Geoscience Reference
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Fig. 1. Locality map
3. Fuzzy theory
A fuzzy set is defined mathematically as follows: if X = {x} is a finite set (for space) of points,
then the fuzzy set A in X is the set of ordered pairs:
A = {x,
A
(x)} x X
(1)
where
A
(x) is known as the grade of membership of x in A and x X mean that x is
contained in X. For all A,
A
(x) represents the grade of membership of x in A and is a real
number in the interval [0, 1], with 1 representing full membership of the set and 0 non-
membership (Zadeh, 1965). In practice, X = { x
1
, x
2
…, x
n
) and the Eq. (1) can be written as:
A = {x
1
,
A
(x
1
); x
2
,
A
(x
2
); ... ; x
n
,
A
(x
n
)}
(2)
4. The Soil Conservation Service Curve Number (SCSCN) hydrologic model
The SCSCN model is a well known archetype for estimating the storm runoff depth from
storm rainfall depth for watershed and thus, stream flow, infiltration, soil moisture content
and transport of sediments. Therefore, the model can assist hydraulic projects, soil
conservation projects and flood control (SCS, 1972; Engel et al., 1993; Mack, 1995; Johnson &
Miller, 1997; Thompson, 1999; Pullar & Springer, 2000;
In the SCSCN model, the physical characteristics of the watershed, such as hydrologic soil
group (HGS), land cover and antecedent moisture conditions, are important because these
characteristics determine the curve number (CN) parameter that estimate the runoff from a
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