthern Australia Agr Forest Meteorol 151 1417ndash1428httpsdoiorg101016jagrformet201103002 2011

Imer D Merbold L Eugster W and Buchmann N Temporaland spatial variations of soil CO2 CH4 and N2O fluxes at threedifferently managed grasslands Biogeosciences 10 5931ndash5945httpsdoiorg105194bg-10-5931-2013 2013

Irvine J Law B E and Hibbard K A Postfire carbon poolsand fluxes in semiarid ponderosa pine in Central Oregon GlobalChange Biol 13 1748ndash1760 httpsdoiorg101111j1365-2486200701368x 2007

Irvine J Law B E Martin J G and Vickers D In-terannual variation in soil CO2 efflux and the response ofroot respiration to climate and canopy gas exchange in ma-ture ponderosa pine Global Change Biol 14 2848ndash2859httpsdoiorg101111j1365-2486200801682x 2008

Jacobs C M J Jacobs A F G Bosveld F C Hendriks DM D Hensen A Kroon P S Moors E J Nol L Schrier-Uijl A and Veenendaal E M Variability of annual CO2exchange from Dutch grasslands Biogeosciences 4 803ndash816httpsdoiorg105194bg-4-803-2007 2007

Jiang C and Ryu Y Multi-scale evaluation of global gross pri-mary productivity and evapotranspiration products derived fromBreathing Earth System Simulator (BESS) Remote Sens Envi-ron 186 528ndash547 2016

Joiner J Guanter L Lindstrot R Voigt M Vasilkov AP Middleton E M Huemmrich K F Yoshida Y andFrankenberg C Global monitoring of terrestrial chlorophyllfluorescence from moderate-spectral-resolution near-infraredsatellite measurements methodology simulations and ap-plication to GOME-2 Atmos Meas Tech 6 2803ndash2823httpsdoiorg105194amt-6-2803-2013 2013

Joiner J Yoshida Y Guanter L and Middleton E M Newmethods for the retrieval of chlorophyll red fluorescence fromhyperspectral satellite instruments simulations and applicationto GOME-2 and SCIAMACHY Atmos Meas Tech 9 3939ndash3967 httpsdoiorg105194amt-9-3939-2016 2016

Jung M Reichstein M Margolis H A Cescatti A RichardsonA D Arain M A Arneth A Bernhofer C Bonal D ChenJ Gianelle D Gobron N Kiely G Kutsch W Lasslop GLaw B E Lindroth A Merbold L Montagnani L MoorsE J Papale D Sottocornola M Vaccari F and WilliamsC Global patterns of land-atmosphere fluxes of carbon diox-ide latent heat and sensible heat derived from eddy covariance



satellite and meteorological observations J Geophys Res-Biogeosci 116 g00J07 httpsdoiorg1010292010JG0015662011

Kato T Tang Y Gu S Hirota M Du M Li Y andZhao X Temperature and biomass influences on interan-nual changes in CO2 exchange in an alpine meadow on theQinghai-Tibetan Plateau Global Change Biol 12 1285ndash1298httpsdoiorg101111j1365-2486200601153x 2006

Kattge J and Knorr W Temperature acclimation in a biochemicalmodel of photosynthesis a reanalysis of data from 36 speciesPlant Cell Environ 30 1176ndash1190 2007

Keenan T Sabate S and Gracia C Soil water stress and coupledphotosynthesisndashconductance models Bridging the gap betweenconflicting reports on the relative roles of stomatal mesophyllconductance and biochemical limitations to photosynthesis AgrForest Meteorol 150 443ndash453 2010

Keenan T Baker I Barr A Ciais P Davis K Dietze M Drag-oni D Gough C M Grant R Hollinger D Hufkens KPoulter B McCaughey H Raczka B Ryu Y Schaefer KTian H Verbeeck H Zhao M and Richardson A D Terres-trial biosphere model performance for inter-annual variability ofland-atmosphere CO2 exchange Global Change Biol 18 1971ndash1987 httpsdoiorg101111j1365-2486201202678x 2012

Keenan T F Prentice I C Canadell J G Williams CA Wang H Raupach M and Collatz G J Recentpause in the growth rate of atmospheric CO2 due to en-hanced terrestrial carbon uptake Nat Commun 7 13428httpsdoiorg101038ncomms13428 2016

Keenan T F Migliavacca M Papale D Baldocchi D Reich-stein M Torn M and Wutzler T Widespread inhibition ofdaytime ecosystem respiration Nat Ecol Evolut 3 407ndash415httpsdoiorg101038s41559-019-0809-2 2019

Kilinc M Beringer J Hutley L B Tapper N J and McGuireD A Carbon and water exchange of the worldrsquos tallest an-giosperm forest Agr Forest Meteorol 182ndash183 215ndash224httpsdoiorg101016jagrformet201307003 2013

Knohl A Schulze E-D Kolle O and Buchmann N Largecarbon uptake by an unmanaged 250-year-old deciduous for-est in Central Germany Agr Forest Meteorol 118 151ndash167httpsdoiorg101016s0168-1923(03)00115-1 2003

Kok B On the interrelation of respiration and photosynthe-sis in green plants Biochim Biophys Acta 3 625ndash631httpsdoiorg1010160006-3002(49)90136-5 1949

Kurbatova J Li C Varlagin A Xiao X and Vygodskaya NModeling carbon dynamics in two adjacent spruce forests withdifferent soil conditions in Russia Biogeosciences 5 969ndash980httpsdoiorg105194bg-5-969-2008 2008

Landsberg J J and Waring R H A generalised model of for-est productivity using simplified concepts of radiation-use effi-ciency carbon balance and partitioning For Ecol Manage 95209ndash228 1997

Lasslop G Reichstein M Papale D Richardson A Ar-neth A Barr A Stoy P and Wohlfahrt G Separa-tion of net ecosystem exchange into assimilation and res-piration using a light response curve approach critical is-sues and global evaluation Global Change Biol 16 187ndash208httpsdoiorg101111j1365-2486200902041x 2010

