Transpiration from the leaf depends on two major factors: the difference in water vapor concentration between the leaf air spaces and the the external air and, the diffusional resisitance (r) of this pathway. This concept of transpiration is analogous to the flow of electrons in an electric circuit. Indeed, an electrical analog is commonly used as a model for water vapor loss from the leaf.

In this analog, resistances are associated with each part of the pathway; the major ones are the resistance at the stomatal pore (r_s) and the resistance due to the layer of unstirred air at the surface of the leaf (r_b) (the so-called boundary layer). Transpiration rate (E, in mol m^–2 s^–1) may be related to diffusional resistances (r, in s m^–1) by the following equation:

Web Equation 4.4.1  

Let’s examine the factors in Web Equation 4.4.1 in greater detail. The difference in water vapor concentration is expressed as c_{wv (leaf)} – c_{wv (air)}. (Sometimes vapor pressures are used instead of concentrations, and the difference is called the water vapor pressure deficit. Water vapor pressure (p_wv) is measured in kilopascals (kPa) and is proportional to water vapor concentration (Web Table 4.4.A) where c_{wv (leaf)} is the water vapor concentration inside the leaf and c_{wv (air)} is the water vapor concentration of the air outside the leaf, both expressed in moles per cubic meter (mol m^–3). Resistance (r) is the inverse of conductance; that is, resistance = 1/conductance. Thus, a high resistance is the same as a low conductance. Expression of this value in terms of resistances is preferred over expression in terms of conductances in some instances because resistances in series may be summed to calculate a total resistance, as in the above equation, whereas a similar calculation of conductances in series is more complicated. In the leaf, the total resistance is due mostly to the diffusion limitation imposed by the stomatal pore, but other parts of the pathway for water vapor loss, such as the boundary layer (which we will discuss shortly), may contribute significantly to r.

Vapor pressures and concentrations are equivalent; in our analysis we will use the latter. The water vapor concentration of bulk air (c_{wv (air)}) can be readily measured, but that of the leaf (c_{wv (leaf)}) is more difficult to assess. We can estimate it by assuming that the air space in the leaf is close to water potential equilibrium with the cell wall surfaces. This approximation is not strictly true, because water is diffusing away from these surfaces. However, it introduces little error because the major resistance to vapor loss is at the stomatal pore. Moreover, the volume of air space inside the leaf is small, whereas the wet surface from which water evaporates is comparatively large. Air space volume is about 5% of the total leaf volume for pine needles, 10% for corn leaves, 30% for barley, and 40% for tobacco leaves. The internal surface area from which water evaporates may be from 7 to 30 times the external leaf area. This high ratio of surface area to volume makes for rapid vapor equilibration inside the leaf.

Making the assumption of equilibrium, we can calculate the water vapor concentration in the leaf air spaces if we know: (1) the water potential of the leaf (which is the same as the water potential of the wall surfaces from which water is evaporating), and (2) the leaf temperature. Let’s take as an example a leaf with a water potential of –1.0 MPa. To reach vapor equilibrium, water evaporates from the cell wall surfaces until the water potential of the air inside the leaf equals the water potential of the leaf. The water potential of the air is given by the following equation:

Web Equation 4.4.2  

where R is the gas constant, T is temperature (in degrees Kelvin), V–_w is the partial molar volume of liquid water, and RH is the relative humidity of the air. Relative humidity is the water vapor concentration expressed as a fraction of the saturation water vapor concentration, c_wv(sat.):

Web Equation 4.4.3  

RH varies between 0 and 1; RH multiplied by 100 is the percentage relative humidity.

Web Table 4.4.A shows RH values as a function of water potential, calculated from Web Equation 4.4.2. This table shows that the air spaces of living leaves must have a high RH, a value of nearly 1 (100%), when water potentials are in the physiological range. Moreover, outside air, with RH of, for example, 0.5 (50%), has a remarkably low water potential.

Web Table 4.4.A  Note: These data are for 20°C. ^aCalculated using Web Equation 4.4.2, with a value of 135 MPa for RT/V_w.

To convert from RH to c_wv, we need to know c_wv(sat.). The saturation water vapor concentration is strongly dependent on temperature. As the air temperature rises, the water-holding capacity of air increases sharply, (Web Figure 4.4.A). In the range of 10 to 35°C, an increase in air temperature of 12°C doubles the water vapor concentration of saturated air. This is an important observation. If our leaf with a water potential of –1.0 MPa warms up abruptly from 20 to 32°C, the relative humidity in the leaf air space drops abruptly from 99.3 to almost 50%. This drop in RH results because the water-holding capacity of the air, c_wv(sat.), doubles. As a result of the drop in RH, water will evaporate in the air space until RH returns to a value of 99.3% and the air is again in water potential equilibrium with the leaf. As a consequence of this change in temperature, c_wv(leaf) (the water vapor concentration of the leaf air space) increases from 0.95 to 1.87 mol m^–3, which makes for a steeper concentration difference driving the diffusional loss of water from the leaf. For this reason, leaf temperature is an important determinant of the transpiration rate.

Web Figure 4.4.A  Concentration of water vapor in saturated air as a function of air temperature.

Textbook Table 4.1 illustrates how RH, c_wv, and water potential change at various points in the transpiration pathway. We see that c_wv decreases along each step of the pathway from the cell wall surface to the bulk air outside the leaf. Keep in mind that RH can increase along part of this pathway because the external air temperature may be lower than the temperature of the leaf. The important points to remember are (1) that the driving force for water loss from the leaf is the absolute concentration difference (difference in c_wv, not in RH), and (2) that this difference depends on leaf temperature.