A morpho-climatic instantaneous unit hydrograph model for urban catchments based on the kinematic wave approximation

Abstract

Summary Stormwater models are valuable tools in urban planning as well as stormwater system design and management. Although the hydraulic simulation of pipes and channels in these models is often quite sophisticated, the hydrologic simulation of the flow contributing to the hydraulic elements is frequently greatly simplified. Hydrologic simulation of urban catchments is made particularly complex due to the presence of features such as streets, small pipes, and channels. In this study, we develop a new model called the U-McIUH (Urban Morpho-climatic Instantaneous Unit Hydrograph), which defines the IUH as the probability density function of the travel time from a random location in the urban terrain to the outlet. Flow paths are extracted from a specially processed digital elevation model that incorporates hillslopes, streets, pipes, and channels, and travel times are computed in each cell using the average wave celerity from kinematic wave theory. These expressions depend on the upstream contribution of flow and the excess rainfall intensity, so they incorporate the so-called climatic dependence of the IUH, which is the dependence of the unit hydrograph on the rainfall intensity. Rainfall pulses of different intensities are convoluted with their respective IUH and superimposed to generate the response to a given storm event. The application of the model to a real catchment provides good reproduction of observed hydrographs, suggesting that the U-McIUH is able to capture some significant hydrologic properties of the catchment. The model is studied by analyzing the effects of (1) the upstream contribution of flow on the travel time formulation, (2) the variation of flow velocities within the urban catchment, (3) the non-linear dependence of the IUH on the rainfall intensity (i.e. the climatic dependence), and (4) the spatial distribution of imperviousness. Overall, these results suggest that the presence of artificial elements in urban watersheds has a significant role in determining the travel times and thus the hydrologic response of the watershed.