Geoscience Reference
In-Depth Information
larger capacity. He reasoned by means of the GM equation (5.41) that
m
should lie
around (3
4) for channels
with a triangular section; although there was some scatter, an analysis of river recession
flow data (cf. Equation (12.54)) confirmed that
m
was mostly between 0.6 and 0.8.
Interestingly, although it was nonlinear, Horton's approach provided the impetus for
the linear lag-and-route procedures of Clark (1945) and O'Kelly (1955), described in
Section 12.2.2.
A second type of nonlinear runoff model, which has been used in a number of studies,
consists of arrays of nonlinear storage elements, like Equation (12.48), in series and in
parallel representing different components of the basin; the storage arrays are usually
structured in the same arrangement as the actual stream channel network. Such arrays
can be considered nonlinear analogs of the linear ones, examples of which are shown in
Figures 12.16-12.19. One such routing procedure was described by Rockwood (1958),
who used it to forecast streamflow in the entire Columbia River Basin on the basis
of preceding streamflows and forecasts of basin inputs from snowmelt and rainfall.
This large basin was assumed to consist of a number of subbasins, lakes and stream
channels. Each subbasin was assumed to consist of two nonlinear storage elements in
series representing surface runoff, which are placed in parallel with two storage elements
in series representing subsurface runoff. Channel segments, mostly between 30 and
80 km long, were represented by three nonlinear storage elements in series. The routing
procedure consisted essentially of the numerical solution of Equation (12.49) for each
storage element, in which it was assumed that
m
/
5) for channels with a rectangular section, and around (3
/
=
0
.
8 and
K
n
was derived by trial
routings.
Different arrays of nonlinear storage elements, each representing a subarea and each
receiving the excess rainfall input on that subarea plus the outflow from the upstream
storage elements, were devised by Laurenson (1964) and subsequently by Mein
et al
.
(1974) to simulate storm flows from catchments in Australia. In this approach the catch-
ment area is first subdivided in a number of approximately equal subareas along the
major tributaries, and a nonlinear tank is then located at the center of gravity of each of
the subareas and assigned a relative lag time of that location. At first this relative lag - or
storage delay - time was assumed to be proportional to
(
L
S
1
/
0
), where
L
and
S
0
are
the length and slope of the reach through the subarea, and the summation was carried
out from the location of the subarea to the outlet; however, it was subsequently found
that putting it proportional to the distance from the outlet, i.e.
L
, yielded the same
results; this shows that the effects of slope, flow depth and surface roughness become
irrelevant in this type of idealization. The parameter
m
was estimated by observing from
comparison of (12.25) with (12.48) that
/
K
n
y
m
−
1
K
=
(12.50)
Then in accordance with Equation (7.19), logarithmic regression was carried out for
a number of storms between the time from the centroid of the excess rain to that of
the storm runoff and the average storm runoff during the event,
y
; the slopes of the
regression lines were assumed to represent (
m
−
1) of (12.50), and produced (see also
Askew, 1970) a range of roughly 0
.
60
≤
m
≤
0
.
81. These values are very similar to those
