This terrestrial biosphere model (the Integrated Biosphere Simulator ‐ IBIS) which demonstrates how land surface biophysics, terrestrial carbon fluxes, and global vegetation dynamics can be represented in a single, physically consistent modeling framework.
IBIS is designed to integrate a variety of terrestrial ecosystem phenomena within a single, physically consistent model that can be directly incorporated within AGCMs. To facilitate this integration, the model is designed around a hierarchical, modular structure (Figure
1) and uses a common state description throughout. The model is broken into several modules which operate at different timesteps. The current model, IBIS 1.1, consists of four modules:
1.The land surface module uses a two-layer vegetation, six-layer soil scheme to simulate the surface energy, water, carbon dioxide, and momentum balance. In order to capture the importance of variations in biophysical and physiological processes during the diurnal cycle, the land surface module operates on a relatively short time step (between 10 and 60 min), which is similar to the time step used by AGCMs to simulate atmospheric processes (typically 20 to 30 min for spectral AGCMs). In this study, the land surface module uses a 60 min time step to reduce computing requirements.
2.A vegetation phenology module, which operates on a daily time step, is used to describe the winter-deciduous and drought-deciduous behavior of specific plant types in relation to seasonal climatic conditions.
3.The carbon balance module sums gross photosynthesis, maintenance respiration, and growth respiration to yield the annual carbon balance for each of nine plant functional types.
4.Starting with the annual net primary productivity for each plant functional type, the vegetation dynamics module simuiates time-dependent changes in vegetation cover resulting from changes in net primary productivity, carbon allocation, biomass growth, mortality, and biomass turnover for each plant functional type.
A hierarchical organization of model components, each operating at different time steps, is not uncommon in ecosystem modeling [Luan et al., 1996]. For example, the widely used FOREST-BGC model [Running and Gower, 1991; Running and Hunt, 1991] uses a somewhat similar method of organization. Such a hierarchical organization of biospheric phenomena provides a straightforward means of coupling biophysical, physiological, and ecological processes.
Figure 2 illustrates the state description used throughout IBIS 1.1. Atmospheric boundary conditions (air temperature, precipitation, specific humidity, wind speed, atmospheric pressure, downward solar and longwave radiation fluxes, and CO2 concentration) are specified at ~70 m above the surface.
The vegetation cover comprises a combination of plant functional types (PFTs) [Woodward and Cramer, 1996], which are adapted from the list presented by Prentice et al. and Haxeltine and Prentice, [1996b] (Table 1). The definition of plant functional types differentiates several important ecological characteristics: basic physiognomy (trees and grasses), leaf habit (evergreen and deciduous), photosynthetic pathway (C3 and C4), and leaf form (broad-leaf and needle-leaf). To determine which PFTs may potentially exist within each grid cell, the model applies a minimal set of climatic constraints (winter cold tolerance limits, growing degree-day requirements, and minimum chilling requirements).
The structural characteristics of the PFTs are described by the following state variables: leaf area index (LAI) and the living biomass in leaf, transport, and fine root tissues.Two vegetation layers are represented: woody plant functional types (trees) exist in the upper canopy, while herbaceous plant functional types (grasses) are placed in the lower canopy. The vegetation cover of a particular grid cell may then be characterized simply by the sums of leaf area and biomass contributed by each plant functional type.
The six soil layers have top-to-bottom thicknesses of 0.10, 0.15, 0.25, 0.50, 1.00, and 2.00 m, in order to capture the diurnal, seasonal, and interannual variations in soil temperature, soil moisture, and soil ice. In simulating the water balance, the model assumes that PFTs are able to draw water differentially from the soil layers; woody plants can take up more water from deeper soil layers than herbaceous plants.
The state description of the model allows trees and grasses to experience different light and water regimes. Thus the competition among PFTs for these two essential resources may be explicitly represented through shading and differential water uptake. This approach, which asserts that plants compete for common environmental resource pools, may be further adapted to include the mechanisms of competition for mineral nutrients.
1.Land Surface Process
The treatment of biophysical processes is based on the LSX land surface model of Pollard and Thompson  and Thompson and Pollard [1995 a and b]. This design is intended to facilitate the direct incorporation of IBIS within AGCMs and allows for more physical consistency between the simulations of atmospheric and ecological processes.
The model simulates the exchange of energy, water vapor, carbon dioxide, and momentum between the surface, the vegetation canopies, and the atmosphere(Figure 3). Like most land surface formulations, this model explicitly represents the temperature of the soil surface and the vegetation canopies, as well as the temperature and specific humidity within the canopy air spaces. Changes in temperature and specific humidity are driven by the radiation balance of the vegetation and the ground, and the diffusive and turbulent fluxes of sensible heat and water vapor.
