**3.6.1 Stomatal resistance**

Empirically established stomatal resistance, which is the most important factor determining transpiration from high vegetation especially forests, has marked variation within the canopy as well as over the day and the season. Stomatal resistance (*R*t) depends both on soil and atmospheric factors. These factors are short-term changes in leaf water potential, vapour pressure deficit, solar flux, leaf temperature, ambient carbon dioxide concentration and significant drying of the soil (very negative soil water potential). Therefore, there is clearly a need to describe the response of *R*t to atmospheric factors as well as soil water status. Estimation of stomatal resistance has generally involved two approaches;


Baldocchi *et al*. (1991) presented an excellent overview of the strengths and weaknesses of different approaches for estimating canopy stomatal resistance. As discussed in their paper, the above mentioned approaches may not yield the same results. The former is primarily a physiological parameter whereas the latter involves additional eco-physiological factors within the canopy. The latter also includes the contribution of soil evaporation. Baldocchi *et al.* (1991) developed a multi-layer canopy stomatal conductance model in which the spatial variation of canopy structure and the radiative transfer within the canopy were taken into account.

Jarvis (1976) has modelled the stomatal resistance as a function of solar radiation, temperature, specific humidity deficit, leaf water potential, and ambient CO2, using a nonlinear least squares technique. Based on the Jarvis work, Stewart (1988) developed a model in which the stomatal resistance was related to solar radiation, temperature, specific humidity deficit, soil moisture deficit and leaf area index. A semi-empirical stomatal resistance model was proposed by Ball *et al.* (1987). After analyzing Ball's model, Aphalo and Jarvis (1993) have proposed a new model, which views the model as a description of the relationship between CO2 flux rate and stomatal conductance, rather than as a model of stomatal conductance alone. Ball's empirical model was later modified by Leuning (1995).

Soil-Tree-Atmosphere Water Relations 179

Values of boundary layer resistance (*Ra*) for individual leaf components can be estimated using engineering equations or empirical relationships. A comprehensive analysis of how to quantify the leaf boundary layer can be found in work done by Campbell (1977), Grace *et al.*

A tree is an organism with leaves and has a capacity to store water in its boles. The transport of water through the water storage in the tree causes hysteresis between rates of soil water uptake and transpiration (Jones, 1982). Landsberg (1986) pointed out that it becomes necessary to include the fluxes in and out of storage in models that predicts the time course of leaf and other tissue water potentials. Trees use stored water to keep stomata open and maintain transpiration in the face of limiting soil moisture or excessive atmospheric demand. Therefore, water movement can be modelled in terms of water potentials and

Having identified the major soil and environmental variables affecting the movement of water from soil to the atmosphere through trees and the subsequent changes in flow associated with resistances in the previous sections, it is possible to combine all this understanding of below- and above-tree water movement into a predictive model. Soil and root resistances, and soil water potential come from the below-ground models whereas the

densities at the surface and the air temperature. Initial rates of water uptake (*FU*p) and transpiration (*F*TP) are used to estimate the exchangeable water storage (*Vp*) and leaf water potential (ψLp). Since ψLp is a function of *Rtp*, an iterative procedure is required to estimate

It is possible to eliminate the intermediate water potentials mathematically by neglecting any storage of water at the surface or in the tree (Thornley and Johnson, 1990). Campbell (1991) has employed a multi-layered root zone to include variable rooting density

Monteith (1980) stated that latent energy for evaporation must be supplied from an external source (according to the law of conservation of energy), and the saturated water vapor in contact with the wet surface must be swept away and replaced by dry air which becomes saturated in turn. To sustain vaporization, however; there must not only be a continual supply of energy, but also an inward flow of liquid water from the soil or the plant (McIlroy, 1984). Accepting this, it is reasonable to assume that there is exchangeable water stored in the plant (Weatherley, 1970 and Jarvis, 1975). Until recently, tree water storage has been largely ignored in soil-tree-atmosphere models. The exchangeable water in the plant allows transpiration to exceed, equal or be less than water uptake by the roots at any given time. This concept of exchangeable water in the plant was used by Kowalik and Ekersten (1984) to formulate a continuous simulation model for transpiration and was

The flow of water through the soil-tree-atmospheric continuum can be divided into three components: (a) water uptake by roots; (b) exchangeable water in storages; and (c) water

*W*

*<sup>p</sup>*) resistances, vapor

(1987), Gates (1980), Monteith and Unsworth (1990) and Nikolov *et al*. (1995).

above-ground models contribute stomatal (*Rtp*) and boundary layer (*Ra*

**4. Combining below- and above-ground processes** 

resistances via exchangeable water storages.

conditions into the water uptake estimations.

**4.1 Modelling water uptake and transpiration** 

the final value of *F*TP.

solved numerically.

Lacking independent estimates of canopy surface resistance for independent assessments of the Penman-Monteith equation, many researchers assumed that canopy surface resistance is equivalent to the integrated stomatal resistance. The adaptation of this assumption has received theoretical (Finnigan and Raupach, 1987; Kelliher *et al.*, 1994; Raupach, 1995) and experimental (Baldocchi *et al*., 1987) criticism over the years. Under the optimal environmental conditions required to achieve 'minimum' resistance (ample water supply, non-extreme temperature, and fully developed non-senescent leaves), stomatal resistance (*R*t) varies through the canopy only in response to variation in photosynthetically active radiation (Kelliher *et al.*, 1994). However, *R*t decreases with radiation and increases with the vapor pressure deficit of the atmosphere (Lohammar *et al.,* 1980). Soil water content varies with uptake by roots as well as with rainfall and irrigation, and soil water potential directly affects *R*t (Jones, 1982). Air temperature changes in a sinusoidal fashion during the day (Goudriaan and van Laar, 1994) and affects *R*t (Aphalo and Jarvis, 1991). White *et al*. (1999) modified *R*t by describing the response of light, air temperature and vapor pressure deficit, but soil water potential directly affects *R*t in some circumstances (Jones, 1992), but in many cases, soil water potential is considered to affect leaf water potential, which in turn controls *R*t (Lynn and Carlson, 1990). Therefore, *R*t as a function of leaf water potential may be more accurate.

