Prediction of Hydrological Risk for Sustainable Use of Water in Northern Mexico

Among surface hydrologic phenomena, it is common to find series of events of random occurrence in time. Poisson processes lead to probabilistic models that are appropriate to explain the number of events produced by certain phenomena. For instance, in surface hydrology, it is quite frequent to relate the Poisson distribution to the occurrence of rainfall events. The so-called leak distribution consists of the simultaneous use of a Poisson law to represent the probability of occurrence of an event and an exponential distribution applied to the mean magnitude of such event. Originally introduced to simulate gas leaks in distribution networks in France, from where it takes its name, the leak distribution has important applications in hydrology. In this paper, the theoretical basis of the law and the method for the estimation of its parameters are introduced. Some applications are included, such as further knowledge of the precipitation regime of hydrologic region No. 10 in Mexico. In this case, through the knowledge of the two parameters of this law, which can be associated to physical variables, it is possible to determine the temporal and spatial distribution of precipitation in detail. As an additional application, the use of this law in drought analysis is shown. Here, the distribution parameters are related to the Standardized Precipitation Index, SPI, allowing the construction of a modified SPI that much better represents the spatial variability of drought periods in the watershed. According to the results presented in this chapter, the use of the leak distribution in surface hydrology processes allows deeper knowledge of regional climatology.