Geoscience Reference
In-Depth Information
Equation (9.103) produces the vertical pressure distribution of the soil water for any
given rate of evaporation E . For relatively low values of E or for a soil profile with a
water table at a shallow depth d w below the surface, the value of H at the soil surface is
relatively small, i.e. close to zero, and the soil surface is close to saturated. Hence, in such
a case the rate of evaporation is governed by the prevailing atmospheric conditions, and not
by the ability of the soil profile to transmit water. For a given depth of the water table d w ,
as the drying power of the air is increased, the suction H at the soil surface will increase; with
this increased gradient the rate, at which water moves upward and evaporates at the surface,
will also increase. But eventually a limit is approached beyond which E cannot increase; in
the limit E is totally controlled by the ability of the profile to transmit water, regardless of
the drying power of the air. For most practical purposes it is probably sufficiently accurate
to assume that the actual evaporation at any time is the lesser of the potential evaporation
and of the limiting evaporation E lim .
A satisfactory approximation of this limiting value E lim can be obtained by assuming
that the soil surface at z
d w is nearly dry or at field capacity, so that one can assume that
H →∞ and k 0. Integration of Equation (9.103) with (8.37) then produces in general
(Cisler, 1969) the following relationship between the limiting rate of evaporation and the
depth of the water table,
=
a
1 / c
a
c sin( π/ c ) ( a + bE lim )
π
+
bE lim
E lim
d w =
(9.104)
in which a , b and c are the parameters of Equation (8.37). Since in many cases a > ( bE lim ),
this is to a good approximation
E lim = a
c
π
c sin(
d c
w
(9.105)
π/
c )
The assumption of isothermal capillary flow is clearly an oversimplification. Espe-
cially near the soil surface, transport in the vapor phase is also likely to play a role, so
that the limiting evaporation rate is probably larger than the predicted value. However,
Gardner (1958) has estimated that this increase is not likely to exceed 20%. In any event,
Equation (9.105) indicates that the limiting evaporation is proportional to d w . As shown
in Figure 9.22, experimental results by Gardner and Fireman (1958) appear to confirm this.
This gives some support to the isothermal flow assumption. (Note that in Figure 9.22 the
curve is similar to, but not quite the same as (9.105), because the depth of the water table
was simulated in the experiment by maintaining the bottom of the 1 m long column at a
negative pressure rather than zero; however, the difference was shown to be small.) Equation
(9.103) was used by Willis (1960) to study the steady flow from a water table in the case
of a soil profile consisting of two layers of different texture. He concluded that the effect
of stratification was pronounced for a system with the coarse-textured soil overlying the
fine-textured soil, but not for the reversed condition.
9.6.2
Unsteady drying of the soil profile and desorption-based parameterizations
A high water table at a constant depth, as assumed in the previous section, is not a common
occurrence; more often than not the water that evaporates from the soil surface is supplied
by a release from storage in the soil profile. To facilitate the solution of this problem, it is
instructive first to consider this drying process with constant atmospheric conditions.
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