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GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 9, NO. 4, PAGES 471-490, DECEMBER 1995

A global land primary productivity and phytogeography model

F. Ian Woodward

Department of Animal and Plant Sciences, University of Sheffield, Sheffield, England

Thomas M. Smith and William R. Emanuel

Department of Environmental Sciences, University of Virginia, Charlottesville

Abstract. A global primary productivity •nd phytogeogr•phy model is described. The model represents the biochemical processes of photosynthesis •nd the dependence of g•s exchange on stomatal conductance, which in turn depends on temperature •nd soil moisture. C•nopy conductance controls soil w•ter loss by ewpotr•nspir•tion. The •ssignment of nitrogen uptake to leaf l•yers is proportionM to irradiance, •nd respiration •nd m•ximum •ssimil•tion r•tes depend on nitrogen uptake •nd temperature. Total nitrogen uptake is derived from soil c•rbon •nd nitrogen •nd depends on temperature. The long-term •ver•ge •nnu•l c•rbon •nd hydrological budgets dictate c•nopy leaf •re•. Although obserwtions constrain soil c•rbon •nd nitrogen, the distribution of vegetation types is not specified by •n underlying m•p. V•ri•bles simulated by the model •re compared to experimental results. These comparisons extend from biochemical processes to the whole c•nopy, •nd the comparisons •re f•vor•ble for both current •nd elevated COe •tmospheres. The model is used to simulate the global distributions of leaf •re• index •nd •nnu•l net primary productivity. These distributions •re sufficiently reMistic to demonstrate that the model is useful for •nMyzing vegetation responses to global environmenta.1 change.

Introduction

Since the middle of the eighteenth century, fossil fuel use, land use, and other human activities forced steady increases in atmospheric CO2 concentration [Watson et al., 1990; Keeling et al., 1989], and because it affects Earth's energy balance, this increase is expected to alter the climate [Mitchell et al., 1990; Schlesinger and Mitchell, 1985]. Although average global temperature increased about 0.5øC over the last century, the full warming expected to accompany CO2 increase is not yet apparent.

The processes that maintain plants on land depend on both climate and atmospheric CO2 [Woodward, 1987; Latchet, 1980], and thus plants will respond to CO2 increases [Bazzaz, 1990; Woodward et al., 1991] and to any climatic changes that it or other greenhouse gas increases may cause [Melillo et al., 1990]. Vegetation, however, plays an important role in the global carbon cycle's control of changes in atmospheric CO2 and in

Copyright 1995 by the American Geophysical Union.

Paper number 95GB02432. 0886-6236 / 95 /95 GB- 02432 $10.00

the climate system. Thus plant responses allow CO2 increase and climatic change to feed back on the Earth systems that control CO2 and climate.

Because of exchanges between the atmosphere and other reservoirs, particularly the oceans, that collec- tively serve as a carbon sink, the observed increase in the carbon content of the atmosphere is less than past fossil fuel emissions [Post et al., 1990; Keeling et al., 1989; Bolin, 1986]. Estimates of oceanic uptake, however, are not large enough to explain this difference between emissions and the accumulation of carbon in the

atmosphere, and it appears that carbon stocks in plants and soil must have increased during the fossil fuel era [Siegenthaler and Sarmiento, 1993].

Past CO2 increases may have stimulated photosynthesis and caused more carbon storage in terrestrial ecosystems. In order to account for differences between observed CO2 increases and simulated sources and sinks, many geochemically oriented carbon cycle models include CO2 fertilization [Keeling et al., 1989]. In these models, empirical functions express the dependence of primary productivity on atmospheric CO2 concentration, and in some cases, response function parameters are adjusted for best agreement between simulated

471

472 WOODWARD ET AL.' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL

and observed atmospheric CO2. This approach can indicate the magnitudes of terrestrial sinks but provides no insight into the mechanisms involved or their dependence on environmental factors.

Rather simplified models show a substantial capacity of vegetation to influence climate [Shukla and Mintz, 1982], through effects on the global carbon cycle, the terrestrial hydrological cycle, and on the transfer of energy between vegetation and the atmosphere. One feature, therefore, which will improve the capacity of atmospheric general circulation models to predict future climates is the inclusion of improved dynamic representations of vegetation function and distributional changes. The current representations of vegetation in climate models are rather simple [Sato et al., 1989], and none allow the geographical distributions of the global suite of vegetation types to change with climate in a manner which closely simulates natural observations of change [Woodward, 1987].

The strong correlation between ecosystem characteristics and climate has been used for some time to de-

rive from climatic data global distributions of biomes [Emanuel et al., 1985; Prentice, 1990; Smith et al., 1992; Prentice et al., 1993] or variables such as net primary productivity [Rosenzweig, 1968; Lieth, 1975; Box, 1978] or decomposition rate [Meentemeyer, 1978; Raich and Schlesinger, 1992]. These empirical approaches can be used to test global ecosystem sensitivity to climate and have been incorporated into global carbon cycle models [Esser, 1984; Dai and Fung, 1993] and tested within climate models [Henderson-Sellers, 1990]. Estimates of variables such as net primary productivity are also derived from remote sensing data [Goward et al., 1985; Tucker et al., 1986; Fung et al., 1987; Prince, 1991]. Whether climatic or remote sensing data are used, fundamental processes are not explicitly considered, and these empirical approaches cannot be used to identify the mechanisms that are responsible for simulated or observed responses.

Improved understanding of vegetation and soil processes and their interactions within ecosystems is lead- ing to general models of terrestrial element cycling that can be applied globally [Running and Coughlan, 1988; Jenkinson, 1990; Aber et al., 1991; Raich et al., 1991; Running and Gower, 1991; Aber and Federer, 1992; Melillo et al., 1993; Parton et al., 1993; Potter et al., 1993; Goldewijk et al., 1994; Warnant et al., 1994]. Similar process representations are used in land-surface transfer schemes within newer climate models [Dickin- son et al., 1986; Sellers et al., 1995]. These models rely on empirical relationships to varying degrees, and if they are used in global simulations, all are referenced either to assumed maps of vegetation or ecosystem distribution or to remotely sensed data. The ranges over which any empirical functions in these models remain

valid and their assumptions of static ecosystem distributions restricts the utility of these models for investigat- ing responses to global environmental change. However, Bonan [1993] shows that basic plant physiological models can explain continental-scale relationships between ecosystem variables and climate. This demonstration indicates that even more generality is possible in global models.

Within the International Geosphere-Biosphere Pro- gramme, the core project Global Change and Terres- trial Ecosystems has defined research plans that have a high priority to develop a dynamic vegetation model for inclusion in climate and global biogeochemical models [Steffen et al., 1992]. In this paper, we describe plant productivity components of such a model that can simulate aspects of changes in phytogeography.

