A New Physically Based Index to Quantify the Impact of Multiple Reservoirs on Flood Frequency at the Catchment Scale Based on the Concept of Equivalent Reservoir

The presence of multiple reservoirs in a catchment generally induces the attenuation of flood events, thus mitigating their impact in downstream flood-prone areas. Such mitigation results from the superposition of several contributions, coming from the regulated (i.e., altered by reservoir) or unregulated subcatchments as determined by the reservoirs spatial distribution within the catchment. Understanding how multiple reservoirs affect the probability distribution of flood peak at the catchment scale is a difficult task, requiring a detailed and generally costly hydrologic/hydraulic simulation. We provide here a simple yet physically based mathematical framework to account for the effect of multiple reservoirs, located in series along the main channel, on peak flood quantile at the catchment scale. The framework allows to disentangle the role of the main relevant parameters controlling the system behavior, such as the number of reservoirs, their relative location and relative storage coefficient within the catchment, and a climatic parameter governing rainfall variability in time. The combined effect of the reservoirs in reducing the peak flow is represented by a global index R, which is bounded between zero and unit and it is independent of the return period. The index is based on the concept of equivalent reservoir and is easily calculated by the analytical formulas provided in this study, as function of the above parameters.