Leuning R A critical appraisal of a combined stomatal-photosynthesis model for C3 plants Plant Cell Environ 18 339ndash355 1995

Leuning R Cleugh H A Zegelin S J and Hughes D Carbonand water fluxes over a temperate Eucalyptus forest and a tropi-cal wetdry savanna in Australia measurements and comparisonwith MODIS remote sensing estimates Agr Forest Meteorol129 151ndash173 httpsdoiorg101016jagrformet2004120042005

Li X Xiao J He B Altaf Arain M Beringer J Desai A REmmel C Hollinger D Y Krasnova A Mammarella INoe S M Ortiz P S Rey-Sanchez A C Rocha A Vand Varlagin A Solar-induced chlorophyll fluorescence isstrongly correlated with terrestrial photosynthesis for a widevariety of biomes First global analysis based on OCO-2 andflux tower observations Glob Chang Biol 24 3990ndash4008httpsdoiorg101111gcb14297 2018

Lindauer M Schmid H Grote R Mauder M Stein-brecher R and Wolpert B Net ecosystem exchange overa non-cleared wind-throw-disturbed upland spruce forestndashMeasurements and simulations Agr Forest Meteorol 197 219ndash234 httpsdoiorg101016jagrformet201407005 2014

Lloyd J and Farquhar G D 13C discrimination during CO2 as-similation by the terrestrial biosphere Oecologia 99 201ndash215httpsdoiorg101007BF00627732 1994

Long S P Postl W F and Bolhaacuter-Nordenkampf H R Quantumyields for uptake of carbon dioxide in C3 vascular plants of con-trasting habitats and taxonomic groupings Planta 189 226ndash2341993

Luo X Keenan T F Fisher J B Jimeacutenez-Muntildeoz J-C ChenJ M Jiang C Ju W Perakalapudi N-V Ryu Y and TadicJ M The impact of the 20152016 El Nintildeo on global photosyn-thesis using satellite remote sensing Philos Trans Roy Soc B373 20170409 httpsdoiorg101098rstb20170409 2018

Ma S Baldocchi D D Xu L and Hehn T Inter-annual vari-ability in carbon dioxide exchange of an oakgrass savanna andopen grassland in California Agr Forest Meteorol 147 157ndash171 httpsdoiorg101016jagrformet200707008 2007

MacFarling Meure C Etheridge D Trudinger C Steele PLangenfelds R van Ommen T Smith A and ElkinsJ Law Dome CO2 CH4 and N2O ice core records ex-tended to 2000 years BP Geophys Res Lett 33 L14810httpsdoiorg1010292006GL026152 2006

Maire V Martre P Kattge J Gastal F Esser G FontaineS and Soussana J-F The coordination of leaf photosynthesislinks C and N fluxes in C3 plant species PLoS One 7 e38345httpsdoiorg101371journalpone0038345 2012

Maumlkelauml A Hari P Berninger F Haumlnninen H and NikinmaaE Acclimation of photosynthetic capacity in Scots pine to theannual cycle of temperature Tree Physiol 24 369ndash376 2004

Marcolla B Pitacco A and Cescatti A Canopy Architecture andTurbulence Structure in a Coniferous Forest Bound-Layer Me-teorol 108 39ndash59 httpsdoiorg101023a10230277098052003a

Marcolla B Pitacco A and Cescatti A Canopy Architecture andTurbulence Structure in a Coniferous Forest Bound-Layer Me-teorol 108 39ndash59 httpsdoiorg101023a10230277098052003b



Marcolla B Cescatti A Manca G Zorer R Cavagna MFiora A Gianelle D Rodeghiero M Sottocornola M andZampedri R Climatic controls and ecosystem responses drivethe inter-annual variability of the net ecosystem exchange ofan alpine meadow Agr Forest Meteorol 151 1233ndash1243httpsdoiorg101016jagrformet201104015 2011

Matsumoto K Ohta T Nakai T Kuwada T Daikoku K IidaS Yabuki H Kononov A V van der Molen M K KodamaY Maximov T C Dolman A J and Hattori S Energy con-sumption and evapotranspiration at several boreal and temperateforests in the Far East Agr Forest Meteorol 148 1978ndash1989httpsdoiorg101016jagrformet200809008 2008

McHugh I D Beringer J Cunningham S C Baker P J Cav-agnaro T R Mac Nally R and Thompson R M Interactionsbetween nocturnal turbulent flux storage and advection at anldquodealrdquo eucalypt woodland site Biogeosciences 14 3027ndash3050httpsdoiorg105194bg-14-3027-2017 2017

McNevin D von Caemmerer S and Farquhar G DeterminingRuBisCO activation kinetics and other rate and equilibrium con-stants by simultaneous multiple non-linear regression of a kineticmodel J Exp Bot 57 3883ndash3900 2006

Medlyn B E Physiological basis of the light use efficiency modelTree Physiol 18 167ndash176 1998

Medlyn B E Duursma R A Eamus D Ellsworth D SColin Prentice I Barton C V M Crous K Y de AngelisP Freeman M and Wingate L Reconciling the optimal andempirical approaches to modelling stomatal conductance GlobalChang Biol 17 2134ndash2144 2011

Meek D W Hatfield J L Howell T A Idso S B and Regi-nato R J A Generalized Relationship between Photosyntheti-cally Active Radiation and Solar Radiation1 Agron J 76 939ndash945 1984

Merbold L Ardouml J Arneth A Scholes R J Nouvellon Yde Grandcourt A Archibald S Bonnefond J M BoulainN Brueggemann N Bruemmer C Cappelaere B CeschiaE El-Khidir H A M El-Tahir B A Falk U Lloyd JKergoat L Le Dantec V Mougin E Muchinda M Muke-labai M M Ramier D Roupsard O Timouk F Veenen-daal E M and Kutsch W L Precipitation as driver of carbonfluxes in 11 African ecosystems Biogeosciences 6 1027ndash1041httpsdoiorg105194bg-6-1027-2009 2009

