Yude Pan á Jerry M. Melillo á A. David McGuireDavid W. Kicklighter á Louis F. PitelkaKathy Hibbard á Lars L. Pierce á Steven W. RunningDennis S. Ojima á William J. PartonDavid S. Schimel á Other VEMAP members

Modeled responses of terrestrial ecosystems to elevated atmosphericCO2: a comparison of simulations by the biogeochemistry modelsof the Vegetation/Ecosystem Modeling and Analysis Project (VEMAP)

Received: 13 December 1996 /Accepted: 20 November 1997

Abstract Although there is a great deal of informationconcerning responses to increases in atmospheric CO2 atthe tissue and plant levels, there are substantially fewerstudies that have investigated ecosystem-level responsesin the context of integrated carbon, water, and nutrientcycles. Because our understanding of ecosystem re-sponses to elevated CO2 is incomplete, modeling is a toolthat can be used to investigate the role of plant and soilinteractions in the response of terrestrial ecosystems to

elevated CO2. In this study, we analyze the responses ofnet primary production (NPP) to doubled CO2 from 355to 710 ppmv among three biogeochemistry models in theVegetation/Ecosystem Modeling and Analysis Project(VEMAP): BIOME-BGC (BioGeochemical Cycles),Century, and the Terrestrial Ecosystem Model (TEM).For the conterminous United States, doubled atmo-spheric CO2 causes NPP to increase by 5% in Century,8% in TEM, and 11% in BIOME-BGC. Multiple re-

Oecologia (1998) 114:389±404 Ó Springer-Verlag 1998

Y. Pan (&) á J. M. Melillo á D. W. KicklighterThe Ecosystems Center, Marine Biological Laboratory,Woods Hole, MA 02543, USAFax: +1-508-4571548; e-mail: yudepan@lupine.mbl.edu

D. McGuireU.S. Geological Survey, Alaska Cooperative Fishand Wildlife Research Unit, University of Alaska Fairbanks,Fairbanks, AK 99775, USA

L. F. PitelkaAppalachian Environmental Laboratory,University of Maryland,Frostburg, MD 21532, USA

K. Hibbard á S. W. RunningSchool of Forestry, University of Montana,Missoula, MT 59812, USA

L. L. PierceDepartment of Biological Sciences,Stanford University, Stanford,CA 94305, USA

D. S. Ojima á W. J. PartonNatural Resource Ecology Laboratory,Colorado State University, Ford Collins,CO 80523, USA

D. S. SchimelNational Center for Atmospheric Research,Boulder, CO 80307, USA

Other VEMAP members:J. Borchers á R. NeilsonU.S. Department of Agriculture Forest Service,Oregon State University, Corvallis, OR USA

H.H. Fisher á T.G.F. Kittel á N.A. RossenbloomNational Center for Atmospheric Research,Boulder, CO USA

S. FoxU.S. Department of Agriculture Forest Service, Raleigh, NC,USA

A. Haxeltine á IC. Prentice á S. SitchUniversity of Lund, Lund, Sweden

A. JanetosNational Aeronautics and Space Administration, Washington,DC, USA.,

R. McKeownNatural Resource Ecology Laboratory,Colorado State University,Fort Collins, CO, USA

R. NemaniUniversity of Montana, Missoula, MT, USA

T. PainterCenter for Remote Sensing and Environmental Optics,University of California, Santa Barbara, CA, USA

B. Rizzo á T. SmithDepartment of Environmental Sciences,University of Virginia,Charlottesville, VA, USA

F.I. WoodwardDepartment of Animal and Plant Sciences,University of She�eld,She�eld, UK

gression analyses between the NPP response to doubledCO2 and the mean annual temperature and annualprecipitation of biomes or grid cells indicate that thereare negative relationships between precipitation and theresponse of NPP to doubled CO2 for all three models. Incontrast, there are di�erent relationships between tem-perature and the response of NPP to doubled CO2 forthe three models: there is a negative relationship in theresponses of BIOME-BGC, no relationship in the re-sponses of Century, and a positive relationship in theresponses of TEM. In BIOME-BGC, the NPP responseto doubled CO2 is controlled by the change in transpi-ration associated with reduced leaf conductance to watervapor. This change a�ects soil water, then leaf area de-velopment and, ®nally, NPP. In Century, the response ofNPP to doubled CO2 is controlled by changes in de-composition rates associated with increased soil mois-ture that results from reduced evapotranspiration. Thischange a�ects nitrogen availability for plants, whichin¯uences NPP. In TEM, the NPP response to doubledCO2 is controlled by increased carboxylation which ismodi®ed by canopy conductance and the degree towhich nitrogen constraints cause down-regulation ofphotosynthesis. The implementation of these di�erentmechanisms has consequences for the spatial pattern ofNPP responses, and represents, in part, conceptual un-certainty about controls over NPP responses. Progressin reducing these uncertainties requires research focusedat the ecosystem level to understand how interactionsbetween the carbon, nitrogen, and water cycles in¯uencethe response of NPP to elevated atmospheric CO2.

Key words Global change á Carbon dioxide áBiogeochemistry á Net primary production (NPP) áVegetation/Ecosystem Modeling and Analysis Project(VEMAP)

Introduction

During the past 250 years, the combustion of fossil fuelsand deforestation have increased atmospheric carbondioxide (CO2) from preindustrial levels of approximately280 ppmv to 358 ppmv in 1994 (IPCC WGI 1996). TheIS92a projection of the Bern carbon cycle model is thatCO2 concentrations will reach approximately 450 ppmvby the year 2040 and 700 ppmv by the year 2100 (IPCCWGI 1996). These increases may have substantial e�ectson the global carbon cycle by in¯uencing carbon as-similation and storage in terrestrial ecosystems (Melilloet al. 1996).

The e�ects of elevated CO2 on carbon cycling havebeen experimentally investigated at the tissue, plant, andecosystem levels (Strain and Cure 1994; McGuire et al.1995a; Curtis 1996; Koch and Mooney 1996; KoÈ rnerand Bazzaz 1996). Studies at the tissue level have fo-cused primarily on the response of net photosynthesisand plant respiration. In contrast to studies at the tissue

level, those at the level of the individual plant have fo-cused primarily on the response of growth. Studies at theecosystem level focus primarily on how growth respondsto elevated CO2 in the context of plant and soil inter-actions. Although there is a great deal of informationconcerning responses at the tissue and plant levels,substantially fewer studies have investigated ecosystem-level responses in the context of integrated carbon, wa-ter, and nutrient cycles. The experimental e�ort at theecosystem level has lagged, in part because of the ex-pense and complexity of investigating responses in thecontext of plant and soil interactions. Understandingderived from ecosystem-level studies is crucial if plantand soil interactions are important in the response ofecosystems to elevated CO2. The experimental commu-nity studying CO2 responses has substantially increasedthe e�ort at the ecosystem level in recent years (Drakeet al. 1989, 1996; Curtis et al. 1990; Grulke et al. 1990;Mooney et al. 1991; KoÈ rner and Arnone, 1992; Norbyet al. 1992, 1996; Oechel et al. 1993, 1996; Owensby et al.1993, 1996, 1997; Zak et al. 1993, 1996; Kemp et al.1994; Jackson et al. 1994; Rice et al. 1994; Arnone andKoÈ rner, 1995; Ellsworth et al. 1995; Cardon 1996; Dayet al. 1996; Field et al. 1996, 1997; Hungate et al. 1996,1997; Johnson et al. 1996; Bernston and Bazzaz, 1997;Franck et al. 1997; KoÈ rner et al. in press; Schortemeyeret al. in press; Stocker et al. 1997). Synthesis of the ex-perimental e�ort at the ecosystem level is just beginningto emerge (e.g., Canadell et al. 1996; Koch and Mooney1996). Because synthesis of experimental information atthe ecosystem level is incomplete, modeling is a tool thatcan be used to investigate the role of plant and soil in-teractions in the response of terrestrial ecosystems toelevated CO2.

