Occurrence des sécheresses dans le bassin de la Medjerda (Tunisie) Drought occurrence in the Medjerda basin

Résumé

La probabilité d'occurrence des sécheresses dans le bassin de la Medjerda (Tunisie) est calculée en se basant sur les totaux pluviométriques annuels de 35 postes sur une période de quarante ans. Les moments statistiques des volumes de déficits face à une demande en eau fixée sont estimés par la méthode des séries. Une fonction de répartition marginale des volumes de déficits est proposée, ainsi que des fonctions de répartition conditionnelles pour des durées sèches de un à six ans. Plusieurs lois de probabilité couramment utilisées en hydrologie sont étudiées. Des applications de ce modèle sont présentées.

Mots-clés:

• Sécheresse,
• méthode de séries,
• pluviométrie

Abstract

The probability of occurrence of drought in the Medjerda basin (Tunisia) is estimated using the stochastic process based on the measurement of total annual rainfalls taken in 35 stations over a period of 40 years.

Marginal and conditional distributions of shortage volumes are analytically proposed at each location. Mean, standard deviation and skewness coefficients of shortage volumes are used for setting up a Person type III model. Then, similarly to I-D-F curves, drought duration curves are plotted within a given threshold. A general formulation of statistics of shortage volume population is given. It is expressed in terms of the position, the location and the scale parameters of the rainfall generator process, for a given threshold value. As an application, some useful distributions in hydrology are examined (Normal, Galton, Gamma, Weibull) and expected drought volumes are estimed.

Model verification is performed using three stations of the basin for which the observed sample was extended to a period of 58 years. Comparison between observed and calculated statistics of shortage shows a good agreement. Expected shortage volumes are mapped using the average rainfall at each station as a threshold. A second threshold was based on an agricultural water demand. The corresponding water supply expected was mapped.

Keywords:

• Drought,
• run,
• rainfall