Merbold L Eugster W Stieger J Zahniser M Nel-son D and Buchmann N Greenhouse gas budget (CO2CH4 and N2O) of intensively managed grassland fol-lowing restoration Global Change Biol 20 1913ndash1928httpsdoiorg101111gcb12518 2014

Meyer W S Kondrlovagrave E and Koerber G R Evaporationof perennial semi-arid woodland in southeastern Australia isadapted for irregular but common dry periods Hydrol Process29 3714ndash3726 httpsdoiorg101002hyp10467 2015

Michaletz S T Weiser M D Zhou J Kaspari M HellikerB R and Enquist B J Plant Thermoregulation EnergeticsTrait-Environment Interactions and Carbon Economics TrendsEcol Evol 30 714ndash724 2015

Migliavacca M Meroni M Busetto L Colombo R ZenoneT Matteucci G Manca G and Seufert G Modeling GrossPrimary Production of Agro-Forestry Ecosystems by Assimila-tion of Satellite-Derived Information in a Process-Based ModelSensors 9 922ndash942 httpsdoiorg103390s90200922 2009

Monson R K Turnipseed A A Sparks J P Harley P C Scott-Denton L E Sparks K and Huxman T E Carbon sequestra-tion in a high-elevation subalpine forest Global Change Biol8 459ndash478 httpsdoiorg101046j1365-2486200200480x2002

Montagnani L Manca G Canepa E Georgieva E Acosta MFeigenwinter C Janous D Kerschbaumer G Lindroth AMinach L Minerbi S Moumllder M Pavelka M Seufert GZeri M and Ziegler W A new mass conservation approach tothe study of CO2 advection in an alpine forest J Geophys Res114 D07306 httpsdoiorg1010292008jd010650 2009

Monteith J L Solar Radiation and Productivity in TropicalEcosystems J Appl Ecol 9 747ndash766 1972

Moors E Water Use of Forests in The Netherlands PhD thesisVrije Universiteit Amsterdam 2012

Myneni R Knyazikhin Y and Park T MOD15A3HMODISCombined Terra+Aqua Leaf Area In-dexFPAR Daily L4 Global 500 m SIN Grid V006Data set NASA EOSDIS Land Processes DAAChttpsdoiorg105067MODISMCD15A3H006 2015

Myneni R Knyazikhin Y and Park T MOD15A2HMODISTerra Leaf Area IndexFPAR 8-Day L4 Global500 m SIN Grid V006 Data set NASA EOSDIS Land ProcessesDAAC httpsdoiorg105067MODISMOD15A2H0062020

Nakai T Kim Y Busey R C Suzuki R Nagai SKobayashi H Park H Sugiura K and Ito A Char-acteristics of evapotranspiration from a permafrost blackspruce forest in interior Alaska Polar Sci 7 136ndash148httpsdoiorg101016jpolar201303003 2013

Noormets A Chen J and Crow T R Age-DependentChanges in Ecosystem Carbon Fluxes in Managed Forestsin Northern Wisconsin USA Ecosystems 10 187ndash203httpsdoiorg101007s10021-007-9018-y 2007

Oquist G and Huner N P A Photosynthesis of overwinteringevergreen plants Annu Rev Plant Biol 54 329ndash355 2003

Papale D Migliavacca M Cremonese E Cescatti A AlbertiG Balzarolo M Marchesini L B Canfora E Casa R DuceP Facini O Galvagno M Genesio L Gianelle D Magli-ulo V Matteucci G Montagnani L Petrella F Pitacco ASeufert G Spano D Stefani P Vaccari F P and Valen-tini R Carbon Water and Energy Fluxes of Terrestrial Ecosys-tems in Italy in The Greenhouse Gas Balance of Italy 11ndash45Springer Berlin Heidelberg httpsdoiorg101007978-3-642-32424-6_2 2014

Pelkonen P and Hari P The Dependence of the Springtime Re-covery of CO2 Uptake in Scots Pine on Temperature and InternalFactors Flora 169 398ndash404 1980

Pilegaard K Ibrom A Courtney M S Hummelshoslashj P andJensen N O Increasing net CO2 uptake by a Danish beech for-est during the period from 1996 to 2009 Agr Forest Meteorol151 934ndash946 httpsdoiorg101016jagrformet2011020132011

Porcar-Castell A Tyystjaumlrvi E Atherton J van der Tol CFlexas J Pfuumlndel E E Moreno J Frankenberg C and BerryJ A Linking chlorophyll a fluorescence to photosynthesis forremote sensing applications mechanisms and challenges J ExpBot 65 4065ndash4095 2014



Posse G Lewczuk N Richter K and Cristiano P Carbon andwater vapor balance in a subtropical pine plantation iForest ndashBiogeosci Forest 9 736ndash742 httpsdoiorg103832ifor1815-009 2016

Post H Hendricks Franssen H J Graf A Schmidt M andVereecken H Uncertainty analysis of eddy covariance CO2flux measurements for different EC tower distances using anextended two-tower approach Biogeosciences 12 1205ndash1221httpsdoiorg105194bg-12-1205-2015 2015

Powell T L Bracho R Li J Dore S Hinkle C R andDrake B G Environmental controls over net ecosystem carbonexchange of scrub oak in central Florida Agr Forest Meteorol141 19ndash34 httpsdoiorg101016jagrformet2006090022006

Prentice I C Dong N Gleason S M Maire V and WrightI J Balancing the costs of carbon gain and water transporttesting a new theoretical framework for plant functional ecologyEcol Lett 17 82ndash91 httpsdoiorg101111ele12211 2014

Prentice I C Liang X Medlyn B E and Wang Y-P Re-liable robust and realistic the three Rrsquos of next-generationland-surface modelling Atmos Chem Phys 15 5987ndash6005httpsdoiorg105194acp-15-5987-2015 2015

