Abstract. During the last decades, the urban hydrological cycle has been strongly modified by the built environment, resulting in fast runoff and increasing the risk of waterlogging. Nature-Based Solutions (NBS), which apply green infrastructures, have been more and more widely considered as a sustainable approach for urban stormwater management. However, the assessment of NBS performance still requires further modelling development because of their hydrological responses sensitively depends on the representation of multiscale space variability of both the rainfall and the NBS distribution. Indeed, we initially argue this issue with the help of the multifractal intersection theorem. To illustrate the importance of this question, the spatial heterogeneous distributions of two series of NBS scenarios (porous pavement, rain garden, green roof, and combined) are quantified with the help of their fractal dimension. We point out consequences of their estimates. Then, a fully-distributed and physically-based hydrological model (Multi-Hydro) was applied to consider the studied catchment and these NBS scenarios with a spatial resolution of 10 m under two different types of rainfall: distributed and uniform, and for three rainfall events. These simulations show that the impact of spatial variability of rainfall on the uncertainty of peak flow of NBS scenarios ranges from about 8 % to 17 %, which is more pronounced than those of the total runoff volume. In addition, the spatial variability of the rainfall intensity at the largest rainfall peak responds almost linearly to the uncertainty of the peak flow of NBS scenarios. However, the hydrological responses of NBS scenarios are less affected by the spatial distribution of NBS. Finally, the intersection effects of the spatial variability of rainfall and the spatial arrangement of NBS seem more pronounced for the peak flow of green roof scenarios and the total runoff volume of combined scenarios.
On dual versions of Krull's intersection theorem