Models are important tools in identifying potentialecosystem responses to global change because they areable to synthesize information in a quantitative fashion(Rastetter 1996). Ecologists are now developing whole-ecosystem models that consider responses to plant andsoil CO2 fertilization, and the more complex responsesof ecosystems to simultaneous changes in climate andatmospheric CO2 concentration. Di�erent models con-ceptualize the role of interactions between plant and soilprocesses in di�erent ways. The simulations of di�erentmodels can be compared to explore the consequences ofhow di�erent conceptualizations about plant and soilinteractions in¯uence the response of terrestrial ecosys-tems to elevated atmospheric CO2. Thus, comparison ofmodels has the potential to provide valuable insight thatmay be useful in designing experiments to elucidatecontrols over CO2 responses at the ecosystem level.

The Vegetation/Ecosystem Modeling and AnalysisProject (VEMAP; see VEMAP members 1995; Pan et al.1996; Schimel et al. 1997) compared the responses ofthree biogeochemistry and three biogeography modelsto climate change and a doubling of atmospheric CO2

for the conterminous United States. The biogeochemis-try models, BIOME-BGC (Hunt and Running 1992;Running and Hunt 1993), Century (Parton et al. 1987,

390

1988, 1993), and TEM (Raich et al. 1991; McGuire et al.1992, 1993, 1995b, 1997; Melillo et al. 1993, 1995), weredriven by a common input database (Kittel et al. 1995,1996). The three biogeochemistry models were run underdi�erent scenarios, combining a doubling of atmo-spheric CO2 with climate changes projected by threegeneral circulation models (GCMs), and vegetation mapsproduced by three biogeography models (BIOME2,MAPSS, and DOLY). When atmospheric CO2 wasdoubled from 355 ppmv to 710 ppmv without climatechange, equilibrium simulations among the three modelsprojected an increase of net primary production (NPP)between 5% and 11% and an increase of carbon storagebetween 2% to 9% for the conterminous United States(VEMAP members 1995). Although each of thesemodels represents interactions among the cycles ofcarbon, nitrogen, and water in ecosystems, interactionsamong the cycles are represented di�erently by themodels (see VEMAP members 1995; Schimel et al.1997). Because of the large number of responses in thefactorial design of VEMAP (three biogeography models,three biogeochemistry models, three climate changescenarios, and two levels of atmospheric CO2), we didnot fully analyze the mechanisms responsible for theresponses of the models to doubled atmospheric CO2 inVEMAP members (1995).

In this study, we analyze in more detail the responseof NPP to doubled CO2 estimated by the three biogeo-chemistry models (BIOME-BGC, Century, and TEM) inVEMAP. To determine the doubled-CO2 response, eachbiogeochemistry model was run to equilibrium at eachCO2 concentration for the potential vegetation (biomes)of each 0.5° grid cell (latitude ´ longitude) in the con-terminous United States. In this analysis, we ®rst reviewthe continental-scale responses of NPP to doubled CO2.We then evaluate the NPP responses of biomes and gridcells along climatic gradients of temperature and mois-

ture to gain insight into the mechanisms controllingthe CO2 responses of the models. Finally, we analyzeeach model for the mechanisms that control the CO2

responses of NPP across the spatial scope of theconterminous United States.

Patterns of NPP response along climatic gradients

Doubled atmospheric CO2 causes simulated increases inNPP for the conterminous United States of 5% inCentury, 8% in TEM, and 11% in BIOME-BGC (VE-MAP members 1995). These increases are substantiallylower than the 25±50% growth response to doubled CO2

that has been observed in greenhouse studies that supplyplants with su�cient nutrients and water (Kimball 1975;Gates 1985). As noted in VEMAP members (1995) andSchimel et al. (1997), these models all have optimal re-sponses similar to those observed experimentally, whichmay be constrained by a number of modeled ecosystemprocesses. We examine patterns of NPP responses forbiomes and grid cells along climatic gradients to un-derstand the constraints that are operating in each of themodels.

For BIOME-BGC, the NPP responses of biomes todoubled CO2 range from increases of 4% in temperatedeciduous savanna to 27% in alpine tundra (Table 1).Among the 17 biomes in the conterminous UnitedStates, the NPP response of BIOME-BGC is generallygreater in cooler and drier biomes (Figs. 1a, b, 2a). Anexception to the response pattern along climate gradi-ents is subtropical arid shrubland, which is the hottestand driest biome, where NPP increases 20% in responseto doubled CO2 (Table 1). For Century, the NPPresponses to doubled CO2 range from 2% in cooltemperate mixed forest to 10% in temperate mixedxeromorphic forest (Table 1). Among the biomes, re-

Table 1 Net primary production (NPP) responses to doubled atmospheric CO2 (710 vs. 355 ppmv) simulated by the VEMAP bio-geochemistry models

Biome Temperature(°C)

Precipitation(mm)

NPP response (%)

BIOME-BGC Century TEM

Tundra )0.5 788.2 27.29 7.83 4.73Boreal conifer forest 0.6 733.1 6.05 3.37 3.50Maritime conifer forest 7.2 1505.9 10.09 4.10 7.59Continental conifer forest 3.4 666.9 15.97 4.51 4.12Cool temperate mixed forest 5.4 1016.4 12.74 1.88 3.08Warm temperate/subtropic mixed forest 16.5 1296.2 6.69 2.25 11.82Temperate deciduous forest 11.0 1102.9 15.50 4.16 8.19Temperate mixed xeromophic forest 12.4 518.7 10.94 10.00 21.22Temperate conifer xeromophic forest 8.2 356.6 22.59 4.95 23.31Temperate deciduous savanna 12.3 903.5 4.11 6.45 8.25Warm temperate subtropic mixed savanna 17.2 677.8 5.12 5.21 12.65Temperate conifer savanna 4.2 417.5 26.20 7.99 5.71C3 grasslands 6.6 450.1 22.44 9.85 1.25C4 grasslands 11.1 597.9 4.78 9.89 2.97Mediterranean shrublands 11.8 528.8 8.74 7.68 19.25Temperate arid shrublands 6.2 355.7 23.74 6.50 15.12Subtropical arid shrublands 16.9 277.8 19.64 2.23 26.33

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sponses are greatest in semi-arid systems where annualprecipitation ranges between 400 and 600 mm (e.g.,grasslands and mixed xeromorphic forest; Figs. 1a, 2b).The response of NPP has no relationship with temper-ature (Figs. 1b, 2b). For TEM, the NPP response todoubled CO2 ranges from 1% in C3 grassland to 26% insubtropical arid shrublands (Table 1). Among thebiomes, responses are greater in warmer and drierbiomes (e.g., subtropical and temperate arid shrublands;Figs. 1a, b, 2c).

A multiple regression between the NPP response ofbiomes to doubled CO2 and the mean annual tempera-ture and annual precipitation of biomes indicates thatthere is a tendency for a negative relationship betweenthe response of NPP and precipitation for all threemodels (Table 2). In contrast, there are di�erent rela-tionships between the response of NPP and temperaturefor the three models. There is a negative relationshipin the responses of BIOME-BGC, a positive relationshipin the responses of TEM, and no relationship in theresponses of Century.

At the grid cell level, the relationships between theNPP response to doubled CO2 and the mean annualtemperature and annual precipitation are similar to thebiome-level relationships (Table 2). The models disagreeon the relationship of NPP response with temperature.A negative relationship exists between NPP response

and precipitation for all three models with the slopes forBIOME-BGC and TEM about twice that of Century.Although the NPP responses of BIOME-BGC and TEMare more sensitive to spatial variability in precipitation,little of the grid cell variation in NPP response is ex-plained by the multiple regressions (Table 2).

