Although the response of stomata to environmental and physiological factors is complex, we know that stomatal conductance varies with leaf irradiance, leaf temperature, atmospheric water vapour pressure deficit and CO2 concentration (Cowan 1977; Buckley & Mott 2002). We know additionally that stomatal conductance depends on guard cell and epidermal turgor (Wu, Sharpe & Spence 1985; Mencuccini, Mambelli & Comstock 2000; Franks et al. 2001), and that regulation of turgor in these cells requires metabolic energy (Farquhar & Wong 1984; Assman 1999; Blatt 2000; Netting 2000). Leaf turgor also depends on the balance between loss of water through transpiration and supply of water to the leaf from the soil (Cowan 1977; Mott & Parkhurst 1991; Maier-Maercker 1999; Mott & Franks 2001). A major challenge is to develop a model which accounts for all the factors which control stomatal conductance.
There are presently few, if any, models which combine our mechanistic understanding of stomatal function at the cellular level with descriptions of the coupled fluxes water and CO2 in the soil–plant–atmosphere continuum (SPAC). Instead, the dependencies of stomatal conductance on environmental and physiological factors are included in semi-empirical models, such as the response-function approach of Jarvis (1976), which relates stomatal conductance to leaf temperature, irradiance and leaf and soil water potentials. More recently, Ball, Woodrow & Berry (1987) and Leuning (1990, 1995) developed relationships between stomatal conductance, CO2 assimilation rate and air humidity which summarized successfully the results of many observations of the stomatal behaviour of well-watered plants. Such models have concentrated on leaf-level process, but to account for the various environmental and physiological controls of stomatal conductance, models of photosynthesis, respiration, leaf energy balances and the transport of water from soil to leaves should be fully integrated with stomatal models.
This continuum approach has been adopted by many workers, but there are marked differences in the way stomatal control of water and CO2 fluxes have been modelled. Some emphasize plant physiology (e.g. Leuning et al. 1995) whereas others provide a greater balance between soil, plant and atmospheric processes affecting carbon and water fluxes (e.g. Sellers et al. 1992; McMurtrie et al. 1992; Jensen et al. 1993; Tardieu & Davies 1993; Williams et al. 1996; Baldocchi & Meyers 1998; Whitehead et al. 2002; Dewar 2002). Many such models are satisfactory when soil moisture is adequate, but some do not predict correctly the patterns in conductance, transpiration and CO2 assimilation when soil moisture availability becomes limiting (e.g. Calvet et al. 1998; Grant et al. 1999). Measured fluxes show a marked daytime asymmetry at low soil moisture contents, with higher fluxes of water and CO2 in the morning than the afternoon (Schulze & Hall 1982; Olioso, Carlson & Brisson 1996; Prior, Eamus & Duff 1997; Grant et al. 1999; Eamus, Hutley & O’Grady 2001). Whereas some models are able to capture the observed asymmetry (Tardieu & Davies 1993), those of others are not (Leuning et al. 1995; Leuning, Dunin & Wang 1998; Grant et al. 1999; Ronda, de Bruin & Holtslag 2001), and we suggest this may result from inadequate coupling of stomatal conductance to the dynamics of water transport from soil to the roots and leaves. Many SPAC models which do incorporate the effects of soil moisture on stomatal conductance use an electrical resistance analog for the transport of water from the soil to the roots (Tardieu & Davies 1993; Amthor 1994; Olioso et al. 1996; Williams et al. 1996; Baldocchi & Meyers 1998). Hydraulic resistance to water flow in the soil varies strongly with soil moisture. Cowan (1965) showed that water content, and hence hydraulic resistance, varies significantly with distance from the root surface to the bulk soil once soil water supply starts to limit transpiration. Thus use of mean soil moisture content, rather than the value near to the roots, may lead to incorrect values for the resistance to water flow in the soil. The spatial distribution in moisture content also changes through the day and hence the dynamics of water flow to the roots will not be captured when mean soil moisture content is used to calculate soil hydraulic resistance (Perrier & Tuzet 1998). To overcome this problem, the model presented in this paper solves Richards’ equation for water flow from the soil to roots numerically (Philip 1957; Gardner 1960), rather than using hydraulic resistances.
Water potentials within the leaf are linked to potentials at the soil–root interface by the flux of water across hydraulic resistances in the plant. We assume that leaf water potential controls stomatal conductance (Buckley & Mott 2002; Leuning, Tuzet & Perrier 2003), an assumption that accounts for the effects of supply and demand for water at the evaporating sites on guard cell and epidermal turgor. This removes the explicit dependence of stomatal conductance on atmospheric humidity used by Ball et al. (1987) and by Leuning (1990, 1995), since their models account only for water losses from the leaves by transpiration.
Supply and demand for CO2 by photosynthesis and respiration also affects stomatal conductance through variations in intercellular CO2 concentration (Mott 1988; Assmann 1999). These considerations, along with the above arguments concerning leaf water potentials, have led in this paper to a revision of the stomatal model of Leuning (1995). While retaining the explicit dependence of conductance on CO2 assimilation (and hence on absorbed light and temperature), the original humidity deficit term is replaced by a function of leaf water potential, and CO2 concentration at the leaf surface is replaced by intercellular CO2 concentration. This approach ensures a complete coupling between stomatal conductance, the flux of water through the plant and soil, and CO2 exchange between leaves and the atmosphere.
In the following two sections we briefly describe the new stomatal model and the equations for uptake of water by roots and transport of water through the plants. Appendix A contains details of the rest of the model which describes exchanges of radiant energy, sensible heat, water vapour and CO2 between the soil, plant and the atmosphere. After presenting the initial and boundary conditions, the full model is used to predict diurnal patterns of leaf water potential, water absorption by roots, and canopy transpiration during a drying cycle for soils with varying hydraulic characteristics. Sensitivity of the model to variations in key controlling parameters is investigated, followed by an examination of the relationships between stomatal conductance, CO2 assimilation, transpiration, intercellular CO2 concentrations and atmospheric humidity deficit.