Articles | Volume 21, issue 5
Hydrol. Earth Syst. Sci., 21, 2361–2375, 2017

Special issue: Rainfall and urban hydrology

Hydrol. Earth Syst. Sci., 21, 2361–2375, 2017

Research article 08 May 2017

Research article | 08 May 2017

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 Veldhuis6 Auguste Gires et al.
  • 1HMCo, 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
  • 6Water Management Department, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, the Netherlands

Abstract. Fractal analysis relies on scale invariance and the concept of fractal dimension enables one to characterize 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 five European countries. The aim was to characterize 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 enables one to quantify how well spatial structures of imperviousness were represented in the urban hydrological models.

Short summary
Data from 10 urban or peri-urban catchments located in five EU countries are used to analyze the imperviousness distribution and sewer network geometry. Consistent scale invariant features are retrieved for both (fractal dimensions can be defined), which enables to define a level of urbanization. Imperviousness representation in operational model is also found to exhibit scale-invariant features (even multifractality). The research was carried out as part of the UE INTERREG IV RainGain project.