Fig. 1 Relative net primary production (NPP) responses (%) ofbiomes in the conterminous USA to doubled atmospheric CO2 (355 to710 ppmv) vs. biome annual precipitation (a) and biome mean annualtemperature (b) as simulated by the VEMAP biogeochemistry modelsBIOME-BGC, Century, and TEM

Fig. 2 Relative NPP responses (%) of biomes in the conterminousUSA to doubled atmospheric CO2 (355 to 710 ppmv) vs. biomeannual precipitation and biome mean annual temperature assimulated by the VEMAP biogeochemistry models BIOME-BGC(a), Century (b), and TEM (c)

392

To understand the reasons for similarities and dif-ferences in NPP responses among the models, we ana-lyze the mechanisms responsible for the responses ofNPP. The strategy for this analysis is to examine howelevated CO2 concentration will in¯uence the formula-tions of processes in each model, and how feedbacksassociated with the water and nitrogen cycles ultimatelyin¯uence the response of carbon assimilation. First, forthe model under analysis we present overviews of theformulations for carbon assimilation and other relevantprocesses. We then analyze the e�ects of CO2 that ap-pear to be insensitive to climate in their in¯uence onparameters or formulations of the model. Finally, weanalyze the e�ects of CO2 that are sensitive to climate togain insight into how interactions of the carbon, water,and nitrogen cycles represented by the model in¯uencethe response of carbon assimilation to elevated CO2.

Mechanisms that control CO2 responsesof NPP in BIOME-BGC

Overview of canopy carbon assimilation

Canopy carbon assimilation in BIOME-BGC is expres-sed as:

PSN � f Amax�G;TS; �LN �; �CO2:i��; a;LAI, PAR, T� � �1�where Amax is a function representing maximum rate ofphotosynthetic CO2 uptake, G is canopy conductance towater vapor, TS is transpiration based on the Penman-Monteith formulation, [LN] is leaf nitrogen concentra-tion, [CO2:i] is the concentration of intercellular CO2, ais the photosynthetic e�ciency (CO2 ®xed per photonabsorbed), LAI is the leaf area index of the canopy,PAR is photosynthetically active radiation, and T is airtemperature. The biochemistry of the C3 photosyntheticpathway in BIOME-BGC is represented by Amax, aMichaelis-Menton function (Farquhar et al. 1980; Le-uning 1990) that simulates the rate of carbon assimila-tion at maximum photosynthetic photon ¯ux density(ppfd), optimum temperature, leaf nitrogen concentra-tion ([LN]), canopy conductance (G), and intercellular

CO2 concentration ([CO2:i]). Intercellular CO2 concen-trations are linearly related to atmospheric CO2. Thecomponents in Eq. 1 are expressed as:

G � f �CO2:a�;LAI, LWP, VPD, T� � �1a�LWP � 0:2�1=�SWP�� �1b�SWP � SWC/MAXH2O �1c�TS � f�LAI, T, VPD, PAR, G� �1d�a � f �CO2:a�; �CO2:i�;LAI; T� � �1e�where [CO2:a] is concentration of atmospheric CO2,LWP is the leaf water potential, VPD is vapor pressurede®cit, SWP is the soil water potential, SWC is thesoil water content, and MAXH2O is the maximumwater-holding capacity (Running and Coughlan 1988;VEMAP members 1995).

In BIOME-BGC, NPP is half of the carbon assimi-lated by the canopy. The doubled-CO2 response of NPPis in¯uenced by a number of variables and processes inthe canopy carbon assimilation model of BIOME-BGCthat are sensitive to increases in atmospheric CO2

(Table 3). We ®rst examine responses that are insensitiveto climate and then examine those that are sensitive toclimate.

CO2 responses not in¯uenced by climatic gradients

In BIOME-BGC, the doubled-CO2 responses of inter-cellular CO2, canopy conductance, and leaf nitrogenconcentration are prescribed and do not in¯uence theresponse of NPP along climatic gradients. IntercellularCO2 increases with a rise in atmospheric CO2 becausethese two quantities are linearly related in the model.The observation that leaf-level stomatal conductance isreduced by elevated CO2 is represented in BIOME-BGCby prescribing an �20% reduction in canopy conduc-tance for a doubling of atmospheric CO2. Similarly,BIOME-BGC represents the observation that elevatedCO2 reduces leaf nitrogen concentration by prescribing a40% reduction in conifers, 30% reduction in broadleafforests and shrublands, and a 20% reduction in C3

Table 2 Multiple regression analysis of the relative NPP response (%) of biomes (n = 17) and grid cells (n = 3168) to doubled CO2:relationship with the mean annual temperature and annual precipitation

Model Coe�cients P-value R2

Constant Precipitation Temperature Precipitation Temperature

BiomesBIOME-BGC 27.50 )0.0101 )0.681 0.051 0.042 0.414Century 8.75 )0.0034 )0.055 0.089 0.655 0.204TEM 9.80 )0.0094 +0.845 0.046 0.009 0.496

Grid cellsBIOME-BGC 26.50 )0.0077 )0.619 <0.0001 <0.0001 0.153Century 8.50 )0.0035 )0.012 <0.0001 <0.2371 0.174TEM 4.94 )0.0066 +0.869 <0.0001 <0.0001 0.334

393

grasses for a doubling of atmospheric CO2. Thus, carbonassimilation increases as intercellular CO2 increases, anddecreases as canopy conductance and leaf nitrogenconcentration decrease.

CO2 responses in¯uenced by climatic gradients

Temperature

Responses of photosynthetic e�ciency and transpirationare sensitive to temperature. Because photosynthetice�ciency decreases with increasing temperature, therelative doubled-CO2 response of NPP is sensitive totemperature (McMurtrie et al. 1992). Although NPP issensitive to the temperature sensitivity of photosynthetice�ciency, the e�ect in BIOME-BGC is small (Hunt andRunning 1992).

Although the doubled-CO2 changes in canopy con-ductance do not directly in¯uence the relative responseof NPP along climatic gradients, changes in canopyconductance in¯uence transpiration, which is sensitiveto climate. Decreases in canopy conductance reduceleaf-level transpiration, which increases soil water andleaf water potential to increase leaf area index (Runningand Gower 1991). Thus, reductions in leaf-level tran-spiration will enhance the response of NPP. We ana-lytically evaluate the sensitivity of the doubled-CO2

response of transpiration along climatic gradients tounderstand the climatic sensitivity of NPP responses todoubled CO2.

In BIOME-BGC, transpiration (TS) is represented bythe Penman-Monteith equation, and is expressed as:

TS � SLOPE RAD� �CP PA�VPD/RASLOPE + GAMMAf1� 1=�G RA�g

DAYL

LE 1000

� ��2�

where TS is canopy transpiration (m3 day)1); SLOPEis the derivative of humidity de®cit (mbar °C)1) atambient air temperature (T); RAD is average canopynet radiation (W m)2); CP is speci®c heat of air(J kg)1 °C)1); PA is density of air (kg m)3); VPD isvapor pressure de®cit from canopy to air (mbar); RAis canopy aerodynamic resistance, which is ®xed at1.0 s m)1 for trees and shrubs, and 0.01 s m)1 for allgrasses; G is leaf conductance (s m)1); GAMMA is thepsychometric constant (mbar °C)1); LE is latent heatof vaporization of water (J kg)1); and DAYL is day-length (s day)1). Fundamental components of thePenman-Monteith TS formulation include absolutehumidity de®cit (VPD) and the derivative of humidityde®cit with temperature (SLOPE), which are directlycontrolled by average daily air temperature (T) andrelative humidity. We simplify Eq. 2 by replacingterms that do not depend on temperature and mois-ture with constants (mx) (see Appendix), and expressthe absolute change in leaf-level transpiration todoubled CO2 as:

DTS � ÿ0:25m4 m5 m1 SLOPE�m2 VPD� �=G1�CO2

SLOPE�m3 � 1:25m4=G1�CO2� � SLOPE�m3 �m4= G1�CO2

� ��3�

where G1�CO2is canopy conductance at 1� CO2.

