Estimation des valeurs extrêmes de débits maximaux annuels en Tunisie : un retour par l'approche multifractale

Estimation of peak annual river discharges in Tunisia: a Multiscaling approach

¹ Ecole Nationale d'Ingénieurs de Tunis.
² Intitut National des Sciences Appliquées et de Technologie.

Abstract

Following Eagleson (1967), the river discharge Q(S, t) may be considered as a time-space process of the basin area S and the time t. Thus, for an given rainfall event, the peak discharge Q_max (S) is a spatial process according to the watershed area. And its multifractal behavior (Lovejoy and Schertzer (1995 a and b) ; Pandey and al. (1998) is investigated. Estimated parameters for multiplicative cascade model are the multifractal index α =1.77, the codimension of the mean C₁ = 0.1 and the deviation from conservation conditions H = 0.414. We find that the critical moment after which statistical moments diverge in the observed series is q_D = 2.2. Developments about consequences for the hydrologic risk assessment (p is the non exceedance value) lead to R_λp ∝ p^-0.45. They constitute an objective basis for the development of runoff-area regression relationships. Owing to the hyperbolic rather than exponential probability tail, this method leads to estimated quantiles for T = 100 years and 1 000 years which are greater then those we obtained through regional and frequency approachs.