Abstract
Hydraulic and hydrologic analysis in urban catchments is typically accompanied by a number of uncertainties, such as a lack of required information for modeling purposes or complex loops inside a drainage network. In this article, Gibbs’ stochastic network model is utilized in order to achieve a dendritic network that corresponds to a fully looped network in terms of the peak of the runoff hydrograph at the outlet. A synthetic catchment with a drainage network composed of 8 × 8 grids is introduced to investigate the behavior of a fully looped network for a given rainfall event using the Storm Water Management Model. Dendritic networks are generated from the Gibbsian model for a given value of the parameter, β. The results showed that the shape of the hydrograph and the peak flow of a fully looped network are heavily dependent on the catchment slope. Moreover, the results showed that it is possible to find the corresponding dendritic networks generated by the Gibbsian model that match the fully looped network depending on the catchment slope in terms of peak flows. The results of this study imply the potential improvement of drainage network analysis providing a relationship between the catchment slope of a fully looped network and the corresponding dendritic network generated by the Gibbsian model.
Highlights
From a hydraulic and hydrologic engineering point of view, urban drainage problems can be classified into two types: design purpose and prediction purpose for forecasting and operation [1]
Dendritic networks are generated from the Gibbsian model for a given value of the parameter, β
The result shows that a transition exists in the relation between the catchment slope and the peak flows of a fully looped network as shown in Figure 3b; the relation between the catchment slope and peak flows is logarithmic but the slope of peak flow with respect to the catchment slope changes near the catchment slope of 9 × 10−3
Summary
From a hydraulic and hydrologic engineering point of view, urban drainage problems can be classified into two types: design purpose and prediction purpose for forecasting and operation [1]. While the design purpose problem utilizes hypothetical rainstorms with a relatively simple temporal and spatial distribution of rainfall, more precise and detailed analysis is required for the prediction purpose problem for the operation and management of a system. One of the recent approaches of hydrologic analysis in urban drainage problems is based on the Geomorphologic Instantaneous Unit Hydrograph (GIUH) [4,5]. Rodriguez et al [6,7] suggest a morpho-climatic approach incorporating rainfall intensity in order to obtain the Instantaneous Unit. Gironas et al [8] developed a morpho-climatic instantaneous unit hydrograph model for urban catchments based on the kinematic wave approximation
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