Equation 3 indicates that canopy transpiration is po-tentially reduced at doubled CO2, (i.e., DTS is negative)when a prescribed reduction in canopy conductance isimplemented in association with doubled CO2. BecauseVPD and SLOPE increase with temperature (see Ap-pendix), the relative reduction in transpiration mono-tonically decreases with increasing temperature (seeFig. 3a).

Table 3 List of parameters, variables, and processes in¯uenced by doubled atmospheric CO2 for each of the VEMAP biogeochemistrymodels

BIOME-BGC Century TEM

1. Intercellular CO2 increase withdoubled atmospheric CO2

1. E�ect of atmospheric CO2 on potentialproduction rate increases withdoubled atmospheric CO2

1. Intercellular CO2 increases with doubledatmospheric CO2

2. Prescribed 20% reduction incanopy conductance 2. Prescribed 20% reduction in

transpiration

2. The amount of the increase in intercellularCO2 concentration varies with canopyconductance

3. Prescribed 20 � 40% reduction inleaf nitrogen concentration. 3. Soil moisture increases with the

prescribed reduction in transpiration3. Potential production increases with the

increase of intercellular CO24. Photosynthesic e�ciency (a) increaseswith doubled atmospheric CO2 4. Prescribed 20% increase in C:N

ratio of foliage4. Nitrogen constraints on the construction

of new tissue cause down-regulation ofphotosynthesis

5. Transpiration is reduced with theprescribed reduction in canopyconductance

5. Decomposition rate decreases withthe lower N concentration in litterfall 5. The degree of down-regulation depends on

soil moisture, air temperature, amount ofcarbon in the vegetation, and the amountsof soil inorganic nitrogen and vegetation-labile nitrogen

6. Soil moisture increases with thereduction in transpiration

6. E�ect of water on decompositionincreases with the increase in soilmoisture

7. Leaf water stress decreases withthe increase in soil moisture 7. Nitrogen availability for plant increases

with the increase in decomposition

394

Moisture

To evaluate the moisture sensitivity of the doubled-CO2

response of transpiration, we further simplify Eq. 3 sothat it does not depend on temperature-sensitivevariables (see Appendix):

DTS � ÿ0:25 m6

�m7 G1�CO2�2 � 1:25 �m4�2

G1�CO2

� 2:25m4 m7

�4�

By di�erentiating Eq. 4 with respect to G, we determinethat the maximum reduction in transpiration occurswhen canopy conductance equals 0.000174 m s)1 at10°C temperature (see Appendix). Because canopyconductance is related to soil moisture (SWC) throughsoil water potential and leaf water potential (see Eq.1a±c), we are able to determine that the relationshipbetween the reduction in transpiration and soil mois-ture is optimized when soil moisture equals 30.8 mm(see Appendix and Fig. 3b). For di�erent temperatures,the relationship is similar to that in Fig. 3b. Thus, thelargest potential reduction in transpiration associatedwith doubled CO2 occurs when soils are substantiallydry, but not extremely dry. Because reductions intranspiration translate into increases in leaf area (see

Appendix), the greatest relative increases in NPP tendto be associated with the largest potential reduction intranspiration.

Mechanisms that control CO2 responses of NPPin Century

Overview of plant carbon assimilation

The equation of potential NPP (NPPp) in Century isexpressed as:

NPPP � NPPmax TpMpSp ACO2 �5�where NPPmax is a biophysically de®ned maximum NPP,Tp is the e�ect of temperature on NPP, Mp the e�ect ofsoil moisture, Sp the e�ect of self-shading, and ACO2 isthe e�ect of atmospheric CO2. The functional forms forTp, Mp, and Sp are given in Parton et al. (1993).

To determine when NPPP is constrained by nutrientavailability, a nutrient-limited NPP (NPPN) is calcu-lated to estimate the fraction of NPPP that can beachieved while maintaining appropriate tissue C:Nstoichiometry:

NPPN �X�Navail Rtimp�Ninput� Fi� �C:Ni

i � 1 to n�6�

where n is the number of plant pools. The term Navail isthe available mineral N in the soil solution plus N inplant storage pools; plant storage results from N that isresorbed from senescent foliage and is available for newgrowth in the spring, or following drought in perennialvegetation. The term Rtimp is a weighting factor forplant nutrient uptake based on root biomass; Rtimp is 1at an upper threshold of biomass and 0 if root biomass iszero. The term Ninput is the N available from ®xationand deposition. The terms Fi and C:Ni are the fraction oftotal N uptake (Navail Rtimp + Ninput) allocated toplant part i, and the C:N ratio of plant part i, respec-tively; plant parts include roots, leaves, and ®ne andcoarse wood. In Century, allocation between plant poolsand C:N ratios of plant pools are speci®ed for eachvegetation type (Schimel et al. 1994; VEMAP members1995) based on observations at sites used to parame-terize the model.

The ®nal calculation of NPP is de®ned by:

NPP � min�NPPN;NPPP� �7�Although NPPN is nearly always less than NPPP, ifNPPP increases, NPP will generally follow because the¯oating C:N ratios are based on a linear N supply/demand equation until the lower critical C:N thresholdis reached (see Parton et al. 1993). Experimental evi-dence supports ¯oating C:N ratios between years(Schimel et al. 1991). If N availability goes up (e.g., ifN mineralization increases because of warmer or wettersoils: Schimel et al. 1994), NPP will increase as NPPNapproaches NPPP.

Fig. 3 The relative reduction in transpiration (TS) for BIOME-BGCassociated with a doubled atmospheric CO2 along gradients of airtemperature (a) and soil moisture (b). Relative reduction intranspiration is calculated as (TSA ) TSE)/TSA where TSA istranspiration at ambient atmospheric CO2 and TSE is transpirationat doubled (elevated) CO2

395

The doubled-CO2 response of NPP is in¯uenced bya number of variables and processes in Century thatare sensitive to increases in atmospheric CO2 (Ta-ble 3). We ®rst examine responses that are insensitiveto climate and then examine those that are sensitive toclimate.

Overview of decomposition

In Century, decomposition for surface and soil struc-tural material is calculated as:

dCi

dt� Ki Lc f�T � f�M� Ci �8�

and for active soil organic matter (SOM) as:

dCi

dt� Ki f�T � f�M� Tm Ci �9�

where Ci is the amount of carbon in a particular soilcarbon pool, Ki is the maximum decomposition rate, Lcis the impact of lignin content on decomposition ofstructural organic matter, f(T) is the e�ect of soil tem-perature on decomposition (Fig. 4a), f(M) is the e�ect ofsoil moisture on decomposition (Fig. 4b), and Tm is thee�ect of soil texture on SOM turnover. The maximumdecomposition rate (Ki) varies for each pool of soilorganic matter.

CO2 responses not in¯uenced by climatic gradients

In Century, the doubled-CO2 responses of ACO2 in Eq.5, C:N in Eq. 6, and transpiration in the water balancemodel are prescribed and do not directly in¯uence thepattern of NPP along climatic gradients. The variableACO2 monotonically increases according to a nonlinearrelationship relative to the baseline CO2 level:

ACO2 � 1� CO2effÿ 1

log10�2:0�log10

CO2conc

CO2bas

� ��10�

where the CO2e� is the potential e�ect of increasing CO2

concentrations above the baseline, CO2conc is the ele-vated concentration of CO2, and CO2bas is the baselineconcentration of CO2. Because the parameter CO2e� is1.2, ACO2 will increase 20% with a doubling of atmo-spheric CO2. Thus, the multiplicative e�ect of ACO2 inEq. 5 will enhance NPPP by 20% for a doubling ofatmospheric CO2.

In Century, the C:N ratios of leaf biomass are in-creased by 20% with a doubling of atmospheric CO2,which causes NPPN to increase by 20% for no change inNavail. Because doubled CO2 levels tend to increaseboth NPPN, through the response of C:N ratios, andNPPP, through the response of ACO2, by 20%, theprescribed reduction in leaf nitrogen concentrationresults in lower litter quality, which tends to decreasedecomposition rates and Navail (Parton et al. 1995).Elevated CO2 does not in¯uence the e�ect of soil tem-perature on decomposition (Fig. 4a).

