Environmental Engineering Reference
In-Depth Information
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
2
0
2
2.5
Quick Res. Time (days)
3
20
40
60
Slow Res. Time (days)
Figure 7.4
Uncertainty in the estimated residence times for the River canning DBM model based on the RIVCBJ estimates and MCS
analysis.
pathway with a residence time of 18.66 days, accounting
for the remaining 41.6% of the flow. It is this latter
pathway that leads to an extended tail on the associated
hydrograph and can be associated with the slowly
changing baseflow in the river. (For a more detailed
explanation and other examples, see Young, 1992, 1993a,
1998, 2001b, Young and Beven, 1994; Young
et al
., 1997.)
Note, however, that the DBM model is stochastic and
so the uncertainty associated with these estimates of the
physical characteristics can be quantified. For example,
Figure 7.4 shows the uncertainty in the two residence
times, as obtained by MCS analysis based on the estimated
model parameters and their associated covariance matrix
(see e.g. Young, 1999a, 2001b, 2004). These normalized
histograms, which are computed from 20 000 MCS real-
izations, show that the short residence time is estimated
reasonably well in relation to its estimated value of 2.574
days, with 95% confidence bounds of
rainfall nonlinearity is a function of flow. Although
this relationship is physically impossible, the analysis
produces such a clearly defined relationship of this sort
that it must have some physical connotations. The most
hydrologically reasonable explanation is that the flow is
acting as a surrogate for soil-water storage. Of course,
it would be better to investigate this relationship directly
by measuring the soil-water storage in some manner and
incorporating these measurements into the SDP analysis.
Unfortunately, it is much more difficult to obtain such
soil-moisture measures and they were not available in the
present example. Sometimes temperature measurements
(Jakeman
et al
., 1990) or simple first-order storage
models (Young, 2003) are used to generate an estimate
of the soil-water storage in these kind of rainfall-flow
models but, in general, these do not tend to explain the
data as well as the above DBM model and there is clearly
a need for more research on this topic.
Finally, what are the advantages of the present
continuous-time, differential equation model (7.2a) or
(7.4) in relation to the previous discrete-time models of
the same data described in the previously cited references?
First, it is clear that there is only one continuous-time
model, which is independent of the sampling interval
.
However, the long residence time is quite uncertain, with
a decidedly skewed distribution towards higher residence
times and 95% confidence bounds of
{
2
.
318 2
.
871
}
{
14
.
30 28
.
85
}
,in
relation to its estimated value of 18.66 days.
The most paradoxical and, at first sight, least
interpretable model characteristic is that the effective
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