Model Description

In a research news article, Baskin [1993] briefly described our global productivity and phytogeography model. The model simulates both functional variables, such as rates of primary productivity, as well as structural variables, such as leaf area index, and under varying assumptions, can be applied from local to global scales. The aim of the full model is to fulfill the re-

quirements described in the previous section, including incorporation into a climate model. The model is developed in modules, which can be used independently. The central plant ecophysiological model (Figure 1) is described here. It first predicts the uptake of nitro-

SOIL

I

I

l t

NITROGEN UPTAKE

WATER UPTAKE

PHOTOSYNTHESIS

RESPIRATION

CONDUCTANCE

CANOPY ET

CANOPY NPP

CLIMATE

C02

Figure 1. Block diagram. Information on soil nutrient status, water holding capacity, climate, and CO2 concentration are used for the first step to predicting leaf and canopy gas exchange. The second step predicts leaf photosynthesis, dark respiration, and stomatal conductance, and finally these responses are run through a year to predict canopy evapotranspiration (et) and net primary productivity (npp). The dashed arrow indicates feedback from canopy processes to plant uptake of water and leaf gas exchange.

WOODWARD ET AL.' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL 475

gen and water from the soil. The rate of nitrogen uptake determines the rates of leaf photosynthesis, dark respiration, and stomatal conductance [Woodward and Smith, 1994a,b]. These rates are then integrated to provide predictions of canopy evapotranspiration and net assimilation (photosynthesis minus respiration). Leaf area index is set to the maximum value that satisfies

annual moisture and carbon balances.

The background research to the subunits of the ecophysiological model is as follows. Nitrogen and water uptake from the soil and the influence of the rate of nitrogen uptake on photosynthetic potential have been previously described [Woodward and Smith, 1994a,b]. The model of leaf photosynthesis is the model described by Farquhar, Von Caemmerer, and Berry [Farquhar et al., 1980; Wullschleger, 1993], also incorporating the effects of variations in temperature, CO2, and stomatal conductance [Harley et al., 1992; Reynolds et al., 1992; McMurtrie and Wang, 1993]. The rate of dark respiration is defined from the rate of nitrogen uptake into the leaves [Charles-Edwards et al., 1986; Ryan, 1991; Reynolds et al., 1992]. Soil water content controls leaf stomatal conductance, probably through changes in the flux of abscisic acid to the stomata [Davies and Zhang, 1991; Gollan et al., 1992; Tardieu and Davies, 1993]. This response is modeled using the asymptotic responses described by Gollan et al. [1992].

Evapotranspiration by a canopy of leaves is predicted by adding the stomatal conductances of each leaf layer of the canopy (when the leaf area index is greater than one) and combining this with an estimate of boundary layer conductance for inclusion in the Penman-Monteith equation of transpiration [Monteith, 1981]. Leaves in- tercept some precipitation, and this moisture is also evaporated according to the Penman-Monteith equation but with only canopy boundary layer conductance [Woodward, 1987; Friend and Woodward, 1990].

Biochemical Processes

Farquhar et al. [1980] describe a widely used model of the biochemical control of photosynthesis. The model is able to simulate the net photosynthetic effects of changes in photorespiratory rate, for example in response to changes in CO2 concentration or irradiance. The photosynthetic rate of a leaf is determined by the minimum rate of at least two processes: (1) the rate of carboxylation Wc due to the amount, kinetic prop- erties, and activation state of ribulose hisphosphate carboxylase-oxygenase (Rubisco) and (2)the rate of carboxylation Wj controlled by the rate of ribulose hisphosphate (RuB P) regeneration in the Calvin cycle, a process that is limited by the rate of electron transport. oCharkey [1985] and Harley and oCharkey [1991] also con- sider the control of photosynthetic rate by triose phosphate utilization U, and a corresponding carboxylation

rate Wp, particularly at high internal CO• concentration and irradiance [Harley et al., 1992].

The net rate of CO• assimilation implied by biochemical processes is

Ab -- Vc 1 ';r• - Rd, (1) where the rate of carboxylation Vc - min{Wc, 14•, Wp }. The variables Po and Pc are the internal partial pressures of O• and CO• respectively; r is the specificity factor of Rubisco for CO• relative to O2 [Jordan and Ogren, 1984], and Ra is the rate of respiration in light due to processes other than photorespiration [Harley et al., 1992]. Typical values of Po and Ra are 21,000 Pa and 0.82 ymol m -• s -1. The specificity factor r depends on temperature [Harley et al., 1992]'

-(3.949-2s.• ) (2) •(T•) - e o.oo• ,

where T• is absolute temperature. If Rubisco controls photosynthesis, then the carboxy-

lation rate is

= + + ' where V• • is the maximum rate of carboxylation by Rubisco. The parameters K• and Ko are Michaelis coefficients for carboxylation and the competing process of oxygenation by Rubisco [Farquhar et al., 1980; Harley et al., 1992]. These coe•cients depend on temperature'

•0.5

35.8- 0.0•T• (4)

Ko(T•)- 1000e•'•-ø'2•k•. (5) Substituting (3)for V• in (1),

( A•- p•+K•(l+•o/Ko) 1 • -R•. (6) Solving for Vff • in (6),

vFx _ + + + - - ' (7) The maximum rate of carboxylation V• •x is calculated from (7) with internal CO• partial pressure P• equal to 70% of its atmospheric partial pressure P• - 35 Pa [Friend, 1991; Reynolds et al., 1992], and with A• - Am•, the maximum, light-saturated, rate of photosynthesis. A subsequent section will describe the rep- resentation of Amax. Alternative values of P• can also be considered. A response function kv(T), derived from a general function by McMurtrie and Wang [1993], further describes the effects of temperature on maximum carboxylation rate'

(S)

474 WOODWARD ET AL.: GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL

where VJ is the carboxylation rate derived from (7). The temperature response function is

= + -2.48 x 10-4(T- 25) 2(9) -8.09 x 10-5(T- 25) 3,

where T is temperature. If the rate of RuBP regeneration limits, then carboxy-

lation rate 14• depends on the rate of electron transport J [Farquhar and Von Caemmerer, 1982]:

Wj: 4(Pc + Po/r)' (10) Irradiance I drives electron transport J [Farquhar et al., 1980; Harley et al., 1992]:

-

where Jm•x is the light-saturated rate of electron transport. The parameter a = 0.24 mol electrons/mol photons is the efficiency of light conversion [Harley e! al., 1992].

