Geoscience Reference
In-Depth Information
a triangular PDF is assumed and the mean and standard deviation for each value of
T
are
determined accordingly.
As mentioned above the pre-established rating curves are used to obtain discharges
from water levels and
vice versa
. The only information available about the precision of
the rating curves is that the calculated discharges could vary by 10% to as much as 30%.
This information is insufficient to make a sensible estimate about the moments of the
distributions for the results of the rating curve conversions. Therefore, instead of
estimating directly the standard deviation or variance of the distribution, an estimate
about the coefficient of variation (CoV) is used. The conventional definition of the CoV
is used as follows:
(6.10)
where
)
Q
,
$
Q
and are, respectively, the coefficient of variation, standard deviation
and mean value of the discharge estimated using the rating curve.
There are five uncertain parameters. Three parameters on rating curve conversions,
one each for the three stations, and two parameters on the flow propagation time for the
two reaches. The estimated mean values and the standard deviations for the flow
propagation time
T
for the two segments are given in Table 6.1.
The flood data of April 1998 are used. In the first part of the assessment, an
assumption of 0.1 CoV is used to estimate the uncertainty in the forecast water levels.
The 95 percent confidence bounds are computed from the estimated uncertainty and are
plotted against the measured water levels at different forecast hours. The forecasts are
carried out from 4 hours to up to 48 hours for two cases: (i) for the rising flow situation
and (ii) for the subsiding flow situation.
Table 6.1:
Properties of the propagation time
T
for different river reaches (means and
standard deviations are computed assuming triangular PDFs).
River reaches
Properties of the propagation time,
T
(h):
Mean
Standard deviation
Givry-Gien
24
3.27
Gien-Orleans
20
2.45
6.2.2
Results of analysis
The uncertainty contributions of each of the five parameters are presented in terms of the
standard deviation of the water levels in Figure 6.4. For the rising flow case, the
contribution of the rating curve conversions remains more or less constant, whereas the
contribution of the propagation time is increasing with increasing forecast lead-time. The
trend however, is not very distinct for the subsiding flow case.
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