WIMOVAC Leaf Gas Exchange Module

Introduction

There is a strong basis for expecting an interactive effect of rising atmospheric CO₂ (C_a) and concomitant temperature changes on the assimilation of C by photosynthesis into ecosystems. A wide range of C₃ and C₄ vegetation has now been examined and most types show a significant alteration in photosynthetic behavior and dry matter production in response to increased C_a. For many C₃ crops and wild species, a pronounced increase in photosynthesis and consequent dry matter production has been observed, at least in the short term {Cure, 1985 #871;Drake, 1991 #1753;Lawlor, 1991 #1234;Lawlor, 1991 #1234}. For individual C₄ species the magnitude and direction of the effects of increased C_a and temperature are less certain but not less significant. Experimental results suggest that for some C₄ species there will be a net increase in C assimilation due to the effect of increased temperature and C_a whilst for others there may be a net decline due to increased respiratory load associated with higher temperature.

Despite this evidence some of the most commonly used models have either ignored the direct effects of C_a or have considered these as an independent effect. The approach proposed by Esser {1987, 1991}{Esser, 1987 #1245; Esser, 1991 #1755}, for example, underlies the Biosphere model and has been used to access future potential changes in global primary productivity and spatial pattern, and yet ignores the direct implications of rising C_a and interactions with temperature. Similarly the vegetation component of the Century model proposed by Parton (1993){Parton, 1993 #1957} has been used to predict the likelihood of ecosystem feedback’s on rising atmospheric C_a on the water use efficiency of vegetation and yet this model only considers the effect of rising C_a on water use efficiency and not its direct effects on photosynthesis. Further the models of Parry (1988,1990){Parry, 1988 #1243; Parry, 1990 #1244} used to predict regional patterns of change in crop production for the UNEP World Climate Impact Studies Program make no allowance for any direct effect of rising C_a.

A number of authors justify the absence of model sensitivity to C_a effects in the photosynthesis component of their models by stating that the stimulatory effects of C_a on carbon uptake are only transient and the effect attenuated by other limiting factors such as water, nutrients and light in the longer term.

A number of controlled environment studies have shown, however, that the initial stimulation of photosynthesis of plants grown at current C_a and transferred to doubled C_a declines with time but nevertheless the end result is almost invariably increased plant biomass and litter {Long, 1991 #1725}. A number of field studies have examined the long term effects of continual stimulation of elevated C_a on natural vegetation. In a tundra environment a doubling of current ambient C_a produced only a transient initial stimulation of community CO₂ uptake in a 3 year study {Oechel, 1985 #557}. In a warm, temperate wetland, a doubling of C_a has produced an approximate doubling of canopy photosynthesis and biomass {Curtis, 1989 #925; Drake, 1991 #1754}.

The ability to predict net carbon exchange and production of vegetation in response to increases in C_a and temperature is therefore critical to assessing the potential impacts of these changes and because this requires prediction beyond experience mechanistic rather than empirical models are needed. An outline of the mechanistically rich approach adopted by wimovac is given in the form a relational diagram in Figure 1

Basis of leaf model

As the primary control interface between the site of photosynthesis (leaf mesophyll cells) and the atmosphere, the stomata play a vital role in determining the character of vegetation response to climate change and any reasonable model predictions of these responses should therefore include stomatal behavior {Dewar, 1995 #1960;Thorpe, 1984 #764; Ball, 1987 #1930;Leuning, 1990 #1844;Leuning, 1995 #1961}. A significant potential weakness in many existing vegetation models is the limited incorporation of such stomatal responses to increased C_a and temperature. Many existing models exhibit either no stomatal response at all or use a broadly empirical approach {Farquhar, 1984 #1776}. Empirical models typically incorporate a modifying function at the canopy level to vary potential transpiration calculations in a fairly artificial manner to give modified vegetation water use characteristics. Such approaches typically do not account for the concomitant effects of stomatal conductance changes on CO₂ gas exchange at the leaf level. Although a truly mechanistic understanding of stomatal behavior currently eludes us the Ball and Berry model provides a robust phenomenological approach which has proved workable in a broad range of vegetation types {Ball, 1984 #868;Ball, 1987 #1277; Collatz, 1992 #1805;Harley, 1992 #1836;Leuning, 1995 #1961}.