]/V•Hsc•e[ege• [1993] and Re•o[•s e! aL [1992] show that the maximum rate of carboxylation l/c max and the light-saturated rate of electron transport •rnax are closely correlated, a response which is expected from the optimization theory of Che• e! aL, [1993]. Light- saturated electron transport is linearly dependent on maximum carboxylation rate with parameters derived by l/V•Hschlege• [1993] from data on 106 plant species:

Jm•x = 29.1 + 1.64V• m•x. (12)

Again, a response function describes the effect of leaf temperature on light-saturated electron transport. It is assumed that V• m•x = V[ evaluated by (7)is for a temperature of 25øC, and

Jm•x - (29.1 + 1.64U)kj(T),

where the temperature response function is

1 + 0.041(T- 25) -1.54 x 10-3(T- 25) 2 -9.42 x 10-5(T- 25) 3

(14)

If triose phosphate utilization limits photosynthesis, the rate of carboxylation is

0.5 Wmin Po

% - 3v + ' where Wmin is the minimum of Wc and Wj. Just as V• m•x and Jm•x are closely correlated, so also are U and Jmax [Wullschleger, 1993], and a linear function describes this relationship:

U = 5.79 x 10 -7 q-0.0569Jm•x. (16)

The question arises as to which process might exert the strongest effect in determining the carboxylation rate Vc. Three sources of evidence indicate that, at least for current partial pressures of CO2, the Rubisco- limited rate Wc is likely to dominate. This conclusion is supported from biochemical studies [Woodrow and Berry, 1988; Stiff, 1991], from a review of 164 response curves of photosynthesis to CO2 concentration [Wullschleger, 1993], and from a theory of nitrogen optimization in leaves [C hen et al., 1993]. The latter example needs some expansion. Chen et al. [1993] propose that plants allocate nitrogen to a canopy of leaves in order to maintain an optimal balance of Wc and 14•. Therefore under a particular average incident irradiance, the optimal photosynthetic response to CO2 will be at the balance between Rubisco and RuBP limita-

tion. If this optimization theory is correct in that it appears to provide an efficient prediction of nitrogen allocation and photosynthesis within a canopy, then it may be assumed that the estimate of maximum assimilation rate is closely related to Wc and 14• at the typical operational value of intercellular CO2 concentration.

Carbon Dioxide Supply

Stomatal conductance controls the diffusion of CO2 from the atmosphere into the intercellular air spaces and thus the supply of CO2 that affects the rates of carboxylation We, Wj, and Wp, (3), (10), and (15). Internal CO2 adjusts to balance supply by diffusion and demand by photosynthetic processes. The stomatal conductance varies with a range of environmental conditions, including CO2 concentration [Jones, 1992]. Therefore as the photosynthetic rate A varies, so does stomatal conductance, and vice versa [Harley et al., 1992].

The assimilation rate implied by the diffusion gradi- ent in CO2 concentration from the atmosphere into the intercellular air spaces is

(Pa - Pc), - (17)

where g• is stomatal conductance to water vapor. Ball et al. [1987] describe a composite empirical relationship for representing stomatal conductance responses to a wide range of environmental conditions that we modify in order to include the effects of soil moisture:

gs ---- (go(T) q- gl(T)At•n/Pa) kg(ws),

where Rn is relative humidity of the air surrounding the leaf. The parameter go is the stomatal conductance when Ad is zero at the light compensation point, and gl is an empirical sensitivity coefficient. The function kg(w•) describes the response of stomatal conductance

WOODWARD ET AL' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL 475

to soil water content w,. There are some problems in the appropriateness of some of the response variables, that is, the relative humidity lAphalo and Jarvis, 1991, 1993]; however, in the absence of a mechanistic model of stomatal conductance to parallel the photosynthesis model, this formulation, with some modification, is used.

An analysis of stomatal conductance measurements from different climates [Woodward and Smith, 1994b] indicates that go and gl are approximately linearly dependent on temperature:

go(T) - 142.4 - 4.8T (19)

g•(T) - 12.7- 0.207T. (20)

The values of these parameters, however, are restricted: 8 _< go _< 80/•mol m -2 s -1 and 6.9 _< gl _< 10.

The effects of the aerial environment on photosynthesis and stomatal conductance work in parallel with the influences of the water status of the soil. It is a long- held theory in plant physiology that the water potential of the soil and leaf are critical in controlling stomatal conductance [Jones, 1980; Kramer, 1988], and it appears to be a safe conclusion that stomata close once the leaf water potential falls below a particular threshold value [Jones, 1980, 1992]. More recent evidence clearly demonstrates that reductions in stomatal conductance

occur as the soil water content declines, even though the leaf water potential remains unchanged [Gollan et al., 1986, 1992; Davies and Zhang, 1991; Tardieu et al., 1992; Tardieu and Davies, 1993]. This response is at- tributed to nonhydraulic communication between the root and the shoot, probably by abscisic acid (ABA) with a response of decreasing stomatal conductance to an increasing rate of ABA supply to the leaves [Gollan et al., 1992; Tardieu and Davies, 1993]. Tardieu and Davies [1993] describe the dual action of ABA and leaf water potential on stomatal conductance. If leaf water potential is greater than a threshold value, then ABA exerts a control on conductance that depends on leaf water potential.

Stomatal conductance is assumed to respond to ABA and soil water content alone [Gollan et al., 1992]. The influences of leaf water potential as a threshold and as a modifier of response to soil water need to be incorporated in terms of the unique responses of different functional types of plants. A simple example is the difference between very drought resistant evergreen species and mesophytic drought sensitive species [Latchet, 1980]. Rooting depth should also be considered.

The influence of soil water content w,, on stomatal conductance g, in (18) is defined by a hyperbolic response function based on data presented in Gollan et al. [1992]'

kg(ws) - 81(ws - 80) (21) w• - 2s0 + s2

where the s coefficients define the water holding capacity of the soil and the shape of the response curve of stomatal conductance to soil water content. The parameter so is the value of the soil water content at which stomatal conductance is zero, Sl defines the slope of the response of conductance to increases of soil water content above so, and s2 is the rate at which the conductance response fiattens as soil water reaches its maximum value.

The internal CO2 partial pressure Pc is determined by iteratively solving the nonlinear equation that arises by setting assimilation rate implied by the diffusion gra- dient (17) equal to assimilation derived from the Far- quhar model (1) with carboxylation rate Vc equal to the minimum of We, W), and Wp [Harley et al., 1992].

Canopy Conduc•ance• Pho•osyn•hesis• and Respiration

Leaf area is distributed into layers each with unity leaf area index. The number of layers equals the leaf area index of the canopy. The mean irradiance I be- neath a leaf area index La is derived from Beer's law [Monsi and Saeki, 1953; Woodward, 1987]'

I- Ioe -kt• , (22)

where I0 is the incident irradiance on the canopy. The parameter k is an extinction coefficient; a typical value is 0.5.

The estimates of stomatal conductance g, for each leaf layer of the canopy are added to determine the canopy stomatal conductance go. Transpiration and soil moisture calculations involve conductances in nonmolar units. Nonmolar stomatal conductance is related to

the conductance in molar units [Friend and Woodward, 1990]'

8.3144T•,gc (23) gn -- 1000Pa Boundary layer conductance is derived from a stan-

dard logarithmic function of vegetation height h [Friend and Woodward, 1990; Jones, 1992]'

3.36

ga ln2(2000_7• ) , (24) h

where height is derived from a simple function of leaf area index [Shugart, 1984]'

h -- 0.807L22 '127. (25)

Wind speed is assumed to be uniformly 20 m/s at a height well above the highest predicted canopy (200 m); however, observed winds will be considered in future model applications.