Solar radiation is treated using a two-stream approximation within each vegetation layer, with separate calculations for direct and diffuse radiation in two wavelength bands (visible from 0.4 to 0.7 |Xm and near-infrared from 0.7 to 4.0 ^im). Within the canopies, infrared radiation is treated as if each vegetation layer is a semi-transparent plane with an emissivity that depends on the foliage density. The wind regime is modeled using mixing-length logarithmic profiles above and between the layers and a simple diffusive model of air motion within each layer.
Total evapotranspiration is simulated as the sum of three water vapor fluxes: evaporation from the soil surface,evaporation of water intercepted by vegetation canopies, and canopy transpiration. Rates of transpiration, which depend on stomatal conductance (see Section 2.2), are calculated independently for each PFT. In order to account for evaporation from intercepted rain, the model describes the cascade of precipitation through the canopies.
A multilayer formulation of soil allows the model to simulate both diurnal and seasonal cycles of heat and moisture in the upper few meters. Each soil layer is characterized by three prognostic variables: temperature, fractional liquid water content relative to ice-free pore space (i.e., soil moisture), and fractional ice content relative to the total pore space (i.e., soil ice). The soil model calculates the time rate of change of liquid phase soil moisture as a function of the vertical gradient of soil water flux using Richard's equation. The vertical flux of water is modeled according to Darcy’s law, where the water flux responds to gravitational and soil matric potentials. In the model, soil matric potential varies with soil moisture and texture following Clapp and Hornberger, The boundary conditions at the bottom of the soil model allow zero liquid and zero heat diffusion and free gravitational drainage of water. A three-layer thermodynamic model represents snow cover in terms of temperature, fractional coverage, and total snow thickness.
The exchange of water vapor and carbon dioxide between vegetation canopies and the atmosphere is strongly controlled by the physiological processes governing photosynthesis and stomatal conductance. Traditionally, physiological processes have been parameterized empirically as passive functions of environmental conditions, light, temperature, and water vapor pressure. However, more mechanistic treatments of photosynthesis [Farquhar et aL, 1980; Farquhar and Sharkey, 1982] and stomatal functioning [Ball et aL, 1986; Lloyd, 1991; Lloyd and Farquhar, 1994; Friend, 1995; Leuning, 1995] have been formulated and tested extensively with gas exchange measurements. In these formulations, photosynthesis rates are a function of absorbed light, leaf temperature, carbon dioxide concentration within the leaf, and the Rubisco enzyme capacity for photosynthesis. Stomatal conductance is a function of the photosynthetic rate and the concentrations of carbon dioxide and water vapor. This framework provides a linked functional relationship between the fluxes of water and carbon in the canopy (Figure 3 and Table 2).
Because of the highly non-linear response of leaf physiological processes to varying light conditions within the canopy, the model divides the canopy into sunlit and shaded fractions [Norman, 1993]. The model performs separate photosynthesis and stomatal conductance calculations for each portion of the canopy and determines a weighted average to arrive at the whole-canopy fluxes. This scaling technique accounts for the attenuation of light through the canopy but does not consider variations in temperature, humidity, or wind speed within canopies.
C3 photosynthesis, which is used by all trees and many herbaceous plants, is expressed as the minimum of three potential capacities to fix carbon following the simplified Farquhar equations [Farquhar et ai, 1980] adopted by Collatz et al. . The gross photosynthesis rate per unit leaf are, Ag (mol CO2 m-2 s-1) may be expressed as
The light-limited rate of photosynthesis is given as
where Qp is the flux density of photosynthetically activeradiation absorbed by the leaf (Einstein m-2 s-1)，α3 is the intrinsic quantum efficiency for CO2 uptake in C3 plants（Einstein m-2 s-1)，Ci is the cincentration of CO2 in the intercellular air spaces of the leaf(mol mol-1) and Γ * is the compensation point for grosss photosynthesis(mol mol-1),given by
where [O2] is the atmospheric oxygen concentration (0.209mol mol-1) and τ is the ratio of kinetic parameters describing the partitioning of enzyme activity to carboxylase or oxygenase function.
where [O2] is the atmospheis the Rubisco-limited rate of photosynthesis, where Vm is the maximum capacity of Rubisco (mol C〇2 m-2 s-1) to perform the carboxylase function and Kc and K0 are the Michaelis-Menten coefficients (mol mol-1) for CO2 and O2, respectively. Under conditions of high intercellular C〇2 concentrations and high irradiance, photosynthesis is limited by the inadequate rate of utilization of triose phosphate [Sharkey, \9%5\ Harley and Sharkey 1991]. We account for this third limitation using the formulation
where T is the rate of triose phosphate utilization. Tmd Vm are correlated and Amthor  finds from an analysis of published results [Wullschleger^ 1993] that 7T=Fm/8.2. Jp is defined in (6a) (see below).