At the centre of wimovac is the gas exchange module consisting of the Farquhar and von Cammerer (1980){Farquhar, 1980 #1922} and Collatz models (1992){Collatz, 1992 #1805} for C₃ and C₄ photosynthesis respectively. Tightly coupled with this are C₃ and C₄ versions of the Ball and Berry (1987){Ball, 1987 #1840} model of stomatal conductance. Incorporation of stomatal response characteristics at the leaf level provides many advantages: i). realistic estimates of leaf conductance for use in leaf energy budget calculations give a physically correct leaf temperature, ii). calculated stomatal conductance can be converted to stomatal resistance and used to calculate actual evapo/transpiration rather than potential evapo/transpiration which falsely assumes a zero resistance. iii). improved estimates of leaf temperature should give a better understanding of potential climate change temperature effects on leaf photosynthetic rates. iv). Improved predictions of evapo/transpiration should improve estimates of vegetation water use efficiency with ‘downstream’ improvements in estimates of water availability and potential impacts on long term C uptake and source-sink relationships.

Cheeseman (1991) and others have suggested that the incorporation of stomatal patchiness, both in the physical distribution and number of stomata and in their relative conductance’s, may be an important component of successfully modelling leaf stomatal conductance. Wimovac includes the statistical approach to leaf stomatal conductance suggested by Cheeseman (1991){Cheeseman, 1991 #1285} but the extra complexity and difficulty with parameterisation it represents prohibits its general use in the already complex models described in this work.

Photosynthesis

The mechanistic model of C₃ leaf photosynthesis developed by Farquhar & von Caemmerer (1980, 1982) has been widely used and validated {Long, 1985 #1155;Long, 1991 #1200;Harley, 1992 #1229} and consists of a model of the regulation of ribulose-1,5-bisphosphate carboxylase and electron transport. The key assumption behind the model is that non limiting processes of photosynthesis are regulated to balance the capacity of limiting processes. At steady state photosynthetic biochemistry is assumed to be regulated so that rubisco consumes RuBP at a rate equal to that at which RuBP is regenerated. According to Farquhar & von Caemmerer (1980) the rate of RuBP use (R) equals the carboxylation rate (V_c) plus the rate of oxygenation (V_o).

When limited by rubisco, R can be described as

where W_c is the rubisco limited rate of carboxylation. When assimilation is limited by the thylakoid reactions the rate of RuBP regeneration is assumed to reflect the electron transport rate and the RuBP rate equals.

The equations originally derived by Farquhar & von Caemmerer (1980) and given in Long and Drake (1991) have been modified in wimovac (Equation 29) to also include a potential phosphate limitation (W_p) arising from the failure of triose phosphate utilisation (starch and sucrose production) to keep up with triose phosphate production in the Calvin cycle {Sharkey, 1985 #1914}. From Farquhar & von Caemmerer (1980) the rubisco limited rate of carboxylation (W_c) is given by Equation 27, where V_cmax is the potential maximum velocity of fully activated rubisco that is inhibitor free, O_i is the oxygen concentration in the stroma, K_c is the Michaelis constant for rubisco for CO₂ and K_o is the Michaelis constant for rubisco for oxygen. J is the potential rate of electron transport under a given set of conditions and is used by Farquhar & von Caemmerer (1980) to calculate W_j as shown in Equation 28.

The direct effects of temperature on the kinetic properties of carboxylation and RubP regeneration use the equations of Farquhar & von Caemmerer. (1980), but are modified here to take account of changes in the solubility and Rubisco affinity, for CO₂ and O₂ {Long, 1991 #1200}. Solubility’s for O₂ and CO₂ were recalculated (Equation 23, Equation 24) relative to their values at 25° C using polynomial relationships fitted to tabular values of solubility at different temperatures {Linke, 1965 #1906;Kaye, 1973 #1916;Jordan, 1984 #373Harley, 1992 #1836}. Jordan and Ogren (1984) provided data on the response of the kinetic constants of Rubisco to temperature and activation energies have been determined from these plots (Long, 1991), and are used here in preference to those proposed by Farquhar & von Caemmerer (1980) in Equation 17. The quantum yield (f ) of CO₂ uptake is estimated in the model as the predicted initial slope of assimilation (A) versus I_abs (Equation 32). The light compensation point is also derived from this slope (Equation 33).