Nitrogen is allocated to leaf layers of the canopy in proportion to the mean irradiance of the leaves:

I

700 ' where N is the rate of leaf nitrogen uptake, and NT is the rate of total nitrogen uptake. This response ade- quately simulates field observations of nitrogen distribution in canopies [Field, 1983; Hirose and Wetget, 1987; Chen et al., 1993]. There is evidence that changes in the atmospheric CO2 concentration may influence leaf nitrogen concentrations [Woodward et al., 1991]. It is possible, however, that this reflects differences in the developmental age of tissues at different CO2 concentrations, and that there are no direct effects of CO2 on nitrogen distribution, with observations most easily explained as a size-dependent phenomenon [Coleman et al., 1993]. In addition, the observations of large increases in leaf starch with CO2 enrichment [Thomas and Strain, 1991] might also be expected to influence the leaf nitrogen concentration by dilution. However, this effect appears to be small when measurements are per unit of leaf area, rather than per unit of leaf weight [Thomas et al., 1993]. As a consequence, nitrogen distribution does not currently depend directly on CO2 concentration in this model.

Dark respiration rate of a leaf layer depends on its nitrogen uptake and temperature [Harley et al., 1992]:

,-2(•) R N r•(T)- 8 3•44T• . - --e ß (27) 50

The temperature response functions are

rl(T)- 20 q- 36e -0'14T (28)

r2(T) - 50,000 + 81,000½ -0'14T. (29)

The response of dark respiration to temperature shows an initial steep increase in rate with temperature and then a falling rate as temperature increases further, a response which better fits observations than a constant temperature coefficient [Robson, 1981]. A subsequent section dealing with nitrogen uptake further describes the temperature dependence of dark respiration.

An empirical function, derived from the data sum- marized by Woodward and Smith [1994a,b], relates the maximum, light-saturated rate of photosynthesis in any leaf layer to nitrogen uptake:

190N

Amax = 360 +•' (30) This rectangular-hyperbolic response is similar to that described elsewhere [.•gren and Ingestad, 1987; Hilbert, 1990; Reynolds et al., 1992].

Plant Nitrogen Uptake and Maximum Assimilation

The traditional interpretation of the responses of leaf photosynthesis to nitrogen is that there is a strong and positive correlation with leaf nitrogen concentration [Field and Mooney, 1986; Evans, 1989]. This reflects the positive correlation between the nitrogen concentration of the leaf and the concentration of the major photosynthetic enzyme Rubisco and of chlorophyll [Farquhar et al., 1980; Evans, 1989]. There is, however, a very large variation in this relationship for different species, even at photosynthetic light saturation [Evans, 1989]. In addition this approach avoids the problem of the process and rate of nitrogen uptake from the soil.

Some of the considerable interspecific and interhabi- tat variation in the relationship between leaf nitrogen and photosynthesis may be accounted for by the proportion of leaf nitrogen as Rubisco and in the activity of Rubisco itself[Friend, 1991; Lloyd et al., 1992]. How- ever, Woodward and Smith [1994a,b] have shown from experimental and observational evidence that the large scatter observed in leaf nitrogen and the relationship between leaf nitrogen and photosynthesis is strongly controlled by soil nutrient status.

The basis of a generalized global model able to account for the impact of soil nutrient status on photosynthesis emerges from a mycorrhizal study by Read [1990]. In this study, the rate of nitrogen supply to plants cor- relates with the mycorrhizal status and type of the host plants. These patterns can be clearly recognized at the global scale. There is an increasing dominance of a mycorrhizal supply of nitrogen to the host plant, extracted from organic nitrogen in the soil, as the organic nitrogen in the soil increases and the pH and litter decomposition rate decrease [Read, 1990]. This increasing dependence on the mycorrhizal supply of nitrogen parallels a decreasing capacity of the host plant's roots to extract and supply the same resource and a decreased proportion of the xylem flux of nitrogen as nitrate [Read, 1990; Stewart et al., 1992]. The increasing dependence on nitrogen supply from mycorrhizas as soil organic nitrogen and carbon increase, however, leads to decreasing rates of nitrogen uptake [Read, 1990], and these decreasing rates are paralleled by decreasing rates of photosynthesis [Reid et al., 1983; Woodward and Smith, 1994a,b]. Similar negative correlations between increasing soil organic nitrogen content and photosynthetic rates are implied in other terrestrial ecosystem models [Raich et al., 1991; Hunt et al., 1991; McGuire et al., 1992]. Ana- lyzing global soils data, Woodward and Smith [1994a,b] showed that these concepts are generally applicable and derived an empirical relationship for the dependence of plant nitrogen uptake on soil carbon and nitrogen contents:

WOODWARD ET AL.' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL 477

Np - 120min{sn/600, 1)e -8X1ø-%c, (31) where sc and sn are soil carbon and nitrogen per unit land area, respectively. Although Woodward and Smith [1994a,b] validated this relationship for a wide range of vegetation types and soils, it was derived from observations near 20øC and is not applicable over a wide temperature range.

The dependence of nitrogen uptake on soil carbon and nitrogen (31) is modified to include temperature dependence based on uptake kinetics, derived from experimental systems operated at a range of temperatures [Clarkson and Warner, 1979; Bravo and Uribe, 1981; Clarkson, 1985]. The response is based around the concept of the activation energy required for a process [Jones, 1992]. Temperature-dependent nitrogen uptake is

e(U• - o.oo83•Tk ) =

1 + e ( o.oo• ) U 1 -- 40.8 + 0.01T- 0.002T 2

u2 - 0.738 - 0.002T

(33)

(34)

ua = 97.412 - 2.504 In Np. (35)

A response function k•r(T) accounts for soil carbon that does not influence nitrogen uptake because of freezing IBonan, 1992]. Where soil carbon s• is greater than 13,000 g/m • and temperature is less than 15øC,

kT(T)-(1+(15-T)/30) 1+so- 10,000 ' (36) Otherwise, the value of the response function k•.(T) is 1. Figure 2 shows the temperature responses of nitrogen

• 12o

m 100 ,

o

E 80

',," 60

:• 40 z

O 20

z 0

10

SOIL CARBON = 1000 g/m 2 _ SOIL CARBON = 5000 g/m 2

, , , , I , , , , i , , , , i , , , , i , , , ,

15 20 25 30 35

TEMPERATURE (øC)

Figure 2. Nitrogen uptake as a function of temperature for 5000 and 1000 g/m 2 of soil carbon and 600 g/m 2 of soil nitrogen.

I i i i i .... SOIL CARBON = 1000 g / m 2 • SOIL CARBON = 5000 g / m 2 _

v 3 E o

z 2 _.o

n 1

0 , • [ , I , • , , I , , • , I • , , , I , , , ,

10 15 20 25 30 35

TEMPERATURE (øC)

Figure 3. Temperature responses of dark respiration at two levels of soil carbon, 5000 and 1000 g/m 2.

uptake for soils with soil carbon values of 1000 and 5000 g/m 2 and with soil nitrogen greater than 600 g/m 2. At this value of soil nitrogen, the processes represented by (31) do not limit nitrogen uptake. Figure 3 shows the dependence of dark respiration on temperature and nitrogen uptake (27) at two levels of soil carbon storage, 1000 and 5000 gC/m 2.

