La modélisation stochastique des étiages: une revue bibliographique

Abstract

SUMMARYThe increasing pressure on the water resources requires better management of the water déficit situations may it be unusual droughts or yearly recurring low-flows. It is therefore important to model the occurrence of thèse déficit events in order to quantify the related risks. Many approaches exist for the modeling of low-flow/drought events. We présent hère a literature review of the stochastic methods. We start by clarifying the différence between lowflows and droughts, two ternis which are often used interchangeably. We then présent some low-flow and drought indicators.The stochastic approach may be divided into two catégories: Frequency analysis and stochastic processes. Most frequency analysis studies aim to assign to a flow value X a cumulative frequency, either directly using empirical distribution fonctions, or by fitting a theoretical distribution. This allows the computation of a critical flow x T corresponding to a return period T, such that P(X < x T ) = -Thèse studies use mostly the annual minima of daily flows T where the hydrological data is assumed independent and identically distributed. It is also common to analyze Q m , the annual minimum of the m-consecutive days average flow, m being generally 7,10,30, 60, 90, or 120 days, and to adopt as critical flow the m-day average having a return period of T years. The distributions which are used include the Normal, Weibull, Gumbel, Gamma, Log-Normal (2) In conclusion, we remark that frequency analysis does not take into account well the duration aspects and uses simplifying stationarity hypothesis. Séries analysis provides duration distributions for simple flow processes. The advantage of point processes is that they can model complex, dépendent and nonstationary processes. Furthermore, alternating point processes can be used to model déficit durations and generate synthetic data such as occurrences of déficit and surplus events. We argue that the duration of low-flows is an important issue which has not received a lot of attention.

A method for low-flow estimation at ungauged sites: a case study in Wallonia (Belgium)

“…Matalas (1963), Joseph (1970), Condie and Nix (1975), Tasker (1987), Leppärjärvi (1989) and Yue and Pilon (2005), amongst many others, have compared various distributions and methods to estimate parameters. The best-adjusted distribution is usually different according to the study region and the low-flow index (Abi-Zeid and Bobée, 1999). In other methods, the understanding of the generating processes of low flows contributes to the choice of distribution (Pacheco et al, 2006).…”