Return Period and Risk of Hydrologic Events. I: Mathematical Formulation

In this study, the rational method is expanded into the rational hydrograph method in which the time of concentration is considered as the system memory and the contributing rainfall depth to the present runoff rate is defined as the accumulated precipitation over the past up to the time of concentration. In doing so, the complete runoff hydrograph can be generated under a continuous nonuniform hyetograph. When the continuous hyetograph is uniform in time, the rational hydrograph method is reduced to the rational method. Using the moving average formulas developed in this study, the event-averaged time of concentration and runoff coefficient can be derived by the least-square method. A new formula for estimating the time of concentration was derived from 25 rainfall/runoff events observed in four urban watersheds. This approach was tested by laboratory observations, and rainfall/runoff events recorded from small watersheds in states of Maryland and Colorado.