Analytical derivation of reservoir routing and hydrological risk evaluation of detention basins

This paper presents two related subjects of urban hydrology, i.e., a closed-form reservoir routing equation for peak outflow; and the evaluation of the hydrological risk of an uncontrolled detention basin, where the latter requires the coupling of reservoir routing and a risk assessment method. Here, the hydrological risk is defined as the probability that peak outflow from the detention basin exceeds the target value set for preventing downstream flooding. Among the available risk assessment methods, the mean-value first-order second-moment (MFOSM) and advanced first-order second-moment (AFOSM) methods are known as giving a good balance between accuracy and computational requirements, and are chosen in this study. To facilitate the application of the MFOSM and AFOSM methods, a closed-form equation is derived for reservoir routing. The developed routing model yields an estimate of peak outflow very close to the value obtained from iterative methods, and exhibits a great improvement over similar closed-form equations proposed in earlier studies. Then, the developed routing model is coupled with the MFOSM and AFOSM methods to evaluate the hydrological risk of detention basins. The coupled scheme incorporates uncertainties residing in peak inflow, inflow duration time, ratio of peak inflow time to inflow duration time, total cross-sectional area of orifice outlets, orifice coefficient, constant surface area of reservoir, and orifice formula error correction factor. The developed methodology offers a technique applicable for the quantitative evaluation of the hydrological risk of urban storm water storage facilities.