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zero. This means that (
1, so that from Darcy's law (8.19) it follows that the
rate of infiltration f c approaches the value of the saturated hydraulic conductivity, or
h
/∂
z )
→−
lim
( f c )
=
lim
z = 0
t →∞
( q z )
=
k 0
(9.4)
t
→∞
The problem of intermediate times of infiltration capacity is dealt with in Section 9.3.
9.1.2
Rainfall infiltration
Like the infiltration capacity, the infiltration of precipitation on the soil surface is gov-
erned by the Richards equation (9.1), but the boundary conditions are quite different
from (9.2). Because in this case the water supply rate at the surface is smaller than the
maximal rate the soil is capable of taking in, the surface water content
θ s is smaller than
θ 0 by an unknown amount; the only known feature of the flow at the surface is the supply
rate or precipitation intensity, and thus the flow rate into the soil. As long as the water
supply rate is maintained, this unknown surface water content
θ s gradually increases.
If the precipitation rate is large enough, eventually the surface water content reaches
the maximum possible value
θ 0 ; after this occurs, water starts to pond the surface. If t p
denotes the time from the start of the rainfall until the inception of ponding, the boundary
conditions can be formulated as follows
θ = θ i
H
=
H i
z
>
0
t
=
0
D w ∂θ
Pk
H
(9.5)
z +
k
=
z +
k
=
Pz
=
00
<
t
t p
θ = θ 0
H
=
0
z
=
0
t
t p
where P
P ( t ) is the intensity of the precipitation. The first condition represents again
an initially constant water content
=
θ i throughout the soil profile. The second condition
indicates that the flux is known at the surface; the third shows that, after ponding starts,
the surface is satiated but the flux is no longer known. If the precipitation rate is small,
however, the surface soil layer never becomes fully satiated; thus t p →∞
and the third
condition of Equation (9.5) is redundant. Further details on the solution of the rain
infiltration problem are covered in Section 9.4.
9.2
INFILTRATION CAPACITY IN THE ABSENCE
OF GRAVITY: SORPTION
Sorption, that is horizontal infiltration of water into a partly but uniformly saturated soil,
when the movement of the displaced air is unimpeded, is a problem of long standing
in the hydrologic literature. Although by itself this type of one-dimensional horizontal
flow may not be very common in nature, the solution of this problem is of practical
importance. First, it gives a good description of the initial stages of vertical infiltration
of water ponded on the soil surface, that is the short-time behavior, while the effects of
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