a process-based, terrestrial biosphere model of ecosystem … · 2011-01-02 · a numerical...

ELSEVIER Ecological Modelling 95 (1997) 249-287

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A process-based, terrestrial biosphere model of ecosystem dynamics (Hybrid v3.0)

A.D. Friend a, *, A.K. Stevens a, R.G. Knox b, M.G.R. Cannell a

a Institute of Terrestrial Ecology. Edinburgh Research Station, Bush Estate, Penicuik, Midlothian EH26 OQB, UK b NASA /Goddard Space Flight Center, Biotpheric Sciences Branch, Greenbelt, MD 20771, USA

Received 9 May 1995; accepted 19 April 1996

Abstract

A numerical process-based model of terrestrial ecosystem dynamics is described and tested. The model, Hybrid v3.0, treats the daily cycling of carbon, nitrogen, and water within the biosphere and between the biosphere and the atmosphere. It combines a mass-balance approach with the capacity to predict the relative dominance of different species or generalised plant types (such as evergreen needleleaved trees, cold deciduous broadleaved trees, and C3 grasses). The growth of individual trees is simulated on an annual timestep, and the growth of a grass layer is simulated on a daily timestep. The exchange of carbon, nitrogen, and water with the atmosphere and the soil is simulated on a daily timestep (except the flux of tree litter to the soil, which occurs annually). Individual trees and the grass layer compete with each other for light, water, and nitrogen within a 'plot ' . Larger and taller plants shade smaller ones; they also take up a greater proportion of the available water and nitrogen. The above-ground space in each plot is divided into 1 m deep layers for the purposes of calculating irradiance interception; horizontal variation in the plot environment is not treated. The soil is represented as a single layer, with a daily hydrological budget. Decomposition of soil organic matter is calculated using an empirical sub-model. The initial size of each tree seedling is stochastic. To predict the mean behaviour of the model for a particular boundary condition it is necessary to simulate a number of plots. Hybrid v3.0 has been written with three major requirements in mind: (i) the carbon, water, and nutrient cycles must be fully coupled in the soil-plant-atmosphere system; (ii) the internal constraints on the model's behaviour, and the driving forces for the model, must be the same as those which operate in nature (e.g., climate, nitrogen deposition, and the atmospheric concentrations of CO 2 and 02); and (iii) the model must be constructed so that it is capable of predicting transient as well as equilibrium responses to climate change. These conditions have largely been met by constructing the model around a set of fundamental hypotheses regarding the general constraints under which plants and soils behave, independently of any particular location or time. The model is thus potentially capable of making reliable predictions of ecosystem behaviour and structure under future, new, amaospheric conditions. The model is tested for a site in eastern North America. A quasi-equilibrium is reached after approximately 250 years with 10 plots. It is found that more plots are not necessary in order to obtain a reliable estimate of mean behaviour. Predictions of productivity, leaf area index, foliage nitrogen, soil carbon, and biomass carbon are all within the range expected for this location.

* Corresponding author. Tel.: + 44-131-4454343; fax: + 44-131-4453943; e-mail: [email protected].

0304-3800/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0304-3 800(96)00034-8

250 A.D. Friend et al. / Ecological Modelling 95 (1997)249-287

Mortality is shown to be a necessary model component; without it large trees reach a maximum size, and then remain in dynamic equilibrium with the climate, without dying. The model runs at a rate of 0.176 s plot- ~ year- t on a workstation (a 500 year simulation, with 10 plots, thus takes approximately 15 min). A sensitivity analysis demonstrates the importance of the parameterisation of phenology, photosynthesis, and foliage/fine root carbon and nitrogen partitioning for the overall carbon balance of the modelled ecosystem. Hybrid v3.0 has been written with the intention of using it to represent the terrestrial biosphere in a total earth system model. This would be achieved by linking it to models of other components of the earth system, such as the climate and the oceans, in a fully coupled manner. This total earth system model could then be used to answer a large range of questions concerning global environmental change. © 1997 Elsevier Science B.V. All rights reserved

Keywords: Model; Ecosystem; Competition; Trade-offs; Forest; Types; Productivity

1. Introduction

One of the greatest challenges in environmental research, equivalent to the 'grand challenges' in physics, is to develop comprehensive, predictive numerical models of the total earth system. Only then shall we be able to predict the impact of changes in atmospheric composition and land use on future climates and vegetation.

The terrestrial biosphere is an integral part of both the global carbon and hydrological cycles. Every year about 14% of the carbon in the atmospheric is exchanged with the terrestrial biosphere, and about 20% of the water added to the atmosphere annually derives from evapotranspiration from the land (Wesfall and Stumm, 1980). In addition, the properties of vegetation and soils regulate the partitioning of energy into latent and sensible heat over significant areas of the land surface, as a result of short-term changes in stomatal conductance, and longer-term changes in vegetation cover and height, leaf area, rainfall interception, and albedo. Consequently, changes in the type and behaviour of vegetation and soils may have appreciable effects on atmospheric CO 2 levels by acting as a net carbon source or sink (Gifford, 1993), and on local and perhaps global climate, by altering sensible and latent heat fluxes, atmospheric humidities, cloud-cover, rainfall, and temperature (Friend and Cox, 1995). Vegetation is also the primary source of energy for virtually all the world's biota, as well as fibre for construction, fuel, and clothing, and is thus of immense importance in its own right.

Any terrestrial biosphere sub-model of the total earth system must be capable of predicting the impacts of vegetation and soils on the atmosphere (climate and CO 2 concentration), as well as the impacts of climate and changing CO z concentrations on vegetation and soils. In our view, such a sub-model should be truly dynamic and should not contain parameterisations that are valid only for particular conditions - - in particular, it should not be constrained by parameters that pertain only to present-day conditions. Our central philosophy has been to build a model from concepts that are general in nature and capture the basic biological constraints, trade-offs, and physical processes that are common to all plant-soil-atmosphere systems.

It is now well accepted that static equilibrium models that rely entirely on correlations between present day climate and vegetation distribution and properties are unreliable tools to predict responses to future climates and CO 2 levels (Emanuel et al., 1985; Woodward and Smith, 1994). Consequently, in recent years a number of models have been written that are, to various degrees, mechanistic (Cramer and Leemans, 1993; Fischlin et al., 1995; McGuire et al., 1992; Monserud and Leemans, 1992; Prentice et al., 1993; Prentice et al., 1992; Raich et al., 1991). However, most models still rely on input parameters that are derived from statistical relationships between vegetation properties and climate. These relationships serve as surrogates for the underlying biological processes that respond to climate. In addition, many models deal only with equilibrium conditions. At present, we are not aware of any models that are truly mechanistic, are totally driven by climate, and deal with dynamic growth processes to enable a treatment of transient behaviour.

The model described here, Hybrid v3.0, was built with three major requirements in mind. First, the carbon,

A.D. Friend et al. / Ecological Modelling 95 (1997) 249-287 251

water, and nutrient cycles must be fully coupled in the soil-plant-atmosphere system. Ecosystems consist of complex interactions between the cycling of matter, primarily carbon, water, and nutrients, and of energy, primarily in the form of radiation, sensible and latent heat fluxes, and chemical bonds. There are, consequently, many interactions and feedbacks between vegetation, soils, and the atmosphere. Ecosystem models have limited predictive capability if the matter and energy cycles are not represented in the fully integrated manner in which they occur in nature.

Secondly, the external constraints on the model's behaviour, and the driving forces for the model, must be the same as those which operate in nature. That is, the constraints must, as far as possible, be fundamental biological and physico-chemical processes and the driving variables must only be climate and inputs from the atmosphere such as CO 2 and nitrogen. That is, the model behaviour must not be predetermined by statistical relationships between climate and ecosystem properties or function - - particularly relationships dependent on current climate (Prentice et al., 1992; and cf. Austin, 1992).

Thirdly, the model must be constructed so that it is capable of predicting transient as well as equilibrium responses to climate change. This means that the model must represent vegetation growth and all of the major processes that occur in an ecosystem over time, such as plant birth and death, litter production, and the fate of litter in the soil. It is for this reason that Hybrid v3.0 is based on a plot model approach that simulates the growth of individuals. Some dynamic vegetation models use rules or observations to fix the vegetation or biome type in each climate, thus separating the cycling of matter and energy from the ecosystem structure (e.g., Meliilo et al., 1993; Prentice et al., 1992; Woodward et al., 1995). By contrast, the use of an individual-based plot approach has the consequence that vegetation types, and transitions between types, are predicted as the outcome of competition for environmental resources (light, water, and nitrogen in our model).

In short, the challenge was to construct a model which was capable of predicting (i) ecosystem behaviour, such as the exchange of carbon and water with the atmosphere, (ii) ecosystem structure, such as the vegetation type, leaf area, and the amount of carbon in vegetation and soil, and (iii) dynamic processes, such as the development of biomass and the replacement of one vegetation type by another, all from climate alone. The

vegetation types and changes in soil properties must be derived as outputs, resulting from the climatic variables and the fundamental properties of ecosystems; they must not be supplied as inputs.

This paper presents a detailed description of the model Hybrid v3.0, which has been developed as a terrestrial biosphere model with the above philosophy, and largely meets the criteria given above. The model is based on Hybrid vl.0, described by Friend et al. (1993), which in turn was based on FOREST-BGC, described by Running and Coughlan (1988), and ZELIG, described by Urban (1990). Some parts of Hybrid v3.0, such as the photosynthesis, stomatal conductance, and soil sub-models, have been described in detail elsewhere (Friend, 1995; Parton et al., 1993; Stewart, 1988) and the equations given here are generally limited to those that have not previously been published. A version of Hybrid intermediate between the one described by Friend et al. (1993), and that described here, was used by Stevens et al. (in press) to simulate the responses of forests to transient climate and atmospheric CO 2 change. This work highlighted the importance of CO:/temperature interactions for net photosynthesis, the importance of mineral nitrogen leaching as a result of increased precipitation, and the effect of increased temperature on plant respiration through an increase in decomposition rates and hence nitrogen availability.

The model presented here represents a set of general hypotheses about how the principal components of terrestrial ecosystems function. These hypotheses are stated explicitly as equations and parameter values which do not change in time or at different places on the globe. If, through testing the model, it appeared to be necessary to change the parameter values in time and/or space in order to simulate observed conditions, our response would not be to give the parameters concerned different values at different times and places, but rather to attempt to internalise the prediction of the parameters from underlying processes (that is, to regard the parameters as variables). Potentially, the use of this principle can highlight key areas of plant physiology, soil dynamics, and overall ecosystem behaviour where our knowledge needs to be increased through experimental work.

252 A.D. Friend et al. / Ecological Modelling 95 (1997) 249-287

2. Overview of model features, structure and operation

2.1. Overall model features

Table 1 outlines the key features of Hybrid v3.0. It is an individual-based plot model, and is driven by daily weather. It combines a mass-balance approach with the capacity to predict the relative dominance of different species or generalised plant types (GPTs: general groups into which individual species can be classified), and how they dynamically interact with atmospheric and soil processes. The key features listed in Table 1 all derive from the philosophy of our approach, outlined in the Introduction.

2.2. Processes, hypotheses and parameters

Table 2 summarises the main processes represented in Hybrid v3.0, the approach used to represent each process, and the primary source of the approach and/or parameters. Table 3 gives the parameters that are specific to given GPTs - examples are given for C3 grass, cold deciduous broadleaved tree, and evergreen needleleaved tree. Table 4 gives the model parameters that apply to all GPTs. A full description of the previously unpublished process equations and of the derivation of the parameters in Tables 3 and 4 is given below.

2.3. Model structure and operation

Hybrid v3.0 uses the approach taken in more recent 'gap' models to describe the irradiance environment of a forest canopy, within which individual trees compete for light (Leemans, 1991). A grass layer is included, and in Hybrid v3.0 individual trees and the grass layer share a common one-layered soil nitrogen and water pool; light, water, and nitrogen are assumed to be homogeneously distributed, horizontally, within each plot. The size of the plots is fixed, and is set to approximate the size of a canopy dominant tree (cf. Shugart and West, 1979).

Individual trees and grass are classified as belonging to either particular species or particular GPTs, depending on the requirements of the simulation. Here, three GPTs are used: C3 grass, cold deciduous broadleaved tree, and evergreen needleleaved tree. The species, or GPT, of an individual or the grass layer determines its fundamental morphological and physiological parameterisation (Table 3).

The model operates on two timesteps (Fig. 1). Photosynthesis, maintenance respiration, nitrogen Uptake, and transpiration are calculated daily for each individual tree and the grass layer. The allocation of carbon and nitrogen and litter production within the grass layer, soil decomposition, and nitrogen mineralisation also all occur on a daily timestep. Grass structure is divided into foliage, support, and fine root compartments. It is assumed that total daily net photosynthesis, transpiration, and night-time respiration of each individual tree and the grass layer all scale linearly with their mean rates - - that is, that there is no need to calculate these rates on a shorter timestep than either the day or the night. The net annual individual tree increments in carbon and

Table 1 Key features of the Hybrid v3.0 model

Constraints Driving variables

Mass balance approach Integration Modular Timestep

fundamental physiological and biophysical relationships and parameters daily climate above the canopy (see Table 5), atmospheric CO 2 concentration, nitrogen wet and dry deposition and fixation rote carbon, nitrogen, and water pools and fluxes fully balanced matter and energy cycles coupled each component of the model is a separate subroutine, allowing easy maintenance and development daily flux and grass allocation calculations, annual tree carbon and nitrogen allocation


Table 2 Processes represented in Hybrid v3.0, the approach taken, and the sources that are either totally responsible for the approach used, or its principal precursor

Process Approach Sources

Competition gap model (individuals compete for light): Prentice and Leemans (1990)

Photosynthesis

Maintenance and growth respiration Stomatal conductance Transpiration Nitrogen uptake Phenology Litter production AlLocation

Tree mass and height from diameter Decomposition Plot hydrology

vertically explicit, horizontally homogeneous leaf: Farquhar biochemistry canopy: optimisation (Eqs. (6) and (8)) nitrogen and empirical models (Eqs. (7), (9), and (10)) empirical function plot conductance and energy balance demand/supply hypothesis (Eq. (13)) parallel chilling/heat sum model (Eq. (14)) largely empirical optimise foliage area fixed foliage/sapwood area ratio (Eq. (32)) fixed foliage/fine root ratio (Eq. (33)) fixed diameter/height allometry and form factors (Eqs. (28) and (29)) Century model, empirical single layer bucket

Farquhar and von Caemmerer ( 1982); Friend (1995) Sellers et al. (1992) Ryan (1990); Ryan (1991b)

Jarvis (1976); Stewart (1988) Friend ( 1995); Monteith and Unsworth (1990) this paper Cannell and Smith (1983) this paper this paper Shinozaki et al. (1964) and this paper this paper this paper and Cannell (1984)