Soil Water Dynamics

Stomatal conductance (18) and the rate of photosynthesis (17) depend on soil moisture, which varies in response to rainfall and losses by evapotranspiration. Stomatal conductance is assumed to change instanta- neously in response to changes in soil moisture, and the rate of change in the mass of soil water per unit area

/ is W s d • d-•W, - rp- E•, (37)

where Fp is precipitation throughfall to the soil, and ET is the evapotranspiration flux. The Penman-Monteith equation describes the loss of soil water by evapotranspiration ET [Montelib and Unsworth, 1990]:

sl•n + cppgaD (38) ET -- • (s + 7(1 + ga/gn))' where cp is the specific heat of air. Again, gn is stomatal conductance (23), and ga is boundary 1wet conductance (24). The dependence of stomatal conductance on soil moisture is expressed in terms of soil water content w• (21). Soil water content is related to the mass of soil

t. water per unit area w•

(39) Ws -- W s

where kw is a form of soil bulk density assuming a known soil depth.

478 WOODWARD ET AL.- GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL

Leaf Area and Annual Net Primary Productivity

Net CO2 assimilation A is evaluated by (1) for the limiting rate of carboxylation Vc - min{Wc, Wj, Wp } and at the internal CO2 partial pressure Pc that matches the assimilation rate implied by biochemical processes to the supply of COd by diffusion into the intercellular air spaces (17). Dark respiration R, which depends on nitrogen uptake and temperature (27), further re- duces the photosynthesis product available for synthe- sizing and maintaining tissue. Thus over the interval tl _< t _< t2, typically 1 year or a growing season, the amount of photosynthate that is available for tissue synthesis and to meet maintenance respiration require- ments is

t2(A- R)dt. (40) 1

If rn• is the mass of leaves, in CO2 equivalents, synthesized during the period tl _< t _< t2 and if synthesis respiration for leaves is assumed to be one third of the mass synthesized [Hay and Walker, 1989], then the amount of photosynthate available to synthesize tissue other than leaves and for maintenance is

(A- R)dt- 1 + rn•. (41) 1

Respiration to maintain tissue other than leaves depends on the mass of living tissue and on temperature:

I•m - km mw I• a ( Tk ) , (42)

where rn•v is the mass of tissue other than leaves. The parameter k,• is the constant of proportionality for the dependence of maintenance respiration on the mass of tissue; a typical value is k,• - 0.35. The temperature response function for maintenance respiration, derived from material presented by Hay and Walker, [1989] and by Paembonan e! al., [1991] is

5.367X lO 4

21.6- •:•i;•q•-• (43) - .

Thus over the period tl _< t _< ta, the maintenance respiration requirement for nonleaf tissue is

R'• - k,• m•(t)RR(Tk)dt. (44)

' is the mass of nonleaf tissue synthesized during If m w the period tl _< t _< t2 and synthesis respiration for that d-_'_ _ 1

ussue is again assumed to be one third of the mass synthesized, then

i I tu (t)RR(T•)dt (1 + õ)m w +km fta mw -- (45) (1 + A part of the photosynthetic product (40) is used to

maintain tissue that is present at the beginning of the interval tl. However, as it dies, the maintenance re- quirements of that tissue decrease du'ring the period tl < t < t2. Likewise, synthesis of new tissue during the interval tl < t < t2 increases maintenance demands. If the mass of tissue other than leaves is assumed constant

and equal to the total mass of nonleaf tissue synthesized, than an approximate allocation of photosynthetic products can be derived:

' ' - (1 + «)m w + k,•m w ft? R• (46) ftt•(n- R)dt- (1 q- 31-) rn•,

and the mass of nonleaf tissue synthesized is

, ftt•(n- R)dt- (1 q- «)rn• (47)

- + al_) + Under this approximation, net primary productivity over the interval t l < t < t2 is

1 PN = (m• q- mr). (48)

t2 - tl

Woodward [1987] shows that leaf area index, and from it vegetation structure and mass, can be predicted from a hydrological budget. Leaf mass and related structural variables, such as canopy height, should maintain average values over the long term that do not deplete soil moisture and such that the respiration to synthesize and maintain plant tissues does not exceed net assimilation in leaf layers under the most severe resource limitations. With annual climate represented by long-term monthly mean values, the model adjusts leaf area index to the maximum value such that both hydrological and primary productivity constraints are satisfied.

For a particular leaf area index L•t, the model first tests that net assimilation is sufficient to synthesize the implied mass of leaf tissue:

ft (1), 1

(49)

where the mass of leaves synthesized is that implied by the leaf area index La'

1

m• - •LL La. (50) The parameter kœ is specific leaf area; a typical value derived from data assembled by Cannell, [1982] is 0.18. If the implied leaf tissue can be synthesized, the model tests that net primary productivity can be maintained:

P• > O, (51)

and that net assimilation occurs in the leaf layer at the bottom of the canopy:


t•(A• - R•)dt > O, (52) 1

where the subscript n indicates the bottom layer. Fi- nally, if these carbon constraints are satisfied, the model tests that precipitation meets or exceeds moisture loss:

•t t• •t I I

Model Tests

Data on photosynthesis in cotton plants [Harley et al., 1992] provide a basis for testing the model at the cell and leaf levels. Since the Harley data do not include information on soil carbon and nitrogen, we varied those variables in the model until simulated dark respiration at 35 Pa CO2 and 17øC matched the observations. With these derived values of soil variables, the model was then solved for V• •x and light-saturated Jn•x for 18, 26, 29, and 34øC. The results, displayed in Figure 4, agree well with additional Harley measurements at these temperatures. Such agreement might, however, be expected as the temperature sensitivities of the Michaelis-Menton coefficients were taken from Harley et al. [1992], but since these values are likely to be conservative across species [Farquhar and Von Caemmerer, 1982], this does not detract from the test. In addition, the responses of net assimilation A to CO2 partial pressure Pc were also simulated at 29øC, 45% relative humidity, and an irradiance of 1500/•mol m -1 s -1, and again the results compare favorably with observations on cotton (Fig- ur½ 5).

250 • 200 7 .•-' • 150 _• 100

50 m•

0 ', I .... I .... I ..... ,

0 50 100 150 200 250 300 350

OBSERVED

[igure 4. Maximum rates of carboxylation V• •x and electron transpor• Jm•x. Simulated values at tempera- Lures of 18, 26, 29, and 34øC are compared with observations on cotton [Barlev el •1., 1992]. The solid line is a regression of predicted values against obserwtions; the goodness of fit is r2 = 0.95, and the slope of this regression is not significantly different from uniW. The dashed line indicates exact agreement.