Prescher A-K Gruumlnwald T and Bernhofer C Landuse regulates carbon budgets in eastern Germany FromNEE to NBP Agr Forest Meteorol 150 1016ndash1025httpsdoiorg101016jagrformet201003008 2010

Priestley C H B and Taylor R J On the Assessment of SurfaceHeat Flux and Evaporation Using Large-Scale Parameters MonWeather Rev 100 81ndash92 1972

Prober S M Thiele K R Rundel P W Yates C J Berry S LByrne M Christidis L Gosper C R Grierson P F Lem-son K Lyons T Macfarlane C OrsquoConnor M H Scott J KStandish R J Stock W D van Etten E J Wardell-JohnsonG W and Watson A Facilitating adaptation of biodiversity toclimate change A conceptual framework applied to the worldrsquoslargest Mediterranean-climate woodland Clim Change 110227ndash248 httpsdoiorg101007s10584-011-0092-y 2012

R Core Team R A Language and Environment for Statistical Com-puting R Foundation for Statistical Computing Vienna Austriaavailable at httpswwwR-projectorg (last access 6 March2020) 2016

Rambal S Joffre R Ourcival J M Cavender-Bares J andRocheteau A The growth respiration component in eddyCO2 flux from a Quercus ilex mediterranean forest GlobalChange Biol 10 1460ndash1469 httpsdoiorg101111j1365-2486200400819x 2004

Reichstein M Falge E Baldocchi D Papale D AubinetM Berbigier P Bernhofer C Buchmann N GilmanovT Granier A Grunwald T Havrankova K Ilvesniemi HJanous D Knohl A Laurila T Lohila A Loustau D Mat-teucci G Meyers T Miglietta F Ourcival J-M PumpanenJ Rambal S Rotenberg E Sanz M Tenhunen J Seufert GVaccari F Vesala T Yakir D and Valentini R On the sep-aration of net ecosystem exchange into assimilation and ecosys-tem respiration review and improved algorithm Global ChangBiol 11 1424ndash1439 2005

Reverter B R Saacutenchez-Cantildeete E P Resco V Serrano-Ortiz POyonarte C and Kowalski A S Analyzing the major drivers

of NEE in a Mediterranean alpine shrubland Biogeosciences 72601ndash2611 httpsdoiorg105194bg-7-2601-2010 2010

Richardson A D Hollinger D Y Aber J D Ollinger S Vand Braswell B H Environmental variation is directly re-sponsible for short- but not long-term variation in forest-atmosphere carbon exchange Global Change Biol 13 788ndash803httpsdoiorg101111j1365-2486200701330x 2007

Rogers A The use and misuse of Vcmax in Earth System Mod-els Photosynt Res 119 15ndash29 httpsdoiorg101007s11120-013-9818-1 2014

Rogers A Medlyn B E Dukes J S Bonan G von CaemmererS Dietze M C Kattge J Leakey A D B Mercado L MNiinemets U Prentice I C Serbin S P Sitch S Way D Aand Zaehle S A roadmap for improving the representation ofphotosynthesis in Earth system models New Phytol 213 22ndash42 httpsdoiorg101111nph14283 2017

Ruehr N K Martin J G and Law B E Effects ofwater availability on carbon and water exchange ina young ponderosa pine forest Above- and below-ground responses Agr Forest Meteorol 164 136ndash148httpsdoiorg101016jagrformet201205015 2012

Running S Mu Q and Zhao M MOD17A2H MODISTerraGross Primary Productivity 8-Day L4 Global 500 m SINGrid V006 Data set NASA EOSDIS Land Processes DAAChttpsdoiorg105067MODISMOD17A2H006 2015

Running S W Nemani R R Heinsch F A Zhao MReeves M and Hashimoto H A Continuous Satellite-Derived Measure of Global Terrestrial Primary Produc-tion BioScience 54 547ndash560 httpsdoiorg1016410006-3568(2004)054[0547ACSMOG]20CO2 2004

Ryu Y Baldocchi D D Kobayashi H van Ingen C Li JBlack T A Beringer J van Gorsel E Knohl A LawB E and Roupsard O Integration of MODIS land andatmosphere products with a coupled-process model to esti-mate gross primary productivity and evapotranspiration from1 km to global scales Global Biogeochem Cy 25 4httpsdoiorg1010292011GB004053 2011

Ryu Y Berry J A and Baldocchi D D What is global pho-tosynthesis History uncertainties and opportunities RemoteSens Environ 223 95ndash114 2019

Sabbatini S Arriga N Bertolini T Castaldi S Chiti T Con-salvo C Njakou Djomo S Gioli B Matteucci G and PapaleD Greenhouse gas balance of cropland conversion to bioen-ergy poplar short-rotation coppice Biogeosciences 13 95ndash113httpsdoiorg105194bg-13-95-2016 2016

Saxton K E and Rawls W J Soil Water Characteristic Estimatesby Texture and Organic Matter for Hydrologic Solutions SoilSci Soc Am J 70 1569ndash1578 2006

Schroder I Kuske T and Zegelin S Eddy Covariance Datasetfor Arcturus (2011ndash2013) Geoscience Australia CanberraTech rep httpsdoiorg10210010014249 2014

Scott R L Jenerette G D Potts D L and Huxman T E Ef-fects of seasonal drought on net carbon dioxide exchange froma woody-plant-encroached semiarid grassland J Geophys Res114 G4 httpsdoiorg1010292008jg000900 2009

Scott R L Hamerlynck E P Jenerette G D Moran M S andBarron-Gafford G A Carbon dioxide exchange in a semidesertgrassland through drought-induced vegetation change J Geo-



phys Res 115 G3 httpsdoiorg1010292010jg0013482010

Scott R L Biederman J A Hamerlynck E P and Barron-Gafford G A The carbon balance pivot point of southwest-ern US semiarid ecosystems Insights from the 21st cen-tury drought J Geophys Res-Biogeosci 120 2612ndash2624httpsdoiorg1010022015jg003181 2015a