A procedure to describe the behavior of *R*t can be given as a function of photosynthetically active radiation, vapor pressure difference, air temperature and soil moisture deficit. Although *R*t is considered to be influenced by changes of CO2 concentration (Hall, 1982), it is typically not included, because in most cases it was found to be almost constant (about 4 ppm variation) (Yang *et al.*, 1998). Baker (1996) also supported the case for insignificant variation of the CO2 profile in forests.

As the radiation interception and scalar profiles are formulated for each sub-canopy within the crown, it is possible to estimate *R*t individually for each sub-canopy, and thus avoid the integration of *R*t for the whole canopy. Similarly, *R*a calculated for each sub-canopy in the canopy is not required to be integrated over the total leaf area of the canopy. One can observe that stem resistance also contributes to the overall resistance of the canopyatmosphere system. However, in resistance studies by Melchior and Steudle (1993), it was found that resistance to water flow was usually negligible where the xylem had already matured.

#### **3.6.2 Leaf boundary layer resistance**

The average thickness of the boundary layer is related to the leaf size. Thus small leaves have thin boundary layers which give small boundary layer resistances whereas large leaves have thick boundary layers with large boundary layer resistances and temperatures which may differ substantially from that of the surrounding air (Grace, 1983). At high wind speeds, the boundary layer is thinner than at low speeds and the resistance correspondingly smaller. The canopy slows down the air flow and creates a turbulent boundary layer. Transport of heat or water vapor through this layer occurs by turbulent diffusion, at a rate determined by the turbulent structure of the air which, in turn, is determined by the wind speed and the aerodynamic roughness of the canopy. The main determinants of boundary layer resistance are therefore leaf size and wind speed, with leaf form exerting a secondary effect through its effect on turbulence (Nikolov *et al*. 1995).

Lacking independent estimates of canopy surface resistance for independent assessments of the Penman-Monteith equation, many researchers assumed that canopy surface resistance is equivalent to the integrated stomatal resistance. The adaptation of this assumption has received theoretical (Finnigan and Raupach, 1987; Kelliher *et al.*, 1994; Raupach, 1995) and experimental (Baldocchi *et al*., 1987) criticism over the years. Under the optimal environmental conditions required to achieve 'minimum' resistance (ample water supply, non-extreme temperature, and fully developed non-senescent leaves), stomatal resistance (*R*t) varies through the canopy only in response to variation in photosynthetically active radiation (Kelliher *et al.*, 1994). However, *R*t decreases with radiation and increases with the vapor pressure deficit of the atmosphere (Lohammar *et al.,* 1980). Soil water content varies with uptake by roots as well as with rainfall and irrigation, and soil water potential directly affects *R*t (Jones, 1982). Air temperature changes in a sinusoidal fashion during the day (Goudriaan and van Laar, 1994) and affects *R*t (Aphalo and Jarvis, 1991). White *et al*. (1999) modified *R*t by describing the response of light, air temperature and vapor pressure deficit, but soil water potential directly affects *R*t in some circumstances (Jones, 1992), but in many cases, soil water potential is considered to affect leaf water potential, which in turn controls *R*t (Lynn and Carlson, 1990). Therefore, *R*t as a function of leaf water potential may be more

A procedure to describe the behavior of *R*t can be given as a function of photosynthetically active radiation, vapor pressure difference, air temperature and soil moisture deficit. Although *R*t is considered to be influenced by changes of CO2 concentration (Hall, 1982), it is typically not included, because in most cases it was found to be almost constant (about 4 ppm variation) (Yang *et al.*, 1998). Baker (1996) also supported the case for insignificant

As the radiation interception and scalar profiles are formulated for each sub-canopy within the crown, it is possible to estimate *R*t individually for each sub-canopy, and thus avoid the integration of *R*t for the whole canopy. Similarly, *R*a calculated for each sub-canopy in the canopy is not required to be integrated over the total leaf area of the canopy. One can observe that stem resistance also contributes to the overall resistance of the canopyatmosphere system. However, in resistance studies by Melchior and Steudle (1993), it was found that resistance to water flow was usually negligible where the xylem had already

The average thickness of the boundary layer is related to the leaf size. Thus small leaves have thin boundary layers which give small boundary layer resistances whereas large leaves have thick boundary layers with large boundary layer resistances and temperatures which may differ substantially from that of the surrounding air (Grace, 1983). At high wind speeds, the boundary layer is thinner than at low speeds and the resistance correspondingly smaller. The canopy slows down the air flow and creates a turbulent boundary layer. Transport of heat or water vapor through this layer occurs by turbulent diffusion, at a rate determined by the turbulent structure of the air which, in turn, is determined by the wind speed and the aerodynamic roughness of the canopy. The main determinants of boundary layer resistance are therefore leaf size and wind speed, with leaf form exerting a secondary effect through its

accurate.

matured.

variation of the CO2 profile in forests.

**3.6.2 Leaf boundary layer resistance** 

effect on turbulence (Nikolov *et al*. 1995).

Values of boundary layer resistance (*Ra*) for individual leaf components can be estimated using engineering equations or empirical relationships. A comprehensive analysis of how to quantify the leaf boundary layer can be found in work done by Campbell (1977), Grace *et al.*
