Rational Method Time of Concentration Can Underestimate Peak Discharge for Hillslopes

Abstract

The Rational Method remains one of the most widely used approaches for estimating peak discharge in small catchments. In one widely used interpretation of the Rational Method, the maximum possible peak discharge produced by a storm with a given return period is predicted by setting the storm duration equal to the time of concentration. Whether the time of concentration maximizes peak flow for a rainfall return period, however, depends on the relationship between contributing area and storm duration. Here, we show that under many conditions, using the time of concentration in the Rational Method leads to an underestimation of peak discharge. This underestimation is illustrated using two case studies on idealized hillslopes on which runoff occurs as sheet flow. We suggest that practitioners should become cognizant of the differences between the critical duration (the storm duration that maximizes peak discharge) and the time of concentration within the Rational Method and be alert to morphology and land-use patterns that are likely to cause these timescales to diverge.