Scott R L Biederman J A Hamerlynck E P and Barron-Gafford G A The carbon balance pivot point of southwest-ern US semiarid ecosystems Insights from the 21st cen-tury drought J Geophys Res-Biogeosci 120 2612ndash2624httpsdoiorg1010022015jg003181 2015b

Serrano-Ortiz P Marantildeoacuten-Jimeacutenez S Reverter B R Saacutenchez-Cantildeete E P Castro J Zamora R and Kowalski A S Post-fire salvage logging reduces carbon sequestration in Mediter-ranean coniferous forest Forest Ecol Manage 262 2287ndash2296httpsdoiorg101016jforeco201108023 2011

Shao C Chen J Li L Dong G Han J Abraha M andJohn R Grazing effects on surface energy fluxes in a desertsteppe on the Mongolian Plateau Ecol Appl 27 485ndash502httpsdoiorg101002eap1459 2017

Shi P Sun X Xu L Zhang X He Y Zhang D and YuG Net ecosystem CO2 exchange and controlling factors in asteppendashKobresia meadow on the Tibetan Plateau Sci ChinaSer D 49 207ndash218 httpsdoiorg101007s11430-006-8207-4 2006

Singsaas E L Ort D R and DeLucia E H Vari-ation in measured values of photosynthetic quantumyield in ecophysiological studies Oecologia 128 15ndash23httpsdoiorg101007s004420000624 2001

Smith E L THE INFLUENCE OF LIGHT AND CARBONDIOXIDE ON PHOTOSYNTHESIS J Gen Physiol 20 807ndash830 1937

Smith N G and Dukes J S Plant respiration and photosynthesisin global-scale models incorporating acclimation to temperatureand CO2 Glob Chang Biol 19 45ndash63 2013

Smith N G and Dukes J S Short-term acclimation to warmertemperatures accelerates leaf carbon exchange processes acrossplant types Global Chang Biol 23 4840ndash4853 2017

Smith N G Keenan T F Colin Prentice I Wang H WrightI J Niinemets U Crous K Y Domingues T F GuerrieriR Yoko Ishida F Kattge J Kruger E L Maire V RogersA Serbin S P Tarvainen L Togashi H F Townsend P AWang M Weerasinghe L K and Zhou S-X Global photo-synthetic capacity is optimized to the environment Ecol Lett22 506ndash517 2019

Stevens R M Ewenz C M Grigson G and Conner S M Wa-ter use by an irrigated almond orchard Irrig Sci 30 189ndash200httpsdoiorg101007s00271-011-0270-8 2011

Stocker B fLUE httpsdoiorg105281zenodo1158524 2018Stocker B rpmodel v104 httpsdoiorg105281zenodo3560169

2019aStocker B sofun v120 httpsdoiorg105281zenodo3529466

2019bStocker B eval_pmodel httpsdoiorg105281zenodo3632308

2020aStocker B rsofun httpsdoiorg105281zenodo3632328

2020b

Stocker B D GPP at FLUXNET Tier 1 sites from P-modelhttpsdoiorg105281zenodo3559850 2019c

Stocker B D Zscheischler J Keenan T F Prentice I C Pentildeue-las J and Seneviratne S I Quantifying soil moisture impactson light use efficiency across biomes New Phytol 218 1430ndash1449 2018

Stocker B D Zscheischler J Keenan T F Prentice I CSeneviratne S I and Pentildeuelas J Drought impacts on terres-trial primary production underestimated by satellite monitoringNat Geosci 12 264ndash270 httpsdoiorg101038s41561-019-0318-6 2019

Suni T Rinne J Reissel A Altimir N Keronen P RannikUuml Maso M Kulmala M and Vesala T Long-term measure-ments of surface fluxes above a Scots pine forest in Hyytiaumllaumlsouthern Finland Boreal Environ Res 4 287ndash301 2003

Suzuki Y Makino A and Mae T Changes in the turnover ofRubisco and levels of mRNAs of rbcL and rbcS in rice leavesfrom emergence to senescence Plant Cell Environ 24 1353ndash1360 2001

Tagesson T Fensholt R Guiro I Rasmussen M O Hu-ber S Mbow C Garcia M Horion S Sandholt I Holm-Rasmussen B Goumlttsche F M Ridler M-E Oleacuten N OlsenJ L Ehammer A Madsen M Olesen F S and Ardouml JEcosystem properties of semiarid savanna grassland in WestAfrica and its relationship with environmental variability GlobalChange Biol 21 250ndash264 httpsdoiorg101111gcb127342014

Tanja S Berninger F Vesala T Markkanen T Hari P MaumlkelaumlA Ilvesniemi H Haumlnninen H Nikinmaa E Huttula TLaurila T Aurela M Grelle A Lindroth A Arneth AShibistova O and Lloyd J Air temperature triggers the recov-ery of evergreen boreal forest photosynthesis in spring GlobalChange Biol 9 1410ndash1426 httpsdoiorg101046j1365-2486200300597x 2003

Tedeschi V Rey A Manca G Valentini R Jarvis P Gand Borghetti M Soil respiration in a Mediterranean oak for-est at different developmental stages after coppicing GlobalChange Biol 12 110ndash121 httpsdoiorg101111j1365-2486200501081x 2006

Tramontana G Jung M Schwalm C R Ichii K Camps-VallsG Raacuteduly B Reichstein M Arain M A Cescatti A KielyG Merbold L Serrano-Ortiz P Sickert S Wolf S andPapale D Predicting carbon dioxide and energy fluxes acrossglobal FLUXNET sites with regression algorithms Biogeo-sciences 13 4291ndash4313 httpsdoiorg105194bg-13-4291-2016 2016

Ulke A G Gattinoni N N and Posse G Analysisand modelling of turbulent fluxes in two different ecosys-tems in Argentina International J Environ Pollut 58 52httpsdoiorg101504ijep2015076583 2015