The principles developed by Farquhar & von Caemmerer (1980) have been incorporated into a further model of one of the two known variants of C₃ photosynthesis, so called C₄ photosynthesis by Collatz et al. (1992). This model is also included in wimovac, and users may specify with a single switch whether their simulation is for C₃ or C₄ vegetation. Collatz et al. (1992) in their model derive a simple biochemical intercellular transport model that includes inorganic carbon fixation by PEP carboxylase, light dependent generation of PEP and RuBP, rubisco reaction kinetics, and the diffusion of inorganic carbon and oxygen between the bindle sheath and mesophyll. The underlying assumption of the model is that once again these processes can be described simply as three potentially limiting steps. i). At rate limiting light intensities the efficiency of CO₂ fixation with respect to light (quantum yield, f ) is assumed to determine the rate of photosynthesis. ii). At low CO₂ concentrations photosynthesis is assumed to be limited by the initial rate of fixation of CO₂ by PEP less the leakage rate back across the bundle sheath cells. iii). When light and CO₂ are not directly limiting, the rate of assimilation is assumed to be limited by the capacity for CO₂ fixation by rubisco within the bundle sheath cells. The high CO₂ concentration in the bundle sheath chloroplasts under these conditions is close to saturating for rubisco and consequently the predicted rate approaches V_cmax. Equation 34 to Equation 38 represent an analytical solution to the coupled C₄ photosynthesis-stomatal conductance model in which these three potentially rate limiting conditions are expressed as a quadratic which may be solved to give leaf a predicted assimilation rate in terms of variables C_i, O_i and I_abs.

The C₃ and C₄ biochemical sub-models form the core of the photosynthesis module in wimovac (Figure 2, Figure 20) and allow prediction of leaf photosynthetic rates of CO₂ uptake and the significance of changes in climatic and atmospheric variables via their effects at the level of carboxylation and oxygenation of RubP, and regeneration of RubP, or in the case of the C₄ sub-model carboxylation and regeneration of PEP.

Leaf photosynthetic responses. i) C3 light response curve for a range of CO2 concentrations, 25°C. ii) C3 A/Ci response curve for a range of temperatures, Ileaf=1500µmol m-2 s-1. iii) C3 temperature response curves for a range of light intensities, Ca=350µmol mol-1 iv). C3 and C4 light response characteristics at 25 °C, Ca=350mmol m-2 s-1 . Parameters and values as specified in appendices I & II.

The leaf biochemical models use C_i (intercellular CO₂ concentration) rather than C_a (atmospheric CO₂ concentration) as a driving variable since C_i approximates to the concentration of CO₂ at the site of reaction. C_i is determined within the leaf from the interaction between assimilation of CO₂ and stomatal conductance to CO₂. To be useful in predicting leaf response to varying environmental conditions, therefore, the biochemical model of CO₂ assimilation must be integrated with a model of stomatal behaviour.

Equations from {Long, 1991 #1393;Farquhar, 1980 #1756;Farquhar, 1982 #1231;Linke, 1965 #1906;Kaye, 1973 #1916;Jordan, 1984 #373Harley, 1992 #1836}. Parameters and values for 25° C unless stated otherwise in appendices I & II were E is 65800 (K_c), 1400 (K_o), 66405 (R_d), 68000 (V_cmax). J_max,210 m mol m^-2 s^-1, K_c, 460 m mol mol^-1, Ko, 330 mmol mol^-1, O_a, 210 mmol mol^-1, R_d,0.21 m mol m^-2 s^-1, V_cmax, 98 m mol m^-2 s^-1, V_omax, 0.21V_cmax.

Equations from {Collatz, 1992 #1805}.{Collatz, 1992 #1805}. Parameters and values as specified in appendices I & II.

Stomatal conductance

A mechanistic understanding of the control processes involved in regulating stomatal conductance remains incomplete. However Ball et al. (1987) developed a phenomenological expression for the regulation of stomatal conductance which has proved very robust. The expression used here is that of Harley et al. (1992) who modified the Ball et al. (1987) expression to provide a more practical version requiring C_a and relative humidity in the air outside the boundary layer, rather than the values within the boundary layer which cannot easily be estimated or measured (Equation 42). Because assimilation of CO₂ and stomatal conductance are inter-dependent, the value of C_i and assimilation rate have been solved numerically in the C₃ model by iteration (Figure 23).

Schematic of Newton/Raphson iterative stomatal conductance calculation.

The Collatz, et al. (1992) C₄ model couples a modified version of the Ball et al. (1987) stomatal conductance calculations directly with the photosynthesis model to give an analytical solution which does not require iteration.

It has been known for some time that stomatal conductance in many plants is also sensitive to the water status of the plant and a number of researchers have proposed a direct relationship between leaf water potential and stomatal conductance {Campbell, 1991 #1958;Jarvis, 1980 #1898}. The water stress model (Equation 43, Equation 0.41) assumes a simple linear relationship between reduction in the stomatal conductance g₁ parameter and decreasing leaf water potential below a threshold value. The gradient of the linear relationship corresponds to the species sensitivity to water stress - a larger gradient gives a more pronounced effect on stomatal closure for a given reduction in leaf water potential.

C₃ and C₄ stomatal responses. i) Light response curve. ii) CO₂ response curve, I_leaf=1500µmol m^-2 s^-1 .