Parton et al. (1993) Running and Coughlan (1988)

nitrogen, together with any stored carbon from the previous year, are allocated at the end of each year to the different tree compartments. Trees are assumed to die when there is insufficient carbon to produce any foliage. The carbon and nitrogen contained in dead trees enter the soil pools at the end of each simulation year (on 31

Table 3 Generalised plant type (GPT) parameters used in Hybrid v3.0 for C3 grass, cold deciduous broadleaved, and evergreen Not shown are the parameters that are either the same for all GPTs, or are only relevant to one (these are given in Table parameters required to predict broadleaf winter phenology)

needleleaved trees. 4, along with those

Symbol Parameter Grass Broadleaf Needleleaf Units

KSW

KpAR

a

b

a o

Jb L, A fu,f sla

f~sw

O/pA R

r/F r/f

P~

shortwave irradiance extinction coefficient (Eqs. (2) and (3)) 0.48 0.48 0.37 photosynthetically active irradiance extinction coefficient (Eqs. (2), 0.65 0.65 0.50 (3), (6) and (8)) allometry coefficient for H (height) from D (diameter) (Eq. (29)) - - 28.51 32.95 allometry exponent for H (height) from D (diameter) (Eq. (29)) - - 0.4667 0.5882 intercept in regression used to calculate JN.o (fraction of foliage N 0.67 0.67 0.83 not used in Rubisco or thylakoids; Eq. (47)) ratio of bark thickness to D (diameter; Eq. (31)) - - 0.033 0.01 fraction of wood plus bark below ground (Eq. (28)) - - 0.220 0.222 fraction of sapwood alive (Eqs. (35) and (37)) --- 0.170 0.0708 turnover rate of foliage (Eqs. (20) and (21)) 1.13 1.00 /).33 specific leaf area (Eqs. (32) and (38)) 36 36 12 shortwave irradiance reflectiola coefficient (Eq. (5)) 0.20 0.20 0. I 1 photosynthetically active irradiance reflection coefficient (Eq. (5)) 0.05 0.05 0.03 tree form factor (Eq. (28)) - - 0.60 0.56 ratio between foliage area and sapwood area (Eq. (32)) - - 4167 3333 ratio between gmax and Rubisco nitrogen 1359 1672 2223

Mean wood plus bark density (Eq. (28)) 305 205

dimensionless dimensionless

| in m

dimensionless fraction

m m ¸1

fraction fraction fraction year m 2 kgC - I

fraction fraction dimensionless m 2 m 2

mol m 2 s i / ( k g

(Rubisco N), m- 2 ) k g C m -3


Table 4 Definition of model parameters (other than those that are GPT-specific, see Table 3) used in the main text to describe Hybrid v3.0. N.B.: Other parameters in Hybrid v3.0 are defined in Friend (1995), Friend (in press), Stewart (1988), Parton et al. (1993), and Comins and McMurtrie (1993)

Symbol Def'mition Value Units

Vegetation parameters r~ fL.r fL.w fRg ft.f fv,s! fw.m

~C,f,n 7/C,w

nu -~Rub/cM ~C:N(f/p) )(C;N(f/r)

temperature threshold for phenology sub-model 6 tree fme root turnover rate (Eq. (17)) 2 fraction of wood plus bark that goes to litter (Eqs. (16) and (22)) 0.01 growth respiration coefficient (F_,qs. (17), (18), (25), (27), and (39)) 0.25 fraction of foliage N retranslocated (Eq. (24)) 0.5 fraction of live sapwood available for storage (Eq. (35)) 0.67 minimum fraction of available C allocated to wood (Eq. (25)) 0.1 accuracy of Cw.inc (annual woody biomass increment; Eq. (27)) 0.001 night foliage respiration coefficient (Eq. (9)) 42.60 × 103 wood respiration coefficient (Eq. (10)) 83.14 ratio between fine root carbon and foliage carbon (Eq. (33)) 1.0 N uptake coefficient (Eq. (13)) 0.036 Rubisco N/chlorophyll N ratio 9.13 relative C:N ratio between foliage and bark plus sapwood (Eq. (43)) 0.145 relative C:N ratio between foliage and fine roots (Eq. (44)) 0.86

Site parameters ( j = do or rv)

farm FN.d

z~ fdo,rv

f~c kj.max lat td(fSo) Xnc,lV

o C

fraction year- l

fraction year- 1

fraction fraction fraction fraction year- l

%

kg C kg N - I s - l kg Ckg C - I s - t kgC kg C -1 m× k g C - l d - I kg N kg N - l

kg C kg N - I (kg C kg N - I) - l kg C kg N - ' (kg C kg N - l ) - l

atmospheric CO 2 concentration 356 rate of addition to soil mineral N pool through fixation and atmospheric 5.48 × 10- 7 deposition plot area (Eqs. (2), (6), and (8)) 200 m 2 fraction of C lost to microbial respiration between soil organic matter a fraction pools do and rv (Eqs. (48)-(51)) ratio between soil water saturation and field capacities (Eq. (54)) 1.72 fraction maximum decomposition rate of soil organic matter pool j (Eq. (52)) a day- latitude (Eq. (15)) 41.25 degrees autumn daylength required for leaf fall in the cold deciduous GPT Eq. (15) s N:C ratio of soil organic matter pool rv (Eqs. (49) and (51)) a kg N kg C- 1

/xmol mol- l kg N m - 2 day- i

a See Patton et al. (1993) for values,

December), along with wood, leaf, and fine root litter from living trees. As mentioned, litter production from grass is calculated each simulated day, and so enters the soil pools daily.

The tree regeneration routine is not yet fully developed. At present, seedlings of each species or GPT are introduced to each plot each year. The initial tree seedling diameter is set as a uniform random number between 0.001 and 0.002 m, with the height set to 1 m. Grass regeneration is simulated by assuming a minimum grass leaf area index of 0.01. Grass is always assumed to occupy only the lowest 1 m layer in each plot, although it has access to the same soil water and nitrogen pools as the trees.

During a simulation some individual trees will grow faster than others because of differences in initial size, and/or because they belong to different species or GPTs (and so are affected by the environment differently). The grass layer is treated in a similar manner to an individual tree, and competes with the trees for resources. Smaller, shorter individuals will be shaded by taller ones, and will take up smaller proportions of the available water (through leaf area differences) and nitrogen (through fine root mass differences) from the soil. Thus, some individuals will eventually have a negative annual carbon balance due to respiration being greater than photosynthesis, and will die. Given an even mix of species or GPTs amongst the seedlings, Hybrid v3.0 is hence potentially able to predict which species or GPTs dominate in different climates. In addition, the model is able


~m~ H20

T H

~ p 1 ~ i ¢ CO 2

1.

Fig. 1. Flow diagram showing the main flows of carbon, water, and nitrogen in a plot in Hybrid v3.0. Grey arrows indicate water flows and thick black arrows indicate carbon and /o r nitrogen flows. The two dashed horizontal lines divide the system into atmospheric, canopy, and soil components. Boxes contain state variables, with shaded boxes indicating both carbon and nitrogen pools. Soil organic matter pools are shown within the square brackets. The structural, metabolic, and active (microbial) pools are each divided into surface and below-ground components. Decomposition, shown by the arrows between these pools, results in the release of mineral nitrogen ( 'N rain.') and CO 2. For clarity, the addition of mineral nitrogen through deposition and fixation, and the leaching of nitrogen and carbon from the soil, are not shown. The partitioning of nitrogen and carbon from their plant stores occurs on a daily timestep in grass and annually in trees. All other flows occur on a daily timestep. The daily partitioning of carbon and nitrogen within the grass does not include heartwood and 'bark and sapwood' is replaced by a structural compartment. See main text for a full description of the model.

to predict the replacement of one vegetation type by another as might occur if the climate changes. Respiration increases more than photosynthesis as a tree increases in size due to a limit on the amount of light that can be intercepted, making old trees vulnerable to a period of environmental stress (such as drought). However, the risk of death is reduced by the presence of storage reserves in the sapwood (see below).

More than one plot is needed in a simulation in order to obtain a general prediction for a given climate. This is because at any one time any given plot will be at a unique stage with respect to the growth dynamics of the


individuals, and thus may not be typical (e.g. a large tree may have just died). Each of the plots in a simulation is completely independent.

Key linkages between the carbon, water, and nitrogen cycles can be identified in natural ecosystems, and many are included in the model described here. The principal points of coupling between these three cycles that are included in Hybrid v3.0 can be broadly described as follows:

plant productivity is dependent on soil water content through stomatal conductance, and on the availability of mineral nitrogen through its effect on internal plant nitrogen status, and hence photosynthetic capacity; stomatal conductance and photosynthetic capacity are important determinants of carbon uptake, and stomatal conductance also controls water uptake from the soil and loss to the atmosphere; soil water content is controlled by inputs from throughfall (partly dependent on foliage area) and outputs to outflow and evapotranspiration;

• outflow results in the leaching of some mineral nitrogen and carbon from the soil; soil carbon content is controlled by inputs from plant litter and outputs to heterotrophic respiration and leaching; soil heterotrophic respiration and nitrogen mineralisation are both influenced by soil water content (as well as soil temperature); total soil nitrogen content is controlled by inputs from plant litter and a fixed rate of atmospheric deposition (assumed to include fixation), and outputs to plant uptake and leaching; litter production and water and nitrogen uptake by the plants are all influenced by productivity, principally through the effects of fine root and foliage biomasses. Thus, many of the feedbacks known to operate in nature are represented in the model.

3. Climate inputs and starting values

Daily climate is the principal boundary condition for Hybrid v3.0, and is provided by a daily weather generator (Friend, in press). This sub-model simulates daily rainfall using a first-order Markov chain and a two-parameter gamma probability function. Other climate variables are then simulated as multivariate normal random variables, conditioned on the precipitation status of the day (Richardson, 1981). These are the 24 h maximum and minimum air temperatures, daily precipitation, daily shortwave irradiance, and daytime atmospheric water vapour pressure (Table 5). Mean 24 h and daytime air temperatures are required by the model, and are calculated from the weather variable inputs using the algorithms of Running et al. (1987), Eq. (1). Mean night-time air temperature is also required, and is calculated as twice the 24 h mean air temperature, minus the daytime air temperature. Soil temperature is assumed to equal mean 24 h air temperature. Daylength is required in a number of calculations (see below). It is calculated from yearday and latitude using the method described by France and Thomley (1984) (Eq. (6.13)), with formulation of Spitters et al. (1986) (Eq. (16)).

Mean daytime shortwave irradiance is given by:

/ s w = 1 X 10 6 " I j / t d ,

solar declination calculated from yearday using the

(1)

where lsw is mean daytime shortwave irradiance at the top of the plot, Ij is 24 h shortwave irradiance at the top of the plot, and t o is daylength. The units of all parameters and variables used in this paper are given in the Tables.

Mean daytime photosynthetically active irradiance (/PAR) is calculated from shortwave irradiance as in Friend (1995) (Eq. (39)).

At the start of a simulation for a given location, each plot is initialised with the soil carbon, nitrogen, water, and snowpack contents given in Table 5. Initial grass leaf area index is also given in Table 5. The model is then

A.D. Friend et al. / Ecological Modelling 95 (1997) 249-287

Table 5 Initial values and daily climate input variables for Hybrid v3.0

257

Initial values

Soil water content 0.5 m Snowpack 0 m Grass leaf area index 0.01 m 2 m- 2 Mineral nitrogen 0.004 kg N m - 2

Soil organic matter pools carbon (kg m 2 ) nitrogen (kg m 2)

Surface metabolic 0 0 Surface structural 0.5 0.00333 Soil metabolic 0 0 Soil structural 0.5 0.0333 Surface active (microbe) 0.04 0.002 Soil active (microbe) 0.3 0.02 Slow 5 0.25 Passive 8 0.8

Daily climate variables

Variable units

Precipitation m day- l Maximum 24 h temperature °C Minimum 24 h temperature °C Shortwave radiation (lj; Eq. (1)) MJ m -2 day t Water vapour pressure Pa

The daily climate variables are converted to the appropriate units for internal use by the model.

run to an equilibrium across a number of plots, a n d / o r perturbed by various influences such as changes in

climate, atmospheric CO 2 concentration, a n d / o r nitrogen deposition rates.

4. Model description

A description is given below of the equations used in the model, their derivation or source, and the method

used to derive any parameter values. All variables used in this description are defined in Table 6.

4.1. l rradiance calculations

Accurately determining the amount of radiation absorbed by each individual, and the grass layer, is essential for determining individual growth rates, and hence competitive success or failure, as well as plot and site

productivity (Monteith, 1981).

Following the methods used by the gap model FORSKA (Prentice and Leemans, 1990) to characterise a forest canopy, the foliage area of each individual tree crown is divided equally across the 1 m deep layers in the plot which it occupies. The term 'c rown ' is used here for the foliage of an individual, ' canopy ' is used for the sum of the crowns within a plot. Each layer in a plot could contain foliage from many different individuals. Grass foliage area is evenly distributed within the lowest 1 m layer. The plot foliage distribution, and the distribution of radiation down through the entire canopy of each plot, relative to that received at the top of each


Table 6 Definition of model variables used in main text to describe Hybrid v3.0

Symbol Definition Units

Individual variables

Carbon ( j = a, b, f, h, i, p, r, sw, v, w, or V)

Cj C (Eqs. (10)-(13), (16)-(18), (20), (21), (23), (24)-(26), (28), (32), (33), (35)-(38), (42)-(44)) kg tree-

Nitrogen ( j = a, f, h, p, r, w, or V)

N mean foliage N in uppermost leaf (Eqs. (8) and (47)) kg m -2 Nay N available for allocation (Eqs. (41) and (45)) kg m - 2 Nj N (Eqs. (8), (9), (13), (22)-(24), (40), (41), and (45)) kg tree- t

Area ( j = h, i, sw, or w)

Z r foliage area (Eq. (38)) m 2 tree- l Zj cross-sectional area at breast height (Eqs. (19), (20), (28,) (32), and (34)) m 2 tree- l Ze. i total foliage area in layer i (Eq. (3)) m 2 tree- i

Litter ( j = a, f, r, or w)

L x.j litter production (Eqs. (16)-(18), (20)-(24), and (26)) kg X tree- l year - i L N total individual litter (Eq. (41)) kg N tree- t year- J

Other individual structural variables ( j = h, i, or w)

Dj diameter at breast height (Eqs. (29)-(31 )) m H b height to base of crown m Hj height to apex (from ground) (Eqs. (28) and (29)) m i¢ number of layers in crown (Eqs. (19) and (20)) tree- i

