Closed Formulas for Design of Combined Detention Ponds

Urban development leads to persistent increase in the number of detention ponds, mostly for flood control purposes. Adding a detention pond soon leads to the need for planning detention ponds over successive subbasins in a coordinated manner, which are here named combined detention ponds. This study analyzes these detention pond combinations using the rational method and kinematic wave routing for arbitrary climate, morphology, and surface conditions. Input and output hydrographs are obtained with three decision variables (downstream admissible flow, distance at the channel, and pond storage volume) and five dimensional parameters (intense rainfall formula exponent, return period, channel wave celerity, runoff coefficient, and basin area). The dimensionless variables and parameters allowed two closed formulas, one for a pond placed downstream in the same channel and the other for a pond also placed downstream, but in a channel’s tributary. The results demonstrate that both the distance between ponds in the same channel and the downstream pond storage can always be solved given the channel admissible flow, whereas a tributary pond can only be solved if the channel admissible flow increases downstream from the tributary. In both cases, the storage volume increases downstream by a factor of 2–5 depending on the channel’s distance from the upstream detention pond and on the upstream admissible flow. Because the peak of tributary outflow anticipates the peak of the lateral flow, tributary ponds are less sensitive to placement and need less storage volume, but the channel’s admissible flow must significantly increase downstream.