Urbanski S Barford C Wofsy S Kucharik C Pyle E Bud-ney J McKain K Fitzjarrald D Czikowsky M and MungerJ W Factors controlling CO2 exchange on timescales fromhourly to decadal at Harvard Forest J Geophys Res 112httpsdoiorg1010292006jg000293 2007a

Urbanski S Barford C Wofsy S Kucharik C Pyle E Bud-ney J McKain K Fitzjarrald D Czikowsky M and MungerJ W Factors controlling CO2 exchange on timescales from



hourly to decadal at Harvard Forest J Geophys Res-Biogeosci112 G2 httpsdoiorg1010292006JG000293 2007b

Valentini R Angelis P Matteucci G Monaco R Dore S andMucnozza G E S Seasonal net carbon dioxide exchange of abeech forest with the atmosphere Global Change Biol 2 199ndash207 httpsdoiorg101111j1365-24861996tb00072x 1996

Veres J S and Williams III G J Time course of photosynthetictemperature acclimation in Carex eleocharis Bailey Plant CellEnviron 7 545ndash547 1984

Verhoeven A Sustained energy dissipation in winter evergreensNew Phytol 201 57ndash65 2014

von Caemmerer S and Farquhar G D Some relationships be-tween the biochemistry of photosynthesis and the gas exchangeof leaves Planta 153 376ndash387 1981

Wang H Prentice I C Keenan T F Davis T W Wright I JCornwell W K Evans B J and Peng C Towards a universalmodel for carbon dioxide uptake by plants Nat Plants 3 734ndash741 2017a

Wang L Zhu H Lin A Zou L Qin W and Du Q Evalua-tion of the Latest MODIS GPP Products across Multiple BiomesUsing Global Eddy Covariance Flux Data Remote Sensing 9 5httpsdoiorg103390rs9050418 2017b

Way D A and Yamori W Thermal acclimation of photosynthesison the importance of adjusting our definitions and accounting forthermal acclimation of respiration Photosynth Res 119 89ndash100 2014

Weedon G P Balsamo G Bellouin N Gomes S Best M Jand Viterbo P The WFDEI meteorological forcing data setWATCH Forcing Data methodology applied to ERA-Interim re-analysis data Water Resour Res 50 7505ndash7514 2014

Wehr R Munger J W McManus J B Nelson D D ZahniserM S Davidson E A Wofsy S C and Saleska S R Sea-sonality of temperate forest photosynthesis and daytime respira-tion Nature 534 680ndash683 httpsdoiorg101038nature179662016

Wen X-F Wang H-M Wang J-L Yu G-R and Sun X-M Ecosystem carbon exchanges of a subtropical evergreenconiferous plantation subjected to seasonal drought 2003ndash2007Biogeosciences 7 357ndash369 httpsdoiorg105194bg-7-357-2010 2010

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Wohlfahrt G Hammerle A Haslwanter A Bahn M TappeinerU and Cernusca A Seasonal and inter-annual variability of thenet ecosystem CO2 exchange of a temperate mountain grasslandEffects of weather and management J Geophys Res 113 D8httpsdoiorg1010292007jd009286 2008

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Yan J Zhang Y Yu G Zhou G Zhang L Li KTan Z and Sha L Seasonal and inter-annual variationsin net ecosystem exchange of two old-growth forests insouthern China Agr Forest Meteorol 182ndash183 257ndash265httpsdoiorg101016jagrformet201303002 2013

Yee M S Pauwels V R Daly E Beringer J Ruumldiger CMcCabe M F and Walker J P A comparison of opti-cal and microwave scintillometers with eddy covariance de-rived surface heat fluxes Agr Forest Meteorol 213 226ndash239httpsdoiorg101016jagrformet201507004 2015

Zeller K and Nikolov N Quantifying simultaneous fluxesof ozone carbon dioxide and water vapor above a sub-alpine forest ecosystem Environ Pollut 107 1ndash20httpsdoiorg101016s0269-7491(99)00156-6 2000

Zeng Y Badgley G Dechant B Ryu Y Chen Mand Berry J A practical approach for estimating theescape ratio of near-infrared solar-induced chlorophyllfluorescence Remote Sens Environ 232 111209httpsdoiorg101016jrse201905028 2019

Zhang Y Xiao X Wu X Zhou S Zhang G Qin Y andDong J A global moderate resolution dataset of gross primaryproduction of vegetation for 2000ndash2016 Sci Data 4 170165httpsdoiorg101038sdata2017165 2017

Zhao M Heinsch F A Nemani R R and Running S W Im-provements of the MODIS terrestrial gross and net primary pro-duction global data set Remote Sens Environ 95 164ndash176httpsdoiorg101016jrse200412011 2005

Zhu Z Bi J Pan Y Ganguly S Anav A Xu L SamantaA Piao S Nemani R R and Myneni R B GlobalData Sets of Vegetation Leaf Area Index (LAI)3g and Frac-tion of Photosynthetically Active Radiation (FPAR)3g De-rived from Global Inventory Modeling and Mapping Studies(GIMMS) Normalized Difference Vegetation Index (NDVI3g)for the Period 1981 to 2011 Remote Sens 5 927ndash948httpsdoiorg103390rs5020927 2013

Zielis S Etzold S Zweifel R Eugster W Haeni M andBuchmann N NEP of a Swiss subalpine forest is significantlydriven not only by current but also by previous yearrsquos weatherBiogeosciences 11 1627ndash1635 httpsdoiorg105194bg-11-1627-2014 2014