Individual physiological variables

m o FC,Rg Fc, f,d Fc,f,n Fc,r fc.w.d Fc.w.n FN.u Ra Vc, max ddreq

fT gmax

mean daytime rate of net photosynthesis of uppermost leaf (Eq. (6)) annual growth respiration (Eq. (39)) daytime C balance of foliage (Eq. (6)) night-time foliage respiration (Eq. (9)) 24 h free root respiration (Eq. (11)) daytime wood respiration (Eq. (10)) night-time wood respiration (Eq. (10)) 24 h N uptake (Eq. (13)) mean daytime dark respiration in crown (Eq. (7)) maximum rate of carboxylation by Rubisco (Eq. (7)) degree day requirement for budburst (Eq. (14)) N uptake temperature factor (Eq. (13)) maximum stomatal conductance to water

kg C m-2 s - I kg C tree- J year- kg C tree- i day- kg C tree - j day - l kg C tree- ~ day- kg C tree- l day- i kg C tree- I day- J kg N tree- l day- l kgC m-2 s -~ k g C m -2 s - l °C dimensionless mol H20 m -2 s -x

Other individual variables

Cj, inc lt, o fI.H../I ft.i f~.o/, fN.¢hl fN.o fN,Rub

annual C increment (Eqs. (26), (27), (39), and (40)) mean radiation absorbed by top leaf (Eq. (4)) radiation penetrating plot canopy incident on top layer (Eq. (5)) radiation incident on layer i absorbed in layer (Eqs. (2) and (3)) radiation incident at top of plot incident on the top layer (Eqs. (4), (5)) foliage N bound in chlorophyll (Eq. (46)) foliage N not bound in Rubisco or chlorophyll (Eqs. (46) and (47)) foliage N bound in Rubisco (Eq. (46))

kg C tree - j year -~ W m -2 and mol m -2 s - t fraction fraction fraction fraction fraction fraction

A.D. Friend et a l . / Ecological Modelling 95 (1997) 249-287 259

Table 6 (continued)

Symbol Def'mition Units

fl radiation incident on top layer absorbed in crown (Eqs. (6) and (8)) fraction ft.nh+, radiation incident on top layer absorbed by bottom layer (Eq. (12)) fraction

Meteorological variables

I I mean daytime irradiance at top of plot (Eq. ( 1 )) W m - 2 or mol m- 2 s - l Ij 24 h shortwave irradiance at top of plot (Eq. (1)) MJ m 2 s - T air temperature (Eq. (10)) K T d mean daytime air temperature K T t mean daytime canopy temperature K T n mean night-time air temperature (Eq. (9)) K T s mean 24 h soil temperature K ed chilling days (Eq. (14)) days t d daylength (Eq. (1), (11), etc.) s day- 1

Plot variables ( j = do or rv)

Cj C in soil pool j (Eqs. (48)-(51)) kg C m -2 ET decomposition soil temperature modifier (Eq. (52)) proportion EM decomposition soil moisture modifier (Eqs. (52) and (53)) proportion Nj N in soil pool j (Eqs. (49)-(51)) kg N m -2 Nmi n soil mineral N pool (Eq. (13)) kg N m- -~ Nmin(do,rv) N mineralisation associated with flux of C from pool do to rv (Eq. (51)) kg N m-2 day- Rn~do.rv) microbial respiration associated with flux of C from pool do to rv (Eq. (50)) kg C m- 2 day- WFPS soil water-filled pore space (Eqs. (53) and (54)) % Zf, i foliage area in layer i (Eqs. (2), (3)) m 2 fl.i mean fraction of irradiance incident at top of layer i absorbed in layer i fraction

(Eqs. (2), (3)) decomposition rate of soil organic matter pool j (Eqs. (48)-(52)) soil water field capacity (Eq. (54)) soil water content (Eq. (54))

kj day- i SWC m

0 s m

Derived site variables

C v carbon in vegetation on l January kg C m -2 C s carbon in soil on 1 January kg C m-2 ZE annual evapotranspiration MJ m- 2 year- J GPP annual gross primary productivity kg C m -2 year-- LA1 annual maximum leaf area index m 2 m - 2 NPP annual net primary productivity kg C m -2 year-- R . annual heterotrophic ( 'soil ') respiration kg C m -2 year--

All foliage areas are on a projected basis. The term 'breast height' refers to 1.37 m above ground level. The subscript j used in the main text to denote individual is omitted for clarity. Where appropriate units are per plot: for grass they are per day where appropriate (e.g., litter production); 'individual' refers to the whole grass layer in a plot as well as a tree. Radiation and irradiance refer to photosynthetically active radiation (PAR) or shortwave (SW); subscript ! denotes PAR or SW. Elements given by: C = carbon, N = nitrogen. Subscript j defined as follows: V = non-heartwood, a = storage, b = lowest foliage layer balance, do = donor soil organic matter pool, f = foliage, h = heartwood, i = inside bark, p = bark and sapwood, r = fine roots, rv = receiver soil organic matter pool, sw = sapwood, v = live sapwood, and w = wood plus bark (excluding storage). X = C or N. N.B.: Other variables in Hybrid v3.0 are defined in Friend (1995), Friend (in press), Stewart (1988), Parton et al. (1993), and Comins and McMurtrie (1993).

p lo t , a re c a l c u l a t e d e a c h t i m e the f o l i a g e a r ea o f an i n d i v i d u a l t ree in the p lo t c h a n g e s . T h e r e l a t i ve a m o u n t o f

r a d i a t i o n a b s o r b e d b y i n d i v i d u a l s in t he l o w e s t l a y e r is r e - c a l c u l a t e d da i ly ( a n d u s e d to u p d a t e t he to ta l r e l a t i ve

i n d i v i d u a l a b s o r p t i o n s ) b e c a u s e g r a s s a l l o c a t i o n o c c u r s e a c h day .


Beer's law is used to calculated the attenuation of photosynthetically active radiation (PAR: 400-700 nm) and shortwave radiation (SW: 400-3000 nm) down through each plot canopy. The attenuation of PAR and SW wavebands are calculated separately because they interact with the foliage in different ways.

In each plot, the fractions of PAR and SW incident on the top of a 1 m deep layer that are absorbed in that layer are assumed to be:

f/a = 1 - exp - K l , j . Zf, i, j , (2)

where fJ,i is the fraction of radiation incident on layer i that is absorbed in layer i (the subscript I denotes either PAR or SW), Kt, j is the radiation extinction coefficient of individual j (N.B. the subscript j is sometimes omitted for clarity), Z f j j is the foliage area of individual j in layer i, Zp is the area of the plot, and n is the number of individuals in the plot. The fraction of radiation incident on each layer that is absorbed by each individual in that layer is calculated from the relative contribution of each individual to the total absorption in the layer:

K1, j . Z f , i, j f , . , j = f , . , . , . ( 3 )

E Zi,,j j = l

where f~,cj is the fraction of radiation incident on layer i that is absorbed by individual j in that layer. The fraction of radiation incident on the top layer of each individual that is absorbed by that individual in each layer that it occupies is calculated by multiplying the total transmissions (1 -f1,~), and individual absorptions (ft,~.j), down through each crown. Summing down through the layers in each crown then gives the total fraction of radiation incident on the top layer of each individual that is absorbed by the individual (f~j). The parameter feAR,j is directly related to the FPAR parameter of Sellers et al. (1992), but applied to individual crowns rather than the whole canopy. This equivalence is used in the calculation of crown photosynthesis (see below).

The quantities of PAR and SW absorbed by the top leaf of each crown are used as inputs to the net photosynthesis and stomatal conductance routines. These quantities are calculated from the daily mean irradiances at the top of the plot:

l,.j,o = f l , j . o / t " KI , j " II , (4)

where ll,j, o is mean radiation absorbed by the top leaf of the crown of individual j , f z . j ,o / t is the fraction of radiation incident at the top of the plot that is incident on the top layer of individual j, and I I is the irradiance at the top of the plot. The fraction of plot radiation incident on the top layer of each individual is assumed to be:

f , . ; .o / , = (1 - . f , . , . . j , . ( s )

where oQ is the species or GPT reflection coefficient and f~ # j/, is the fraction of radiation that penetrates the plot canopy that is incident on the top layer of individual j ~calculated by multiplying f~.; down through the plot); the subscript t denotes the top of the plot and H,,,i is the height to the top of the crown of individual j. Heights are rounded to the nearest 1 m for use in the radiation calculations.

Mean values for the GPT-specific parameters (K1,j and oz I) are required. Jarvis and Leverenz (1983) reported that values of KpA R vary from 0.5 to 0.8 for broadleaved forests, and from 0.4 to 0.6 for coniferous forests. The means of these ranges (0.65 and 0.50 for cold deciduous broadleaved and evergreen needleleaved tree GPTs, respectively) are used here (Table 3). Foliage absorbs a higher proportion of PAR than SW; thus KpA R tends to be higher than Ksw. Measured values for the ratio KpAR/Ksw are relatively conservative, and lie between 1.3 and 1.4 (Green, 1984, quoted by Russell et ai., 1989, p. 24), hence 1.35 is used here. Using the estimates of KpA R given here, this results in values for Ksw of 0.48 and 0.37 for cold deciduous broadleaved

A.D. Friend et al. / Ecological Modelling 95 ( 1997 J 249-287 261

and evergreen needleleaved tree GPTs, respectively (Table 3). For simplicity, in Hybrid v3.0 the C3 grass GPT is assumed to have the same radiative properties as the cold deciduous broadleaved tree GPT.

Spitters (1986) presented an equation to calculate the reflection coefficient of a green, closed, canopy (% in Eq. (5)) from solar elevation and the single-leaf scattering coefficient. Using a scattering coefficient of 0.2 for PAR (Spitters, 1986), and assuming a mean solar elevation of 45 °, C~eA R is then 0.05 according to this equation. This is the same value as that given by Jones (1992) as typical for all vegetation types. Jones gave a corresponding value of 0.2 for C~sw (Table 2.4 of Jones, 1992), and these two values for the two wavebands are used for the cold deciduous broadleaved tree and C3 grass GPTs (Table 3). Moore (1976) measured a value for O~sw of 0.11 in a needleleaved forest. Applying the ratio of PAR to SW reflectance given by Jones results in a value of 0.03 for ~eAR for the needleleaf tree GPT. These values are used in Hybrid v3.0 (Table 3), with % for each plot being weighted by the relative foliage areas of the different GPTs.

4.2. N e t p h o t o s y n t h e s i s

The amount of radiation absorbed by each individual is critical to determining its productivity because of the central role of PAR in photosynthesis. In Hybrid v3.0, each day the mean rate of total crown net photosynthesis, and the mean rate of net photosynthesis in the lowest crown layer, are calculated for each tree. The mean rate of grass net photosynthesis, and the mean rate of net photosynthesis in the lowest 10% of the grass foliage, are also calculated each day for each plot. A significant assumption employed in this model is that foliage physiological properties (such as nitrogen and Rubisco content) decrease down through each tree crown, and the grass foliage, with the same gradient as time-averaged PAR. This hypothesis is based on the assumption that photosynthetic capacity is distributed optimally, with respect to radiation, within the canopy and/or each individual's crown. A detailed discussion of this viewpoint, and its implications, was presented by Sellers et al. (1992). Significant savings in execution time are obtained by adopting this hypothesis because the alternative would be to calculate photosynthesis and transpiration separately for each foliage layer of each crown. However, application of this optimisation hypothesis has the consequence that, for a given set of environmental conditions and a given total crown foliage nitrogen content, only one calculation of photosynthesis is necessary to obtain the rate of the entire crown. This is because total canopy, or crown, net photosynthesis emerges as being linearly related to the rate of photosynthesis of the uppermost leaf at all values of /PAR (Sellers et al., 1992):

fPA R Fc. f . a = A o • Zp" KpAR , (6)

where Fc, r. d is the mean daytime rate of crown net photosynthesis (subscript C denotes carbon, f foliage, and d daytime), A o is the mean daytime rate of net photosynthesis of the uppermost leaf, Zp is the plot area, and f e A R

is the fraction of PAR incident on the uppermost foliage layer that is absorbed by the entire crown (see above; note that the subscript for individuals is omitted from now on). Furthermore, as a result of the optimisation hypothesis, the mean daytime rate of net photosynthesis in the lowest layer of each crown is a linear function of Fc,r. d (see below). From Eq. (6) it might appear that reducing KpA R will increase crown photosynthesis. However, the amount of PAR absorbed by the top leaf will be reduced (Eq. (4)), providing a limit to the influence of K e A a on productivity. KpA R also affects the amount of nitrogen in the top leaf (see Eq. (8) below).

Net photosynthesis is calculated using the PGEN v2.0 model of Friend (1995). This model uses the well characterised biochemical formulations of Farquhar and co-workers (Farquhar and yon Caemmerer, 1982; Farquhar et al., 1980). All equations (for photosynthesis, transpiration, and energy relations) in Friend (1995) are used in Hybrid v3.0 except for those used to calculate leaf water potential (Eqs. (5), (20), (21), (33), (34), and (37) of Friend, 1995), absorbed radiation (Eqs. (38), (40), and (47) of Friend, 1995), optimal stomatal conductance (Eqs. (1) and (2) of Friend, 1995), and the co-limited rate of net photosynthesis (Eq. (18) of Friend, 1995). Leaf water potential and optimal stomatal conductance are not required because stomatal conductance is

262 A.D. Friend et a l . / Ecological Modelling 95 (1997) 249-287

calculated using an empirical (as opposed to optimisation) function, in which soil water potential is assumed to influence stomatal conductance directly (see below). The radiation absorption equations of PGEN are replaced in Hybrid v3.0 by the canopy radiation scheme described above (the value of absorbed PAR used to calculate A o is given by Eq. (4)). The concept of co-limitation of net photosynthesis by the carboxylation-limited or ribulose-bisphosphate (RuBP) regeneration-limited rate (Eqs. (3) and (4) of Friend, 1995, respectively) is replaced by one of taking the minimum of these two rates, resulting in savings in execution time. Atmospheric pressure is assumed to be 101325 Pa throughout Hybrid v3.0 (it is an input to PGEN v2.0).

Three further simplifications have been made in adapting PGEN v2.0 for use in Hybrid v3.0: (i) Rather than calculate the rate of daytime dark respiration (of the top leaf) from foliage temperature and a foliage nitrogen factor (Eq. (26) of Friend, 1995), the simpler approach of relating respiration directly to the maximum rate of carboxylation, as suggested by Collatz et al. (1991), is used:

e d = 0.015. We.ma x , (7)

where R d is the mean rate of dark respiration and Wc,ma x is the maximum rate of carboxylation by Rubisco (Eq. (22) of Friend, 1995), of the uppermost leaf. Because Ve,ma x is dependent on temperature and Rubisco content (which in turn is dependent on foliage nitrogen, see below), this approach maintains the temperature and foliage nitrogen dependencies of the original PGEN v2.0 formulation. (ii) The radiative 'resistance' to heat loss is assumed to be fixed at 213.21 s m -1 in Eq. (50) of Friend (1995). (iii) Leaf thickness is assumed to be 300 × 10 -6 m in the calculation of the resistance to CO 2 transfer from the leaf surface to outside the mesophyll liquid phase (Eq. (31) of Friend, 1995). And (iv) the slope of the saturation vapour concentration versus temperature is calculated between air temperature and air temperature plus 0.1 K, rather than between air and foliage temperature (Eq. (53) of Friend, 1995). This last approximation is necessary because no iteration to solve the energy balance is used, yet this slope needs to be known to calculate foliage temperature.

