Runoff peaks from two-dimensional laboratory watersheds

Abstract

Abstract Based upon 578 laboratory hydrographs, a method has been developed to describe the magnitude and time of occurrence of the peak discharge. The experiments were conducted on a 40 × 40-ft. (12.2 × 12.2-m) large watershed and on portions of it. The independent experimentation variables were the rainfall intensity (up to 12 in.hr.−1 or 305 mm hr.−1), the rainfall duration (up to 8 min.), the main watershed slope (0.5–3%), the area exposed to rainfall (nine different configurations) and the surface roughness (two different materials). A time of concentration has been defined as the time from the initiation of the rainfall until the time when the discharge begins with a gradual approach towards its equilibrium state. This approach is described by a straight inclined line on a semilog plot of the hydrograph. The time of concentration is found to be proportional to the product of the rainfall intensity and the watershed slope raised to a power of −0.25. The proportionality coefficient is larger for the rougher surface, and also for watersheds (configurations) where the area exposed to rainfall is not adjacent to the outlet. The time of concentration, as is defined here, is not related to the length of flow along the watershed. The ratio of the peak discharge to the supply rate is found here as a linear function of the ratio of the rainfall duration to the time of concentration. A rainfall whose duration is equal to the time of concentration results in a runoff whose peak is equal to the supply rate. The functional relationship between the ratio of the peak discharge to the supply rate and the rainfall duration, that has been found in the laboratory, is identical to the original relationship for outdoor urban watersheds from which the rational formula was developed almost a century ago. The ratio of the time of peak to the time of concentration is found to be proportional to the ratio of the rainfall duration to the time of concentration raised to a power of ∼0.5. A similarity has been found between these results and the peak reduction factor found for small outdoor watersheds in Illinois.