Determining Probability Distribution of Hillslope Peak Discharge by Using an Analytical Solution of Kinematic Wave Time of Concentration.

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Abstract

Hillslope hydrology is fundamental for understanding the flood phenomenon and for evaluating the time ofconcentration. The latter is a key variable for predicting peak discharge at the basin outlet and for designing urbaninfrastructure facilities. There have been a multitude of studies on the hydrologic response at the hillslope scale,and the time of concentration has been derived for different approaches. One approach for deriving hillsloperesponse utilizes, in a distributed form, the differential equations of unsteady overland flow, specifically developedat the hydrodynamic scale, in order to account for the spatial heterogeneity of soil characteristics, topography,roughness and vegetation cover on the hillslope. Therefore, this approach seemingly mimics the completehydraulics of flow. However, the very complex patterns generated by spatial heterogeneity can cause considerableerror in the prediction even by very sophisticated models. Another approach that directly operates at the hillslopescale is by averaging over the hillslope the soil hydraulics, the topography, and the roughness characteristics. Aphysically-based lumped model of hillslope response was first proposed by Horton (1938), under the assumptionthat the flow regime is intermediate between laminar and turbulent regimes (transitional flow regime), by applyingthe mass conservation equation to the hillslope as a whole and by using the kinematic wave assumption forthe friction slope (Singh, 1976, 1996). Robinson et al. (1995) and Robinson and Sivapalan (1996) generalizedHorton’s approach, suggesting an approximate solution of the overland flow equation that is valid for all flowregimes. Agnese et al. (2001) derived an analytical solution of a nonlinear storage model of hillslope response thatis valid for all flow regimes, and the associated time of concentration.Recently, the well-known kinematic wave equation for computing the time of concentration for impervioussurfaces has been extended to the case of pervious hillslopes, accounting for infiltration. In particular, an analyticalsolution for the time of concentration for overland flow on a rectangular plane surface was derived using thekinematic wave equation under the Green-Ampt infiltration (Baiamonte and Singh, 2015). The objective ofthis work is to apply the latter solution to determine the probability distribution of hillslope peak discharge bycombining it with the familiar rainfall duration-intensity-frequency approach.
Original languageEnglish
Number of pages1
Publication statusPublished - 2016

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