Abstract
Abstract. This paper develops a theoretical framework to investigate the core dependence of peak flows on the geomorphic properties of river basins. Based on the theory of transport by travel times, and simple hydrodynamic characterization of floods, this new framework invokes the linearity and invariance of the hydrologic response to provide analytical and semi-analytical expressions for peak flow, time to peak, and area contributing to the peak runoff. These results are obtained for the case of constant-intensity hyetograph using the Intensity-Duration-Frequency (IDF) curves to estimate extreme flow values as a function of the rainfall return period. Results show that, with constant-intensity hyetographs, the time-to-peak is greater than rainfall duration and usually shorter than the basin concentration time. Moreover, the critical storm duration is shown to be independent of rainfall return period as well as the area contributing to the flow peak. The same results are found when the effects of hydrodynamic dispersion are accounted for. Further, it is shown that, when the effects of hydrodynamic dispersion are negligible, the basin area contributing to the peak discharge does not depend on the channel velocity, but is a geomorphic propriety of the basin. As an example this framework is applied to three watersheds. In particular, the runoff peak, the critical rainfall durations and the time to peak are calculated for all links within a network to assess how they increase with basin area.
Highlights
A number of hydrological analyses require the evaluation of the highest peak-flow values expected to occur with a given return period
This paper develops a simplified theory based on the concepts of geomorphologic instantaneous unit hydrograph (GIUH) and of width function (Rinaldo et al, 1991, 1995; D’Odorico and Rigon, 2003)
We use the framework of the GIUH theory to determine the rainfall duration that causes the highest peak flow
Summary
A number of hydrological analyses require the evaluation of the highest peak-flow values expected to occur with a given return period. Most of the methods addressing this issue – from the simple rational method Mulvaney (1851), Doodge (1957) to the use of distributed rainfall-runoff models (e.g., Beven, 2001) – have been developed with the purpose of providing quantitative predictions of peak flows for engineering applications more than a synthesis of their dependence on the geomorphic and hydrodynamic characteristics of the watershed To this end, this paper develops a simplified theory based on the concepts of geomorphologic instantaneous unit hydrograph (GIUH) and of width function (Rinaldo et al, 1991, 1995; D’Odorico and Rigon, 2003).
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