BIVARIATE EXPONENTIAL MODEL APPLIED TO INTENSITIES AND DURATIONS OF EXTREME RAINFALL

The Poisson model for rainfall occurrences in which storm intensity and duration are represented by two independent random variables is extended to consider intensity and duration as bivariate random variables each with a marginal exponential distribution. A numerical optimization method using annual maxima is adopted for parameters estimation. Comparison is made with the results of a numerical procedure which uses the Gumbel distribution as an approximation to the probability distribution of the extremes of the bivariate exponential model. A case study is presented using data from 18 raingauge stations in northern Italy. For rainfall durations of practical interest the theoretically derived relationships between probabilities and intensities compare favourably with observed relationships.