In the model, the rate of carboxylation-limited net photosynthesis is a linear function of foliage nitrogen. Thus, this rate per unit of foliage nitrogen need be calculated only once, on each day, for each GPT in each plot (stomatal conductance will vary between plots as a function of soil water and absorbed PAR, see below). This value can then be scaled with the foliage nitrogen content of the top leaf to get the rates for each individual, resulting in substantial savings in execution time. However, RuBP-regeneration limited net photosynthesis is a saturating function of both foliage nitrogen and PAR, and must therefore be calculated for each individual each day, although the shared parameters between all individuals of the same GPT in each plot need be calculated only once.

As a consequence of the assumptions that foliage nitrogen is allocated optimally within each crown (see above), and photosynthetic capacity is a linear function of foliage nitrogen (Friend, 1995), it follows that the nitrogen content of each leaf must be directly proportional to the time-averaged PAR absorbed by that leaf relative to the whole crown. Therefore, the nitrogen content of the uppermost leaf of each individual tree, and the grass layer, is:

KpAR N = feA------~ " N f / Z p , (8)

where N is the nitrogen content of the uppermost leaf and Nf is the total foliage nitrogen of the individual crown or the grass canopy. Calculation of Nf is described below. During initial application of Eq. (8) within Hybrid it was found that, under high leaf area conditions, unrealistically high top-leaf nitrogen contents were obtained. To overcome this, the observed approximate maximum limit of 4 × 10 -3 kg m -2 (see Evans, 1989, Fig. 1) has been imposed on N in Hybrid v3.0. It is undesirable to require such a limit, but previous model simulations (not shown) demonstrated its necessity. The need for this limit suggests that the optimisation theory is either incorrect, or that the relationship between nitrogen, photosynthesis, and respiration is not fixed down through the canopy. There is a need for experimental work to help understand the relationships between radiation, foliage nitrogen, photosynthesis, and respiration in canopies. Nevertheless, without overwhelming


information to the contrary, it is sensible (and often computationally efficient) to assume that plants make optimal use of their resources.

4.3. Maintenance respiration

The daily maintenance respiration fluxes from each living tissue compartment are important components of a plant's daily carbon balance. The term 'maintenance respiration' refers to the CO 2 evolution from plants that is principally the result of protein repair and replacement and the respiratory processes that provide energy for the maintenance of ion gradients across cell membranes (Penning De Vries, 1975).

The mean night-time foliage maintenance respiration rate of each tree, and the grass layer, are assumed to be linear functions of the total foliage nitrogen contents and exponential functions of air temperature (after Ryan, 1991b):

Fc.f,n = n C , f , n "N f" e -6595/T" , (9)

where Fc,f. n is night-time foliage maintenance respiration (subscript n denotes night-time), "qc,f,n is a constant, and Tn is mean night-time air temperature. The value of the constant "qC.f,n was estimated from Ryan (1991b) to be 42.60 × 103 kg C kg N-~ s-1, and this value is used for all GPTs (Table 4). Total nitrogen, rather than Vc.ma ~ (Eq. (7)), is used in Eq. (9) because night-time respiration is related to the total metabolic activity of the foliage rather than to potential photosynthetic pathway activity. The temperature term in Eq. (9) is the same as that used by Friend (1995), the constant 6595 K being the activation energy (J mo1-1) divided by the gas constant, and is equivalent to a Q~0 of 2.1. This temperature dependence is used in Hybrid v3.0 for all non-growth respiration rates.

Mean fine root maintenance respiration over each 24 h period (Fc. r) is calculated from fine root nitrogen content (Nr), and mean 24 h soil temperature (T~), using the same formulation as for Fc,f, n (Eq. (9)). Separate values of Fc, r for the daytime and night-time are not calculated because soil temperature is not expected to change greatly over any given 24 h period.

In nature, tree sapwood respiration is required to maintain the living sapwood parenchyma cells, which are present in the sapwood of all living trees; the support tissue in grass also respires. Tree sapwood respiration is clearly a carbon cost, but is balanced by certain advantages resulting from possessing living sapwood in Hybrid v3.0 as in nature (see below). Sapwood and grass support tissue maintenance respiration rates are assumed to be linear functions of living carbon mass, and exponential functions of air temperature (after Ryan, 1990):

Fc. w = r/c.wC v • e -6595/r, (10)

where Fc. w is wood maintenance respiration, "qC.w is a constant, Cv is the mass of living carbon, and T is air temperature. The constant in Eq. (10) is calculated from the measurements of Ryan (1990) to be 83.14 kg C kg C- 1 s- i, and this value is used for all GPTs (Table 4). Two mean daily fluxes of sapwood and grass support tissue respiration are calculated, one for the daytime and one for the night-time (Fc.w, d and Fc.w. . using T d (daytime air temperature) and T n respectively in Eq. (10)).

4.4. Total daily tree carbon balance

Each day, the individual tree and grass layer carbon stores, are incremented by their daily net carbon balances. In trees, if the carbon store is positive at the end of the year (after allowing for any additional carbon required to support foliage or fine root turnover that occurred during the year), this carbon is allocated to new growth and growth respiration (see below). In grass, allocation or subtraction of the carbon store to/from the total biomass occurs on each day (see below). The daily change in the carbon store (AC a) of all GPTs is given by:

AC a = td " ( F c , f , d - - F c , w . d ) - - (86400 - to) " ( F c . f . n + F c . . . . ) - 86400-Fc, r, (11)


where C a is the carbon store, Fc,f. d (Eq. (6)) and Fc.~. . (Eq. (9)) are the respective mean daytime and night-time fluxes of carbon between the foliage and the atmosphere, Fc.w. d and Fc.w. . are the respective mean daytime and night-time fluxes of carbon from the living wood, or structure (Eq. (10)), Fc. r is the mean daily flux of carbon from the fine roots, t d is the daylength, and the constant 86400 is the number of seconds in 24 h. C a may become negative, and this is allowed for at the end of each year (or each day in grass) in the allocation routine (see below).

4.5. Carbon balance of the lowest foliage layer

The carbon balance of the lowest foliage layer of each tree crown, and the lowest 10% of the grass foliage layer, is calculated daily. If, at the end of each year for trees, or each day for grass, an individual's accumulated carbon balance in this layer is negative, the foliage area of that individual is reduced by the amount present in the layer in trees, or by 10% in grass. This results in the foliage area being optimised on an annual timestep in trees and daily in grass. Because it is assumed that foliage physiological properties fall down through each crown at the same rate as time-averaged PAR (see above), it follows that the rates of photosynthesis and respiration of any layer in the crown are linear functions of the rate of the top leaf (see above), and indeed of the whole crown (assuming that the relative proportion of radiation reaching each leaf is the same as the time-mean relative proportion, as is the case in this model). Consequently, the carbon balance of the lowest foliage layer is a linear function of the whole crown rates of daytime photosynthesis and night-time respiration:

dCb = fPAR,nb., . (ta.Fc,f.a _ (86400 - td)-Fc,f,n) , (12) dt fPAR

where C b is the carbon balance of the lowest 1 m foliage layer in the tree crown, or the lowest 10% of the foliage layer in grass, and fPAR.nb., is the fraction of radiation incident on the uppermost layer of the individual that is absorbed by its lowest crown layer (indexed by the height to the base of the crown, H0, plus 1 m).

4.6. Stomatal conductance

Stomatal conductance controls the flux of C O 2 into, and water out of, the leaves of higher plants. C O 2 is required for photosynthesis, and transpiration depletes soil water; transpiration is also an important determinant of leaf temperature. These effects are all included in Hybrid v3.0. The mean daytime stomatal conductance of the uppermost leaf of each individual tree, and the grass layer, is calculated for each day. This is achieved using empirical relationships between stomatal conductance and irradiance (/PAR.o), soil water potential, above-canopy air temperature, above-canopy water vapour pressure deficit (vpd), and above-canopy CO 2 concentration. Stewart (1988) found that a multiplicative model based on the model of Jarvis (1976), and using non-linear functions of solar radiation, specific humidity deficit, air temperature, and soil moisture deficit, could explain 73.3% of the variance in surface conductance (calculated from water flux measurements) over 90 days in a pine forest near Thetford, England. We attempted to calibrate the full PGEN v2.0 model of leaf physiology (Friend, 1995) with these Thetford data. In this version of PGEN, stomatal conductance is calculated using an optimisation concept by assuming that conductance maximises short-term carbon gain (the cost function being related to leaf water potential). However, we were unable to achieve as good a fit (as measured by the r 2 statistic) as even half that obtained using the Stewart/Jarvis model. Much of the discrepancy between the two models and the data was in the vpd response, particularly in the comparison between PGEN and the data. The data exhibit a marked closing response to vpd, much stronger than was (or indeed could be) predicted by PGEN v2.0. In addition, Lloyd et al. (1997) found that a multiplicative model of the Stewart/Jarvis type produced a very good fit to the flux measurements made over the Amazon rainforest. Two alternative models (the 'Lamdba' model, based on an optimisation theory: Lloyd and Farquhar, 1994, and the 'Ball-Berry' empirical model: Leuning, 1990) did not provide as good a fit to the data (Lloyd et al., 1997).


In view of these comparisons, the Stewart/Jarvis model is used here, and with the same parameterisation for the functions (though not the maximum stomatal conductance, see below) as used by Stewart (1988) in his non-linear version, except for the soil water response function. This function is replaced by a function which effects a linear closing response between soil water potentials of - 0 . 2 MPa and - 1.5 MPa, as is typically observed (e.g., Turner et al., 1985). A linear closing response to increasing atmospheric CO 2 concentration, in which" the stomata close by 40% for a doubling of atmospheric CO 2, with no further closure above an atmospheric CO 2 partial pressure of 80 Pa, has been added. This degree of closure is, again, typically observed (e.g., Friend and Leith, in press). The use of empirically-derived relationships with air parameters, rather than foliage parameters (such as leaf temperature), results in large savings in execution time by avoiding the need for iteration. Nevertheless, it should be noted that the Stewart/Jarvis model has six free parameters, and thus might be expected to fit any single dataset with a high degree of success. The generality of a given parameterisation has not been tested; this will be done as more flux measurements become available.

The maximum stomatal conductance to water (gmax) is required by the stomatal conductance sub-model. In order to make the stomatal conductance function more realistic and dynamic than in its original conception, gmax is assumed to vary with foliage photosynthetic capacity. It is widely observed that stomatal conductance and photosynthesis are correlated with one another (Farquhar and Wong, 1984), presumably because of their functional relationship. KSrner (1994) collated 73 field observations of maximum stomatal conductance and net photosynthesis (Area x) pairs in l l major vegetation types, and found that the slope of the relationship differs between types. His values of maximum stomatal conductance are not the same as gmax used here. gmax is a hypothetical parameter that is unlikely ever to be reached, whereas the parameter quoted by KSrner is measured in the field at the leaf level. The values of gmax used in Hybrid v3.0 for different GPTs and photosynthetic capacities were calculated from the maximum stomatal conductance values of K~Srner by assuming that these were measured under the following, favourable, environmental conditions: an air temperature of 25°C, a PAR flux of 1500 /~mol m -2 s - l , a relative humidity of 70%, an atmospheric CO 2 concentration of 350 p, moi mol- ~, and no soil water limitation. Putting these values into the appropriate functions (Stewart, 1988; plus the CO 2 response given here) yields a total factor of 0.37. Dividing the values given by KSmer by this factor gives the ratios between gmax and Am~ x required for each GPT. Because Area x is not used directly in Hybrid, gmax is actually calculated from the amount of foliage nitrogen bound in Rubisco; a reasonable surrogate for Area x within vegetation types (Field and Mooney, 1986). Consequently, gmax is re-calculated each time foliage nitrogen changes (i.e., daily for grass and annually for trees).

A relationship between gmax and Rubisco is now required. Evans (1989) presented the results of photosynthetic measurements across a range of species and foliage nitrogen contents. He found that at a foliage nitrogen content of 1.4 × 10 -3 kg m -2, the greatest value of Area × w a s about 28 /xmol CO 2 m -2 s - I . Using the mean gma×/Amax ratio of KSrner (1994) for herbaceous graminoid species (the maximum photosynthetic rates of Evans were measured in wheat) gives gmax equal tO 0.375 mol m -z s - l for this nitrogen content. Then, assuming that the fraction of foliage nitrogen bound in Rubisco is 0.23 (a typical value: Evans, 1989), the ratio between gmax and the amount of foliage nitrogen bound in Rubisco (r/g,~) is 1359 m o lm -2 s- ~/(kg (Rubisco N) m-2). This ratio is used for grass in Hybrid v3.0, and is scaled using the data of K6rner to give ratios of 1672 mol m -2 s -~/ (kg (Rubisco N) m -2) for cold deciduous broadleaved trees and 2223 mol m -2 s - I / ( k g (Rubisco N) m -2) for evergreen needleleaved trees (Table 3).

A minimum foliage (cuticular) conductance to CO z of 48.1 × 10 - 6 m S-1 is assumed for all plant types.

4.7. Foliage energy balance and transpiration

The daytime canopy energy balance must be solved each day in order to calculate the foliage temperature and rate of transpiration of each plot. Transpiration influences soil water content and foliage temperature influences net photosynthesis and dark respiration. The mean daytime canopy temperature of the entire plot (Tf) is calculated following the methods described by Friend (1995), (Eqs. (41)-(53), but with changes as detailed

266 A.D. Friend et al . / Ecological Modelling 95 (1997) 249-287

above) prior to the physiological calculations. Total plot canopy conductance is calculated as the sum of all the individual-based conductances. These are each calculated on a ground area basis by scaling the predicted stomatal conductance of the uppermost leaf of each crown (see above), vertically to the whole crown, using fPAR and KpA R as for net photosynthesis (Eq. (6)). A plot boundary layer conductance is calculated following Friend (Eq. (41) of Friend, with the leaf characteristic dimension set to 0.04 m), and added to the individual stomatal conductances. The isothermal net radiation of the entire plot canopy is calculated on a ground area basis by summing the absorbed shortwave radiation across individuals (reflection is subtracted from each individual as in Eq. (5)). This value is then used to replace the first term (i.e. absorbed shortwave radiation) of the calculation of isothermal net radiation in Friend (Eq. (45) of Friend; the remaining terms allow for long-wave radiation absorptance and emmittance). Incident shortwave radiation on each individual is calculated from total plot radiation by multiplying mean daytime shortwave plot irradiance (Eq. (1)) by the fraction of plot irradiance incident on the top of the individual ( f s w . o / t ; Eq. (5)) and fsw- Plot transpiration is calculated from the canopy-to-air vapour density deficit and total resistance (the inverse of conductance) to water flux as in Friend (Eq. (19) of Friend), but with the saturation density of water at leaf temperature calculated using the updated treatment given by Jones (1992), (Appendix 4, p. 359).