40

v 30 E

o

-• 2o

• 10

0 10 20 30 40

OBSERVED A (p. mol m -2 S '1)

Figure 5. Net CO2 assimilation rate A. Simulated values are compared to observations on cotton [Harley et al., 1992] over a range of internal CO2 partial pressures. The solid line is a regression of predicted values against observations; the goodness of fit is r 2 = 0.99, the slope of this regression is not significantly different from unity. The solid line indicates exact agreement.

We compared the function that describes the dependence of stomatal conductance on soil moisture (21) to observations. Figure 6a shows the comparison for wheat [Gollan et al., 1986], and Figure 6b, the comparison for sycamore [Khalil and Grace, 1993]. In both cases, the parameters in the function were adjusted for the best fit between observations and predictions, as these values were not available. Therefore the test only demonstrates the capabilities of the function to represent the observations with parameter adjustment.

We compared simulated canopy photosynthesis and evapotranspiration to gas exchange measurements in a 12-year-old regenerating forest of Eucalyptus maculata and Acacia longifolia. Wong and Dunin [1987] measured gas exchange in a ventilated chamber that covered a small group of trees with maximum canopy height of 10 m and a leaf area index of 3.3. Gas exchange was measured for most of the daylight hours at CO2 partial pressures of about 34 and 68 Pa. Environmental condi-

tions in the model were set to values provided by Wong and Dunin [1987], and we used soil carbon and nitrogen levels from Attiwill and Leeper [1987].

The model predictions agree closely with observations for both canopy photosynthesis (Figure 7) and canopy transpiration (Figure 8). The greatest differences occur during the early morning and late evening, particularly under CO2 enrichment. It is clear from the published results [Wong and Dunin, 1987] that the daily trends in gas exchange for the canopy differ between a day at ambient and a day at enriched CO2; however, it is not possible to explain the difference, and thus to unequiv- ocally ascribe the variance in agreement to either the

480 WOODWARD ET AL.' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL

5OO

400

300

200

lOO

o

o.oz ß o o.o5o o.o6o o.o7o 0.080 o.o9o O.lOO

SOIL WATER CONTENT (g/g)

140

•, 120 E o

E lOO E

v

LU 80 O z

• 60 o

:=) 40 z O ' (9 20

0

0.00 0.10 0.20 0.30 0.40 0.50

SOIL WATER CONTENT (g/g)

Figure 6. Stomatal conductance response to soil moisture. The response function for stomatal conductance, the solid curve, is compared to data: (a) on wheat [Gal- lan e! al., 1986] and (b) on sycamore [Khalil and Wrace, 1993].

5O

•-• 45

-• 40

.• 35

• 30

• 25

2O

20

riCO 2 '- 34 Pa ..-' [] A CO 2 .- 68 Pa

• , , , I , , , , I • , , , I , , , , I .... I , , , ,

25 30 35 40 45 50 OBSERVED .4 (p, mol ITI '2 S '1)

Figure 7. Canopy photosynthesis A. Simulated values are compared to observations at atmospheric CO2 partial pressures of about 34 Pa and 68 Pa. The solid line is a regression of predicted values against observations; the goodness of fit is r 2 = 0.66, and the slope is not significantly different from unity. The dashed line indicates exact agreement.

morning radiation is assumed, and values are scaled by the number of daylight hours to approximate the effects of the diurnal cycle.

We used the Holdridge classification [Holdridge, 1967] to organize comparisons of globally simulated values of maximum assimilation rate Amax with field observations. Simulated values for each 0.50 cell were as-

signed to a Holdridge type based on the climate of the cell. Woodward and Smith [1994a,b] assembled field ob-

10

model or to possible artifacts occurring during a corn- 'E 8 plex field campaign. •

In order to evaluate the model globally, data on E climate and soils are required [Woodward and Smith, • 6 1994a,b]. We used climate data assembled by Leemarts r• and Cramer [1991] and soil carbon and nitrogen data m assembled by Zinke and co-workers [Zinke et al., 1984' <

m 4 Post et al., 1982, 1985]. These data sets allow evalu- • ation of the model for each 0.50 latitude x 0.50 lon- m

gitude cell on the Earth's land surface over a year of 2

climate derived from long-term monthly mean values of 2 temperature, rainfall, and relative humidity. Standard methods were used to calculate solar radiation through the year on each grid cell [Hungerford et al., 1989].

In the absence of hourly climate data, we approximate the influences of the diurnal cycle. The model evaluates variables daily at interpolated values of temperature and relative humidity and with rainfall distributed uniformly across the days of the month. Mid-

[] CO 2 -- 34 Pa A A CO 2 -- 68 Pa

I I I , , ,

4 6 8 10

OBSERVED E•. (mmol ITI '2 S '1)

Figure 8. Canopy evapotranspiration ET. Simulated values are compared to observations at atmospheric CO2 partial pressures of about 34 Pa and 68 Pa. The solid line is a regression of predicted values against observations; the goodness offit is r 2: 0.81, and the slope is not significantly different from unity. The dashed line indicates exact agreement.


4O

E 30 o

20

' 10

0

0 10 20 30 40

OBSERVED Am• (•mol m '2 s '1)

Figure 9. Maximum assimilation rate Amax. Predicted values are assigned to a biome classification for comparison with field observations. The solid line is a regression of predicted values against observations; the goodness of fit is r 2 - 0.97; the slope of this regression is significantly different from unity, indicated by the dashed line.

servations of Amax and extracted maximum values for each biome; assuming that they do not reflect a true ob- servation of Amax, lower values were excluded. Figure 9 compares the simulated and observed values of Amax for each Holdridge type. The agreement is good, but a regression of predicted against observed values indicates consistently higher predictions at high values of Amax. The correlation between predicted and observed values remains high if mean values of observations that include lower values of observed Amax are used.

Finally, Plates I and 2 display simulated global distributions of leaf area index and net primary productivity. Field observations of these variables are subject to significant errors. These errors include measurement error, particularly in measuring belowground productivity, error through ignorance of marked spatial variation in both attributes, errors associated with choosing average or characteristic sites, and variations with suc- cessional stage. Therefore comparison with field data is not a strong test of our model.

We compared leaf area index (Plate 1) against observations at 35 sites [Woodward, 1987], ranging from sparse tundra and arid vegetation to tropical rain forest, Figure 10. Simulated and observed leaf area index at the sites are strongly correlated, although simulated values tend to be low. We compared simulated annual net primary productivity (Plate 2) with field observations assembled by Raich et al. [1991] and by McGuire et al. [1992]. As shown in Figure 11a, the comparison at 19 sites, ranging from tundra to tropical evergreen forest, again shows reasonable correlation between observations and predictions. For seven

sites where predicted values in our global simulation differed significantly from observations, we solved the model with climatic variables specified by data from the nearest weather station in the M•'ller [1982] collec- tion. Except for the addition of estimates for a site in Puerto Rico, values of soil carbon and nitrogen were unchanged. As shown in Figure 11b, significant discrep- ancies between simulated and observed values decrease

substantially when nearby climate data are used rather than values derived by interpolating a set of observed

Discussion and Conclusion

We developed the model described in this paper to provide a means of analyzing vegetation responses to global changes including atmospheric CO2 increase and climatic change. We anticipate using the model to investigate the role of vegetation in climate and in the global biogeochemical cycles that control atmospheric greenhouse gas concentrations as well as to assess the general impacts of global change on terrestrial ecosystems. It is difficult to fully validate the model for these applications, but our tests indicate that while numer- ous refinements and modifications are warranted, the model in its present form can provide useful insight about global vegetation. We find that representations of basic plant processes can be combined to simulate reasonable and realistic, if not yet fully accurate, global vegetation responses to environmental change.

