Ces 10 dernières années, certains épisodes pluvieux marquants ont entraîné une prise de conscience du risque encouru par les agglomérations modernes face à des phénomènes hydrologiques particuliers. La gestion du risque pluvial passe par une amélioration de la connaissance de l'aléa pluvieux. Dans cet article, on développe une approche stochastique exploitant le potentiel d'informations contenu dans un échantillon d'épisodes pluvieux extrêmes ayant ou ayant pu engendrer des crues dévastatrices. Une approche spatiale est utilisée pour caractériser l'aléa pluvieux. A partir d'un jeu d'épisodes extrêmes sélectionnés sur une région méditerranéenne entre 1958 et 1993, on estime l'aire des surfaces où les précipitations dépassent un seuil de pluviométrie fixé. L'estimation des aires des surfaces pluvieuses nécessite le recours à un modèle d'interpolation spatiale des hauteurs de pluie. La justification du krigeage climatologique est présentée ainsi que l'estimation des paramètres du modèle retenu. Les distributions des aires des isohyètes, à différents seuils de pluviométrie, sont ensuite analysées. Il apparaît que quelle que soit l'isohyète considérée, une loi gamma peut être ajustée sur l'échantillon de surface. Une relation entre les paramètres des lois permet une généralisation du modèle probabiliste à n'importe quel seuil de pluie compris entre 50 et 300 mm.
In the last 10 years many cities in southern Europe have been affected by heavy rainfall events leading to severe runoffs. The assessment of rainfall risk requires a better knowledge of the climate hazards and particularly rainfall hazards. The most usual rainfall risk assessment is based on a stochastic approach and point rainfall frequency analysis remains the most-used method. However, in the Mediterranean region great variations of rainfall depth frequencies can be observed according to the point considered, and according to the period of observation. Moreover the recent hydrological catastrophes which have affected the south of France have been studied on an individual basis and studies based on a global approach, using the whole information contained in a sample of several observations, remain unusual.A rainfall risk assessment has been proposed in the Languedoc-Roussillon, a 28,000 km2 region along the Mediterranean sea. This study has been based on a sample of 93 daily extreme rainfall events, which have occurred in the region. They have been extracted from the Météo-France database for the 1958-1993 period of observation, if a rainfall depth greater or equal to 190 mm in 24 hours or 48 hours (because of the sampling constraints) has been observed at one rain gauge in the region at least. The spatial extension of the rainy surfaces defined at different rainfall thresholds, varying from 50 to 250 mm/24 hours and 50 to 300 mm/48 hours, have been investigated. For a given threshold, the area of the rainy surface corresponding to a given frequency has been estimated.The estimation of the rainy surfaces area has required the choice of a spatial interpolation method: the climatological kriging method has been used. This method is based on the assumption that all the rainfall events came from the same meteorological situation, but some studies have shown that there may be different meteorological situations (TOURASSE, 1981; RIVERAIN, 1997). Thus the sensitivity of the interpolation model according to this assumption has been tested. A different interpolation model has been estimated for each season because the information about the meteorological situations which have generated the selected events is not available. Only the variogram over June to August differs significantly from the "annual" variogram. The differences between the rainy surfaces area estimated with the "seasonal" variogram and the "annual" one did not exceed 10% in proportion of the areas estimated with the "annual" variogram. The rainy surface areas are less sensitive to the climatological assumption. For each time step and each rainfall threshold considered, it has been observed that the two parameter Gamma law could best fit the frequencies of the rainy surface areas. The relation between each of the Gamma law parameters and the rain threshold has been estimated (relations R1 and R2). The quantiles of the rainy surface areas have been estimated with two methods :- directly from the fitting of a Gamma function to the sample of rainy surface areas; - using the previous relation to estimate the Gamma function parameters. It has been observed that the quantiles estimated with the second method were close to those estimated with the first method, even if the fitting errors of the R1 and R2 relations were considered. Such a result allows one to estimate the regional frequency of a rainy surface areas defined at each threshold between 50 and 300 mm/48 hours or 50 and 250 mm/24 hours. However extrapolations beyond the studied threshold intervals should not be done because the R1 and R2 relations are empirical.The isohyets area quantiles have been defined: they represent the isohyet area corresponding to a given rainfall threshold and a given return period. The isohyet area quantiles may be very large; for example at the 200 mm / 48 hours threshold the isohyets area represents 15% of the region (4500 km2). This can be explained by the time step dt. The isohyets area represents the dynamics of the convective cells integrated over dt, which remains unknown but is greater than 48 hours. Moreover for a given rainfall threshold and a given event, several separate isohyets could be observed. However in this study only the all areas corresponding to the different isohyets have been estimated. Thus it could give a very large area when the event affects the all region.The ratio between the isohyet area quantiles at the 48-hour and 24-hour time steps evolved from 1.3 to 20: it increased with the rainfall threshold for a given return period. This can be explained by the strong dynamics of the convective cells which generate the highest rainfall depths, compared to the rain cells at a larger spatial scale, which generate lower rainfall depths. Thus the isohyet areas defined at a high rainfall threshold are sensitive to the time steps than isohyet areas defined at a smaller rainfall threshold.The frequencies estimated in this study have been regional frequencies, but it appears that the isohyet areas are not independent of the event's location. However, at this stage the sample is too small to allow a study of conditional frequencies. In order to perform this study the sample has already been enlarged by considering all the French Mediterranean region which have been affected by heavy rainfall depths. It has been based on all the information included in the Météo-France data base over this region (since 1870). The rainfall threshold used to select the rainfall events has been diminished to 90 mm/ 24 hours to include the high intensity events over short time steps which could generated severe floods, especially over small catchments.Combined with the information about the meteorological situations, the development of this work should allow improved studies of the relations between the rainy surfaces and the meteorological situations at the origin of the rainfall events.