4.8 . N i t r o g e n u p t a k e

Uptake of mineral nitrogen by each tree, and the grass layer, occurs each day. In trees, this uptake is accumulated in a store (N a) for allocation at the end of the year; in grass, allocation occurs each day (see below). The daily uptake of nitrogen is positively related to fine root mass, soil mineral N content, and the C to N ratio of the entire plant (excluding the C and N bound in the heartwood):

FN, u = flu . f T . Cr . Nmin . C v . / N v , (13)

where FN. o is the daily uptake of nitrogen from the soil by the individual (or grass), "qu is a constant, fT is a factor to allow for the effect of soil temperature (given by Eq. (la) of Thomley, 1991, with his constants), C r is the fine root carbon mass, Nmi n is the soil mineral nitrogen content, C v is the non-heartwood plant carbon mass, and N v is the non-heartwood plant nitrogen mass. Eq. (13) includes control of nitrogen uptake by soil nitrogen supply (Nmin), demand by the plant ( C v / N v ) , and the ability of the plant to access nitrogen in the soil (Cr). It is assumed that the plant does not take up any nitrogen if C v / N v is lower than 10 kg C kg N- ~ and/or N (the nitrogen content of the top leaf, Eq. (8)) is greater than (or equal to) 4 × 10 -3 kg m -2. ~Tu is set to 0.036 m 2 kg C-~ d - ' (ignoring C:N units) for all GPTs (Table 4; calculated from Thornley, 1991). It is assumed that there is no leaching of nitrogen from the plant, nor any direct input of nitrogen into the leaves from the atmosphere.

4.9. P h e n o l o g y

The ability to sense when foliage display will yield carbon gains, without undue risk of frost damage, is an important adaptive feature of all cold deciduous plant species. The biochemical processes underlying the acquisition and release of dormancy (expressed as the inability of organs to grow at favourable temperatures) are unknown, but there is compelling evidence for the progressive loss of dormancy with increased chilling. This loss of dormancy is measured as an increase in the growth rate of the organs as a function of temperature, otherwise expressed as a decrease in the heat sum required to reach a given stage of budburst (Cannell, 1988). In accordance with this evidence, in Hybrid v3.0 the date of budburst of the cold deciduous broadleaved tree GPT is predicted using a parallel chilling/heat sum sub-model (Cannell and Smith, 1983). This sub-model considers the effects on dormancy of temperatures both above and below a critical threshold, and has been found to perform well across a wide range of species (Murray et al., 1989). The heat sum required for budburst is reduced as the number of chilling days increases. This heat, or degree-day, sum, is measured as the sum of the positive differences between the daily mean temperatures, and some threshold temperature (Tth), following

A.D. Friend et al./ Ecological Modelling 95 (1997) 249-287 267

some predetermined date; the chilling-day sum is the number of days on which the mean temperature was below Tth following some, usually earlier, predetermined date.

The parallel chilling/heat sum model of Cannell and Smith (1983) was fitted to the eastern USA white oak (Quercus alba) spring phenology data of Wickham and Box (1989), using daily temperature data from the US Historical Climate Network database (Karl et al., 1990) for stations closest to the phenological observations. We followed Wickham and Box (1989) in choosing a threshold temperature of 6°C (Table 4) and a degree-day start date of 1 February (Julian day 32), and Cannell and Smith (1983) in choosing a chilling day start date of 1 November (Julian day 305). For sites in the Southern Hemisphere, the equivalent dates are 3 August (Julian day 215) and 3 May (Julian day 123), respectively.

Because Wickham and Box (1989) reported phenology data for only one year, it was necessary to tune the fitted equations to include the effect of between-year variation. This was achieved using the temporally extensive (but single location) dataset of Smith (1915). The asymptote of the equation (see below) was adjusted until a good fit to both datasets was achieved. The following equation for the degree-day requirement for budburst in Quercus alba was derived, using the data of Wickham and Box (1989) for sites in Michigan, Pennsylvania, Virginia, and South Carolina:

ddre q = 178.8 + 2731 • e -°°414cd, cd > 31, (14)

where ddre q is the degree-day requirement for budburst in the cold deciduous GPT and cd is the chilling day sum. Because Q. alba has a very wide distribution in the USA (Little, 1971), this parameterisation is used for the cold deciduous broadleaved tree GPT in this paper. The minimum chilling day limit of 31 days was calculated from Wickham and Box (1989); if cd is less than 31, ddre q is set to the value obtained for 31 days (i.e. 935.5°C). It is assumed that 10 days elapse from leaf emergence until the foliage is a net exporter of carbon, and so considered as displayed in the model. This delay was calculated from Smith (1915) as half the time from leaf emergence to full leaf area.

The day on which the foliage of the cold deciduous broadleaved GPT ceases to be a net exporter of carbon, due to autumn senescence, is empirically calculated from latitude (lat) and daylength. The daylength of this day is assumed to be:

ta(rso) = 39132 + 1.088 (11at1+60"753), (15)

where td(fS0) is the autumn daylength required for leaf fall in the cold deciduous broadleaved GPT. The constants in Eq. (15) were derived from the data on winter bud formation of Kaszkurewicz and Fogg (1967) for Populus deltoides, with a correction to predict the daylength for 50% colour change using the data of Smith (1915). The use of absolute latitude enables this equation to be used in the Southern Hemisphere.

However, the parameterisation of the phenology equations described here cannot be confidently applied outside the eastern USA because relationships between the risk of frost damage, climate, and latitude vary from region to region. This issue will be addressed in a subsequent paper.

4.10. Grass litter production

Constant fractions of grass foliage, support structure, and fine root carbon and nitrogen pools are assumed to enter the litter pools each day prior to allocation. The rate of carbon and nitrogen litter production is assumed to be 0.31% day-1 (equivalent to 113% per year), a value calculated from the data of Kinyamario and Imbamba (1992) for a savanna grassland in Kenya (no difference between above- and below-ground turnover rates was detected).

4.11. Tree litter production

As in grass, tree carbon and nitrogen litter production is also calculated, prior to allocation, using a largely empirical approach. However, unlike in grass this is done only at the end of each year. More mechanistic


treatments of tree and grass litter production (especially fine root turnover, see below) will be considered in later versions of the model.

4.11.1. Carbon litter and related equations The annual flux of carbon from trees to the soil, through non-individual mortality (i.e. normal litter

production), is calculated as follows. Wood plus bark litter carbon is assumed to be linearly proportional to wood carbon mass:

LC.w =fL,w " Cw, (16) where Lc. w is annual wood plus bark litter carbon (N.B. including heartwood), fL,w is the fraction of wood that goes to litter each year, and C w is the total wood plus bark carbon mass. It is assumed that an equal proportion of the stored carbon also goes to litter (Lc, a; the production of wood plus bark litter is assumed to be largely the result of damage, and so will include the storage compartment), fL.w is given the nominal value of 0.01 (Table 4).

Annual fine root litter carbon is calculated from the fine root turnover rate (fL,r)" If this rate is greater than 1, then the additional carbon required is subtracted from the carbon store, C a , after allowing for growth respiration (the assumption is made that the carbon store was used during the year to support fine root turnover). If C a is then negative, in order to conserve carbon the fine root litter carbon amount must be re-calculated based on the carbon available, hence:

Lc,r=min(( fL .r 'Cr);(Cr + Ca" (I --fRg)) (17)

where Lc. r is annual fine root litter carbon and fRg is the fraction of carbon used for growth which is lost as growth respiration; this fraction is set to 0.25 (Ryan, 1991a; Table 4).

Fine root turnover is potentially a very important component of a tree's carbon budget, and indeed can represent the largest flux of carbon to the soil (Cannell, 1989). Observations and estimates indicate that fine roots turnover 2 to 5 times per year, (Cannell, 1989); here it is assumed that fL.r is fixed at 2 for both tree GPTs (i.e. fine roots turn over twice per year). It is known that fine root turnover is affected by the availability of water and nutrients (Cannell, 1989), though these effects are not included in Hybrid v3.0.

Following wood plus bark and fine root litter production, the storage carbon pool is updated by ACa:

A C a = - t c , a - - max(0;( Lc. r - Cr ) / (1 - fR~)) - (18)

This expression allows for storage litter carbon (Lc, a) and the depletion of carbon from the store for fine root turnover up to, but not exceeding, that which can be supported by the carbon available (C a) at the end of the year. It also allows for any growth respiration resulting from this additional fine root turnover. No feedback to plant performance is allowed for if lack of stored carbon results in fine root production being below that required.

If, at the end of a year, the annual carbon balance of the lowest foliage layer of an individual tree (Cb; Eq. (12)) is below zero, then the foliage carbon in that layer enters the foliage litter pool, and the sapwood that was supplying the foliage in that layer with water (and nutrients) is transformed into heartwood. Thus, the heartwood area is increased by the amount required to maintain a fixed foliage area to sapwood area (at breast height) ratio:

Z h :=Z h +Zsw/ i c, (19)

where Z h is heartwood area, Zsw is sapwood area at breast height, and i c is the number of layers in the crown (Hw - Hb). The basis for this assumption is discussed below. Following an increase in heartwood area by this means, the height to the base of the crown (H b) is increased by 1 m. Annual foliage litter carbon is then calculated using the following expression, where the first part gives the carbon mass of the foliage in the lowest layer, and the second part gives the annual turnover of the remaining foliage:

Cf +fL,f" C f - - (20) Lc "f "~" l"~- i c '

where Lc, f is annual foliage litter carbon and fL.f is the foliage turnover rate.

A.D. Friend et aL / Ecological Modelling 95 (1997) 249-287 269

If the carbon balance of the lowest foliage layer was positive at the end of the year, annual foliage litter carbon is calculated as a linear function of foliage carbon:

Lc, f =fL.f • Cf, (21)

where fL, t" is assumed to be 1 (hence deciduous) for the broadleaved and 0.33 (hence evergreen) for the needleleaved tree GPTs (Table 3).

4.11.2. Nitrogen litter Annual tree wood plus bark litter nitrogen (LN. w) is calculated in the same way as wood plus bark litter

carbon (Eq. (16)):

Ly.w =fL.w "Sw, (22)

where N w is the nitrogen mass in the wood plus bark (N.B. including heartwood). Annual storage litter nitrogen (LN,~,) is calculated in the same manner as storage litter carbon (see above).

It is assumed that no fine root nitrogen is re-translocated into the tree prior to litter production (as is consistent with some of the few observations that have been made, such as Nambiar and File, 1991). Annual fine root litter nitrogen (LN. ~) is calculated as a linear function of fine root litter carbon. Because fine root litter carbon can be greater than the total amount of fine root at any one time (see above), fine root litter nitrogen might also be greater than fine root nitrogen. Consequently, a check is made that sufficient nitrogen in the fine roots and store is available to support the required annual fine root litter nitrogen (LN,r):

LN, r = min(( Lc. r • Nr/Cr); ( N~ + Na) ). (23)

Annual foliage litter nitrogen (LN. f) is assumed to follow foliage litter carbon, after allowing for any re-translocation:

Uf LN,, =ft .r" Lc,f" C- 7 , (24)

where ft.f is the fraction of foliage nitrogen not re-translocated into the plant prior to litter loss. Measurements (Boerner, 1984; Chapin III and Van Cleve, 1989; Nambiar and Fife, 1991) suggest a mean value of about 0.5 for this fraction, and this is used for all GPTs (Table 4).

4.12. Allocation in grass

The allocation of carbon and nitrogen to the foliage, support structure (stem, tiller, and coarse root), fine root, and storage compartments of the grass in each plot occurs each day, following litter production. All grass carbon and nitrogen (i.e. foliage, support structure, fine root, and storage) is assumed to be labile for the purposes of allocation. Constant ratios of 10:1 between the support structure and foliage carbon masses, and 1:1 between the foliage and fine roots carbon masses, are used to calculate a maximum foliage carbon mass from the available carbon. If the carbon balance of the lowest 10% of the foliage was below zero the previous day, then the actual foliage mass is restricted to a maximum of 90% of its value on the previous day. If the potential foliage mass from the available carbon is greater than this, then the additional carbon is allocated to the storage compartment, together with the required amount from the structural and fine root compartments to maintain the required ratios. Growth respiration is calculated as 25% of carbon allocated to each compartment, as in trees (see above). Grass support structure carbon is used to calculate maintenance respiration on each day using Eq. (10). Nitrogen is allocated to the foliage, structure, and fine root compartments so as to maintain constant relative C:N ratios, as in trees (see below). The total C:N ratio of the grass is not allowed to fall below 10; if it does then the required amount of nitrogen is routed to litter prior to nitrogen allocation. This may be necessary if respiration exceeds photosynthesis for a significant period, thus reducing grass carbon but not grass nitrogen.

270 A.D. Friend et aL / Ecological Modelling 95 (1997) 249-287

If, following allocation, foliage carbon mass is less than that required to produce a leaf area index (LAI) of 0.01, then the compartments are all reset to produce this LAI, and nitrogen is allocated to give a total C:N ratio of 25. The use of a minimum grass biomass in this way is a substitute for regeneration. In a future version of Hybrid we will include direct soil moisture and temperature controls on grass growth (cf. Woodward and Friend, 1988).

4.13. Allocation in trees

A number of different modelling approaches have been used to calculate the allocation of carbon and nitrogen within trees. It is outside the scope of this paper to discuss their relative merits and limitations, suffice to say that, as for stomatal conductance, a truly mechanistic model (i.e. one which correctly treats the actual significant mechanisms involved) is still lacking. In Hybrid v3.0, the approach to carbon allocation is to use methods which encapsulate the basic functional constraints between the different tree parts, with nitrogen allocation following carbon allocation using mostly empirical principles.

Tree carbon and nitrogen allocation is calculated following litter production, within each individual, at the end of each year. Three constraints are used to calculate carbon allocation. First, it is assumed that there is a fixed allometric relationship between diameter at breast height and woody carbon mass (Eqs. (28) and (29) below). Secondly, it is assumed that foliage area is linearly proportional to the sapwood area at breast height (Eq. (32)) and that there is a fixed fraction of sapwood that is alive (fv; see Eq. (37) below). And thirdly, it is assumed that there is a fixed ratio between the foliage and fine root carbon masses (Eq. (33)). These constraints are parameterised differently for each GPT (see below). Following carbon allocation, nitrogen is partitioned so as to maintain constant relative C:N ratios between the sapwood plus bark, foliage, and fine root compartments. As heartwood grows (see above), sapwood carbon and nitrogen become locked up until released by soil decomposition.