In Century, doubled atmospheric CO2 causes a pre-scribed 20% decrease in transpiration per unit leaf mass.By modifying the available water in the soil, the changein transpiration rate in¯uences Mp in Eq. 5. The functionMp is linearly expressed as:

Mp � a�rainfall + stored H2O�=PETÿ b �11�where coe�cients a and b depend on soil texture. On®rst inspection, elevated CO2 will tend to increase Mpbecause reduced transpiration translates into an increasein soil moisture. However, increased soil moisture en-hances leaf area, which partially compensates for thereduced transpiration per unit leaf mass. Changes in Mpassociated with reduced transpiration have the potentialto di�erentially in¯uence decomposition along moisturegradients.

CO2 responses in¯uenced by climatic gradients

In Century, the e�ect of soil moisture on decompositionincreases monotonically with soil moisture (Fig. 4b).Because the prescribed reduction of transpiration inCentury tends to increase soil moisture, the response ofdecomposition to doubled CO2 is relatively higher withincreasing 1 ´ CO2 soil moisture (Fig. 5a). By taking theratio of the 1 ´ CO2 and 2 ´ CO2 decomposition re-sponses in Fig. 5a, the relative response of decomposi-tion tends to be greater in semi-arid regions where the

Fig. 4 The scalar functions in the Century decomposition formula-tion for the e�ects of soil temperature (a) and soil moisture (b) ondecomposition

396

ratio of precipitation plus stored soil water to PET isapproximately equal to 0.4 (Fig. 5b). Because the rela-tive response of decomposition in Fig. 5b tends to causegreater relative responses of nitrogen availability insemi-arid regions, the responses of NPP to elevated CO2

tend to be greater in semi-arid regions (Figs. 1, 2b).

Mechanisms that control CO2 responses of NPP in TEM

Overview of plant carbon assimilation

Carbon assimilation in TEM is represented by grossprimary production (GPP), which is expressed as:

GPP � Cmax f(PAR) f(LEAF) f�T �f(Ca;GV� f(NA) �12�where Cmax is the maximum rate of C assimilation, PARis the photosynthetically active radiation, LEAF is leafarea relative to the maximum annual leaf area, T isthe monthly air temperature, Ca is the atmosphericconcentration of carbon dioxide, GV is relative canopyconductance, and NA is nitrogen availability. NPP iscalculated as the di�erence between GPP and plantrespiration. A doubling of CO2 directly in¯uences f(Ca,

GV) and in¯uences f(NA) through feedbacks of the ni-trogen cycle that in¯uence GPP (Table 3).

CO2 responses not in¯uenced by climatic gradients

In TEM, the term f(Ca, GV) is described by the hyper-bolic (Michaelis-Menton) function:

f(Ca;GV� � Ci=�Ci � kc� �13�where Ci represents the intercellular concentration ofCO2 in the canopy and kc is the half-saturation constantfor CO2 uptake. Similar to BIOME-BGC, Ci increaseslinearly with Ca. In TEM, this dependence is described byGV ´ Ca (see Raich et al. 1991). Similar to the response ofleaf area in BIOME-BGC to potential reductions intranspiration, TEM implicitly assumes that the alloca-tion of leaf area to carbon uptake responds so thatoverall canopy conductance and actual evapotranspira-tion (AET) do not change in response to elevated CO2.Although leaf area is assumed to change, the e�ect ofrelative leaf area on GPP, f(LEAF), is not a�ected byelevated CO2. This assumption is based on the hypothesisthat increases in leaf area will o�set decreases in tran-spiration per unit leaf area (see Eamus and Jarvis 1989).The half-saturation constant kc has been chosen to in-crease f(Ca, GV) by 37% for a doubling of atmosphericCO2 from 340 ppmv to 680 ppmv with GV equal to 1,i.e., f(680, 1)/f(340, 1) � 1.37. When relative canopyconductance (GV) is a constant, the function f(Ca, GV)monotonically increases according to a hyperbolic rela-tionship with elevated atmospheric CO2 (Fig. 6a). Al-though GPP is potentially enhanced by 37% in responseto doubled atmospheric CO2 for no water or nitrogenlimitation, the actual response along climatic gradientsdepends on both water and nitrogen availability.

CO2 responses in¯uenced by climatic gradients

The e�ects of moisture availability on CO2 response areimplemented through Eq. 13, where relative canopyconductance, GV, increases monotonically with the ratioAET and PET (see Appendix). Because the intercellularCO2 concentration depends on both canopy conduc-tance and atmospheric CO2 (GV ´ Ca), the e�ect ofmoisture availability on canopy conductance in¯uencesthe potential response of GPP to elevated atmosphericCO2. Under conditions of very low moisture availability,GPP may increase by more than 90% if nitrogen avail-ability does not limit production (Fig. 6b). Thus, thepotential response of GPP to elevated CO2 tends toincrease along gradients of decreasing precipitation.

In TEM, the carbon-nitrogen status of the vegetationin¯uences the calculation of GPP through the feedbackof nitrogen availability on carbon assimilation. Thisfeedback, which is represented by f(NA) in Eq. 12, isdetermined by the status of nitrogen supply which is thesum of nitrogen uptake (NUPTAKE) plus nitrogen

Fig. 5 a The ambient-CO2 (355 ppmv) and doubled-CO2 (710 ppmv)scalar functions in the Century decomposition formulation for thee�ect of soil moisture on decomposition, f(M), vs. soil moisture levelsat ambient atmospheric CO2 (1 ´ CO2); relative to the soil moisturelevel at ambient CO2, the reduction of transpiration e�ectively shiftsthe scalar function to the left. b The ratio of the doubled-(elevated)CO2 scalar function, f(M)E, to the ambient scalar function, f(M)A, forthe e�ects of soil moisture on decomposition in Century vs. soilmoisture levels at ambient atmospheric CO2 (1 ´ CO2)

397

mobilized from the vegetation labile nitrogen pool(NMOBIL). The feedback represented by f(NA) is dy-namically determined by comparing the calculation ofGPP based on nitrogen supply and the calculationof GPP for no constraints of nitrogen supply. The Cto N ratio of production, which is represented by theparameter Pcn, is multiplied by the sum of NUPTAKEand NMOBIL to determine the amount of NPP that canbe supported from the nitrogen supply. Nitrogen supplyconstrains production when the calculation of uncon-strained GPP, i.e, potential GPP (GPPp) for f(NA) equalto 1, exceeds the sum of autotrophic respiration (RA)and NPP that is determined from nitrogen supply.Therefore, the feedback of nitrogen availability oncarbon assimilation, f(NA), is the ratio of GPP to GPPp(see Appendix). The ability of the vegetation to incor-porate elevated atmospheric CO2 into production asformulated by Eq. 13 depends on the degree to whichproduction is limited by nitrogen supply.