Abstract

Introduction

Theory

Balancing carbon and water costs

Introducing Jmax limitation

Methods

The light use efficiency model

Temperature dependence of the intrinsic quantum yield of photosynthesis

Soil moisture stress

Simulation protocol

Site-scale simulations

Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data

Calibration and evaluation data

Data for site-scale simulations

Data for global-scale simulations

Evaluation methods

Components of variability

Drought response

Results

Calibration results

GPP variability across scales

Seasonal variations

Spatial and annual variations

Drought response

Uncertainty from fAPAR input data

GPP target data

LUE

Global GPP

Discussion

Conclusions

Code and data availability


Appendix B Temperature and pressure dependence of photosynthesis parameters

Appendix B1 Photorespiratory compensation point

Appendix B2 Deriving

Appendix B3 MichaelisndashMenten coefficient of photosynthesis

Appendix B4 Atmospheric pressure

Appendix C Corollary of the prediction

Appendix C1 Stomatal conductance

Appendix C2 Intrinsic water use efficiency

Appendix C3 Maximum carboxylation capacity

Appendix C4 Dark respiration Rd




Appendix F1 Deriving

Appendix F2 Deriving the Jmax limitation factor

Appendix F3 An alternative method for introducing the Jmax limitation

Appendix G The rpmodel() function of the rpmodel R package

Author contributions

Competing interests

Acknowledgements

Financial support

Review statement

References


1 Introduction

Realistic reliable and robust estimates of terrestrial photo-synthesis are required to understand variations in the car-bon cycle monitor forest and cropland productivity and pre-dict impacts of global environmental change on ecosystemfunction (Prentice et al 2015) Understanding how photo-synthetic rates depend on temperature humidity solar ra-diation CO2 and soil moisture is at the core of this chal-lenge Process-based dynamic vegetation models (DVMs)and Earth system models (ESMs) in use today almost al-ways use some form of the Farquharndashvon CaemmererndashBerry(FvCB) model for C3 photosynthesis (Farquhar et al 1980von Caemmerer and Farquhar 1981) in combination withstomatal conductance (gs) models (Ball et al 1987 Leun-ing 1995 Medlyn et al 2011) that couple water and carbonfluxes at the leaf surface

The FvCB model describes the instantaneous saturatingrelationship between leaf-internal CO2 concentrations (ci)and assimilation (A) and how this relationship depends onabsorbed photosynthetically active radiation (APAR) It sim-ulates A as the minimum of a light-limited and a RuBisCO-limited assimilation rate AJ and AC respectively

A=min(AJAC) (1)

Although the FvCB model is standard for leaf-scale pho-tosynthesis and its environmental response on timescales ofminutes to hours DVMs and ESMs using FvCB produce di-vergent results for ecosystem-level fluxes and their responseto the environment at longer timescales (Rogers et al 2017)This is due to assumptions that have to be made about pho-tosynthetic parameters that are not predicted by the FvCBmodel stomatal conductance (gs) and the maximum ratesof RuBisCO carboxylation (Vcmax) and electron transport(Jmax) for ribulose-15-bisphosphate (RuBP) regenerationwhich together determine the relationship between ci and ACommon approaches for determining the values of Vcmax andJmax in DVMs and ESMs are to prescribe fixed values perplant functional type (PFT) and attempt to simulate the dis-tribution of PFTs in space or to use empirical relationshipsbetween leaf N and Vcmax and simulate leaf N internally orprescribe it per PFT (Smith and Dukes 2013 Rogers 2014)

While the FvCB model describes a non-linear relation-ship between instantaneous assimilation and absorbed lightecosystem production integrated over weeks to monthsscales proportionally with APAR (Monteith 1972 Medlyn1998) This observation underlies the general light use effi-ciency (LUE) model which describes ecosystem-level photo-synthesis (gross primary production GPP) as the product ofAPAR and LUE

GPP= PAR middot fAPAR middotLUE (2)

where PAR is the incident photosynthetically active radiationand fAPAR is the fraction of PAR that is absorbed by green

tissue The LUE model is the basis for observation-drivenGPP models that use fAPAR and PAR based on remote sens-ing data and combine this with different approaches for sim-ulating LUE (Running et al 2004 Zhang et al 2017 Fieldet al 1995) and for some forest growth models (Landsbergand Waring 1997) Other remote-sensing-data-based models(Jiang and Ryu 2016) apply the FvCB model in combinationwith vegetation cover and type data and prescribed Vcmax fora set of PFTs

Here we describe a model referred to as the P-model thatunifies the FvCB and LUE models following the theory de-veloped by Prentice et al (2014) and Wang et al (2017a)The model assumes an optimality principle that balances theC cost (per unit of assimilation) of maintaining transpirationand carboxylation (Vcmax) capacities It thus predicts how theratio of leaf-internal to ambient CO2 (ci ca = χ ) acclimatesto the environment given temperature (T ) water vapourpressure deficit (D) atmospheric pressure (p) and ambientCO2 concentration (ca) (Prentice et al 2014) The P-modelalso assumes that the photosynthetic machinery tends to co-ordinate Vcmax and Jmax in order to operate close to the inter-section of the light-limited and RuBisCO-limited assimila-tion rates (coordination hypothesis Chen et al 1993 Haxel-tine and Prentice 1996 Maire et al 2012) under mean day-time environmental conditions By further assuming equalityin the marginal cost and benefit of Jmax daily-to-monthlyaverage assimilation rates can then be described as fractionsof absorbed PAR ie as a LUE model (Eq 2) (Wang et al2017a)

Thus the P-model embodies an optimality-based theoryfor predicting the acclimation of leaf-level photosynthesisto its environment and for simulating LUE In combinationwith prescribed PAR and remotely sensed fAPAR it esti-mates GPP across diverse environmental conditions (Wanget al 2017a) Its prediction for acclimating photosyntheticparameters reduces the number of prescribed (and temporallyfixed) values and avoids the distinction of model parameter-isation by vegetation types or biomes (apart from a distinc-tion between the C3 and C4 photosynthetic pathways) TheP-model has a further advantage over other data-driven GPPmodels (Running et al 2004 Zhang et al 2017) and em-pirically upscaled GPP estimates (Jung et al 2011) in that itaccounts for the influence of changing CO2 and that it usesfirst principles (rather than imposed functions) to representeffects of T D and p (Sect 2) The theory underlying theP-model regarding the waterndashcarbon trade-off has been de-scribed by Prentice et al (2014) and applied by Keenan et al(2016) to simulate how changes in primary production havedriven the terrestrial C sink over past decades and by Smithet al (2019) to explain variations in observed Vcmax Wanget al (2017a) complemented the theory by including effectsof limited electron transport capacity (Jmax) and predictedvariations in observed χ across environmental gradients Toresolve model biases under conditions of low soil moisture





