Patrick Arnaud

Using a stochastic model for generating hourly hyetographs to study extreme rainfalls

Abstract A stochastic model for generating hourly hyetographs has been developed using data from observed precipitation records to simulate rainfall patterns. This model makes it possible to study maximum precipitation distributions for normal or exceptional frequencies over long periods of time. The modelling provides observations (up to 10-year frequency) of quantiles similar to those observed by directly fitting a law of statistical distribution onto an observed distribution. Differences occur for rare frequency quantiles. Modelled rainfall frequency distributions behave in an over-exponential way (i.e. greater than strictly exponential) at infinity, yielding higher results than those obtained using standard fittings. One factor that is considered in modelling can explain this behaviour: the persistence of storms within a rainfall episode which causes high rainfall accumulation. Thus modelling the observed phenomenon provides an innovative approach in studying extreme occurrences.

Sensitivity of hydrological models to uncertainty in rainfall input

Abstract Different approaches used in hydrological modelling are compared in terms of the way each one takes the rainfall data into account. We examine the errors associated with accounting for rainfall variability, whether in hydrological modelling (distributed vs lumped models) or in computing catchment rainfall, as well as the impact of each approach on the representativeness of the parameters it uses. The database consists of 1859 rainfall events, distributed on 500 basins, located in the southeast of France with areas ranging from 6.2 to 2851 km2. The study uses as reference the hydrographs computed by a distributed hydrological model from radar rainfall. This allows us to compare and to test the effects of various simplifications to the process when taking rainfall information (complete rain field vs sampled rainfall) and rainfall–runoff modelling (lumped vs distributed) into account. The results appear to show that, in general, the sampling effect can lead to errors in discharge at the outlet that are as great as, or even greater than, those one would get with a fully lumped approach. We found that small catchments are more sensitive to the uncertainties in catchment rainfall input generated by sampling rainfall data as seen through a raingauge network. Conversely, the larger catchments are more sensitive to uncertainties generated when the spatial variability of rainfall events is not taken into account. These uncertainties can be compensated for relatively easily by recalibrating the parameters of the hydrological model, although such recalibrations cause the parameter in question to completely lose physical meaning. Citation Arnaud, P., Lavabre, J., Fouchier, C., Diss, S. & Javelle, P. (2011) Sensitivity of hydrological models to uncertainty of rainfall input. Hydrol. Sci. J. 56(3), 397–410.

Evaluating flash-flood warnings at ungauged locations using post-event surveys: a case study with the AIGA warning system

Abstract This article presents a comparison between real-time discharges calculated by a flash-flood warning system and post-event flood peak estimates. The studied event occurred on 15 and 16 June 2010 at the Argens catchment located in the south of France. Real-time flood warnings were provided by the AIGA (Adaptation d’Information Géographique pour l’Alerte en Crue) warning system, which is based on a simple distributed hydrological model run at a 1-km2 resolution using radar rainfall information. The timing of the warnings (updated every 15 min) was compared to the observed flood impacts. Furthermore, “consolidated” flood peaks estimated by an intensive post-event survey were used to evaluate the AIGA-estimated peak discharges. The results indicated that the AIGA warnings clearly identified the most affected areas. However, the effective lead-time of the event detection was short, especially for fast-response catchments, because the current method does not take into account any rainfall forecast. The flood peak analysis showed a relatively good correspondence between AIGA- and field-estimated peak values, although some differences were due to the rainfall underestimation by the radar and rainfall–runoff model limitations. Editor Z.W. Kundzewicz; Guest editor R.J. Moore Citation Javelle, P., Demargne, J., Defrance, D., Pansu, J. and Arnaud, P., 2014. Evaluating flash-flood warnings at ungauged locations using post-event surveys: a case study with the AIGA warning system. Hydrological Sciences Journal, 59 (7), 1390–1402. http://dx.doi.org/10.1080/02626667.2014.923970

Uncertainties of extreme rainfall quantiles estimated by a stochastic rainfall model and by a generalized Pareto distribution.

