A holistic stochastic model for precipitation events

In the western United States, much of the annual precipitation falls during relatively few storm events. When precipitation is measured as daily (or hourly, etc.) accumulations, these events appear as sequences of various durations. We describe a trivariate probability distribution and assert that it provides a natural description for the durations, magnitudes, and maximum intensities of such events. We show that this distribution, in its most straightforward application, indeed describes precipitation events composed of daily observations at most long-term weather stations across the western United States, allowing for a flexible assessment of specific event probabilities and return periods with respect to their three defining components. This characterization opens the door to further understanding of risk associated with out-of-sample meteorological events.