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ASSESSMENT OF THE USE OF RAINFALL-RUNOFF MODELS
FOR FLASH-FLOOD FORECASTING
L. MOULIN, E.GAUME, C. OBLED*
Centre d'Enseignement et de Recherche Eau Ville Environnement,
Ecole Nationale des Ponts et Chaussées, 77455 Marne la Vallée Cedex 2, FRANCE,
moulin@cereve.enpc.fr, gaume@cereve.enpc.fr
* LTHE/ENSHMG, BP 53, 38401 Grenoble Cedex 9, FRANCE obled@hmg.inpg.fr
ABSTRACT
While operational flood management requires timely and accurate forecasts and whereas
many hydrological modelling tools exist, in most cases they are not used in operational
conditions, especially on fast-reacting catchments where flash floods occur. The present
work attempts to assess the usefulness of these models for forecasting issues. In a first part,
performances of various lumped rainfall-runoff models were evaluated on 11 catchments of
the upper Loire river basin (France) with areas ranging from 20 to 3200 km². Using specific
criteria reflecting the objectives of flash flood forecasting, a first evaluation shows low
performances of conceptual models, and accuracy of results depends on anticipation of
forecasts. In a second part, for the purpose of quantifying the role of input uncertainties in
forecasting errors, areal rainfall uncertainty was estimated with geostatistical tools and a
model of temporal correlation of estimation error was proposed.
Keywords: Hydrological modelling; Rainfall uncertainty; Forecasting; Flash floods
Introduction
Among various renewable energy sources, hydroelectricity is widely used: hydroelectric power
supplies about 20% of world electricity, for instance 715 gigawatts (GW) in 2004. To manage
hydroelectric dams, accurate forecasts are necessary, especially in case of floods: in such a case, dam
managers have to release dam water before the beginning of flood, to be able then to store the
maximum volume of water in the dam reservoir. But this released water will not be used to produce
electricity, which corresponds to a loss of money. Therefore with the use of hydrological forecasts, a
compromise has to be found. In addition to management of hydroelectric dams, flood forecast is also
very crucial for urban protection and for water resources management.
Hydrological models or rainfall-runoff (RR) models convert a meteorological input (precipitation,
evapotranspiration) into a hydrological output. They are widely used and studied by scientists and
researchers. Nevertheless they are seldom used in operational context. This work tries to assess the use
of such models to forecast particular hydrological occurrences very difficult to forecast because of
their small response time and then to study the possible role of rainfall uncertainties on quality of
hydrological simulations.
Data and Methodology
The surface selected for this study is the upper Loire river basin. It is located in the central part of
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France with a total area of about 3200 km². Many hydroelectric plants with their reservoirs are present
on this area.
This region has up to 40 precipitation stations from three networks with an hourly time step. The
owners are State flood forecasters (Cristal), National Weather service (Meteo France) and the main
electricity generation and distribution company in France (EDF). This region is quite mountainous:
elevations vary from 400 to 1600 m a.s.l. The location of this region within France is shown on
Figure 1. 11 watersheds were chosen for this study with an area from 20 to 3200 km². Figure 1 shows
the location of 40 hourly raingage stations.
Fig. 1. Upper Loire River Basin and location of measurement stations
Several hydrological models, widely used by hydrologists, were selected for this study and it has been
decided to work with lumped and continuous versions of Topmodel [1], GR4J [2], HBV [3] and
IHAC [4]. Goodness-of-fit of hydrological simulations is usually estimated with a Nash and Sutcliffe
Efficiency [5] or a classical estimation of root mean square error (RMSE), whereas hydrological
forecasts are evaluated with a persistence criterion. Here, we have purposed other criteria,
corresponding more specifically to flash-floods issues. They allow us to estimate the goodness-of-fit to
the maximal value of peak, his timing and to the total flood volume.
Results
We compared 4 rainfall-runoff models. Results show that (a) if we consider a particular flood it is
possible to find better simulation from one model but (b) it is not possible to significantly discriminate
models in term of performance for all floods. In addition, performances with flood specific criteria (on
timing, volume, and peak) are low. It shows how complex the flash flood forecasting is. For the 11
studied catchments (that means about 190 floods), a timing error superior or equal to 2h is found for
36% of floods, an error on peak value superior to 20% is found for 47% of floods and an error on
volume superior to 20% is found for 28% of floods, that means only 20% of floods are correctly
simulated according to these three criteria. To explain this low performances one possibility comes
from uncertainty on areal rainfall.
Rainfall uncertainty
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The aim of this section is to characterize uncertainty on the rainfall input used by hydrological models.
From a geostatistical point of view, the rainfall over a basin is modelled as a stochastic process, a
random function. This approach allows to study variability of the rainfall process in space and time
and to quantify uncertainty on the areal rainfall estimate.
Fig. 2. Maps of estimation standard deviation (accuracy) for a time step of 1h (left) and 1day (right).
First step consists to carry out that the model proposed by Lebel [6] for a neighbouring area, can be
used with our precipitation data (a climatologic isotropic spherical semivariogram model with no
nugget effect and a range of 25 km for 1h time step and a range of 76 km for a daily time step).
Figure 2, showing normalized standard deviation of estimation on our study site, was obtained with
this model. Furthermore, cross-validation procedure was implemented to compare the estimated and
measured values. The data of a given location are removed from the data set and the variable at this
location is predicted using the remaining locations. If the mean standardised error is nearly (estimated
with a test of Student, for instance) equal to 0 and the standard deviation nearly (with a test of Fisher)
equal to 1, the model is regarded as acceptable.
In a second step, we proposed a model of temporal correlation of estimation errors.
Error (t )    Error (t  1)  
where  is a Gaussian variable and α is estimated with a trial and error procedure. When checking this
temporal correlation model with cross validation (Figure 3), values of α=0.7 to 0.9, shows acceptable
results. We finally have an estimation of the uncertainty in space and time of the rainfall input.
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Fig. 3. Validation of temporal correlation error model
Conclusions and perspectives
To conclude, let’s remind the main points: hydrological models are not used in operational conditions.
We tried to use some of them for flash floods forecasting on fast reacting catchments of Upper Loire
River basin. Results show no significant difference between models in term of performance and
general low goodness-of-fit. One possible reason for these low results can be due to uncertainty on
rainfall estimate. To characterize it we have used geostatistical tools and we have proposed a model of
temporal correlation of estimation errors. In further works, it would be interesting to introduce rainfall
uncertainties into hydrological models.
Acknowledgements
DIREN Centre and Etablissement Public Loire are thanked for their support to this study and for
providing most of data for our study. Other data were provided by EDF (streamflow and precipitation
data for 2 catchments) and Meteo France provided hourly precipitation data.
References
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