Equations from {Ball, 1987 #1840}. Where g₀ = 81.1, g₁=9.58

Transpiration & energy budget

In order to investigate the effects of elevated C_a and concomitant temperature changes on possible canopy water usage, an expression has been introduced into the wimovac canopy models for the instantaneous transpiration of water vapour from the canopy. Wimovac uses the approach of Penman (1948) and Monteith (1965 and 1973) as expressed in Equation 58 to calculate the instantaneous transpiration from each leaf class within the canopy and sums the leaf classes to give total canopy water loss (Equation 59). The Penman-Monteith expression has been combined here with a boundary layer conductance model expressed as g_a (Equation 49 or Equation 49 may be specified) which describes the transfer of water vapour from the evaporating leaf surface to the bulk air stream in terms of the aerodynamics of the turbulent air above the canopy {Campbell, 1977 #1238;Thornley, 1990 #1283}. The turbulent properties of the air are assumed to be determined by the wind speed (u_a), sink momentum (d) and the roughness of the canopy, usually expressed as empirical roughness coefficients V and V _m.

Transpiration. i). Predicted response of canopy transpiration (E_c) to incident solar radiation (I) for the three transpiration model options. ii). Predicted response of E_c to stomatal conductance (g_s) indicating the difference between potential and actual transpiration. iii). Predicted effect of g_s on leaf temperature (T_leaf). iv). Diurnal pattern of E_c for J_day=190, W =52° , F_canopy=3 for which 4 initial soil water potentials are assumed ranging from well watered (0 kPa) to severely stressed (-1500 kPa). Unless otherwise specified I=1500 m mol m^-2 s^-1, T_air=25 ° C, h_s=0.7, g_s=200 mmol ^m-2 s^-1.

J_a (Equation 45) represents the total solar radiation absorbed by a given canopy leaf class. L_b represents the leaf boundary layer conductance which changes as an empirical function of leaf width and wind speed (U_a), D p_va is the vapour pressure deficit based upon relative humidity values from the macroclimate module and g is the psychrometric parameter derived from the density of dry air (r ), the specific heat capacity of air (c_p) and the latent heat of vaporisation (l ). R_lc is the net long wave radiation assumed to be emitted by the canopy and F _n is the net radiation balance of the canopy.

Equations from {Penman, 1948 #1938; Monteith, 1991 #1810}. = 0.4, d = 0.77h, = 0.026h, m = 0.13h.

Leaf physiological processes such as photosynthesis and leaf expansion are generally strongly temperature dependent. Therefore it is important to be able to estimate the temperature of the canopy in terms of the current environmental conditions. One of the principle features of the Penman-Monteith formulation (Equation 58) is that it describes transpiration independently of the temperature of the canopy. This is achieved in the analysis by using an approximation scheme relating air and canopy temperature. It is equally possible to eliminate transpiration from the equations to derive an expression for the difference between the canopy and air temperature. A derivation of the Penman-Monteith equation in which transpiration has been eliminated, is used in wimovac to calculate the temperature of individual canopy leaf classes using this energy budget approach (Equation 56). The first term in the equation represents the influence of radiation on the temperature difference between the canopy and the air and the second term the diffusion influence.

Default parameter settings for both the transpiration and leaf temperature modules were as for Campbell (1977). The expression relating apparent sink momentum to canopy height, given by Campbell (1977), however was corrected here and has the form, d=0.77h where d is the apparent sink momentum and h is the canopy height in metres. Leaf transpiration, temperature and stomatal conductance are not independent quantities, and so an iterative procedure is used here to establish their respective equilibrium values.

Nitrogen effects

The effects of leaf nitrogen content on C₃ plants are mediated, in wimovac, through the three potentially rate limiting processes central to the Farquhar & von Caemmerer (1980) model and a simple model of leaf dark respiration. The underlying assumption of this approach is that leaf nitrogen is predominantly tied up with protein in the leaf and that this protein exerts a major controlling influence upon photosynthesis via rubisco, which may make upto 40% of the soluble protein content of the leaf, and the proteins involved in electron transport. The model assumes a linear relationship between leaf nitrogen concentration and the maximum rate of carboxylation (V_cmax), light saturated rate of electron transport (J_max) and the rate of triose phosphate utilisation (TPU). Field (1983) in Equation 61 to Equation 63, and Harley et al. (1992) in Equation 64 to Equation 66, both provide suitable coefficients for parameterisation of the model and although the exact formulation of their models differs slightly the predicted response of assimilation to nitrogen concentration{Field, 1983 #1281;Harley, 1992 #1836} is closely comparable.

[ Home ] [ Up ]

Send mail to humph@essex.ac.uk with questions or comments about this web site.
Copyright © 1998 WIMOVAC Ltd.
Last modified: August 19, 1997