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| Titel |
Integration of flow meter devices for optimal discharge estimation during floods |
| VerfasserIn |
G. Corato, T. Moramarco, T. Tucciarelli |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250029223
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| Zusammenfassung |
| Discharge hydrograph estimation in rivers is usually carried out by means of water level
measurements and the use of the so called water depth – discharge relationship. The water
depth – discharge curve is updated rarely by integrating local velocities measured in a given
section at specified water depth values. To update such curve is very expensive
and very often the highest points, used for the peak flow estimation during floods,
are the result of rough extrapolation of points corresponding to much lower water
depths.
Recently, new discharge estimation techniques have been developed. A first one is the use
of a radar that provides the velocity of short waves on the free surface around its intersection
with the beam. The radar can be located on the span of a bridge and the its beam slope is
usually about 45Ë . Locating the radar on the vertical of the maximum water depth, it is
possible to measure the maximum surface velocity. The maximum surface velocity is well
known to be different from the average one, but many researchers have resorted to the use of
the analysis tool based on the entropy theory. Based on this theory, the mean flow
velocity can be estimated after the reconstruction of the solid of flow velocity starting
from the sampled maximum surface velocity and using an entropic parameter, M,
linked to the gauged sites. Numerical integration of the Reynolds equations along
the section can also be used to link the measured local velocity with the average
value.
A second technique is based on the analysis of synchronous water level data recorded in
two different river sections far some kilometers from each other. This methodology is based
only on the analysis of the water levels, the knowledge of the river bed geometry within the
two sections, as well as the use of a diffusive flow routing numerical model, linking the
unknown upstream and downstream discharge hydrographs with the measured water level
hydrographs. The bed roughness, represented by the average Manning coefficient, is the
single parameter of an inverse problem where the water level hydrographs are the measured
data.
The 1D flow routing model is given by the following Saint Venant equations, simplified
according to the diffusive hypothesis:
-Ï-+ -q-= 0
-t -x
(1)
-h+ (S - S ) = 0
-x f 0
(2)
where q(x,t) is the discharge, h(x,t) is the water depth, Sf is the energy slope and S0 is
the bed slope. The energy slope is related to the average n Manning coefficient by the Chezy
relationship:
S = -q2n2-
f Ï2-4-3
(3)
where- is the hydraulic radius and Ï is the river section. The upstream boundary
condition of the flow routing model is given by the measured upstream water level
hydrograph and the upstream discharge hydrograph is a model output. The computational
domain is extended some kilometers downstream the second measurement section and the
downstream boundary condition is properly approximated. This avoids the use of the
downstream measured data for the solution of the system (1)-(3) and limits the model error
even in the case of subcritical flow. The optimal average Manning coefficient is obtained by
fitting the water level data available in the downstream measurement section with the
computed ones.
The results obtained using the data collected in three Italian rivers, where direct discharge
measurements were available for validation, highlight the advantages and the limits of the
adopted analysis. The main advantage is the simplicity of the hardware required for the data
acquisition, that can be easily performed continuously in time, also during very bad weather
conditions and using a long distance control.
The main limit is given by the approximations adopted in the model formulation, like the
absence of significant inflow between the two measurement sections and the roughness
homogeneity inside the sections.
Very good results have been obtained, in all the three tests, using only the upstream
measured water level hydrograph as boundary condition and calibrating the optimal average
Manning coefficient using a single discharge measurement, even very far in time from the
estimated values. We believe that the reason of this good match is that the error in
the computed upstream discharge is affected by the elevation error along all the
modeled reach and an unbiased distribution of these errors provides a limited effect on
the discharge estimation. These results suggest that combining the use of radar
measurement devices with 1D flow routing software could provide a very good and
robust measurements system. Moreover, the surface velocity measurement could be
carried out rarely, even few times a year, using the same instrument for several rivers. |
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