A probabilistic description of rain storms incorporating peak intensities

Design storms with standardized hyetograph shapes and selected combinations of storm depths and durations are widely used in engineering hydrology. The key distinguishing feature between equal-duration design storms is their distinct intensity distributions. Differences in design storm hyetographs do not affect storm frequency, since only the frequency of the combination of storm depth and duration are determined through the use of Depth–Duration–Frequency curves. Probability distributions of peak intensity within rainfall events are not determined in current practice. Some current research applies copulas to joint distributions of rainstorm variables, but most of these are limited to bivariate distributions, and those that are developed for trivariate distributions do not address key variables important to everyday practice, or are limited by complexity of analysis. An alternative approach to characterizing peak storm intensity, intensity peak factor, together with its probability distribution is developed in this paper. An Archimedean copula is applied to describe the joint probability distribution of storm duration with intensity peak factor. That joint distribution is combined with the probability distribution of storm depth, to produce a joint probability distribution for storm depth, duration, and peak intensity. The result is a simple approach to fully characterizing the storm variables of direct interest to practitioners, thereby providing a complete probabilistic description of the return period or frequency of a selected design storm.