Geoscience Reference
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excess process. This situation was addressed by Kirkby (1975; see also Scoging and Thornes,
1982) using an infiltration equation of the form:
f ( t )
=
B/H
+
A
(B5.2.6)
where H is the current depth of storage, A is the long term infiltration rate (which may now
be controlled at depth) and B is a constant. Updating of H at successive time steps allows
application to any irregular sequence of rainfall inputs using:
for r(t) > f(t), d dt
=
r ( t )
f ( t )
and
for r(t) < f(t), d dt
=
r ( t )
A
For steady rainfall inputs, this results in infiltration capacity being an inverse function of time
rather than the square root of time, as in the Philip (1957) equation.
B5.2.6 Time to Ponding and the Time Compression Assumption
Whatever type of function is used to describe infiltration, effective rainfalls are calculated as the
excess of rainfall over infiltration following the time to ponding. For rainfall intensities that are
irregular in time, this is often most easily done in terms of comparing the cumulative rainfall
and cumulative infiltration rates, estimating the time of ponding as the point at which the
cumulative infiltration satisfies one of the solutions above (this is called the time compression
assumption) .
Thus, using the Green-Ampt equation as an example, the cumulative infiltration at any time
up to the time of ponding is the integral of the sequence of rainfall intensities:
t p
F ( t )
=
r ( t ) dt
(B5.2.7)
0
Under the sharp wetting front assumption, this is also equal to
z f ( ˜
F ( t )
=
i )
(B5.2.8)
Thus, at each time step the depth of the wetting front can be calculated and used in Equation
(B5.2.3) to calculate the current infiltration capacity, f t . If this is less than the current rainfall
intensity, r t , then the time of ponding has been reached. Similar arguments can be used for
other surface control infiltration equations to determine the time of ponding (see, for exam-
ple, Parlange et al. , 1999). For storage-based approaches, a minimum storage before surface
saturation can be introduced as an additional parameter if required.
B5.2.7 Infiltration in Storms of Varying Rainfall Intensity
In storms of varying rainfall intensity, the input rate may sometimes exceed the infiltration
capacity of the soil and sometimes not. When input rates are lower than the infiltration capacity
of the soil, there may be the chance for redistribution of water within the soil profile to take
place, leading to an increase in the infiltration capacity of the soil. This is handled easily in
storage capacity approaches to predicting infiltration, such as that of Kirkby (1975) noted above,
but such approaches do not have a strong basis in soil physics. Clapp et al. (1983) used an
approach based on a Green-Ampt or kinematic approach to the infiltration and redistribution
of successive wetting fronts. More recently Corradini et al. (1997) have produced a similar
approach based on a more flexible profile shape than the piston-like wetting front of the Green-
Ampt approach. It is worth noting that methods based on soil physics may also be limited in
 
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