In a nitrogen-limited system we can express f(NA) as:

f(NA) � GPP

GPPp� Pcn (NUPTAKE + NMOBIL)� RA

GPPp�14�

In Eq. 14, NUPTAKE is a function of monthly tem-perature and mean monthly volumetric soil moisture;

autotrophic respiration (RA) is a function of tempera-ture (see Appendix). The behavior of Eq. 14 acrossclimatic gradients is di�cult to analyze in an a priorifashion because simulation is required to determine thee�ects of climate on the pools in the equation (see Ap-pendix). However, we can evaluate how nitrogen feed-back in¯uences nitrogen limitation of NPP in an aposteriori fashion to gain insight into the CO2 responseof production along climatic gradients. The degreeto which GPP is limited by nitrogen availability inTEM can be determined by running the model withnitrogen feedback in the GPP equation turned o�, i.e.,f(NA) � 1, to produce an estimate of GPP that is notlimited by nitrogen availability (see McGuire et al. 1992,1993 for application of this technique). The relativelimitation of GPP by nitrogen availability, i.e., f(NA), iscalculated as GPP/GPPp where GPP is the estimate ofGPP in the nitrogen-limited solution and GPPp is theestimate of GPP in the unlimited solution. For both

Fig. 6 a The hyperbolic scalar function in TEM, f(Ca, GV), for thee�ect of atmospheric CO2 (Ca) and relative canopy conductance (GV)on gross primary production at GV equal to 1 vs. atmospheric CO2

(ppmv). b The ratio of the doubled (elevated) scalar function, f(Ca,GV)E, to the ambient scalar function, f(Ca, GV)A, vs. a gradient ofmoisture availability as represented by actual evaportranspiration(AET) and potential evapotranspiration (PET)

Fig. 7 a For each biome within the conterminous United States, theannual scalar for the e�ect of nitrogen availability on gross primaryproduction, f(NA), vs. mean annual temperature of the biome for twolevels of atmospheric CO2 (355 ppmv and 710 ppmv). The depen-dence of f(NA) at 355 ppmv is represented by solid symbols and at710 ppmv by open symbols; solid lines represent linear regressions(355 ppmv: R � 0.789; P � 0.0002; n � 17; 710 ppmv: R � 0.748,P < 0.0001, n � 17). b The ratio of the regression lines in a, whichrepresents the acclimation response of gross primary production todoubled CO2 along a gradient of biome mean annual air temperature;the pattern represents down-regulation, which occurs when thephotosynthetic capacity of plants grown in elevated CO2 decreasesin comparison to plants grown at baseline CO2

398

contemporary CO2 and doubled CO2, nitrogen limita-tion of GPP decreases [i.e., f(NA) increases] in ecosys-tems with higher mean annual temperature (Fig. 7a;R � 0.789, P � 0.0002 for contemporary CO2;R � 0.748, P < 0.0001 for doubled CO2; n � 17ecosystems), but is unrelated to annual precipitation(R � 0.052, P � 0.8437 for contemporary CO2;R � 0.035, P � 0.8948 for doubled CO2; n � 17).Thus, nitrogen limitation of production tends to increasewith decreasing temperature. This relationship indicatesthat nitrogen supply will tend to constrain the responseof NPP to elevated CO2 more at low temperature than athigh temperature.

The observed acclimation response of carbon assim-ilation, which can be described by the ratio f(NA)2�CO2

=f(NA)1�CO2

(Fig. 7b), is categorized as down-regulation.Down-regulation occurs when the photosynthetic ca-pacity of plants grown in elevated CO2 decreases incomparison to plants grown at baseline CO2, but therate of photosynthesis for plants grown and measured atelevated CO2 is not less than the rate for plants grownand measured at baseline CO2 (Luo et al. 1994). Becausenitrogen supply is least limiting at high temperatures,and the response of NPP tends to be greater forconditions of lower moisture availability, the greatestresponse of NPP to elevated CO2 tends to occur in hotand dry ecosystems (Figs. 1a, b, 2c, 6b, 7b).

Discussion

Among the VEMAP biogeochemistry models, doubledatmospheric CO2 causes simulated increases in NPP forthe conterminous United States to increase between 5%and 11%. These increases are substantially lower thanthe 25±50% growth response to doubled CO2 that hasbeen observed in greenhouse studies that supply plantswith su�cient water and nutrients (Kimball 1975; Gates1985). In this study, we analyzed the climatic sensitivityof the NPP responses simulated by the models to un-derstand how interactions among carbon, water, andnitrogen dynamics constrain the response of NPP to beless than optimal. The comparison among the threebiogeochemistry models in this study indicates that themodels tend to agree on NPP responses to doubled CO2

along precipitation gradients, but tend to disagree on theresponses along temperature gradients.

Because there is little information on the relativeecosystem-level responses of NPP to elevated CO2 alongclimatic gradients, the controls over the response are notwell understood. This lack of understanding has led themodels in this study to di�erent conceptualizationsabout how ecosystem processes control the response ofNPP to elevated CO2. In BIOME-BGC, the NPP re-sponse to doubled CO2 is directly a�ected by increasedintercellular CO2 concentration and e�ciency of quan-tum yield, reduced canopy conductance, and leaf Nconcentration. The e�ects of these factors on NPP donot vary with climate. The patterns of NPP responses

along the climate gradients are controlled by the changein transpiration associated with reduced leaf conduc-tance to water vapor. This change a�ects soil water, thenleaf area development, and ®nally NPP. In Century, theresponse of NPP to doubled CO2 is directly a�ected byincreased CO2 concentration, changes in soil moistureassociated with reduced transpiration, and increasedC:N ratios in plant foliage. The e�ects of these factorsdo not in¯uence NPP responses along climatic gradients.The NPP responses along climate gradients are con-trolled by changes in decomposition rates associatedwith increased soil moisture that results from reducedevapotranspiration. This change a�ects N availabilityfor plants, which in¯uences NPP. In TEM, the NPPresponse to doubled CO2 is controlled by increasedcarboxylation which is modi®ed by canopy conductanceand the degree to which nitrogen constraints causedown-regulation of photosynthesis. These factors a�ectthe NPP response along the climate gradients. The im-plementation of di�erent mechanisms among the modelshas consequences for the spatial pattern of NPP re-sponses estimated by the models, and represents, in part,conceptual uncertainty about controls over NPP re-sponses.

The NPP estimates for contemporary climate andCO2 have been extensively tested at speci®c sites for eachof the models in this study (McGuire et al. 1992; Melilloet al. 1993; Parton et al. 1994; Running 1994). Themodels generally agree on NPP estimates for contem-porary conditions at continental and biome scales, butdisagree on important details of within-biome patterns(VEMAP members 1995; Schimel et al. 1997). Theprocesses controlling the CO2 response of NPP in themodels are a subset of the processes that have beenhighlighted in CO2-enhancement experiments; none ofthe models have attempted to implement all of themechanisms that might play a role in controlling eco-system-level responses of NPP to elevated CO2. Thechoice of processes re¯ects, in part, the di�erent paths ofhistorical development by the models. These biases haveboth strengths and weaknesses.

The BIOME-BGC relies primarily on the hydrologi-cal cycle and water availability for controlling carbonuptake (VEMAP members 1995). The patterns of CO2

response along both temperature and precipitation gra-dients re¯ect, in part, transpiration responses alongthese gradients. The transpiration response in¯uencessoil moisture, which has e�ects on leaf area develop-ment. The explicit treatment of transpiration and leafarea responses is a strength of the BIOME-BGC ap-proach. In contrast to the treatment of hydrological ef-fects, BIOME-BGC does not fully implement the e�ectsof nitrogen availability to control assimilation responsesto elevated CO2. For example, changes in leaf nitrogenare prescribed, and nitrogen cycling plays no role incontrolling nitrogen allocated to canopy biomass.Therefore, the response of BIOME-BGC along tem-perature gradients re¯ects its focus on transpirationrather than on feedbacks from nutrient cycling.

399

In contrast to BIOME-BGC, both Century andTEM rely heavily on the nitrogen cycle and nitrogenavailability for controlling carbon uptake (VEMAPmembers 1995; Schimel et al. 1997). Although feedbacksof the nitrogen cycle are important in both Century andTEM, the models di�er in how temperature and mois-ture availability interact to in¯uence nitrogen avail-ability (VEMAP members 1995). In Century, soil waterstatus and C:N ratios in organic matter in¯uencedecomposition to a�ect nitrogen availability to plants.The CO2-induced changes in soil moisture and C:Nratios of litterfall in¯uence nitrogen availability to a�ectNPP.

