Geoscience Reference
In-Depth Information
B6.1.8 Linking TOPMODEL to the Power Law Rainfall Nonlinearity
In Section 4.3, it was suggested that there is a link between the bilinear power law that has been
shown to be useful in defining the effective rainfall nonlinearity in the data-based mechanistic
(DBM) modelling methodology and the prediction of saturated areas in TOPMODEL. The
starting point for demonstrating this link is the equation for the local deficit calculation in
TOPMODEL which, assuming that the transmissivity is homogeneous in the catchment in
Equation (B6.1.5) may be simplified to:
D
−
D
i
m
−
a
tan
ˇ
=−
ln
(B6.1.29)
The edge of the saturated contributed area
A
c
for any mean deficit
D
is defined by the locus
of points where
D
i
=
0 so that for those points that are just saturated
−
D
m
=−
a
tan
ˇ
ln
(B6.1.30)
and, using B6.1.17 with
=
, the subsurface discharge is given by:
Q
b
=
Ae
−
e
−
ln
tan
ˇ
−
a
(B6.1.31)
We then assume that we can approximate the upper tail of the topographic index curve as
an exponential function of the form:
A
c
=
A
o
exp
n
(
−
a
tan
ˇ
ln
(B6.1.32)
From Equation (B6.1.31)
−
Q
b
Ae
−
a
tan
ˇ
=
ln
(B6.1.33)
and combining with Equation (B6.1.32)
A
o
(
Ae
−
)
n
Q
b
A
c
=
(B6.1.34)
or
A
c
∝
Q
b
(B6.1.35)
This is equivalent to the power law transformation of the rainfall inputs suggested in a number
of DBM SDP analyses as derived from the observations (though not all the SDP transformations
result in this power law form).
Box 6.2 The Soil and Water Assessment Tool (SWAT) Model
B6.2.1 The Pedigree of SWAT
The Soil and Water Assessment Tool or SWAT model is a product of the Agricultural Research
Service (ARS) of the US Department of Agriculture. It is the latest generation of a long line of
USDA ARS models with rainfall-runoff components that includes the Chemical, Runoff and