An advantage of a model describing basic plant processes is that vegetation response mechanisms can be identified. This is important in simulation and sensitivity studies as well as in understanding vegetation changes detected by remote sensing. Different ecosystems can respond to environmental change in similar ways; for example leaf area index may decrease or net primary productivity increase, but for different reasons. Process based models must be used to scrutinize broad

patterns of vegetation change in order to isolate the detailed mechanisms involved so that they can be verified in field and laboratory experiments [Woodward, 1987]. This interest in the mechanisms of vegetation response requires reliable representations of plant processes. Our tests and other studies indicate that the representations in our model of biochemical processes and of the dependence of stomatal conductance on assimilation, temperature, and soil moisture are satisfactory.

The biochemical aspects of our model (1)-(16) have been analyzed and tested extensively. Our tests against data on cotton (Figures 4 and 5) are typical of others. The Farquhar et al. [1980] photosynthesis model appears to simulate the influence of biochemistry on photosynthesis over a wide range of Ca plants and environmental conditions, making it well suited to global vegetation analyses. The utility of our global model, particularly in simulating responses to elevated CO2,

482 WOODWARD ET AL' GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL

? ....... T .............................................. :•' ......................................

ß ,,, :-.•.•, :.

I t :.L '• " , .'.,' " '

'• '' :.

,

i

i ß

,: :.

•.•'..' • ..• .6:•.. • .' .:½:• ..... • • •,,,;

t ,i ' •..

i ' :,, ,

.

i i .'". .•½½ •

1

. t' • . ,

,el- i, i rY

I.z_


o

o o


10

X

[] ,1• •

[]

I , , , I , • • I , , • I , , ,

2 4 6 8 OBSERVED LEAF AREA INDEX

o

o lO

Figure 10. Leaf area index. Simulated values are compared to observations at 35 field sites [Woodward, 1987]. The solid line is a regression of predicted values against observations; the goodness of fit is r 2 - 0.73. The dashed line indicates exact agreement.

can be extended by incorporating a corresponding rep- resentation of C4 photosynthesis [Collatz et al., 1992].

Similarly, the dependence in the model of stomatal conductance on soil moisture (21) agrees well with observations, Figure 6. However, this function is empirical, and its parameter values must be adjusted for agreement with observed responses rather than derived from independent experiments or first principles. The incorporation of a function based on the mechanisms involved awaits further data and better understanding of this important control on photosynthesis. Good agreement between simulated and observed canopy photosynthesis as well as evapotranspiration (Figures 7 and 8) indicates satisfactory coupling of biochemical processes with stomatal conductance responses and partitioning of nitrogen and photosynthesis within leaf layers.

The favorable comparison on a global basis of simulated maximum assimilation rates against field observations (Figure 9) indicates that the assumed dependence of maximum assimilation on nitrogen uptake (30) and in turn the dependence of nitrogen uptake on soil carbon and nitrogen contents as well as temperature (31)-(36) provide a satisfactory means of relating photosynthesis calculations to soil organic matter and nutrient pools for global simulations. In order to investigate ecosystem biogeochemistry, our primary productivity model can be coupled to a model of soil carbon and nitro- ,• ...... 1;,• ,• e.g., is required to fully assess ecosystem responses to rising atmospheric CO2.

The comparisons of simulated and observed leaf area index and net primary productivity (Figures 10 and 11) indicate good agreement with field measurements. The simulated global distribution of leaf area index matches

the general distribution of biomes as expected [Wood- ward, 1987; Prentice et al., 1993], and the simulated geographical patterns of annual net primary productivity generally match those simulated by other models [Melillo et al., 1993; Potter et al., 1993].

Whole plant allocation is not yet well enough under- stood to be properly treated in general models. Thus our scheme for estimating annual net primary productivity (40)-(48) only roughly approximates the required accounting of allocation to synthesis and to meet maintenance demands. We make two critical assumptions in estimating net primary production.

1.2/ ' ' ' i . , . i . , . i . , , i , , , i I I

0.8 .-'" -

0.6 ." - []

0.4 [] 0.2[- [] 0.0E:;,',•, , .... ,•,,,,,, ,

0.0 0.2 0.4 0.6 0.8 1.0 1.2 OBSERVED NPP (kg m '• y'•)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

0.0

i i i I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' '•, •,j b

0.2 0.4 0.6 0.8 1.0 1.2

OBSERVED NPP (kg m '2 y'•)

Figure 11. Annual net primary productivity. Simu- lated values are compared to observations at 19 sites

dicted values are all extracted from the global simulation. (b) Seven predicted values are replaced by values simulated with climate observed at a nearby weather station IMP'lief, 1982]. The solid lines are regressions of predicted values against observations: the goodness of fit in (a)is r 2 - 0.81; while in (b) r • - 0.95. The dashed lines indicate exact agreement.

WOODWARD ET AL.: GLOBAL PRODUCTIVITY AND PHYTOGEOGRAPHY MODEL 485

First, by constraining leaf area index, we are able to partition photosynthate between leaf and other tissue in a consistent, if simplistic, way. In actuality, all of the leaf tissue allowed by carbon and moisture constraints is not necessarily synthesized each growing season or year. Thus more photosynthate is available for synthesis and maintenance of nonleaf tissue than is implied by (41), and the difference is certainly significant in the case of evergreen plants.

An equally critical second assumption in our estimates of annual net primary productivity is that the mass of nonleaf tissue associated with maintenance res-

piration is constant over the growing season or year and is equal to the amount of tissue other than leaves that is synthesized during the period. This assumption requires that the senescence of nonleaf tissue occur at the same rate that nonleaf tissue is synthesized. Again, this assumption is only approximated in actuality and devi- ations can be significant.

At this stage, we do not expect very accurate global simulations of vegetation characteristics. Our model treats only the most fundamental environmental factors and processes that determine variables such leaf area index or primary productivity and is not constrained by observations of such variables. Several very important phenomena are not directly considered at all. For example, disturbance does not affect vegetation structure or function in the model. Thus in savannas where fire is

important, the model predicts values of leaf area index that are probably too large [Frost et al., 1986; Wood- ward, 1987]. Similarly, we do not address land use or management. Where crops replace forest ecosystems, or even in grasslands under grazing, the model simulates unrealistic values of primary productivity or leaf area. At least for some time, forest management can lead to higher values of primary productivity than ecological considerations would suggest should occur under natural conditions. But our simulated large-scale patterns of leaf area index (Plate 1) and annual net primary productivity (Plate 2) are very reasonable, demonstrating the dominant role of climate in determining the distributions of vegetation structure and function.