In TEM, the model assumes that leaf area respondsso that total canopy conductance and actual evapo-transpiration do not change in response to elevatedCO2. The relative response of GPP is potentially greaterfor lower canopy conductance. Thus, the response ofGPP to elevated CO2 is potentially highest in dry en-vironments. The ability of the vegetation to incorporateelevated atmospheric CO2 into production according tothese hydrological and physiological considerationsdepends on the degree to which production is limited bynitrogen supply. The feedback between carbon and ni-trogen uptake is designed to maintain both the carbonto nitrogen ratios of production and overall vegetativebiomass at target ratios that are speci®c to particularvegetation types. These constraints of carbon-nitrogenstatus of the vegetation determine the degree to whichGPP is down-regulated in response to elevated CO2.Because nitrogen availability limits production more atlow temperature than at high temperature, the responseof NPP to elevated CO2 tends to be lowest in coldmesic environments and to be highest in hot xeric en-vironments. Like Century, TEM explicitly considersinteractions between carbon and nitrogen dynamics.Although TEM implicitly considers the interactionsbetween canopy conductance, leaf area, and soil mois-ture, its approach could be improved by explicitlyrepresenting the linkages among these variables. Addi-tionally, the parameters representing the C to N ratiosof production were not altered in the simulations. Thus,the e�ects of lower nitrogen requirement on the abilityof vegetation to incorporate elevated CO2 into pro-duction and the e�ects of higher C to N ratios in re-ducing decomposition rates were not represented. Thesee�ects have been evaluated in an analysis of TEM atthe global scale (McGuire et al. 1997). In that analysis,the response of NPP in simulations that considered thecombined e�ects of lower nitrogen requirements andreduced decomposition rates did not di�er from theresponse in simulations that did not include these ef-fects.

The implementation of the mechanisms by the VE-MAP biogeochemistry models results from the range ofempirical ®ndings observed in various ®eld and labora-tory studies (see reviews in Kimball 1975; Kimballand Idso 1983; Eamus and Jarvis 1989; Poorter 1993;Ceulemans and Mousseau 1994; Idso and Idso 1994;

McGuire et al. 1995a; Wullschleger et al. 1995). How-ever, these empirical studies do not span the range ofenvironmental and ecosystem conditions that were beingsimulated in this study. For example, the recent obser-vations on carbon allocation under elevated CO2 levels(Drake 1992; Owensby et al. 1993) suggest that an in-crease in carbon allocated to ®ne-root production iswarranted. However, because a general and proventheory for a resource-based approach to allocation doesnot yet exist (see Running and Hunt 1993), models areforced to adopt a more conservative approach using®xed partitioning coe�cients to allocate carbon amongplant tissues. Because our experimental understanding ispoor, we are unable to validate or verify the responses ofthe models in this comparison.

In this study, we are able to identify major uncer-tainties that need to be addressed in future experimentaland modeling studies. We have identi®ed four majorresearch priorities from the comparison in this study.(1) What role does the hydrological cycle play in con-trolling the CO2 responses of leaf area and soil moisturealong temperature and moisture gradients? (2) Whatrole does the nitrogen cycle play in the CO2 responsesof leaf area, and leaf nitrogen content along tempera-ture and moisture gradients? (3) What is the relativerole of changes in nitrogen requirements, allocation,tissue C to N ratios, and rates of decomposition in CO2

responses of NPP along temperature and moisturegradients? (4) What are the relative contributions andimportance of interactions between the hydrologicaland nutrient cycles in controlling NPP responses toelevated CO2? These are key areas of divergence inconceptual and quantitative models arising from dif-ferent formulations of the e�ects of CO2 on water andnutrient use, allocation, and on long-term coupling ofcarbon and nitrogen storage (see VEMAP members1995). Our analysis indicates that additional research isrequired to understand how interactions between thecarbon, nitrogen, and water cycles in¯uence the re-sponse of NPP to elevated atmospheric CO2 in terres-trial ecosystems. In future studies of CO2 responses, itis important to simultaneously measure carbon, water,and nutrient ¯uxes and pools in terrestrial ecosystems.Fluxes to be measured should include photosynthesis,decomposition, N uptake, N mineralization, N losses,and evapotranspiration. Pools to be measured shouldinclude soil moisture, and the C and N pools in ®neroots, wood, leaves, and soil. Measurement of these¯uxes and pools is important for understanding theinteractions among processes that control CO2 re-sponses of ecosystems. Progress in understanding theseinteractions is crucial in reducing the uncertaintiesabout terrestrial responses to elevated atmosphericCO2.

Acknowledgement This work was funded by the Electric PowerResearch Institute, NASA, and the USDA Forest Service as acontribution to the Vegetation/Ecosystem Modeling and AnalysisProject (VEMAP).

400

Appendix

Analysis of climatic sensitivity of BIOME-BGC responsesto doubled CO2

Temperature sensitivity of transpiration

Transpiration in BIOME-BGC, which is based on the Penman-Monteith formulation, is expressed as:

TS � SLOPE RAD + (CP PA)VPD/RA

SLOPE + GAMMA f1� 1=�G RA�gDAYL

LE 1000

� ��A1�

where TS is canopy transpiration (m3 day)1); SLOPE is the de-rivative of humidity de®cit (mbar °C)1) at ambient air temperature(T); RAD is average canopy net radiation (W m)2); CP is speci®cheat of air (J kg)1 °C)1); PA is density of air (kg m)3); VPD isvapor pressure de®cit from canopy to air (mbar); RA is canopyaerodynamic resistance, which is ®xed at 1.0 s m)1 for trees andshrubs, and 0.01 s m)1 for all grasses; G is leaf conductance (s m)1);GAMMA is the psychometric constant (mbar °C)1); LE is latentheat of vaporization of water (J kg)1); and DAYL is daylength(s day)1). To determine the temperature and moisture sensitivity oftranspiration, we simplify Eq. A1 by replacing terms that do notdepend on temperature and moisture with constants (mx). Byletting m1 � RAD, m2 � CP PA/RA, m3 � GAMMA, m4 �GAMMA/RA, andm5 � DAYL/(LE 1000), Eq. Al is simpli®ed as:

TS � m1 SLOPE�m2 VPD

SLOPE�m3 �m4=Gm5 �A2�

With a prescribed 20% reduction in canopy conductance (G), thechange in transpiration is expressed as:

DTS � TS2�CO2ÿ TS1�CO2

� m1 SLOPE + m2 VPD

SLOPE + m3 �m4=G2�CO2

m5

ÿ m1 SLOPE + m2 VPD

SLOPE + m3 �m4=G1�CO2

m5

� m1 SLOPE + m2 VPD

SLOPE + m3 �m4= 0:8� G1�CO2� �m5

ÿ m1 SLOPE + m2 VPD

SLOPE + m3 �m4=G1�CO2

m5

� ÿ0:25 m4 m5 m1 SLOPE+m2 VPD� �=G1�CO2

SLOPE+m3 � 1:25m4=G1�CO2� � SLOPE+m3 �m4=G1�CO2

� �(A3)

In Eq. A3, both vapor pressure de®cit (VPD) and SLOPE dependon temperature:

VPD � 6:1078e17:27T=�237:3�T � �A4�and

SLOPE � d(VPD)

dT� 6:1078e17:27T=�237:3�T � 4098� 34:54T

�237:3� T �2 �A5�

where T is temperature. By substituting these relationships intoEq. A3, we are able to calculate the temperature sensitivity of therelative reduction of transpiration associated with doubledatmospheric CO2 (see Fig. 3a).

