Effect of Rainfall Variability On The Hydrological Behaviour of Urban Basins: A Simulation Approach Based On Peano's Basins

The objective of this study is to assess the variability of the flow-rate at the outlet of urban basins due to spatial variability of rainfall. A simulation approach based on PeanoSs basins, assumed representative of the morphology of urban rain sewer networks, is adopted.

The basins are characterised by their outlet distances distribution and by an homoge- neous imperviousness coefficient. The hydrological modelling consists of the deter- mination of the travel time on the flow paths deduced from the morphology of the rain sewer systems. This makes it possible to determine the isochronous zones of the basin and the transfer function represented by a unit hydrograph. The variability of a rain-field is characterised by its coefficient of variation and by its spatio-temporal correlogram, so by a covariance function.

For PeanoSs basins of various surface areas, the influence of the spatial variability of rain-field is studied: - On the unit hydrograph of the basin whose components can be expressed as a function of both the isochronous surfaces and the rainfall variability. The unit hydrograph variability, expressed by the variance of the peak value, is de- duced from the integration, over the main isochronous surface, of the rainfall covari- ance. - On the outflow resulting from a hyetogram lasting several time steps. The com- ponents of the outflow are obtained by convolution of the unit hydrographs weighted by the rainfall intensity. The variability of the peak flow can be expressed from the rainfall spatio-temporal covariance.

This study allows to statistically quantify the peak flow variability due to the spatial variability of rain-field. In particular, the obtained results indicate that the peak flow variability increases when the coefficient of variation of rainfall increases or when the spatial correlation becomes stronger. It seems that this influence decreases when the surface area of the basins increases. These results are significant for PeanoSs basins whose surface does not exceed a few tens of km2. Nevertheless, these results must be validated by results taken from experimental data, this is the next stage of the work.