Geoscience Reference
In-Depth Information
Fig. 7.11 Observed hydrographs
at the inflow end
Q
i
and
at the outflow end
Q
e
(in
m
3
s
−
1
) listed in Table
7.2, and used in
Example 7.2 (heavy
lines). The calculated
outflow hydrographs
(thin lines) are obtained
with the MCD method
with reference flow rate
Q
0
=
2 500 m
3
s
−
1
(triangles) and
Q
0
=
1500 m
3
s
−
1
(circles).
2000
Q
i
Rate
of
flow
Q
e
1000
0
0
5
10
15
20
25
30
Time (h)
Q
0
=
2500 m
3
s
−
1
, the corresponding values are
V
0
=
2.09 m s
−
1
,
h
0
=
7.02 m,
K
=
1.83 h
and
X
0.27. As illustrated in Figure 7.11, the calculated outflows are not strongly
affected by the choice of the reference flow rate
Q
0
. Not surprisingly, a lower value of
Q
0
results in a generally slower wave motion through the reach, and a somewhat delayed
arrival of the peak discharge.
=
7.3.3
Adjustment of calibration parameters on physical grounds
The expressions for the Muskingum parameters derived in the previous section require
a knowledge of the effective channel hydraulic parameters of the channel reach. In this
case, “effective” means that the hydraulic parameters should have values, which produce
the optimal results with the Muskingum procedure. Therefore, effective parameters may
not be easy to ascertain from the available information on the channel characteristics or
even from field surveys. Rather, for a given flood event, they are probably best obtained by
calibration, by means of the procedures explained in Section 7.3.1. However, the parameters
in the Muskingum formulation are not constants, so that for some other flood that must
be routed through a reach for design or forecast purposes, they are not likely to be the
same as those obtained by calibration with past events. Nevertheless, the physically based
expressions (7.53)-(7.56) obtained in the previous section can still be used to adjust or scale
the parameters obtained by calibration, to render them applicable to any other flood event
with different flow rates. This can be done conveniently by taking the peak flow rate, or
some other characteristic flow rate as reference.
The adjustment can be applied to channels of any cross-sectional shape, but it is especially
simple for wide channels, so that
R
h
=
h
. Let the parameters obtained by calibration with
a flood event on record be denoted by
K
r
and
X
r
, and those for the design or forecast flood,
that is to be routed, by
K
d
and
X
d
; use the same subscripts also for the corresponding flow
characteristics in these two events. For example, if the peak velocity
V
ipd
at the inflow end
of the reach is known, one obtains immediately by means of (7.53) the time lag in the reach
for the design or forecast event
K
d
=
K
r
V
ipd
V
ipr
(7.57)
