Development of tail models and scale invariance for regional estimation ofdrought flows

This paper proposes a methodology for the regional analysis of drought flow s. This approach lies on the combination of two procedures. (i) The simple scale invariance method for regional series of drought flows, based on the analysis of the relation moments-surfaces or the relation quantiles-surface s, explains the spatial variability of drought processes by their indexatio n on a series of scale parameters, essentially the size of the drainage bas in. This procedure principally aims at delimitating homogeneous regions, an d this characterizes the first condition of a regional estimation. (ii) Fre quency analysis of minimum flows, with the approach using tail conditional models, consists in adjusting a probability distribution to values that are smaller than or equal to some given threshold. As a fact, this procedure g ives some more weight to the lower part of the distribution by defining a p riori a level of censure, mainly a threshold u(i) called ceiling value. Thi s procedure establishes the second condition of a regional estimation, that is, the determination of a regional estimation model. This methodology has been applied to analyze drought flow characteristics of 187 hydrometric st ations scattered in the province of Quebec. Results have shown that the fir st to the sixth order non-central moments follow a simple scale invariance with respect to the area of the watershed. As a result, analysis of the res iduals of these six moments has allowed classifying hydrologically similar watersheds. On the basis of the results from the analysis on the residuals of the sixth moment, the province has been divided into two homogeneous reg ions. The behaviour of the minimum flows from these different regions has s hown that they, too, followed a simple scale invariance.