Abstract. L (Linear) moments are used in identifying regional flood frequency distributions for different zones Tunisia wide. 1134 site-years of annual maximum stream flow data from a total of 42 stations with an average record length of 27 years are considered. The country is divided into two homogeneous regions (northern and central/southern Tunisia) using a heterogeneity measure, based on the spread of the sample L-moments among the sites in a given region. Then, selection of the corresponding distribution is achieved through goodness-of-fit comparisons in L-moment diagrams and verified using an L moment based regional test that compares observed to theoretical values of L-skewness and L-kurtosis for various candidate distributions. The distributions used, which represent five of the most frequently used distributions in the analysis of hydrologic extreme variables are: (i) Generalized Extreme Value (GEV), (ii) Pearson Type III (P3), (iii) Generalized Logistic (GLO), (iv) Generalized Normal (GN), and (v) Generalized Pareto (GPA) distributions. Spatial trends, with respect to the best-fit flood frequency distribution, are distinguished: Northern Tunisia was shown to be represented by the GNO distribution while the GNO and GEV distributions give the best fit in central/southern Tunisia.

Best-fit distributions of floods in Tunisia are determined based on L-moment diagram and statistical tests. GEV and GLO distributions provided the best fit to seven and three regions of Tunisia respectively. In each homogeneous region, hierarchical approaches and regression models were developed for gauged and ungauged watersheds. The first two parameters of the distributions (GEV and GLO) were estimated from measured data while the third parameter was represented by the regional average value weighted by the record length of all stations in the region. The obtained parameters were correlated to the catchment size. Quantiles obtained by the proposed models were compared with those obtained using local conventional models. Statistical tests showed that the proposed models provided a much better agreement with observed floods than any of the conventional methods generally used in Tunisia.

The method of "historic event" is used to generate synthetic hyetographs based on statistical analysis of precipitation data. A synthetic triangular model was developed based on rainfall data of Zioud watershed (central Tunisia) with a standard time step of one hour. A database of 2799 observed rainfall events was used to provide statistical parameters for a simple triangular-shaped hyetograph model. The developed model provides a synthetic hyetograph in dimensionless form for different storm durations (2, 3 and 4 hours). For a given season and location, the variation of the first dimensionless moment with duration was relatively small, with an average range of 13% for all the stations. The resulting dimensionless hyetographs were found to be nearly identical when they were non-dimensionalized using the rainfall depth and duration, showing some seasonal effect and insignificant effects of the rainfall duration. A good agreement between simulated and observed hyetographs was achieved based on not only visual impressions, but also statistical numerical and graphical tests. Un modèle triangulaire pour la génération de hyétogrammes synthétiquesRésumé La méthode de l'averse historique est utilisée pour générer des hyétogrammes synthétiques moyennant l'analyse statistique de données de précipitation. Un modèle synthétique triangulaire a été établi sur la base des séries pluviométriques du bassin versant de Zioud (Tunisie centrale), avec un pas de temps standard d'une heure. Une base de données de 2799 événements de pluie observés a été utilisée pour fournir les paramètres statistiques d'un modèle de hyétogramme de forme triangulaire simple. Le modèle développé fournit un hyétogramme synthétique sous une forme adimensionnelle pour différentes durées d'averse (2,3 et 4 heures). Pour une saison et un lieu donnés, la variation du premier moment adimensionnel selon la durée est relativement faible, avec une gamme moyenne de 13% pour l'ensemble des stations. Les hyétogrammes adimensionnels obtenus sont presque identiques lorsqu'ils sont normalisés par rapport à la hauteur de pluie et à la durée, présentant un effet saisonnier et une influence non significative de la durée de la pluie. Un bon accord entre les hyétogrammes simulés et observés est obtenu, non seulement en termes d'impressions visuelles mais aussi de tests numériques et graphiques. Mots clés hyétogramme synthétique; modèle triangulaire; analyse statistique; prédétermination hydrologique

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Abstract. L (Linear) moments are used in identifying regional flood frequency distributions for different zones Tunisia wide. 893 site-years of annual maximum stream flow data from a total of 37 stations with an average record length of 24.14 years are considered. The country is divided into two homogeneous regions (northern and central/southern Tunisia) using a heterogeneity measure, based on the spread of the sample L-moments among the sites in a given region. Then, selection of the corresponding distribution is achieved through goodness-of-fit comparisons in L-moment diagrams and verified using an L-moment based regional test that compares observed to theoretical values of L-skewness and L-kurtosis for various candidate distributions. The distributions used, which represent five of the most frequently used distributions in the analysis of hydrologic extreme variables are: (i) Generalized Extreme Value (GEV), (ii) Pearson Type III (P3), (iii) Generalized Logistic (GLO), (iv) Generalized Normal (GN), and (v) Generalized Pareto (GPA) distributions. Spatial trends, with respect to the best-fit flood frequency distribution, are distinguished: Northern Tunisia was shown to be represented by the GEV distribution while the GLO distribution gives the best fit in central/southern Tunisia.