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Case study
SOIL CURVE NUMBERS FOR RAINFALL- RUNOFF RELATIONSHIP
An empirical, black-box approach to predicting
runoff from rainfall is the Curve Number (CN)
approach developed by the United States
Department of Agriculture, Soil Conservation
Service (SCS, 1972). The CN methodology has
been used extensively in the USA for modelling
rainfall-runoff relationships. The fundamental
equation at the heart of the CN method is
described in equation 6.9.
2
(
PS
PS
+
02
08
.
)
(6.12)
Q
=
.
140
CN = 100
CN = 90
CN = 80
CN = 60
CN = 40
120
100
80
60
) 2
PI
PI S
(
−+
a
(6.9)
Q
=
40
a
20
where Q is the surface runoff (mm); P is the storm
precipitation total (mm); I a is the initial
abstractions (all losses before runoff begins, e.g.
surface storage, rainfall interception) (mm); and S
is the so-called retention parameter (mm) defined
in equation 6.10:
0
0
20
40
60
80
100
120
140
Rainfall (mm)
Figure 6.18 Runoff curves for a range of rainfalls.
In the CN methodology antecedent soil moisture
condition is accounted for by having three
different CNs, for dry, average and wet conditions.
The CN method provides a simple solution to
the problem of how to model the rainfall-runoff
relationship. There are other methods to model
the runoff from rainfall, e.g. the modified Green-
Ampt infiltration method is frequently used in
physically-based hydrological models to provide
infiltration and surface runoff estimates. The
simplicity provided by the CN method has many
attractions but it does suffer from consequent
drawbacks. The most notable of these for any
analysis of land use change is that CN varies
according to soil characteristics and land cover.
A land use change from pasture (or suburban
garden) to forest will lead to an alteration in three
factors: the soil infiltration characteristics; the
rainfall interception; and the antecedent soil
moisture conditions. Therefore more than one
factor is likely to be altered in equations 6.9-6.12
and a simple alteration of CN may not be enough
25 4 1000
S
=
.
10
(6.10)
CN
where CN refers to the curve number, which is
derived using lookup tables (see SCS, 1986).
The CN values vary according to soil type, land
use, slope and changes in antecedent soil water
content. The actual number of the curve is repre-
sentative of the percentage of storm rainfall that
runs off as stormflow, i.e. CN of 100 corresponds
to all rainfall occurring as stormflow, such as for
an impervious pavement (Figure 6.18).
Empirical studies on small agricultural
watersheds in the USA suggest that the initial
abstraction term ( I a ) can be approximated using
equation 6.11:
I a = 0.2 S
(6.11)
This reduces equation 6.9 to the form shown in
equation 6.12:
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