This paper proposes a method to easily quantify the attenuation due to a reservoir on downstream flood peak discharges, that is, to the downstream flood frequency curve. Using a parsimonious Instantaneous Unit Hydrograph‐based model, we show that the flood peak attenuation is mainly controlled by three system characteristics: (1) the reservoir position along the river channel, (2) the spillway dimensions, quantified by the reservoir storage coefficient; and (3) the storage capacity. These three system characteristics are quantified by three dimensionless numbers, which are derived analytically for an idealized catchment. The degree of flood peak attenuation increases for increasing storage capacity and spillway dimensions, in different ways depending on the reservoir position along the river channel. An optimal position exists, which maximizes the degree of flood peak attenuation, and is in general different from the outlet of the catchment. Interestingly, for large reservoirs with relatively small spillways, a range of quasi‐optimal positions exists. With the Instantaneous Unit Hydrograph‐based model, we also investigate how the duration of extreme rainfall relevant for determining the maximum flood peaks at the catchment outlet changes depending on the three system characteristics. Some of the assumptions of the method (i.e., catchment simple morphology and linearity of reservoir response) are relaxed in a real‐world example, which demonstrates that the synthetic results approximate well what would be obtained by a more realistic model.

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[1] A stochastic model is developed for the analysis of the traveltime distribution f t in a hillslope. The latter is described as made up from a surficial soil underlain by a less permeable subsoil or bedrock. The heterogeneous hydraulic conductivity K is described as a stationary random space function, and the model is based on the Lagrangian representation of transport. A first-order approach in the log conductivity variance is adopted in order to get closed form solutions for the principal statistical moments of the traveltime. Our analysis indicates that the soil is mainly responsible for the early branch of f t , i.e., the rapid release of solute which preferentially moves through the upper soil. The early branch of f t is a power law, with exponent variable between À1 and À0.5; the behavior is mainly determined by unsaturated transport. The subsoil response is slower than that of the soil. The subsoil is mainly responsible for the tail of f t , which in many cases resembles the classic linear reservoir model. The resulting shape for f t is similar to the Gamma distribution. Analysis of the f t moments indicates that the mean traveltime is weakly dependent on the hillslope size. The traveltime variance is ruled by the distribution of distances of the injected solute from the river; the effect is coined as source zone dispersion. The spreading due to the K heterogeneity is less important and obscured by source zone dispersion. The model is tested against the numerical simulation of Fiori and Russo (2008) with reasonably good agreement, with no fitting procedure.