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In-Depth Information
way in which can be applied to ungauged catchments using default parameters. These are
also reasons why it has been so often used for studies of the impacts of changes in land
management and future climate change. It is relatively simple to make a run to represent
current conditions and then modify the parameter values or inputs to represent potential
future change.
It is relatively simple to do but the question then is how meaningful the resulting predictions
are, given that the SWAT model, like all rainfall-runoff models, is an approximation to the
complexity of the perceptual model of runoff processes in a particular catchment and when
there may be many thousands of parameter values involved. This question of meaningfulness
of such simulations is dependent on how far we can believe that the complexity can be rep-
resented by the effective values of parameters and their stationarity over time. There is still
much to be learned about model calibration and evaluation (see Chapter 7). For the moment
it is suggested that, where possible, the model predictions and particularly predictions of the
impacts of change should be associated with an uncertainty analysis so that the significance
of the difference between simulations can be assessed.
Box 6.3 The SCS Curve Number Model Revisited
B6.3.1 The Origins of the Curve Number Method
The USDA Soil Conservation Service Curve Number (SCS-CN) (now, strictly, the Natural
Resources Conservation Service, NRCS-CN) method has its origins in the unit hydrograph
approach to rainfall-runoff modelling (see Chapter 4). The unit hydrograph approach always
requires a method for predicting how much of the rainfall contributes to the “storm runoff”.
The SCS-CN method arose out of the empirical analysis of runoff from small catchments and
hillslope plots monitored by the USDA. Mockus (1949) proposed that such data could be
represented by an equation of the form:
Q
P
−
I
a
=
1
(10)
−
b
(
P
−
I
a
)
−
(B6.3.1)
or
P
−
I
a
=
1
−
B
(
P
−
I
a
)
Q
−
exp
(B6.3.2)
where
Q
is the volume of storm runoff;
P
is the volume of precipitation,
I
a
is an initial retention
of rainfall in the soil, and
b
and
B
are coefficients. Mockus suggested that the coefficient
b
was
related to antecedent rainfall, soil and cover management index, a seasonal index, and storm
duration.
Mishra and Singh (1999) show how this equation can be derived from the water balance
equation under an assumption that the rate of change of retention with effective precipitation
is a linear function of retention and with the constraint that
B
(
P
−
I
a
)
<
1. Approximating the
right hand side of Equation (B6.3.2) as a series expansion results in an equation equivalent to
the standard SCS-CN formulation
Q
P
−
I
a
=
P
−
I
a
S
max
+
P
−
I
a
(B6.3.3)
where
S
max
=
1
/B
is some maximum volume of retention. Mishra and Singh (1999) propose a
further generalisation resulting from a more accurate series representation of Equation (B6.3.2)
(and giving better fits to data from five catchments) as
Q
P
−
I
a
=
P
−
I
a
S
max
+
a
(
P
−
I
a
)
(B6.3.4)