It has been observed that the transition between these three potential rates of leaf photosynthesis is not sharp, but is rather more gradual. To account for such colimitation between Jei JC9 and JS9 Collatz et aL  used a set of quadratic equations to link them,
where θ and β are empirical constants, governing the sharpness of the transition between the three potential photosynthesis rates.
Photosynthesis in C4 plants, which are mainly the wann grasses, is similarly modeled as the minimum of three potential capacities to fix carbon [Collatz et aL, 1992]. Again, the gross photosynthesis rate is given in principle by the minimum of three potential rates of photosynthesis,
where Jj = α4Qp is the light-limited rate of photosynthesis,Je = Vm is the Rubisco-limited rate of photosynthesis, and Jc = kCi is the CO2-limited rate of photosynthesis at low CO2 concentrations. The compensation point is thus taken to be zero for C4 plants. In the model, the actual calculation of C4 gross photosynthesis rates involves a pair of quadratic equations like (6a) and (6b).
CO2 produced by leaf maintenance respiration, R\eaj(mol CO2 m-2 s-1) is given by
where γ is the leaf respiration cost of Rubisco activity[Collatz et aL, 1991], leaving the net leaf assimilation rate An (mol CO2 m-2 s-1), as
The model also calculates maintenance respiration of stem and fine root biomass,
where β is a maintenance respiration coefficient defined at 15°C (0.02 y1 for stem sapwood biomass and 0.20 y1 for fine root biomass) [Sprugel et aL, 1995; Amthor, 1984; Ryan et ah, 1995], Sapwood is the sapwood fraction of the total stem biomass (estimated from an assumed sap velocity and the maximum rate of transpiration experienced during the previous year)，and y(T) is the Arrenhius temperature function,
where T is the temperature (in degrees Celsius) of the appropriate tissues (stem temperature and soil temperature in the rooting zone), is a temperature sensitivity factor (Table 2), and T0 is set to absolute zero (-273.16°C). Collatz et al. [1991, 1992], Lloyd and Farquhar , Dewar , and others have used semi-empirical models of stomatal conductance based on the formulation of Ball et al. . Here we use a related formulation, developed by Leuning , which takes the form,
where gsiH2O is the stomatal conductance of water vapor (mol H2O Cs is the CO2 concentration (mol mol-1 the leaf surface, Ds is the water vapor mole fraction difference between the leaf and the air (mol mol-1), D0 is a reference value (mol mol-1), and m and b are the slope and intercept of the conductance-photosynthesis relationship.
The photosynthesis and stomatal conductance submodels are linked by considering the flow of CO2 into the leaf as a one-dimensional diffusion process etal. 1991, 1992],
where Ca is the mole fraction of CO2 in the atmosphere(mol mol-1) and gb,CO2 is the boundary layer conductance for CO2 (mol CO2 m-2 s-1).
A review of literature shows that decreased photosynthesis in response to water stress has been attributed to either stomatal limitation or inhibition of the mesophyll photosynthetic capacity or a combination of these [Farquhar and Sharkey, 1982; Chaves, 1991]. More recently, tiie possibility of patchy stomatal closure has been suggested [Terashimaet al.9 1988; Chaves, 1991; Antolin and Sanchez-Diaz^ 1993]. There is some evidence that moderate water stress results only in stomatal closure, but under severe water stress, the stomatal closure can result in feedback inhibition of the biochemistry of photosynthesis [Vassey et aL, 1991; Friend, 1995]. It has also been suggested that water stress might directly inhibit growth rates [Cornell and Dewar, 1994]. Owing to the lack of clear understanding of the mechanism by which water stress influences photosynthesis and growth, we have adopted a simple heuristic approach to represent this influence. We first calculate a stress factor based on plant-available soil moisture. We then directly reduce gross photosynthesis rates by this factor, which is given by
where θ is the soil moisture content (fraction of ice-free pore space) and 0W,// is the soil wilting point. The denominator normalizes the function so that it ranges between 1.0 (0 = 1.0) and 0.0 (O = Owilt)
Typically, models that employ the Farquhar equations prescribe constant values of the Rubisco carboxylation capacity Vm. Here, however, we follow the method suggested by Haxeltine and Prentice [1996a], whereby we predict the value of Vm that would give the maximum (non-water-stressed, and non-nitrogen-stressed) rate of time-averaged photosynthesis. The model employs an algorithm which slowly (over a ~1.5 month time_weighting filter) adjusts the value of Vm to achieve the optimal balance between gross photosynthesis and leaf maintenancerespiration. This formulation reflects the strong evidence for near-optimal nitrogen allocation in a wide variety of canopies [州Merger，1987; FzeW，1983，1991; Sellers et aL, 1992; Evans, 1989; Kull andJarvis9 1995. Sands, 1995] and results in a simple and general photosynthesis prediction that does not require prescribed values of photosynthetic capacity in different biomes.
