Distribution of peak flow derived from a distribution of rainfall volume and runoff coefficient, and a unit hydrograph

An expression for the distribution function of peak runoff is derived, combining results of frequency analysis of rainfall volumes with the traditional concepts of runoff coefficients and the unit hydrograph. Rainfall volume, scaled with respect to its duration, is assumed to follow a gamma distribution, whereas for the runoff coefficient a beta distribution is applied. Hydrograph characteristics are considered to be deterministic variables. A closed form analytical expression is achieved when some minor simplifications are made. The approach is tested and validated against data from 17 small Swiss drainage basins, for which unit hydrographs have been determined. The runoff response of these basins is very different in relation to both the distribution of the runoff coefficient and hydrograph characteristics, which is also reflected in the behaviour of the distribution of peak flow. Four main response classes of basins are identified that can be related to the physiography of the basins.

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