Transpiration and Plant Water Uptake

9.5 Transpiration and Plant Water Uptake

Liquid water moves from soil to and through roots, through the xylem of plants, to the leaves, and eventually evaporates in the substomatal cavities of the leaf. The driving force for this flow is a water potential gradient. In order for water to flow, the leaf water potential must be below that of the soil. The entire system is sometimes thought of as being similar to a

resistor network in an electronic circuit where water and current flow are analogous, and where the potential differences are like voltage differences in the circuit. Ohm's law is then used to describe the flow of water in the

system. The main resistances for liquid water are in the root and in the leaf, so we can calculate the rate of uptake of water from the soil as:

where is the soil water potential, is the leaf water potential, and and

are the root, leaf, and total plant resistances. The uptake in Eq. (9.13) should be thought of as uptake per unit area of soil, not per plant. Campbell (1985) has shown that any distribution of roots and soil water potential can be represented by a single equivalent potential, which is the

(9.13). Forplants growing intypical field situations, almost all of the resistance for uptake of water is in the root (the soil resistance

Water Flow in Soil

is negligible). For this condition, the equivalent soil water potential can

be calculated from

(9.14) where

is the distribution of soil water potential with depth. In Ch. 5 we discussed the fact that the relative humidity inside the stomata of leaves is nearly 1.0. In even severely stressed leaves, it does not drop below 0.98. The humidity of the outside air is usually below

(z) is a depth weighting function for root density and

0.5 during daytime. Therefore, the plant can have no direct effect on its water loss by dropping its leaf water potential. The con- trol of water loss is indirect, through effects of leaf water potential on the stomatal

conductance for vapor. At high leaf water poten- tial stomatal conductance is determined by light, temperature, and concentration. As leaf water potential decreases below some threshold, conductance begins to drop rapidly. A simple mathematical function with these characteristics is:

where and are the plant transpiration and maximum possible transpiration, and

sets the threshold leaf water potential for stomatal closure. The power 10 was chosen somewhat arbitrarily. It determines how rapidly the simulated stomata close.

Going back to Eq. it can be seen that it describes a linear relationship between uptake rate and leaf water potential (for a given soil water potential). Leaf water potential could decrease indefinitely, and uptake increase indefinitely except for the limit placed on leaf water potential by Eq. (9.15). We are interested in finding what that limit is for any given soil water potential. To do that, we convert Eqs. (9.13) and (9.15) to a dimensionless form. When

= and = the leaf water potential will have a value,

Using these values, Eq. (9.13) can

be solved for

(9.16) Substituting Eq. (9.16) into

and defining = as a dimensionless uptake rate,

as a dimensionless leaf water potential, and

= as a dimensionless soil water potential gives

Equation (9.17) is plotted in Fig. 9.8 for two values of the dimensionless soil water potential (straight lines with positive slope intersecting the horizontal axis at @*,

= and

0.5 where = 0).

Transpiration and Plant Water Uptake 141

0.0 0.2 0.4 0.8 1.0 1.2 1.4 1.8 2.0 Dimensionless Leaf or Soil Water Potential

F IG U RE 9.8. Dimensionless water uptake and loss.

Equation (9.15) is already in a dimensionless form. The dimensionless transpiration rate can be defined as E*

The ratio of the potentials is the same as the ratio

dimensionless potentials. Equation (9.15) is also plotted in Fig. 9.8 and it can be seen that the declining part of Eq. (9.15) is closely approximated by a straight line. The equation of the line is

The maximum or potential uptake rate for a given soil water potential is at the intersection of the uptake and loss lines. Solving Eqs. (9.17) and

(9.18) simultaneously to find that point, gives

The actual rate of uptake cannot be higher than this value, but it can be lower if the evaporative demand of the atmosphere is lower. The actual transpiration rate of the plant canopy is therefore equal to the minimum of the evaporative demand of the atmosphere and

These ideas can be related to the depletion of the moisture by defining yet another dimensionless quantity, the available water fraction. The available water fraction can be defined as

where is average water content of the root zone and the subscripts indicate field capacity and permanent wilting water contents. For the simplest case, where it is assumed that water content of the root zone is

Water Flow in Soil

uniform, substitute from Eq. (9.3) to convert Eq. (9.20) to water potential. Dividing through by

to convert to dimensionless soil waterpotentials, and canceling common terms, gives:

Equation (9.21) can be solved for dimensionless soil water potential and combined with Eq. (9.19) to find a relationship between the maximum possible uptake rate and available water in the root zone. Obtaining values for

If = -

and requires the estimation of a scaling potential

J then 1.5 can be substituted for the dimensionless permanent wilt water potential (from Fig. 9.8;

= -1500 J kg-') use 0.02 for the dimensionless field capacity, and assume b = 5 to convert to numerical values. The resulting equation is

Equation (9.22) is shown plotted in Fig. 9.9. It shows that the poten- tial uptake rate is high until about half of the available water has been extracted. With increasing depletion of soil water the uptake rate falls rapidly. It is important to remember that Fig. 9.9 is not showing the ac- tual uptake rate, it is showing the maximum rate for any given soil water

content. If the atmospheric demand is lower than this value, then the up- take will be controlled by the atmospheric demand. The maximum uptake rate when soil is wet is probably about equal to the maximum atmospheric

0.0 0.2 0.4 0.6 1.0 Available Water Fraction

9.9. Maximum rate of plant water uptake as a function of soil available water fraction.

F IG URE

Transpiration and Plant Water Uptake 143

demand on hot days, since plants tend to develop resistances and water potentials which just meet environmental demands.

Example 9.2. Using the same soil properites as in Example 9.1, estimate the available water in

in a 1 m deep root zone if the permanent wilting water potential is -

J kg-'.

Solution.

If we assume that field capacity is at -33 then, from Example 9.1,

0.28 m 3 The available volumetric water content is 0.28 -

0.12 0.16 m 3 With a one meter deep root zone, the available water in mm is obtained as

mm of water. If, on the average, a plant uses 5

then a one meter root zone of this soil could potentially provide water for about 32 days.

Example 9.3. If a shallow-rooted plant (rooting depth 200

is growing in the soil described in Example 9.2 and

= 5 every day, how long will it take before

Solution. The total available water in a 200 mm deep profile would be

0.16 x 200

32 The available water fraction on the first day is

A, = 1 so = 5 It can be assumed that is appropirate for

an entire day so that on the second day the available water is 32

0.84 and on the second day the plant uptake rate can be estimated from Eq. (9.22).

5 mm =

27 mm. Thus A, = 27/32 =

5[1 - (1 + 1.37 x

On day 3, A, =

4.9 This process can be continued until

0.69 so that

Available water mm

Water Flow in Soil

Therefore, 8 days will be required for the transpiration rate to be reduced from 5 to 1

Note how quickly the plant runs out of water at the end of 7 days. This is a consequence of the steepness of the curve in Fig.

9.8. Obviously the plant will virtually stop transpiring on the ninth day.