Water Flow in Soil
is negligible). For this condition, the equivalent soil water potential can
be calculated from
h = 1 F.(z)h(z)dz
(9.14)
where F, (z) is a depth weighting function for root density and @(z) 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
0.5 during daytime. Therefore, the plant can have no sigmficant direct
effect on its water loss by dropping its leaf water potential. The control of water loss is indirect, through effects of leaf water potential on
the stomatal diffusive conductance for vapor. At high leaf water potential stomatal conductance is determined by light, temperature, and COz
concentration. As leaf water potential decreases below some threshold,
conductance begins to drop rapidly. A simple mathematical function with
these characteristics is:
where E p and E,,, are the plant transpiration and maximum possible
transpiration, and @cr 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. (9.13), 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 1Cr, = 0 and U = Epm the leaf
water potential will have a value, @Lm. Using these values, Eq. (9.13) can
be solved for Rp:
@ ~ m
R p = -.
(9.16)
Epmax
Substituting Eq. (9.16) into (9.13), and defining U* = U/EpmX as a
dimensionless uptake rate, @*, = @ L / @ L , as a dimensionless leaf water
potential, and @: = @ s / @ ~ m 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 @*, =
= 0 and @*, = @ ; = 0.5 where U* = 0).
is negligible). For this condition, the equivalent soil water potential can
be calculated from
h = 1 F.(z)h(z)dz
(9.14)
where F, (z) is a depth weighting function for root density and @(z) 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
0.5 during daytime. Therefore, the plant can have no sigmficant direct
effect on its water loss by dropping its leaf water potential. The control of water loss is indirect, through effects of leaf water potential on
the stomatal diffusive conductance for vapor. At high leaf water potential stomatal conductance is determined by light, temperature, and COz
concentration. As leaf water potential decreases below some threshold,
conductance begins to drop rapidly. A simple mathematical function with
these characteristics is:
where E p and E,,, are the plant transpiration and maximum possible
transpiration, and @cr 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. (9.13), 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 1Cr, = 0 and U = Epm the leaf
water potential will have a value, @Lm. Using these values, Eq. (9.13) can
be solved for Rp:
@ ~ m
R p = -.
(9.16)
Epmax
Substituting Eq. (9.16) into (9.13), and defining U* = U/EpmX as a
dimensionless uptake rate, @*, = @ L / @ L , as a dimensionless leaf water
potential, and @: = @ s / @ ~ m 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 @*, =
= 0 and @*, = @ ; = 0.5 where U* = 0).