Geoscience Reference
In-Depth Information
start of ponding is quite different from the initial condition used to describe the infiltration
capacity, i.e. the first of (9.62). In fact, the initial soil water content distribution at the
start of ponding cannot be prescribed in general beforehand, because it will depend on
the specifics of the duration and intensity of infiltration prior to ponding for each rainfall
event. Because a detailed solution of Richards's equation for each rainfall occurrence is
neither practical nor feasible, it is useful to explore further simplification of the problem.
Several parameterizations of rainfall infiltration that have been proposed in the past
involve the concept of
time compression
(also called
time condensation
), or some assump-
tion similar to it. Briefly, the underlying assumption is that the potential infiltration rate,
at any given time after the onset of ponding within a rain storm period, depends only
on the previous cumulative infiltration volume, regardless of the previous infiltration or
rainfall history during that same storm. The time compression approximation (TCA) was
introduced in the 1940s (see Sherman, 1943; Holtan, 1945) in the context of partitioning
the rainfall on a watershed into runoff and infiltration, and was later applied in many
other studies (see Reeves and Miller, 1975; Sivapalan and Milly, 1989; Salvucci and
Entekhabi, 1994; Kim
et al.
, 1996).
Conceptually, TCA can be considered another instance of the application of the
lumped kinematic approach, as formulated in Equation (1.10). Thus the soil profile
is a one-dimensional control volume, the rate of infiltration
f
is the inflow rate
Q
i
, and
the cumulative infiltration
F
is the storage
S
. After the inception of ponding, the inflow
rate
f
is assumed to be a function of the storage
F
only, independent of the precipitation
history.
General formulation
Let
f
F
(
t
) denote the actual infiltration rate and actual cumulative
infiltration, respectively; as these are functions of time, one also has the inverse functions
t
=
f
(
t
) and
F
=
F
c
(
t
) denote the same functions
for the infiltration capacity, that is under potential conditions, as analyzed in Section 9.3.
and subject to boundary conditions (9.2); their inverse can be written, respectively as
t
=
t
(
f
) and
t
=
t
(
F
). Similarly,
f
c
=
f
c
(
t
) and
F
c
=
=
t
(
f
c
) and
t
=
t
(
F
c
). The basic assumption of TCA can be expressed as follows
=
<
f
P
for
t
t
p
(9.90)
f
=
f
c
(
t
(
F
c
=
F
))
for
t
≥
t
p
With a constant (or average) rate of rainfall
P
, the cumulative infiltration at the time
of incipient ponding is (
Pt
p
). Define now the (fictitious) compression reference time
t
cr
as the time period after the start of rainfall that would be required to produce the same
infiltrated volume, but under potential conditions. Thus one has
F
(
t
p
)
=
Pt
p
=
F
c
(
t
cr
)
(9.91)
from which
t
cr
or
t
p
can be estimated. Once
t
cr
and
t
p
are known, the cumulative infiltration
is given by
F
(
t
)
=
Pt
for
t
<
t
p
(9.92)
F
(
t
)
=
F
c
(
t
−
(
t
p
−
t
cr
))
for
t
≥
t
p
