Extreme value modeling for environmental data analysis

Abstract

This article deals with the problem of stochastic modeling the total maximum amount of flushed rainfall in a watershed when data come from daily rainfall measurements in various locations inside a watershed. The annual total maximum \(Y\) of a random number \(N\) of independent total extremes in a given year is of great interest, for instance when dealing with the prediction of the largest flood that might occur in a given year in order to construct hydraulic protections in populated areas. Here, we propose a joint probability model for \(Y\) and \(N\) on the basis of the peaks over a threshold method. From this model, it is possible to obtain the marginal distribution of \(Y\), which includes information contained in the \(N\) variable. It is also possible to obtain the conditional distribution of \(N\) given that \(Y\) is less than a given value \(y\), which provides information about predicting the mean number of extreme events \(N\) in a year. Some discussion is included on two methods for estimating the parameters involved in the distribution of \(Y\). An application of this model is provided where daily rainfall data coming from some basins located in a southeast region of Mexico are analyzed.