Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system
Auguste Gires1, Ioulia Tchiguirinskaia1, Daniel Schertzer1, Susana Ochoa Rodriguez2, Patrick Willems3, Abdellah Ichiba1,4, Li-Pen Wang3, Rui Pina2, Johan Van Assel5, Guendalina Bruni6, Damian Murla-Tuyls3, and Marie-Claire ten Veldhuis61HMCo, École des Ponts, UPE, Champs-sur-Marne, France 2Urban Water Research Group, Department of Civil and Environmental Engineering, Imperial College London, Skempton Building, London SW7 2AZ, UK 3Hydraulics Laboratory, KU Leuven, 3001, Heverlee (Leuven), Belgium 4Conseil Départemental du Val-de-Marne, Direction des Services de l'Environnement et de l'Assainissement (DSEA), Bonneuil-sur-Marne, 94381, France 5Aquafin NV, Dijkstraat 8, 2630 Aartselaar, Belgium 6Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, PO Box 5048, 2600 GA Delft, the Netherlands
Received: 05 Oct 2016 – Accepted for review: 19 Oct 2016 – Discussion started: 26 Oct 2016
Abstract. Fractal analysis relies on scale invariance and the concept of fractal dimension enables to characterise and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in 5 European countries. The aim was to characterise urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2 m × 2 m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enabled to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.
Gires, A., Tchiguirinskaia, I., Schertzer, D., Ochoa Rodriguez, S., Willems, P., Ichiba, A., Wang, L.-P., Pina, R., Van Assel, J., Bruni, G., Murla-Tuyls, D., and ten Veldhuis, M.-C.: Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system, Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-527, in review, 2016.