Impact of detention dams on the probability distribution of floods

Abstract. Detention dams are one of the most effective practices

for flood mitigation. Therefore, the impact of these structures on the basin

hydrological response is critical for flood management and the design of

flood control structures. With the aim of providing a mathematical framework

to interpret the effect of flow control systems on river basin dynamics, the

functional relationship between inflows and outflows is investigated and

derived in a closed form. This allowed the definition of a theoretically

derived probability distribution of the peak outflows from in-line detention

basins. The model has been derived assuming a rectangular hydrograph shape

with a fixed duration and a random flood peak. In the present study, the

undisturbed flood peaks are assumed to be Gumbel distributed, but the

proposed mathematical formulation can be extended to any other flood-peak

probability distribution. A sensitivity analysis of parameters highlighted

the influence of detention basin capacity and rainfall event duration on

flood mitigation on the probability distribution of the peak outflows. The

mathematical framework has been tested using for comparison a Monte Carlo

simulation where most of the simplified assumptions used to describe the dam

behaviours are removed. This allowed demonstrating that the proposed

formulation is reliable for small river basins characterized by an impulsive

response. The new approach for the quantification of flood peaks in river

basins characterized by the presence of artificial detention basins can be

used to improve existing flood mitigation practices and support the design of

flood control systems and flood risk analyses.