A variable source area model of the rainfall‐runoff process based on the Watershed Stream Network

Abstract

A model of the dynamic contributing area during a storm is formulated in terms of the history of precipitation in excess of B horizon permeability. The spatial dynamic contributing area along the main stream is obtaihed under the assumptions that the velocity of flow along the stream network is uniform, the drainage density is a constant within a given watershed, and the first-order streams are uniformly distributed in the basin. The runoff from the dynamic contributing area is then routed through the synthesized stream network to obtain the direct runoff at the basin outlet by making use of a method based on the linearized Saint Yenant equations. The model has been tested in several watersheds in the central United States. INTRODUCTION SYNTHESIS OF THE STREAM NETWORKMany hydrologic phenomena and transport processes occurring in a watershed are associated with rainfall-runoff transfer. Erosion, sedimentation, and transport of plant nutrients, pesticides, and pollutants are examples of phenomena closely associated with the rainfall-runoff process. Hydrologic models of runoff cycles are thus needed not only to simulate water transport in the watershed but also to promote the understanding and simulation of the transport processes of these other conservative substances. In order to trace properly the substances transported, the hydrologic model must indicate where the runoff is likely to originate and how it reaches the stream. Cahill et al. [1974], in tracing the dynamics of phosphorus in a small river system, and Huff and Kruger [1967], in tracing radioactive aerosols from precipitation to water supplies, indicate these requirements.In their classical role, hydrologic models of the runoff cycle have been used to obtain the runoff information necessary to determine the location and size of hydraulic structures. Such models did not require specific information regarding the source of the runoff. More recently, these models have also served to study alternate solutions to water resources developments and associated environmental, economic, and social impacts. Simulation of environmental effects, in particular, requires specific information on the origin and path of the runoff. Lumped deterministic and stochastic systems, which have been successfully used in many hydrologic analyses, do not describe the transport of water irlSide the catchment. Spatially distributed deterministic models would seem ideally suited for describing the internal flows within a watershed. Their analyses require very laborious discretization and tabtl!ation of all the necessary physical and topographical properties of all the infinitesimal areas forming the watershed. Complete simulation of all the combinations of overland flows and of the flows in all the ramifichtions of the stream network is extremely complex, and the necessary data are generally unavailable and too expensive to obtain, except for a few experimental watersheds. An intermediate approach is proposed in this paper. It is based on a syn[hesis of the stream network and on the w...

An isolated event model based upon direct runoff calculations using an implicit source area concept

“…It is proposed to investigate this point in far more detail following the calibration and verification of the model on far more catchments. Lee & Delleur (1976) developed a regression equation relating the main parameter in their direct runoff equation to the storm runoffratio, which in turn was found to be related to rainfall intensity, rainfall volume, minimum daily temperature and a soil permeability index. Further investigations in the catchments studied here as well as others should reveal whether similar relationships can be developed in southern Africa for the parameters of the S-curve model.…”

“…Their method of source area calculation does produce a contracting area during zero rainfall periods. The Lee & Delleur (1976) technique for estimating direct runoff was used with the antecedent moisture storage and routing components of the S-curve model reported here to examine whether a declining source area could be an advantage. The model fit on all the storms tested that had double or complex peaks was very poor indeed, with the second or later peaks being underpredicted quite severely.…”

“…However, the results illustrated in Fig.2(b) indicate that the second peak is modelled quite satisfactorily if the response area remains constant between the rainfall periods. The dynamic contributing area concept was used quasi-explicitly in a catchment model developed by Lee & Delleur (1976) from an earlier hillslope model (Tennessee Valley Authority & North Carolina State University, 1970). Their method of source area calculation does produce a contracting area during zero rainfall periods.…”

“…The unit hydrograph is one of the earliest storm runoff models and requires an external calculation of excess rainfall. More recent developments incorporate the excess rainfall calculation as part of the model structure (Engman & Rogowski, 1974;NERC, 1975;Lee & Delleur, 1976). Total moisture accounting catchment models produce total runoff (storm runoff plus "delayed flow") as output from inputs of gross rainfall by continuously modelling the moisture status of a series of storages (Krzystofowicz & Diskin, 1978).…”

Contribution of directly connected and isolated impervious areas to urban drainage network hydrographs

“…The width function is typically defined as the catchment area at a distance from the outlet (Moussa, 2008). The width function and the area function can be differently defined based on channelization (Lashermes and Foufoula-Georgiou, 2007), but the width function basically represents the distance-area function (Lee and Delleur, 1976). The width function approach is considerably simpler than the GIUH approach because it emphasizes the metric representation of the basin instead of the topologic one (Di Lazzaro, 2009).…”