The stochastic modeling of low flows by the alternating point processes approach: methodology and application

The increasing demand on water resources requires better management of the water deficit situation, may it be unusual droughts or yearly recurring low flows. We propose to use alternating non-homogeneous point processes to model the occurrences and durations of water deficits and surplus. The advantage of this approach is that it is a relatively simple way to model complex, dependent and non-stationary phenomena. It can be used as an alternative to developing more intricate physically based models. Furthermore, alternating point processes can be used to generate synthetic data that may reveal useful for analysis purposes. Most importantly, they allow to subsequently quantify risks related to deficit durations. Our methodology, developed for two types of events under non-homogeneous conditions, consists of six steps: identification of event type, choice of point process, choice of intensity function shape, estimation of intensity function parameters, testing model fitness, and sensitivity analysis. Also included are two new models based on the non-homogeneous Poisson conditional process that take into account external variables such as precipitation and temperatures. We begin with a classification of some point processes and their relation to each other. We describe the procedure for using the pertinent statistical tests. We present our modeling results for 10 Canadian rivers where we observed that in most cases, the simpler point processes were quite adequate.