Parsimonious hydrological modelling in urban areas: Towards integrated modelling

Most popular urban hydrological model used in research and engineering (e.g. MOUSE, SWMM, MUSIC,P8) are spatially distributed with linknode drainage network. If some of them (e.g. PURPS, RUNQUAL, SLAMM, StormTac and WBM) treat the catchment in a lumped fashion, ignoring the drainage network, they are nonetheless unfit for routing of the drainage network and baseflow simulation (Elliott and Trowsdale 2007) . Yet, water science abounds with mathematical tools designed for conceptual lumped hydrological studies, including stochastic and deterministic approaches (see e.g. Singh and Woolhiser (2002) for a review). But so far, these models have been mostly experimented on rural areas where a parsimonious approach seems more natural (Basu, Rao et al. 2010; Jacobson 2011) The objective of this paper is to propose a light mathematical framework to assess continuous flow dynamics at waste water treatment plant (WWTP) inlet and urban river outlet. In this perspective, we adapt existing theory in rural hydrology to the specificity of urban environment. Thus, our model is built as series of three linear and non linear boxes. One box stands to account for “flashy” response on impervious surfaces (Deletic 1998), another for pervious areas and finally one for sub surface flow. This conceptual model totally ignores the complexity of the drainage system. Indeed, pipe network is indirectly considered through the impervious surface box. The model described is calibrated and validated for the Vidy WWTP and the Vuachère River, both being located in a 2000.000 equivalent inhabitants’ city Lausanne, Switzerland. Automatic Monte-Carlo calibration procedure is used to optimize model performance based on Nash-Sutcliffe (NS) and Normal Biais (NB) coefficients. The proposed framework indicates that, despite heterogeneities, a dynamic yet computationally light and parsimonious approach can be successfully employed to simulate the hydrograph response of engineered hydrosystems. It presents the great benefit of insignificant computation time to be run, and thus stands as a valuable and flexible tool for future integrated models that shall develop in a close future. Example of coupling with complex water quality function to assess the risk of “first flush” contaminated rain water on sensitive aquatic species can be found in Coutu et al. (submited to Water Research). Further possibilities of coupling are being developed.