Moisture sensitivity of transpiration

To determine the moisture sensitivity of transpiration, we simplifyEq. A3 by letting m6 � m4 m5 (m1 SLOPE + m2 VPD), andm7 � SLOPE + m3, so that the reduction in transpiration onlydepends on variables that are sensitive to moisture (G, m6, andm7):

DTS � ÿ0:25 m6

m7 G1�CO2� �2�1:25 �m4�2G1�CO2

� 2:25m4 m7

�A6�

The greatest potential reduction in transpiration (most negative)will occur when the denominator of Eq. A6 is minimized. Todetermine canopy conductance, G, associated with the greatestreduction in transpiration we de®ne the variable FG:

FG � m7 G1�CO2� �2�1:25 �m4�2

G1�CO2

�A7�

and di�erentiate as follows:

dFG

dG� �m7 G�2 � 1:25 �m4�2

G

" #� 0 �A8�

and determine that FG is maximized when

G ������������������������1:25�m4�22m7 ÿm7

2

s�

�������������������������1:25�m3=5�22m7 ÿm7

2

s�A9�

The value of G that minimizes FG at 10°C is 0.000174 m s)1, whichis determined by setting m3, which represents GAMMA, equal to0.652 (see Monteith 1973), and calculating m7, which is SLO-PE + m3, as 1.543. Because canopy conductance is related to soilmoisture (SWC) through several equations, we can determine thesoil moisture associated with the greatest potential reduction intranspiration.

In BIOME-BGC, canopy conductance is expressed as:

G � Gmax ÿDGw�LWPÿ LWPmin� �A10�where G is canopy conductance (m s)1); Gmax is maximum canopyconductance (m s)1); DGw is the slope of G vs. LWP (m s)1

)MPa)1) (� 0.00139); LWP is the daily maximum leaf water po-tential ()MPa); and LWPmin is the minimum leaf water potentialinducing stomatal closure, de®ned here as the spring minimumLWP ()Mpa) (� 0.5). Leaf water potential (LWP) in Eq. A10 iscalculated by the equation:

LWP � 0:21

SWC=MAXH2O�A11�

where SWC is soil water content; and MAXH2O is the maximumwater-holding capacity (m3) (� 2350). With Eqs. A10 and A11 wedetermine that the soil moisture that minimizes canopy conductancecorresponds to SWC equal to 30.8 mm. Thus, the potential relativereduction in transpiration ()DTR) to doubled CO2 will monotoni-cally increase with soil moisture when SWC is less than 30.8 mm,and will monotonically decrease with soil moisture when SWC isgreater than 30.8 mm (see Fig. 3b). In BIOME-BGC, potentialreductions in transpiration translate into increases in leaf area.

Leaf area response to potential reductions in transpiration

In BIOME-BGC, decreases in transpiration a�ect allocation to leaftissue through the following relationship:

LAI � CLWP SLA � CLCLWPmaxLWPL

SLA �A12�

where CLWP is carbon available for leaf growth; SLA is speci®c leafarea (m2 kg)1 C); CLC is the upper limit on the carbon available forleaf growth; LWPmax is maximum leaf water potential; and LWPLis the highest simulated predawn leaf water potential. Based onEqs. A11 and A12, we determine that the relationship between leafwater potential and soil moisture is:

LAI2�CO2

LAI1�CO2

�CLC

LWPmax

LWPL2�CO2SLA

CLCLWPmax

LWPL1�CO2

SLA� LWPL1�CO2LWPL2�CO2

� SWC2�CO2

SWC1�CO2

� SWC1�CO2� DSWC

SWC1�CO2

� 1� DSWC

SWC

�A13�

401

where LAI2�CO2is the leaf area index for doubled atmospheric CO2,

LAI1�CO2is leaf area index for contemporary atmospheric CO2,

SWC is the soil moisture for contemporary atmospheric CO2, andDSWC is the potential change in soilmoisture caused by the potentialreduction in transpiration. Thus, in BIOME-BGC, the greatest rel-ative increase in leaf area is associated with the greatest potentialrelative increase in soil moisture, which tends to be associated withthe greatest potential relative decrease in transpiration. Because,increases in leaf area enhance gross primary production (GPP) inBIOME-BGC, increases in leaf area will also enhance NPP.

Canopy conductance and nitrogen feedback in TEM

Calculation of relative canopy conductance

In TEM, relative canopy conductance, GV, can be expressed as:

Gv � ÿ10 AETPET

� �2�2:9AET

PETwhen AET

PET� 0:1

GV � 0:1� 0:9AETPET

when AETPET

> 0:1

8>><>>: �A14�

where AET is actual evapotranspiration and PET is potentialevapotranspiration. GV increases monotonically with the ratio ofAET/PET.

Calculation of f(NA), the nitrogen feedback scalar

In TEM, the feedback of nitrogen availability on carbon assimi-lation, f(NA), is dynamically determined by comparing the calcu-lation of GPP based on nitrogen supply and the calculation ofpotential GPP for no constraints of nitrogen supply. PotentialGPP, GPPp, is calculated as:

GPPp � Cmaxf(PAR) f�LEAF� f�T �f�Ca;GV� �A15�where Cmax is the maximum rate of C assimilation, PAR is thephotosynthetically active radiation, LEAF is leaf area relative tothe maximum annual leaf area, T is the monthly air temperature,Ca is the atmospheric concentration of carbon dioxide, and GV isrelative canopy conductance. Monthly GPP, NPP, and f(NA) arecalculated in TEM as:

NPP = Pcn�NUPTAKE + NMOBIL�GPP = Pcn�NUPTAKE + NMOBIL� � RA

f(NA) = GPP=GPPpwhen Pcn�NUPTAKE + NMOBIL� � RA < GPPp

8>><>>: �A16�

and

NPP = GPPp ÿ RA

GPP = GPPpf(NA) = 1when Pcn�NUPTAKE + NMOBIL� �RA � GPPp

8>><>>: �A17�

where Pcn is the C to N ratio of production, NUPTAKE is ni-trogen uptake, NMOBIL is nitrogen mobilized from the vegetationlabile nitrogen pool, and RA is autotrophic respiration. FromEq. A16, f(NA) in a nitrogen-limited system is expressed as:

f(NA) � GPP

GPPp� Pcn �NUPTAKE + NMOBIL� � RA

GPPp�A18�

In TEM, NUPTAKE is expressed as:

NUPTAKE � Nmax f�NAV;SMV� f�T � f(CA) �A19�where Nmax is the maximum rate of N uptake by the vegetation,NAV is the mean monthly pool of inorganic nitrogen available inthe soil solution, SMV is mean monthly volumetric soil moisture, Tis mean monthly temperature, and CA is carbon availability(see McGuire et al. 1992, 1997). The function f(NAV, SMV) isdescribed by the hyperbolic (Michaelis-Mention) function:

f(NAV;SMV� � �SMV�3 NAV

kn1 � �SMV�3 NAV

�A20�

where kn1 is the half-saturation constant for nitrogen uptake. Thefunction f(T) in the NUPTAKE equation is an exponential func-tion with a Q10 of 2.0. When N supply limits plant growth, f(CA) isequal to 1 because carbon is not a limited factor for N uptake[see McGuire et al. 1992 for more details on f(CA)].

The sum of autotrophic respiration (RA) is expressed as:

RA � Rm � Rg � Kr CV elnQ10r =10� �T � Rg �A21�

where Rm is maintenance respiration, and Rg is growth respiration,Kr is the basal respiration rate of vegetation carbon, CV is vege-tation carbon, Q10r is the Q10 of respiration (see McGuire et al.1992). Because growth respiration is calculated as 20% of thephotosynthate that is available for the construction of new tissue,GPP can be calculated as (see Raich et al. 1991):

GPP � 1:25NPP� Rm �A22�The substitution of Eqs. A19±22 into Eq. A18 yields:

f(NA) � GPP

GPPp� 1:25NPP� Rm

GPPp

� 1:25Pcn�NUPTAKE + NMOBIL� � Rm

GPPp

�1:25Pcn Nmax

�SMV�3NAV

kn1��SMV�3NAV

e0:693T�NMOBIL

!�KrCV e lnQ10r=10� �T

Cmax f(PAR) f(LEAF) f�T � f(Ca; GV�(A23)

Equation A23 indicates that the feedback of nitrogen availabilityon carbon assimilation is in¯uenced by two nitrogen pools (NAV,NMOBIL), one carbon pool (CV), soil moisture (SMV) and airtemperature (T).

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