These global model results indicate that the dependence of the processes and parameters involved in primary productivity on climatic and edaphic conditions can be treated by functional relationships rather than by assigning characteristics and parameter values to vegetation types and adopting a map of vegetation or biome distribution. While the latter approach may yield more accurate simulations of contemporary conditions or of natural conditions under current climate, it is severely limited in simulating conditions expected with global environmental changes that alter parameter values for particular biomes or the distributions of vegetation types over the Earth's land surface.

Moreover, reasonable simulation of the global distribution of leat area index (Plate 1) demonstrates that models based on vegetation process representations can be used to derive the distributions of vegetation structural characteristics in addition to functional variables

such as primary productivity. If vegetation maps are required, they can be derived by classifying the structural and functional variables simulated by our model. Indeed, schemes for relating vegetation and biome distributions directly to climate and edaphic conditions are making increasing use of process representations.

In the absence of global data on variables such as leaf area index or primary productivity, comparison of model results with observations at selected field sites

provides an important, but difficult to interpret, test of global vegetation models. The agreement between our simulated and observed leaf area index (Figure 10) is consistent with the results derived by Woodward [1987] in tests of the basic relationships between vegetation and climate that underly the more detailed model described here. Predicted values of net primary productivity extracted from our global simulations agree re- markably well with the observations used to calibrate the terrestrial ecosystem model of Melillo et al. [1993], as well as do those derived from remotely sensed vegetation data [Potter et al., 1993] or from an alternative model based on process representations but constrained by a map of ecosystem distribution and em- ploying ecosystem specific parameter values [Warnant et al., 1994].

The improvement, however, in the agreement between predicted and observed annual net primary productivity (Figure 11b) signals the need for caution when testing models meant for global simulations against site data. The values of climatic variables assigned to uni- form land units by interpolating weather station data may provide satisfactory representations of climate for simulating the broad patterns of ecosystem variables across continents but show poor agreement when those large-scale simulations are compared to observations at specific sites. As shown in Figure 11b, some of the discrepancy can be resolved by substituting data from a nearby weather station, but this does not fully re- solve the issue. The improvement in agreement between simulated and observed net primary productivity illus- trates the variability in ecosystem variables due to climate that global vegetation models with climate specified by broad-scale estimates do not yet address.

While some of the parameter values and empirical functions in our model are derived from extensive global data sets, others are mean values that are based on available experimental results. In actuality, there is substantial variability in these values. We believe that our global simulations, as well as those of a number of other groups, are sufficiently realistic to warrant work to im-


prove these remaining uncertain parameters and func- s tions. It is also important to assemble better climatic sc data. Monthly mean climatic data are inadequate to s• fully exploit the detailed models now available to global so change studies.

Notation

A

ga

g•

g•

go

gl

h

I

J

k

kL

Ko L,

mw

N

P• P• Po PN

)

assimilation rate, pmol m -2 8 -1. specific heat capacity of air, J g-1 0 C- 1. vapor pressure deficit, Pa. evapotranspiration water flux, g m -2 s-1. precipitation throughfall to the soil, g m

-1 S

bounc•ary layer conductance, m/s. canopy stomatal conductance, mmol m

-1 S ß

nonmolar stomatal conductance, m/s. stomatal conductance, mmol m -2 s -1. stomatal conductance parameter, mmolm -2

-1 S

stomatal conductance parameter. canopy height, m. irradiance, pmol photons m -2 s -1. electron transport rate, pmol electrons m

-1 S

light •xtinction coefficient. soil water response of stomatal conductance. temperature response of maximum electron

transport. specific leaf area, m2/g. maintenance respiration coefficient, s -1. temperature response of soil carbon avail-

ability. temperature response of maximum carboxy-

lation rate.

soil water bulk density, g/m a. carboxylation Michaelis coefficient, J/mol. oxygenation Michaelis coefficient, J/mol. leaf area index.

mass of leaves, pmol/m 2. mass of tissue other than leaves, pmol/m 2. leaf nitrogen uptake rate, mol g-1 composite nitrogen uptake rate, tool

ß

total nitrogen uptake rate, mol g- atmospheric C02 partial pressure, Pa. internal C02 partial pressure, Pa. internal 02 partial pressure, Pa. annual net primary productivity, pmol m -2

-1 S ß

dark respiration rate, pmol m -2 s -•. day respiration, pmol m -2 s-1. relative humidity, %. maintenance respiration, pmol m-2 s- net radiation, W/m 2. temperature response of maintenance respi-

ration.

81

82

T

vapor pressure parameter, Pa/øC. soil carbon, g/m 2. soil nitrogen, g/m 2. stomatal conductance response parameter, g

water/g dry soil. stomatal conductance response parameter. stomatal conductance response parameter, g

water/g dry soil. temperature, 0 C. absolute temperature, Kelvin. triose phosphate utilization rate, pmol m -2

-1 S

carbo•:ylation rate, pmol m-2 s- 1. soil water content, g water/g soil. Rubisco limited carboxylation rate, pmol

m-2 s-1 RuBP limi[ed carboxylation rate, pmol m -2

-1 S

phosphate limited carboxylation rate, pmol m 8

efficiency o{ light conversion, mol electrons per mol photons.

psychrometric constant, Pa/øC. density of air, g/m a. latent heat of vaporization, J/g. specificity factor of Rubisco, J/mol.

Acknowledgments. Part of this work was funded by the Natural Environment Research Council through a grant, GST/02/696, to F. I. Woodward under the Terrestrial Ini- tiative in Global Environmental Research (TIGER). W. R. Emanuel was supported by the U.S. National Aero- nautics and Space Administration Mission to Planet Earth through grant NAGW 2669. T. M. Smith was partially supported by the NIGEC Southeast Regional Office through U.S. Department of Energy Cooperative Agreement DE- FC03-90ER61010. This project is a recognized Core Re- search Project by the International Geosphere Biosphere Programme (IGBP) Core Project on Global Change and Terrestrial Ecosystems (GCTE). We are grateful for critical comments on the manuscript by D. J. Beerling, P. L. Mitchell and S. E. Lee.

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490 WOODWARD ET AL.: GLOBAL PRODUCTIVITY AND •PHYTOGEOGRAPHY MODEL

W. R. Emanuel and T. M. Smith, Department of Environmental Sciences, University of Virginia, Clark Hall, Charlottesville, Virginia 22903 U.S.A. (e-mail: wre6s@Virginia. EDU, tms9a@Virginia. EDU)

F. I. Woodward, Department of Animal and Plant Sci-

ences, University of Sheffield, P.O. Box 601, Sheffield, York- shire S10 2UQ U.K. (e-mail: [email protected])

(Received August 11, 1994; revised August 3, 1995; accepted August 9, 1995.)