Assuming a fixed relationship between sapwood area and foliage area enables stem respiration to be predicted from foliage mass if the fraction of sapwood that is alive is known. The assumption that this live fraction is fixed is at least as important as the assumption that the foliage area/sapwood area is fixed. The latter hypothesis is taken from the 'pipe model' theory of Huber (1928) and Shinozaki et al. (1964).

There are a far greater number of published measurements of foliage area/sapwood area ratios than of living sapwood fractions; and it has emerged that observed within-species variation in the former could be accounted for by climatic differences (Whitehead et al., 1984; Mencuccini and Grace, 1995). Unfortunately, there are insufficient (published) measurements of the latter to enable a similar assessment to be made. Whitehead et al. (1984) suggested a method for predicting the foliage area/sapwood area ratio from tree permeability and hydrological variables; we will investigate the possibility of incorporating this into a future version of Hybrid. Hari et al. (1985) found a very strong linear relationship between the number of non-water conducting tree rings and the number of whorls of dead branches in Scots pine (Pinus sylvestris), showing that heartwood formation is linked to the death of foliage as assumed in Hybrid v3.0 (Eq. (19)). In addition to the functions of foliage water supply and support, sapwood also performs the important function of carbohydrate and nutrient storage, and this function is also incorporated into Hybrid (see below).

4.13.1. Carbon allocation At the end of each year the annual net, positive, carbon balance of each tree (Ca; including any stored carbon

from previous years) is available for growth. If C a is negative (which can occur due to unfavourable climatic conditions), then to conserve carbon the required amount is subtracted from the wood plus bark (Cw). It is assumed that a minimum fraction (fw.m; set to 0.1 for all tree GPTs: Table 4) of any available carbon is always used for new wood plus bark growth. Consequently, C w is incremented by this minimum amount (AC w) prior to any further allocation (growth respiration is allowed for):

ACw =fw,m "Ca" (1 --fRg)" (25)


The carbon available is reduced by this minimum allocation to the wood plus bark, and then partitioned between the foliage, wood plus bark, storage, and fine root carbon compartments. The total changes in these compartments, at the end of each year, are given by the differences between their annual increments (after allowing for growth respiration), Cj.in c, and their annual litter losses:

ocj Ot = Cj'inc - Lcd' (26)

where the subscript j refers to f (foliage), w (wood plus bark), a (store), or r (fine roots). Because storage carbon is used for the foliage, wood plus bark, and fine roots increments, including their growth respirations, it must be tree that:

(Cf.inc + Cw.inc -~" Cr , i nc ) / / ( 1 --fRg) + Ca.in¢ = 0. (27)

These four values of Cj.in ~ are calculated by searching for a new stem diameter at breast height (Dw) within the three constraints given above by simultaneously solving Eqs. (26)-(35) (see below).

As mentioned, an allometric relationship is used to calculate woody mass from diameter. Total tree wood plus bark carbon mass (subscript w), non-storage inside-bark woody carbon mass (subscript i), and heartwood carbon mass (subscript h), are all calculated using the following expression (after Cannell, 1984):

cj = (1 + k , ) F'Hj .Zj "Pw, (28)

where f~t is the below-ground fraction (see below), "0F is the tree form factor, Hj is height to the apex of the relevant compartment, Zj is the cross-sectional area at breast height of the relevant compartment, Pw is the mean wood plus bark density, and the subscript j refers to w, i, or h. Thus it is assumed that this relationship, which was derived for total tree mass, also holds for inside-bark mass and heartwood mass separately.

The global dataset collated by Cannell (1984) was used to estimate mean form factors for the cold deciduous broadleaved and evergreen needleleaved GPTs of 0.60 and 0.56, respectively (Table 3). Also using this source (and assuming that carbon is 50% of oven dry weight), mean wood densities were estimated to be 305 and 205 kg C m -3, respectively (Table 3).

The height to the apex of each compartment from the ground is calculated as an exponential function of the compartment's diameter at breast height:

Hj = a" D b, (29)

where a and b are GPT-specific constants. These height allometry constants, and the below-ground fractions (f~t), were calculated from regressions developed by Young et al. (1980) for tree species in Maine, USA. Regressions for 6 broadleaved and 7 needleleaved species, 30 to 120 cm in height, were used. The mean below-ground fraction was calculated to be 0.220 for the cold deciduous broadleaved tree GPT and 0.222 for the evergreen needleleaved tree GPT. Mean values of a and b for the cold deciduous broadleaved tree GPT were calculated to be 28.51 and 0.4667, respectively, and the mean values for the evergreen needleleaved tree GPT were 32.95 and 0.5882, respectively (Table 3).

The cross-sectional areas at breast height of each component are calculated from their respective diameters: 7/"

Zj = ~- "D~. (30)

The inside-bark diameter at breast height is calculated by assuming that bark thickness is a constant fraction (fb) of total diameter:

D ~ = D w . ( 1 - 2 . f b ) . (31)

This fraction was estimated from Elias (1980) to be 0.033 of for the cold deciduous broadleaved tree GPT, and 0.01 for the evergreen needleleaved tree GPT (Table 3). Heartwood diameter is derived from heartwood area (Eq. (19)) by solving Eq. (30) for D h.


As mentioned, foliage carbon is assumed to be linearly proportional to sapwood area at breast height, thus:

Cf = "qe" Z~w/sla, (32)

where "0f is the foliage to sapwood area ratio, Zsw is the sapwood area at breast height, and sla is the specific leaf area. Mean values of r/f for the cold deciduous broadleaved and evergreen needleleaved GPTs were calculated from Young et al. (1980) to be 4167 and 3333 m 2 m- 2, respectively. Mean specific leaf areas for the cold deciduous broadleaved and evergreen needleleaved GPTs were calculated to be 36.0 and 12.0 m 2 kg C- ~, respectively, from data for 6 species of each type (Knox and Friend, submitted; Table 3).

As mentioned, fine root carbon is assumed to be linearly proportional to foliage carbon, thus:

C r = Tlr/f" C f , (33)

where "qr/f is the ratio between fine root carbon and foliage carbon, and is assumed to be 1 for all GPTs (calculated for lodgepole pine from Pearson et al., 1984; Table 4).

Sapwood area is the difference between the inside-bark and heartwood areas:

Z~w = Z i - Z h . (34)

The storage of carbohydrate and nutrients is an important function of sapwood (Ryan, 1990). These reserves are used to build new leaves and roots as required (McLaughlin et al., 1980), and if low make trees more susceptible to death in a fluctuating environment. Storage also helps trees survive the effects of herbivory (Waring and Pitman, 1985). In Hybrid v3.0, if sufficient carbon is available following allocation to foliage and fine roots, the sapwood storage compartment of each tree is completely filled at the end of each year. This takes priority over any stem growth above the minimum (Eq. (25)). Stored carbon will then be available for allocation at the end of the next year. The maximum potential size of the storage compartment is assumed to be:

ca =fv,s, L Csw, (35) where fv.st is the fraction of live sapwood that can be used as storage, fv is the fraction of sapwood that is alive (see below), and Csw is sapwood carbon, fv.~t is estimated to be 0.67 for all tree GPTs (Table 4). Sapwood carbon is given by:

C~w = C i - Ch. (36)

Any carbon remaining following increments to the foliage, store, and fine roots (if the storage compartment can be filled completely) is added to the wood plus bark (and consequently inside-bark) compartment. This results in an increase in the sapwood area, making iteration then necessary to find the new value of D w.

Therefore, the priority for carbon allocation, once a minimum has been added to the wood plus bark, is first foliage and fine roots, second storage, and third sapwood plus bark. The wood increment (Cw.i, c) is found to an accuracy of 0.001% by iteration of Eqs. (26)-(35) (ca: Table 4).

Because the heartwood area remains constant during the search for the new value of D w, the sapwood area can only remain the same or increase. Consequently it may become apparent (following calculation of the minimum wood increment) that there is not enough carbon available to produce the minimum foliage and fine root requirements based on the current sapwood area. In this case, the heartwood area is increased to keep the foliage area/sapwood area ratio constant, with no allocation to the carbon store nor to the sapwood plus bark (above that given in Eq. (25)).

Once the new diameter at breast height (Dw), heartwood area (Zh), and stored carbon (C a) values have been found, the tree state variables are all re-calculated. The amount of living sapwood is a crucial factor in determining stem respiration (Eq. (10)) and is assumed to be:

Cv=f~-C~w. (37)

Deciduous trees tend to have higher fractions of living sapwood (parenchyma) than evergreen trees (Panshin et al., 1964), presumably because of the larger requirements in the spring for new foliage and fine root growth


(McLaughlin et al., 1980). Values of fv for each tree GPT were calculated from the data for a wide range of North American species presented by Panshin et al. (1964). The mean value for cold deciduous broadleaved trees is 0.170, and that for evergreen needleleaved trees is 0.0708 (Table 3).

Foliage area (Zf) is also calculated following carbon allocation:

ze = sla • c f . (38)

Total individual growth respiration (Fc.Rg) is given by:

Fc.R~ = (Cf.ioc + Cw.inc + C~,inc) "fR~/( 1 --fR,,,). (39)

From the foregoing it can be seen that Hybrid v3.0 explicitly represents the trade-offs associated with sapwood: its role as a water transport medium (Eq. (32)), its role as a storage compartment (Eq. (35)), and its contribution to maintenance respiration (Eq. (10)). The different values of fv and r h between different tree GPTs (Table 3) determine their relative strategic balances between stress tolerance and growth rate (cf. Grime, 1979).

4.13.2. Nitrogen allocation As mentioned, if the annual carbon balance of the lowest foliage layer of the individual, C b (Eq. (12)), is

below zero, a proportion of the sapwood is turned into heartwood (Eq. (19)). Heartwood is also formed if insufficient carbon is available to produce the foliage and fine roots that could have been supported by the sapwood area at the end of the year (see above). If there is an increase in heartwood area. the corresponding increase in heartwood carbon mass is calculated using Eqs. (28)-(30). It is assumed that, in the process of heartwood formation, an equal proportion of sapwood nitrogen is turned into heartwood nitrogen (Nh), and thus made unavailable for any subsequent re-translocation during the life of the tree:

dUn Up dt = Ch'inc " -~pp ' (40)

where Ch,in c is the increase in heartwood carbon mass and Np and Cp are the respective amounts of nitrogen and carbon in the sapwood plus bark.

It is now possible to calculate the amount of labile nitrogen within each tree available for allocation at the end of the year. It is assumed that, after litter production and any heartwood formation, all of the nitrogen in the plant, excluding that bound into heartwood, is available for allocation to the foliage, sapwood plus bark, and fine root compartments. The total amount of labile nitrogen available for allocation (N~,,) is therefore given by:

Nav=N~ +Nf+Np + N r - L N , (41)

where L N is the total amount of litter nitrogen (LN. w + Lx. r + LN. a + LNS; Eqs. (22)-(24)). Nitrogen allocation is calculated empirically to maintain fixed relative C:N ratios between the three

compartments. Thus the C:N ratio of any one tissue will vary as a function of nitrogen uptake and loss, but the relative ratios between tissues will not change. If the partitioning coefficients (i.e. fractions of total nitrogen allocated) to the foliage, sapwood plus bark, and fine roots are c, d, and e respectively, then it can be shown that:

c = 1/(1 -~-(XC:N(f/p)'Cp -{- XC:N(f/r).Cr)/ICf), (42)

and:

and:

d--- XC:N(f/p)" C. Cp/Cf, (43)

e =- Xc:N(f/r) " c. Cr/C f, (44)

274 A.D. Friend et al./Ecological Modelling 95 (1997) 249-287

where XC:N(e/p) and )(C:N(f/r) are the relative C:N ratios between the foliage and sapwood plus bark, and foliage and fine roots, respectively. The first ratio, ,)(C:N(f/p), was calculated to have a mean of 0.145 across 9 species, in data reported by Turner (1980) and Turner and Lambert (1981). This mean was calculated by including a 13% weighting for bark (sapwood and bark nitrogen contents were given separately from sapwood nitrogen). The second ratio, XC:N(f/r), was calculated from the data of Nambiar and Fife (1991) for Pinus radiata seedlings to be 0.86. These two means are used for all GPTs (Table 4).

The new tree nitrogen compartment sizes are then given by:

Nf=C'Nav, Np=d'Nav, Nr=e'Nav, (45)

and N a is set to zero. Foliage nitrogen (Nf) is further divided into three compartments: Rubisco-bound, chlorophyll-bound, and

'other' (Evans, 1989). This partitioning is important for calculating photosynthesis rates. For each mole of nitrogen bound in chlorophyll, 12.5 moles are bound in the thylakoid complex (Evans, 1989), thus:

fN,Rub -{- 12.5 "fN,chl -{-fN,o = l , (46)

where fN,Rub, fN,chl' and fN,o are the fractions of foliage nitrogen bound in Rubisco, chlorophyll, and 'other' compartments, respectively. This other fraction is required by foliage for structural, nuclear, and cytoplasmic material; the rest being available for the thylakoids and Calvin cycle enzymes. It appears logical that these last two compartments should be given priority if foliage nitrogen increases; consequently, the amount of nitrogen in the other fraction will remain constant if leaf structure does not change (Evans, 1989). Therefore, in Hybrid v3.0, it is assumed that f~.o falls as foliage nitrogen increases. Indeed, Evans (1989) reported that when foliage nitrogen in spinach increased from 1.05 g m -2 to 2.80 g m -2 (on a leaf area basis), fN,o fell from 0.595 to 0.470. This exact relationship is used in Hybrid v3.0 for the cold deciduous broadleaved tree and C3 grass GPTs.

It is observed that, on a projected foliage area basis, evergreen species often have higher foliage nitrogen contents, but lower maximum rates of photosynthesis, than deciduous species (Field and Mooney, 1986). A possible explanation for this is that, because the foliage of evergreen species must be displayed for more than one year, it makes evolutionary sense to invest relatively more resources, including nitrogen, in antiherbivory compounds (Gulmon and Mooney, 1986), and so less nitrogen is available for photosynthetic compounds such as Rubisco (Field and Mooney, 1986). This relationship between foliage longevity and fh,o is included in Hybrid v3.0.

