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 scriptR $\mathcal{R}$, 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.

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Factors affecting the probability distribution of floods include climate change, land use modifications and the construction of infrastructures that affect flood generation and propagation. Among such infrastructures, reservoirs play an important role thanks to their storage capacity, also depending on the their purpose and operation. As an example, a limited storage capacity is reserved for flood attenuation above the maximum regulation level in the case of for example, hydropower generation or water supply for civil and irrigation uses. The effect of reservoirs on flood frequency depends on the characteristics of the reservoir but also the climatic and geomorphological factors representing meteorological forcing, runoff generation, and flood propagation within the river network.Local and regional estimates of reservoirs impact on flood frequency are fundamental for risk assessment and planning purposes (including reservoir operation). Several methods exist, ranging from detailed hydrologic/ hydraulic simulations to fast and parsimonious methods based on impact indices. While the former approaches are suitable for local studies, generally requiring a large amount of information, the latter ones are suited for large scale analyses relying on limited information about the structure and the processes. As an example, Fatichi et al. ( 2015) assess the effects of hydraulic infrastructure (including reservoirs) and climate change on the hydrological regime of the Alpine area, by using a fully distributed hydrological analysis. It is important to mention also low-resolution models, which represent an option; however, they are still quite demanding in terms of computational time for the large-scale scenario we are interested in. Indeed, we remind that any hydrodynamic model, regardless of its resolution, requires several computational steps and components (e.g., a hydrological component to evaluate the synthetic hyetograph, a hydraulic component and an iterative procedure for the calculation of the critical discharge). Instead, our focus here is on simplified methods, based on the use of suitable indices that allow for a quick estimate of the impact of reservoirs on floods at the catchment scale; this is useful for global assessments of the impact of reservoirs and a screening analysis, for both risk assessment and planning purposes.