Peak discharge and time to peak scaling in urbain runoff modeling
It is possible to simulate the hydraulic functioning of a given network either with a detailed “microscopic” model at the street section scale or with a global “macroscopic” model which generates total flow rates at the outlet of a basin. The microscopic model is useful when one is concerned with the hydraulic performance of individual conduit sections and the precise locations of problematic areas within a network. Macroscopic modeling is mainly useful when one is interested exclusively by the exit flow rates of a basin. This may be the case in interceptor management where the flow rate is a parameter of the global optimization procedure, within the framework of real time management of regulators. In this case, detailed modeling of a network is unnecessary. On the other hand, detailed modeling requires that a voluminous data base be built and maintained, implying expenditures exceeding the resources of small municipalities. The present work consists in elaborating a systematic method which allows one to substitute simplified hydraulic modeling for detailed modeling of a drainage network. The approach is based on the analysis of the drainage parameters in an urban environment. The non-dimensional groupings retained in this analysis comprise the characteristics a of the basin, of the network and of rainfall. In order to provide a greater generality to this approach, the authors applied the analysis to synthetic networks and rainfalls covering a wide range of specific cases. From a practical viewpoint, the objective was to link the peak flow rates and the time to peak of the global model to those of the detailed model of a basin. Two transfer functions have thus been proposed in order to obtain the peak flow rate and the time to peak of the detailed model as functions of the same parameters provided by the global model. The parameters retained for the transfer function are the density of the drainage network and the rate of filling of the network. In order to implement the proposed method and perform the required hydraulic and hydrological simulations, the authors have used the SWMM program (Storm Water Management Model). 180 simulations have thus been completed, 15 for each type of network and for each type of rainfall. For every combination, one computes the peak flow rate and the time to peak as obtained by the global and detailed models of the basin. The proposed multi-criterion analysis revealed that the total discrepancy between simplified and detailed modeling of a drainage network is very important. Within the range of the assumed densities, the difference can be as great as 50%. This discrepancy between global and detailed modeling is explained by the storage capacity of the different types of networks. Indeed, for a same given drained area, a network provides additional storage with increasing length of the network and therefore with increasing drainage density. On the basis of the above finding, a global model cannot replace a detailed model without the use of required corrections for the computation of peak flow rates for a given specific case. In order to resolve this difficulty, it is recommended to use the empirical models proposed herein to reduce the discrepancy and thereby obtain the appropriate corrections. The proposed method has been subjected to a validation program on basin No.1 of the Verdun borough. Agreement between the flow rates measured at the entrance of the Rhéaume pumping station and those simulated by the proposed method is very satisfactory. The transformation models derived from the analysis allow for the transition from a global model to a detailed one and provide a significant improvement in optimized real time management of drainage networks.