A guide to the relative investment of foliage nitrogen in photosynthesis between cold deciduous broadleaved and evergreen needleleaved tree GPTs can be obtained from a comparison of their relative maximum rates of photosynthesis and specific leaf areas. K~Srner (1994) reported that the maximum rate of photosynthesis in boreal conifer trees is about 29% greater than that in temperate deciduous trees when expressed on a projected foliage area basis. If it is assumed: (i) that the foliage used for these measurements had the sla values given above; (ii) that these maximum rates of photosynthetic are determined by Rubisco and chlorophyll contents; and (iii) that both GPTs have the same foliage C:N ratios, then, to account for the difference in the observed maximum rates of photosynthesis between the two GPTs, it is necessary for the deciduous trees to have allocated 50% more foliage nitrogen to Rubisco and chlorophyll than the evergreen trees. This difference is included in Hybrid v3.0 by making the intercept' (a o) in the relation between fN.o and N (foliage nitrogen content expressed on a leaf area basis: Eq. (8)), a GPT-specific parameter:

fN,o=ao--71.aN, fN,o > 0.1. (47)

The slope of this relationship was derived from Evans (1989) as explained above. With a o set to 0.67 for the cold deciduous broadleaved GPT, and 0.83 for the evergreen needleleaved tree GPT, the difference in fN.o between the GPTs is consistent with the observed maximum rates of photosynthesis (Table 3). Comparison of the relative foliage nitrogen and photosynthesis measurements between non-evergreen and evergreen species,


reported by Field and Mooney (1986), yields similar values to those derived here. It is assumed that C3 grass has the same value of a o as cold deciduous broadleaved trees.

The ratio of fN.Rub to fN.chl (XRub/ch~) represents the relative investment in light harvesting and dark reaction machinery, and so can be considered as an adaptation to different levels of irradiance. Evans (1989) gives values of fY.Rub for a range of crop species, with a mean of approximately 0.21, and values of fY.ch, for a wider range of species, under conditions of both high and low irradiance, with a mean of 0.023. Thus, a reasonable value for XRub/chl is 0.21/0.023 ( = 9.13), and this value is used for all GPTs in Hybrid v3.0 (Table 4). In a future version of Hybrid, XRub/ch~ will be made a function of absorbed irradiance, as is observed (Evans, 1988) and predicted from an optimality argument (Friend, 1991).

4.14. Soil carbon and nitrogen dynamics

In Hybrid v3.0, as well as in nature, soil carbon and nitrogen dynamics largely determine the availability of mineral nitrogen to the plants, the rate of heterotrophic respiration by the ecosystem, and the amount of carbon stored in the soil.

4.14.1. Choice of sub-model We examined several approaches for simulating soil carbon and nitrogen dynamics in Hybrid v3.0, including

those described by Thornley and Verberne (1989), Raich et al. (1991), and a simplified version of the Century soil sub-model developed by ourselves. The full Century soil sub-model (Parton et al., 1987; Parton et al., 1993) was chosen for incorporation into Hybrid because only it gave reasonable predictions of both soil carbon storage, and nitrogen mineralisation rate, for a wide range of litter input rates and climate conditions, without requiring detailed parameterisation of microbial kinetics (as is required by the model of Thornley and Verberne, 1989) or different parameterisations for different vegetation types (as is required by the model of Raich et al., 1991). Simplifying Century by reducing the number of pools resulted in good predictions of nitrogen mineralisation, but low estimates of carbon storage.

4.14.2. Differences from Parton et al. 1993 The soil decomposition sub-model of Hybrid v3.0 is identical to the soil sub-model of Century (Parton et al.,

1993), except for: (i) in addition to foliage and fine root litter, a wood litter input is included (this is not divided into metabolic and structural fractions but enters the surface structural pool only: Comins and McMurtrie, 1993); (ii) foliage and fine root lignin fractions are fixed at 0.2 and 0.16 respectively (Comins and McMurtrie, 1993); (iii) surface and root metabolic litter pool N:C ratios are allowed to vary between the limits of 0.1 and 0.04 (Comins and McMurtrie, 1993); (iv) annual maximum decomposition rates are converted to daily rates; (v) the soil moisture decomposition rate modifier is a function of percentage water-filled pore space (Williams et al., 1992; see below); (vi) clay and sand fractions are site-independent and are both fixed at 0.3 (approximating a loam soil); and (vii) all mineralised nitrogen enters a single mineral nitrogen pool (no differentiation between ammonium and nitrate forms is made; nitrogen uptake, net mineralisation, and net deposition, and leaching are the processes which act on this pool, hence volatilisation, denitrification, and nitrification processes are not included).

The input of mineral nitrogen to the soil by deposition and fixation is assumed to occur at a pre-industrial ra te of 5.48 )< 10 - 7 kg N m -2 day- ~ (FN, d, Table 4; equivalent to 2 kg N ha-1 year- 1), and so this amount is added to the mineral nitrogen pool each day. In addition, leaching of the mineral nitrogen pool is treated; the relative amount is equivalent to the proportion of soil water lost as outflow.

4.14.3. General description of Century mechanics The soil sub-model of Century consists of eight dead organic matter pools. Each is characterised by specific

(constrained) N:C ratios and first order decay rates. This concept is consistent with the observation that soil


organic matter may be defined in terms of fractions differing in age and recalcitrance (Jenkinson and Rayner, 1977), and also with the exponential decay model of Jenny et al, (1949). The driving variables are soil temperature and moisture (which modify all the decay rates), the fractions of sand and clay (which modify microbial respiration), and the fraction of lignin in litter (which determines, with the litter N:C ratio, the separation of litter into metabolic and structural components). The general principles used in the Century model of soil decomposition are illustrated by Eqs. (48)-(52) below.

For two hypothetical organic matter pools, do (donor) and rv (receiver), where the decomposition products of do flow into rv, the change in the carbon mass of pool rv is given by:

dC~v dt = (1 --fd .... ) "kdo" Cdo-- krv'Crv, (48)

where C is the carbon mass of pool do or rv, J~o,~, is the fraction of carbon lost to microbial respiration between pools do and rv, and k is the decomposition rate of pool do or rv. The change in the nitrogen mass of pool rv is calculated using a prescribed N:C ratio of the receiver pool:

dt = Xnc,rv" (1 --fdo.rv) "kdo" Coo - krv "Nrv, (49)

where N~v is the nitrogen mass, and Xn¢.~ the prescribed N:C ratio of pool rv. This use of Xnc,rv acts to make the N:C ratio of pool rv approach this prescribed value; if insufficient nitrogen is available in the donor pool, then immobilisation is assumed to occur to match that required by the receiver pool.

From Eq. (48), it is can be seen that the rate of microbial respiration associated with the flux of carbon from pool do to pool rv (RH(do,rv)) is given by:

RH(do.~v) =fd . . . . "kdo "C do. (50)

The rate of nitrogen mineralisation associated with this carbon flux (Nm~,(do,~)) is the difference between the loss of nitrogen by the donor pool and the amount gained by the receiver pool:

Nmin~do.rv) = kdo "Ndo -- Xn .... " (1 --fdo.~) " kdo" Coo" (51)

The decomposition rate of each pool (k j) is affected by soil temperature and moisture content:

kj = ET- EM. kj,ma ~ , (52)

where j is either do or rv, ET is a decomposition temperature modifier (Comins and McMurtrie, 1993), EM is a decomposition soil moisture modifier, and kj.~a x is the maximum decomposition rate of the carbon pool do or rv. ET and EM are restricted to the range 0 to 1. EM is calculated from the percentage of soil pore space that is filled with water ('water-filled pore space': WFPS) using two equations fitted to Fig. 8 of Williams et al. (1992):

(0"000371" W F P S 2 ( (WFPS~ ~ - 60) 2-iI0748 - WFPS + 4.13, WFPS _> 60 (53)

EM = /exp~ WFPS < 60

WFPS is calculated from soil water content and soil water saturation capacity:

100- 0 s - - , (54) W F P S = f vc " swc

where 0 s is soil water content, fFc is the ratio between saturation capacity and field capacity, and swc is soil water field capacity. Soil water field capacity is assumed to be fixed at 0.5 m, a typical value taken from the Potent ial storage o f water in root zone database of Webb et al. (1991) (Table 4). The ratio between saturation


capacity and field capacity was calculated from the data presented by Raich et al. (1991) to be 1.72 for a loam soil, and this value is used here (Table 4).

4.15. Plot hydrology

Daily precipitation is classed as either rain or snow, depending on whether the minimum night-time temperature is above or below 0°C. Rain intercepted by the canopy is calculated as a linear function of (total plot) leaf area index as in the FOREST-BGC model (i.e. 0.0005 m LAI-~ day-~: Running and Coughlan, 1988); the same value is used for all GPTs. Maximum evaporation of intercepted rain is calculated using the Penman-Monteith equation (Monteith and Unsworth, 1990, Eq. (11.26a), p. 187), and any excess intercepted rain (throughfall) enters the soil. If cold enough, precipitation enters the snowpack. Snowmelt is calculated as in FOREST-BGC, and meltwater is added to soil water. One half of soil water above field capacity, following any inputs from rain, throughfall, and/or snowmelt, and losses due to evapotranspiration, is routed to outflow. This creates the possibility of the soil containing water above field capacity for short periods.

Bulk soil water potential on a given day is calculated from the amount of water remaining in the soil at the end of the previous day and soil water field capacity using the equation of Campbell (1985), with the same parameterisation as in Friend (1995). If the mean 24 h air temperature is below zero, soil water potential is set to - 1 . 5 MPa because the soil is assumed to be frozen. Bulk soil water potential is used to calculate stomatal conductance (see above). An additional effect of water potential on stomatal conductance is assumed to occur due to tree height (Friend, 1993). This effect is represented as a reduction in the effective soil water potential for stomatal conductance by 0.015 MPa for each 1 m of mean crown height (Friend, 1993), on an individual tree basis.

4.16. Output variables

Many variables are predicted by Hybrid v3.0. Those that are most significant for the carbon cycle and vegetation/atmosphere interactions are mean annual gross primary productivity (GPP), net primary productivity (NPP), heterotrophic ('soil ') respiration (RH), latent heat flux (AE), total biomass carbon (on 1 January: Cv), total soil carbon (on 1 January: Cs), and annual maximum leaf area index (LAD. These are all listed in Table 6. Also of interest is relative species, or GPT, dominance, GPP is defined as the annual sum of the individual daytime carbon foliage fluxes (Fc.f,d; Eq. (6)); NPP is defined as GPP minus the annual sum of the individual daily autotrophic respiration fluxes (i.e. Fc,f, n + Fc.w, d + F c . . . . + Fc,r) arid the annual growth respiration flux (Fc.R~; Eq. (39)).

5. Simulations

The simulations presented here were produced by Hybrid v3.0 with parameterisation as described in this paper. All the parameters have been set using estimates derived from literature sources, or, in the few cases where these are unavailable, best guesses. No re-parameterisation, or 'tuning', has been performed in order to make the model behave in a desired manner. The model was tested using climate for a site in south-western Pennsylvania, USA (41.25°N, 80.25°W). This location has a temperate climate, is moist in all seasons, and has a hot summer. Mean annual precipitation is 973 mm, mean July daily maximum temperature is 27.9°C, and mean January daily minimum temperature is -6.7°C. The natural vegetation of this region is winter deciduous oak-hickory forest (Kricher and Morrison, 1988).

The initial conditions for the simulations are given in Table 5, and the atmospheric CO 2 concentration (Cat m) and the rate of nitrogen deposition and fixation are given in Table 4. One year of weather was generated for this site by the daily weather generator (Friend, in press), and used to drive the model for each year of the


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Fig. 2. Simulation I performed by Hybrid v3.0 for a location in Pennsylvania, USA, using the same daily weather each year. The panels show annual means of l0 plots. (a) Gross and net primary productivity (kg C m-2 year- i); (b) leaf area index (m 2 m-2) ; (c) total biomass carbon (kg C m-Z); and (d) total soil carbon (kg C m-2) . See main text for a full description of the simulation.

simulation. Using the same daily weather each year simplifies interpretation of the output by reducing inter-annual variability. It was established that the simulated weather was typical for the site. Hybrid v3.0 was run for 500 years and the mean annual predictions across 10 plots are shown in Fig. 2.

The first significant feature to note is that the model is stable and predicts sensible values. The model contains many different feedbacks, and it is therefore significant that it neither results in the decay of the ecosystem to no stored carbon (due to negative feedbacks), nor to an overshooting of productivity and stored carbon. Indeed, the predictions are very close to what would be expected for this site. All of the trees at the end of the simulation are of the cold deciduous broadleaved tree GPT, although some evergreen needleleaved individuals grew during the first 250 years. Predicted productivity (Fig. 2a) and leaf area index (Fig. 2b) exhibit some initial oscillatory behaviour, followed by a gradual increase up to a quasi-equilibrium after about 250 years. Biomass carbon (Fig. 2c) behaves similarly. The initial fall in soil carbon (Fig. 2d) is due to low productivity when the trees are small (and so have low litter inputs to the soil). Following this fall, soil carbon then increases a little as productivity increases. Tree density reaches a maximum of 1145 trees ha-~ (22.9 trees plot- ~ ) after 27 years, and falls to 350 trees ha- ~ by the end of the simulation. There is no significant growth of grass because of the low levels of radiation penetrating the tree canopy. The low amplitude oscillation in productivity evident after 250 years is due to each of the 10 plots being dominated by 1 tree (with a diameter at breast height of about 0.63 m), which is in dynamic equilibrium with the climate and soil. Each year the stem grows or contracts as a result of feedbacks between photosynthesis and respiration.

The predictions of mean NPP and biomass carbon, during the last 100 years of the simulation, are given in Table 7 (simulation I). These values are well within the ranges measured for temperate deciduous forests (e.g., Art and Marks, 1978). The NPP estimate also closely matches the value predicted for this location's mean

A.D. Friend et al . / Ecological Modelling 95 (1997) 249-287 279

Table 7 Predictions of ecosystem properties, at a site in Pennsylvania, USA by Hybrid v3.0. Values are the means of l0 plots over the last 100 years of a 500 year simulation. Simulations: (I) same climate each year, no stochastic mortality; (II) different climate each year, 1/200 stochastic mortality; (1II) as II except 1/400 stochastic mortality. GPP: gross primary productivity (kg C m 2 year- ~); NPP: net primary productivity (kg C m -2 year- ~); RH: heterotrophic ( 'soil ') respiration (kg C m 2 year- ~); LAI: leaf area index (m 2 m-~) ; Cv: carbon in vegetation (kg C m-2) ; Cs: carbon in soil (kg C m-2) ; )rE: latent heat flux (MJ m -2 year ~)

Simulation GPP NPP R u LAI C~ C s 3- E

I 1.802 0.559 0.567 5.64 8.64 11.63 1387 II 1.141 0.378 0.410 3.06 6.28 9.77 841 III 1.783 0.544 0.577 5.05 10.94 11.70 1319

annual climate by the highly empirical 'Miami' model (Leith, 1978). NPP is predicted to be 31% of GPP, indicating that autotrophic respiration (not including photorespiration or daytime foliage dark respiration) is 69% of carbon fixed. Soil heterotrophic respiration is 1.43% higher than NPP, and consequently soil carbon content is falling slightly at the end of the simulation, as can be seen in Fig. 2d. The mean foliage nitrogen content over the last 100 years of the simulation is 1.9%, a typical value for temperate deciduous forests.