Abstract The hourly rainfall stochastic model SHYPRE generates long hourly rainfall series and enables the estimation of distribution quantiles. Two different uncertainty analyses are proposed, based on frequential and Bayesian methods, to quantify the effect of sampling distribution and parameter uncertainties on the quantile estimations. The results are compared with those of a regional generalized Pareto distribution (GPD) based on extreme value analysis, with a regionally fixed value of the shape parameter. The GPD and SHYPRE are shown to have similar uncertainties. The application of regional approaches is shown to reduce sampling sensitivity in estimations, especially when few data are available. The study is based on a 122-year daily rainfall series in Marseille, France.

La méthode SHYREG débit—application sur 1605 bassins versants en France métropolitaine

Résumé La méthode SHYREG est une approche développée pour la connaissance régionale de l’aléa pluvial (SHYREG pluie) et hydrologique (SHYREG débit) en tout point du territoire français. Elle est basée sur le couplage d’un générateur stochastique de pluie horaire et d’un modèle hydrologique. Cet article présente les résultats de la mise en œuvre de la méthode sur 1605 bassins versants répartis sur la France métropolitaine. Sur les fréquences courantes (c.à.d. périodes de retour inférieures à 10 ans), la méthode restitue correctement les quantiles de débit de crue ajustés à une loi statistique sur les observations (loi GEV, selon le critère de Nash-Sutcliffe). Plusieurs critères sont utilisés pour valider l’extrapolation des débits à des fréquences extrêmes: (a) en la confrontant à de longues chroniques de débits observés, (b) en analysant dans le modèle hydrologique la saturation du réservoir de production synonyme de comportement asymptotique avec les pluies, et (c) en étudiant la stabilité de la méthode à travers les critères statistiques. Editeur Z.W. Kundzewicz; Editeur associé G. Mahé Citation Aubert, Y., Arnaud, P., Ribstein, P., et Fine, J.-A., 2014. La méthode SHYREG débit, application sur 1605 bassins versants en France Métropolitaine. Hydrological Sciences Journal, 59 (5), 993–1005.

Relevance of an at-site flood frequency analysis method for extreme events based on stochastic simulation of hourly rainfall

Abstract Extreme events are rarely observed, so their analysis is generally based on observations of more frequent values. The relevance of the flood frequency analysis (FFA) method depends on its capability to estimate the frequency of extreme values with reasonable accuracy using extrapolation. An FFA method based on stochastic simulation of flood event is assessed based on its reliability and stability. For such an assessment, different training/testing decompositions are performed for a set of data from more than 1000 gauging stations. We showed that the method enables relevant ‘predictive’ estimates, e.g. by assigning correct return periods to the record values that are systematically absent in calibration datasets. The model is also highly stable vis-a-vis the sampling. This characteristic is linked to the use of regional statistical rainfall data and a simple rainfall–runoff model that requires the calibration of only one parameter. Editor D. Koutsoyiannis Associate editor Q. Zhang

Extreme rainfall analysis by a stochastic model: impact of the copula choice on the sub-daily rainfall generation

The hourly rainfall stochastic model SHYPRE is based on the simulation of descriptive variables. It generates long series of hourly rainfall and enables an at-site empirical estimation of distribution quantiles over France. The present study focuses on the improvement of the rainfall generator by modelling storm characteristics dependence by the copula approach. An evaluation framework is proposed to evaluate the goodness-of-fit of a given method over a territory with a particular care for the extreme part of the distribution. It is used to illustrate the impact of the copula choice on the estimation of rainfall quantiles. Contrary to Clayton copula, both the Gumbel’s and Frank’s permit to improve significantly the performance of the model in the sub-daily rainfall generation. According to our criteria, the final version of SHYPRE proposes a better estimation of rainfall quantiles than the classical extreme value distributions.

Nouvelle approche de la prédétermination des pluies extrêmes

A stochastic model generating hourly hyetographs uses information contained in observed rainfall in order to reproduce it. When used over very long simulation periods, it makes it possible to study rainfall on all frequency scales. The modelling of hyetographs leads to a distribution of maximum rainfall with a behaviour that differs from that obtained with more classical models using a simple exponential law. The modelling of the internal structure of the rainy episodes conditions this behaviour by randomly generating strong rainfall events. Moreover, the modelling appears robust and not very sensitive to sampling. This new approach of predetermining the rainfall remains however statistical: its results are conditioned by the hypotheses of the model, as validation is impossible beyond the observed frequencies.