The frequency distributions of rainfall volume, rainfall duration, and interevent time are examined using the historical rainfall record of Toronto, Canada. Exponential probability density functions are found to fit well to the histograms of the rainfall event characteristics. The rainfall-runoff transformation on an event basis is described by an equation which incorporates the hydrologic processes commonly considered in numerical simulation models. On the basis of this equation and the exponential probability density functions of rainfall event characteristics, closed-form analytical expressions are derived for average annual runoff volume and runoff event volume return period. Deterministic continuous simulation of various urban catchments are conducted using the Toronto historical rainfall record as input. Close agreement between simulation model results and those from analytical expressions is obtained. The event-based probabilistic models for the determination of average annual runoff volumes and runoff event volumes with specified return periods from urban catchments are proposed as an alternative to continuous simulation models. ¿ 1998 American Geophysical Union