To evaluate the simulations of the coupled photosynthesis-stomatal conductance formulation, we compared them to observations of physiological processes. The actual quantum efficiency (i.e., not the intrinsic quantum efficiency) of C3 plants is observed to range between 0.04 and 0.07 and in C4 plants to be constant around 0.055 [Ehleringer and Bjorkman, 1977]. Furthermore, observations show that, under ample water supply and moderately high humidity, the stomata respond in a manner that maintains Ci /Ca values in the range of 0.3-0.5 for C4 plants and 0.6-0.8 for C3 plants [Ehleringer and Cerling, 1995; Sage, 1994; Poorter and Farquhar, 1994. Long and Hutchin,1991; Wonget al., 1979, 1985]. Our model gives this same behavior under normal ranges of leaf temperature, C〇2 concentration, and moderate to full light conditions. Figure 4 shows the simulations of net assimilation for a single leaf as a function of different light, carbon dioxide and temperature conditions. The simulated physiological behavior is typical of field and laboratory observations [e.g.5 Long and Hutchin, 1991; Jones, 1983; Ehleringer，1985].
In climates with one or more unfavorable seasons,vegetation has an annual cycle of leaf display (in deciduous trees and herbaceous plants) and leaf physiological activity (in evergreen trees) involving climatic triggers that induce or break dormancy. The model currently uses a very simple rule-based formulation to describe the winter-deciduous and drought-deciduous behavior of particular plant functional types. Winter-deciduous plants (temperate deciduous trees, boreal deciduous trees, cool grasses, and warm grasses) drop their leaves when daily average temperatures fall below a critical temperature threshold (〜5°C for deciduous trees and warm grasses and -0°C for cool grasses); in the spring, the leaves reappear when temperatures rise above the critical temperature threshold. Drought-deciduous plants (tropical deciduous trees) are forced to drop their leaves during the 2 least productive months of the year, defined in terms of the previous year's carbon balance. It is possible to make this module more explicitly process-oriented, by incorporating the inverse relationship between growing degree-day requirements for budburst and chilling period length that has been shown experimentally for both deciduous and evergreen trees [Murray et aL, 1989].
4.Carbon Balance and Vegetation Dynamics
Until recently, models to predict vegetation structure and composition at a global scale have focused on equilibrium vegetation patterns and have been unable to predict the transient dynamics of the vegetation cover. This limitation has existed because the present paradigm of vegetation dynamics models relies on the explicit simulation of patch-scale processes [e.g., Shugart, 1984] and cannot be easily adapted to the global scale.
Our approach uses a highly simplified representation ofvegetation dynamics, where the competition among plantfunctional types is characterized by the ability of plants to capture resources. In particular, our model explicitly simulates the competition for common light and water resource pools. For example, PFTs in the upper vegetation layer are able to capture light first and therefore shade the lower vegetation canopy. However, the lower layer vegetation is able to uptake soil moisture first as it infiltrates through the soil. Thus the model can mechanistically simulate competition between trees and grasses.
Competition between PFTs within the same vegetation layer is driven by differences in the annual carbon balance resulting from different ecological strategies, including differences in phenology (i.e., evergreen versus deciduous), leaf form (i.e., needle leaf and broadleaf), and photosynthetic pathway (i.e., C3 or C4). Therefore the model includes a generalized means of simulating the dynamic competition between plant types within a layer.
The annual carbon balance for each plant functional type is calculated by summing hourly carbon fluxes (gross photosynthesis and maintenance respiration terms). For each plant functional type U the gross primary productivity (GPP) is calculated at the end of each year as
where the integration is carried through the entire year. The net primary productivity (NPP) of each plant functional type is expressed by
where (0.33) is the fraction of carbon lost in the construction of net plant material because of growth respiration [Amthor, 1984].
The basic description of plant functional types resolves carbon in three biomass pools: leaves, transport tissues (i.e., predominantly stems), and fine roots. Changes in the biomass pool j of plant functional type / are described by the differential equation
where aij represents the fraction of annual NPP allocated to each biomass compartment and τij describes the residence time of carbon in the biomass compartment. The residence time of carbon in a biomass compartment is intended to represent the loss of biomass through mortality and tissue turnover. For simplicity，allocation and turnover parameters are assumed to be fixed within a given PFT. The leaf area index (LAI) of each PFT is obtained by simply dividing leaf carbon by specific leaf area (Table 1).