As mentioned, in simulation I the dominant tree in each plot reached an equilibrium size and did not die. To assess whether this was due to the lack of inter-annual climatic variability, the model was also run using different climate for each year (created for the same site by the weather generator), but a single tree still eventually dominated each plot and did not die (not shown). Of course, in nature trees do die, and it would thus appear that the climate produced by the weather generator is either not variable enough to produce extremes of

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Fig. 3. Simulation III performed by Hybrid v3.0 for a location in Pennsylvania, USA, using different climate each year and stochastic mortality. The panels show annual means of 10 plots. (a) Gross and net primary productivity (kg C m -2 year- 1); (b) leaf area index (m 2 m-2) ; (c) total biomass carbon (kg C m-2 ; and (d) total soil carbon (kg C m-2) . See main text for a full description of the simulation.


Table 8 Sensitivity indices for the dependence of the overall carbon status of the modelled ecosystem (a deciduous forest in North America) on each model input parameter and internal constant. Sensitivity index determined as described in text. Reference given where parameter and its usage defined elsewhere

Description of parameter(s) Symbol or default value Sensitivity index

Autumn daylength for leaf fall (Eq. (15)) tdcfso) Daylength (Eqs. (1), etc.) t d Rubisco oxygenation turnover number (Eq. (23) of Friend, 1995) k o Photorespiration comp. CO 2 conc. (Eqs. (3) and (4) of Friend, 1995) F, Constant for electron transport (Eq. (28) of Friend, 1995) 2. I Intercept in Rubisco calculation (Eq. (47)) a o Top leaf limit on N uptake see text Latitude (Eq. (15)) lat Relative foliage to root C:N (Eq. (44)) XC:N(f/r) Atmospheric CO 2 concentration Cat m M - M const, of Rubisco for O 2 (Eq. (3) of Friend, 1995) K o Fine root/foliage C ratio (Eq. (33)) "qr/e M - M const, of Rubisco for CO 2 (Eq. (3) of Friend, 1995) K c Rubisco/chlorophyll N ratio XRub/cm Height/dbh coefficient (Eq. (29)) a Growth respiration coefficient (Eqs. (17), etc.) fRg PAR extinction coefficient KpA R Rubisco carboxylation turnover no. (Eq. (22) of Friend, 1995) k c Maximum e - transport rate (Eq. (29) of Friend, 1995) Jmax Fine root turnover rate (Eq. (17)) fL.r Limit on top leaf N content see text Tree form factor (Eq. (28)) OF Mean wood plus bark density (Eq. (28)) Pw Maximum temperature for stomatal conductance 40°C Foliage turnover rate (Eqs. (20) and (21)) fL. f Relative C:N of foliage and sapwood plus bark (Eq. (43)) XC:N(f/p) Specific leaf area (Eqs. (32) and (38)) sla Fine root respiration rate (Eq. (11)) Fc. r Degree-day requirement for bud burst (Eq. (14)) dd req Constant in photosynthesis equation (Eq. (12) of Friend, 1995) 10.5/4.5 Maximum stomatal conductance/Rubisco N ratio r/g~x Temperature threshold for phenology Tth Stomatal conductance see text Soil decomposition rate of all soil pools (Eq. (52)) k Wood respiration coefficient (Eq. (10)) r/c. w Apparent sky temperature (Eq. (45) of Friend, 1995) T s SW extinction coefficient Ksw Fraction of sapwood alive (Eqs. (35) and (37)) fv Foliage/sapwood area ratio (Eq. (32)) "Of Bark thickness/dbh ratio (Eq. (31)) fb N uptake coefficient (Eq. (13)) "0u Thermal resistance to heat loss (Eq. (42) of Friend, 1995) rnR N deposition rate FN, d Lignin content of litter see text Night foliage respiration coefficient (Eq. (9)) rtc.f, n Atmospheric vapour pressure deficit vpd Water outflow fraction see text Leaf characteristic dimension see text Minimum stem increment (Eq. (25)) fw.m Foliage dark respiration coefficient (Eq. (7)) 0.015 Boundary layer resistance to CO 2 (Eq. (30) of Friend, 1995) re. a

5.122 2.407 0.940 0.928 0.902 0.894 0.877 0.826 0.665 0.584 0.576 0.548 0.522 0.516 0.503 0.487 0.483 0.462 0.440 0.435 0.383 0.373 0.372 0.361 0.345 0.337 0.325 0.316 0.298 0.297 0.281 0.270 0.251 0.221 0.219 0.195 0.189 0.179 0.174 0.172 0.137 0.136 0.124 0.123 0.111 0.108 0.108 0.106 0.099 0.097 0.091


Table 8 (continued)

Description of parameter(s) Symbol or default value Sensitivity index

Wood plus bark turnover rate (Eqs. (16) and (22)) fL.w 0.082 Maximum soil water potential (Eq. (36) of Friend, 1995) l~soil.max 0.081 Soil water filled pore space (Eqs. (53) and (54)) WFPS {).075 Height effect on stomatal conductance see text 0.073 PAR reflection coefficient (Eq. (5)) apA R 0.072 Ratio of soil water saturation to field capacities (Eq. (54)) Jvc 0.070 Plot area (Eq. (2)) Zp 0.062 Soil texture (clay and sand contents); effect on decomposition (Parton et al., 1993) - - 0.061 Soil water holding capacity (Eq. (54)) swc 13.057 Accuracy of pipe model solution (Eq. (27)) e a 0.053 Below ground wood plus bark fraction (Eq. (28)) fst 0.053 Day temperature calculation factor (Running, 1994) 0.212 0.052 SW reflection coefficient (Eq. (5)) asw 0.050 Molecular effect on diffusion (Eq. (6) of Friend, 1995) - - 0.050 Soil water drying curve parameter (Eq. (36) of Friend, 1995) bsoil 0,049 Leaf internal resistance (Eq. (30) of Friend, 1995) re. i 0.044 Canopy interception of precip. (Running and Coughlan, 1988) 0.0005 rn LAI- 1 day- ~ 0.044 Plant C:N for N uptake calculation see text 0.043 Snowmelt coefficient (Running and Coughlan, 1988) 0.0007 m°C - l day- 1 0,042 Exponent of height/dbh relationship (Eq. (29)) b 0,037 N:C ratios of soil pools (Eqs. (49) and (51)) Xnc.rv 0,032 Fraction of live sapwood available for storage (Eq. (35)) iv.st 0,030 Foliage N retranslocation fraction (Eq. (24)) )'i.f 0.029 Soil carbon leach rate (Parton et al., 1993) - - 0.027 Cuticular conductance see text 0.025

drought and temperature capable of killing established trees, a n d / o r the model is not treating the processes necessary for mortality, such as disease, herbivory, and windthrow. In order to assess the potential impact of non-autonomous mortality, a simulation was performed with different weather each year in which each tree was given an annual probabili ty of 1 / 2 0 0 of imposed death, using a random number generator. The results are shown in Table 7 (simulation II).

Imposing random mortali ty clearly has the effect of reducing productivity and LAI, with NPP reduced by 32% (Table 7). This seems a rather large reduction, and so a third simulation was performed as in simulation II but with the annual probabil i ty of mortality halved to 1 /400 , and the results are shown in Fig. 3 and Table 7 (simulation III). Compared with simulation I, NPP and LAI are hardly affected by the increased mortality. However, death of large trees occurred in most plots, resulting in a more realistic simulation than in simulation I. Fig. 3 shows that the simulation is still stable, but with greater inter-annual variability, due largely to climate, but partly also to tree death. The spikes in the soil carbon graph are due to large trees dying and entering the litter pools. Again, the system takes about 250 years to reach an equilibrium.

A simulation was also performed as in III, but with 50 plots (not shown). The mean values over the last 100 years of the simulation were very similar to those of simulation III, indicating that 10 plots are sufficient. The mean rate of simulation III was 0.176 s plot-1 year-~ on a Silicon Graphics R4000 workstation.

6. A sensi t iv i ty ana lys i s

A sensitivity analysis was performed on Hybrid v3.0 using the same conditions as in simulation III in the last section. The sensitivity of model output to changes in all input parameters, and all internal constants, was


measured. Model output for the purposes of this analysis was taken to be those five parameters considered to be the most important for the overall carbon status of the ecosystem, namely GPP, NPP, LM, C v, and C s. The default values of these parameters are given in the last row of Table 7. A sensitivity index was determined for each output parameter as described by Friend et al. (1993). Each input parameter and internal constant was altered in turn by increasing its value by 10%. The resulting sensitivity index for each parameter was then taken as the mean of the absolute values of the sensitivity indices for each output parameter. The results are presented in Table 8. A sensitivity index of 1 indicates that the five output parameters changed by an average of 10% for a 10% change in the tested input parameter or model constant. A higher value indicates a more than linear effect, and a value of below 1 indicates a less than linear effect.

The most important parameter in the model, the autumn daylength for leaf fall, has a very high sensitivity index (5.122). Increasing its value by 10% reduces the length of the growing season by 28 days. Daylength itself also has a high sensitivity index, mainly reflecting the importance of the balance of the photosynthetic and respiratory processes described in Eq. (11). The next few parameters in the table reflect the dominance of the rate of photosynthesis in determining the amount of carbon in the system. The nitrogen uptake coefficient (r/u) has a much lower sensitivity index, reflecting the fact that nitrogen mineralisation is fast enough in this relatively warm climate to keep pace with the supply of carbon through photosynthesis. Latitude is important because it affects both daylength and phenology (Eq. (15)). As might be expected, the ratios of carbon and nitrogen between the foliage and fine roots are also important parameters.

Many parameters are clearly not very important for the overall carbon balance of this modelled ecosystem. These will be examined to assess whether model simplifications are possible. However, the results of this sensitivity analysis must be viewed in the context of the particular climate used, and the output considered. For example, the low sensitivity values obtained for the hydrological parameters indicate the lack of any serious water stress at this location; this will clearly not be the case for many other climates. In addition, it is important to consider the confidence with which the different parameters in Table 8 are known in assessing the significance of their sensitivity indices. For example, the rate of fine root turnover may appear to be less important than the Rubisco oxygenation turnover number, but it is far more uncertain (Hendrick and Pregitzer, 1993).

7. Discussion

The model described here, Hybrid v3.0, meets the three requirements given in the Introduction for a model that is capable of being tested, using the current climate, and then developed to predict with some confidence the interactive processes between vegetation and the atmosphere in past and future climates. These requirements are: (i) full coupling of the carbon, nutrient, and water cycles in the soil-plant-atmosphere system; (ii) that the external constraints on model behaviour be only climate, and that internal parameterisation be kept constant in space and time; and (iii) that the model represents the growth and development of vegetation over time and so can predict transient responses to climate. In one or more of these respects, Hybrid v3.0 differs from all of the other models that have so far been published to examine the effects of vegetation on the global climate and vice versa (e.g., Dickinson et al., 1991; Prentice et al., 1992; Sellers et al., 1996; Woodward et al., 1995).

The next step traditionally is to 'validate' the model, but we would caution here against the normal method of fitting the output of a process-based model to observations. This may be appropriate for a model based entirely on statistically-fitted data, which can then be evaluated against independent data. It would, however, be a meaningless 'validation' of the ability of our model to simulate vegetation from climate simply to adjust various sets of the numerous parameter values to give good fits to global measurements of net primary productivity, leaf area index, evapotranspiration, or any component variable or process. We recall the words of De Wit (1970), who stated that fitting a mechanistic model to data "is a disastrous way of working . . . since there are many parameters and many equations involved this is not difficult . . . the technique reduces into the most cumbersome and subjective technique of curve fitting that can be imagined".


A much more useful and critical procedure is to 'test' and improve the ability of the model to meet our performance criteria. And here our approach has distinct advantages. Because Hybrid v3.0 has only climate as its variable input, it is capable of being rigorously tested by comparing its predictions with present-day conditions. In other words, it can be tested by showing that it is capable of predicting current conditions without altering the internal parameterisation. Significant tests of the model will include prediction of present day (i) fluxes of carbon and water measured at different locations, (ii) geographic distributions of vegetation types on global and regional scales, and (iii) amounts of carbon in different locations. A model that is capable of predicting these present day conditions across a range of climates, with climate as the only input variable, is a model that can be used with some confidence to predict the impacts of future global change. It is our contention that this philosophy and approach will lead to the greatest understanding of biospheric processes as well as to models with the most reliable predictive capability within GCMs and models of the total earth system.

As part of this testing procedure we are currently exploring the ability of Hybrid v3.0 to predict potential vegetation globally at a 0.5 degree resolution, using our daily weather generator (Friend, in press). Simulations for a single location have been included in this paper to allow the model's behaviour to be assessed, with favourable results. We will also be concentrating on predictions along a well-defined transect in North America and at test sites with known natural vegetation that are in partial-equilibrium with climate. The model processes and their parameterisations will be manipulated to determine their impact on model predictions at the test sites. The aim is to identify which processes need to be represented (and at which level of detail), and which parameterisations are required, to be able to predict total carbon, annual net primary productivity, and vegetation types at different sites from climate alone. The results of these tests will be reported separately. In addition, Hybrid v3.0 is being used in an integrated modelling project where forest growth, soil process, thermal, and radiation models are being linked and tested against observations across a range of scales (Levine et al., 1993).

From the foregoing, it is clear that we do not regard the formulations given in this paper as necessarily fixed. We are aware, for instance, of altemative formulations of phenological processes (e.g., H~inninen, 1991), the relationship between foliage area and sapwood area, based on the pipe-model theory (Rennolls, 1994; Mencuccini and Grace, 1995), and the control of stomatal conductance (Dewar, 1995; Friend, 1995; Leuning, 1995; Lloyd et al., 1997; Monteith, 1995) and partitioning (Cannell and Dewar, 1994). We expect that, as a result of our tests of the model, and of new ideas emerging from other modelling and experimental projects, we will be able to make progressive improvements in future versions of Hybrid, gaining increasing confidence in its predictive capability. Nevertheless, the model is complete as v3.0, and constitutes a novel and dynamic tool for the study atmosphere-biosphere interactions.

Acknowledgements

We acknowledge the financial support provided by the NERC TIGER (Terrestrial Initiative in Global Environmental Research) programme (award number GST 91/15: Modelling Carbon Dioxide Exchange at Regional Scales), the EC Environment Research Programme (contracts EV57-CT92-0127 and EV5V-CT94- 0468), and NASA through the FED project (Forest Ecosystem Dynamics, Office of Emission to Planet Earth). We also wish to thank Steve Running, Hank Shugart, and Tom Smith for providing the original idea and impetus for this model, and John Monteith, Roddy Dewar, and John Thornley for many helpful discussions during its development. Deena Mobbs and John Thornley and an anonymous reviewer provided useful comments on an earlier manuscript.

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