Geoscience Reference
In-Depth Information
Liu
et al.
(1998) estimated the error in the TCA solution by comparing it with the exact
solution of rainfall infiltration for the special case of the linearized Richards equation with-
out gravitational effect, that is Equation (9.6) with a constant
D
w
=
D
0
. The differences
between the two solutions were very small, with the largest occurring near ponding. The
maximal error in cumulative infiltration was found to be an underestimate of only 1.3% for
the first TCA procedure with (9.94), and about 2.5% for the second procedure with (9.95)
and (9.96); similarly small errors were obtained for the rates of infiltration. On the other
hand the second procedure underestimated the time to ponding obtained with (9.96) by
about 19%. This illustrates that
t
p
can be a sensitive parameter and that conversely, errors
in
t
p
will cause much smaller error in the resulting
F
or
f
. The sensitivity issue was also
dealt with by White
et al
. (1989).
9.5
CATCHMENT-SCALE INFILTRATION AND OTHER “LOSSES”
So far in this chapter, infiltration has been considered effectively as a point process. In
applied hydrology it is usually necessary to estimate the process over larger areas, often
with typical length scales on the order of kilometers. Over the years engineers, faced with
the task of predicting storm runoff from precipitation, have developed various, mostly
heuristic, approaches to deal with this problem. Some of these are reviewed in what
follows.
9.5.1
Infiltration capacity methods
This approach consists of the simple extension of the available information on point
infiltration over a larger area. It is currently implemented in many catchment water bal-
ance models, by subdividing the catchment area into appropriate subareas with assumed
uniform infiltration characteristics; for each subarea an average or typical infiltration
capacity relationship is adopted, which is then applied with the time compression approx-
imation to deal with precipitation events. The main difficulties with this approach are the
large spatial and temporal variability of soil properties and soil moisture content, that are
normally encountered even in so-called homogeneous field situations. This means that
it is never an easy matter to define an average
f
c
(
t
) function for application over a larger
area. As already pointed out in Section 9.3.4, this problem is still poorly understood and
will have to be the subject of more research.
9.5.2
The loss rate concept
In many of the methods that have been in use to predict streamflow from rainfall obser-
vations for flood-control purposes (see Feldman, 1981), it is necessary to determine a
rainfall
excess
, that is the part of the precipitation which generates the direct storm runoff.
This is usually done by applying a loss rate to the observed precipitation intensity. Most of
this “loss” is assumed to consist of infiltration; however, because it is difficult to consider
them separately, other processes such as initial rainfall detention storage in depressions
and rainfall interception, are usually included in the total loss. Because generally much
