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the effective
S
max
value. Michel
et al.
(2005) note that this is only a way of trying to compensate
for a structural deficiency in the method and suggest a modification so that it can be used as
a continuous soil moisture accounting method.
The background to the SCS-CN method is purely empirical. That is primarily its strength,
but also a limitation in that it does not allow any direct interpretation in terms of process,
except in so far as Mockus originally suggested that the value of
S
max
would be the volume of
infiltration or available storage, whichever was the smaller. More recent studies have attempted
to extend this interpretation. Steenhuis
et al.
(1995) have interpreted the method as equivalent
to assuming a variable contributing area of runoff generation over which the storm rainfall
volume is sufficient to exceed the available storage prior to an event (see also the work of
Lyon
et al.
(2004) and Easton
et al.
(2008) for applications of this interpretation). The implied
proportion of the catchment contributing to runoff for a given effective rainfall value is then
directly related to the value of
S
max
(Figure B6.3.1). They show reasonable fits to observations
for several Australian and American catchment areas (ranging from 16.5 to 7000 ha) with
permeable soils. Adjusting the value of
S
max
for each catchment resulted in a range of values
from 80 to 400mm (see Figure B6.3.2). It is also worth noting that Ponce (1996) recorded, in
an interview, that Vic Mockus later stated that “saturation overland flow was the most likely
runoff mechanism to be simulated by the method”.
Figure B6.3.1
Variation in effective contributing area with effective rainfall for different values of
S
max
(after Steenhuis
et al.
, 1995, with kind permission of the American Society of Civil Engineers); effective
rainfall is here defined as the volume of rainfall after the start of runoff,
P
−
I
a
.
Yu (1998) suggests that a model of the form of the SCS-CN method can be derived on the
basis of assumptions about the spatial variability of (time constant) infiltration capacities and
the temporal variability in rainfall intensities. Under these assumptions, runoff will be produced
anywhere on a catchment where the time varying rainfall rate exceeds the spatially variable
but time constant infiltration capacity (making no allowances for any runon process). For an
exponential distribution of infiltration capacity in space and rainfall intensity in time, Yu shows
that the runoff generated
Q
is given by the SCS-CN equation.
B6.3.4 Applications of the Curve Number Method
A wide variety of models have been based on the curve number method. It has been used
widely in procedures recommended by the USDA, notably in the TR20 and TR55 methods for
estimating peak runoff and hydrographs (USDA-SCS, 1986). A detailed summary of the method
is given by McCuen (1982). It has also provided a runoff component for a succession of water