2 Theory




apart(EA)

partχ=minusb

part(VcmaxA)

partχ (3)


ductance gs

E = 16gsD (4)

and




with

mC =ciminus0

lowast

ci+K (7)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD (8)

with

ξ =

radicβ(K +0lowast)

16ηlowast (9)



with

m=ciminus0

lowast

ci+ 20lowast (11)


m=caminus0

lowast



(12)









1+(

4 ϕ0 IabsJmax

)2

︸︷︷︸L

(13)


partA

partJmax= c (14)


L=

radic1minus

(clowast

m

)23

(15)





with

mprime =m

radic1minus

(clowast

m

)23

(17)



3 Methods




prime MC (19)




ϕ0(T )=aLbL

4(0352+ 0022 T minus 000034 T 2) (20)







β =






















34 Forcing data




341 fAPAR





































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References




2 Theory




apart(EA)

partχ=minusb

part(VcmaxA)

partχ (3)


ductance gs

E = 16gsD (4)

and




with

mC =ciminus0

lowast

ci+K (7)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD (8)

with

ξ =

radicβ(K +0lowast)

16ηlowast (9)



with

m=ciminus0

lowast

ci+ 20lowast (11)


m=caminus0

lowast



(12)









1+(

4 ϕ0 IabsJmax

)2

︸︷︷︸L

(13)


partA

partJmax= c (14)


L=

radic1minus

(clowast

m

)23

(15)





with

mprime =m

radic1minus

(clowast

m

)23

(17)



3 Methods




prime MC (19)




ϕ0(T )=aLbL

4(0352+ 0022 T minus 000034 T 2) (20)







β =






















34 Forcing data




341 fAPAR





































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References







1+(

4 ϕ0 IabsJmax

)2

︸︷︷︸L

(13)


partA

partJmax= c (14)


L=

radic1minus

(clowast

m

)23

(15)





with

mprime =m

radic1minus

(clowast

m

)23

(17)



3 Methods




prime MC (19)




ϕ0(T )=aLbL

4(0352+ 0022 T minus 000034 T 2) (20)







β =






















34 Forcing data




341 fAPAR





































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References





β =






















34 Forcing data




341 fAPAR





































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References







34 Forcing data




341 fAPAR





































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References
































4 Results














43 Drought response
















FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References














FULL 075 069 069 073 027 009BRC 072 065 063 072 025 006ORG 070 063 060 069 024 005NULL 068 065 058 071 021 003





FULL 196 42666 39863 184 155 16697BRC 205 45478 43814 189 154 17054ORG 215 46619 44780 199 154 17254NULL 219 46521 46599 194 158 17371




45 GPP target data





46 LUE










47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References








47 Global GPP



5 Discussion













































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References











































6 Conclusions












Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References









Table A1 Continued





Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References


Table A1 Continued





















p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References














p(z)

p0(B1)



=





TK0 R TK

) (B2)


B2 Deriving 0lowast











hence








K(TKp)=Kc(TK)

(1+

pO2(p)

Ko(TK)

) (B8)









p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References





p(z)= p0

(1minus

Lz

TK0

)gMa(RL)minus1

(B10)





gs =

(1+

ξradicD

)A

caminus0lowast (C1)





iWUE=ca(1minusχ)

16 (C2)


iWUE=1

16(

1+ ξradicD






mprime

mC (C4)
















Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References



Rd = Rd25 fR (C9)

fR = exp(


2K))

(C10)


Rd = b0fR

fVVcmax (C11)








where




where





with


1727 TT + 2373

)(E2)

and

eact =p(z) wair Rv

Rd+wair Rv (E3)



F1 Deriving χ


part(EA)

partχ=

16 Dca (1minusχ)2

(F1)


part(VcmaxA)

partχ=minus

K

ca χ2 (F2)


a16 D

ca (1minusχ)2= b

K

ca χ2 (F3)



and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References


and solved for χ

χ =ξ

ξ +radicD

(F4)

ξ =

radicβK

16ηlowast (F5)


χ =0lowast

ca+

(1minus

0lowast

ca

)ξ

ξ +radicD

(F6)

ξ =

radicb(K +0lowast)

16 a (F7)



ξ +radicD

(F8)



c =m(ϕ0Iabs)

3

4

radic[(ϕ0Iabs)2+ (

Jmax4 )2

]3 (F9)


)23

=1

1+(

Jmax4ϕ0Iabs

)2 (F10)


k =4ϕ0Iabs

Jmax(F11)

and

u=

(4cm

)23

(F12)


11+ kminus2 = u (F13)


(1minus u)12 =1

radic1+ k2

(F14)




where

mprime =m

radic1minus

(clowast

m

)23

(F16)

and

m=caminus0

lowast



(F17)




AJ =

(J

4

)m (F18)




AJ =(m

4




2θ (F20)





with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References


with



4cm

(1minus θ 4c

m

) minus 4θ

(F22)


mprime =mωlowast

8θ (F23)

and





mC (F25)










References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References







References






































































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References






















































































































































































2020b






































Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References

























Abstract

Introduction

Theory



Methods




Simulation protocol


Global simulations

Model calibration

Forcing data

fAPAR

Meteorological data




Evaluation methods


Drought response

Results

Calibration results


Seasonal variations


Drought response


GPP target data

LUE

Global GPP

Discussion

Conclusions





















Competing interests

Acknowledgements

Financial support

Review statement

References

P-model v1.0: an optimality-based light use efﬁciency model for … · 2020. 6. 22. · with...

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Transcript of P-model v1.0: an optimality-based light use efﬁciency model for … · 2020. 6. 22. · with...