Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Abstract

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 subcatchments 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.

Scale effect challenges in urban hydrology highlighted with a distributed hydrological model

“…This means that over this range of scales, the structure of the pluvial networks fills most of the space. These results confirm similar conclusions of a multi-catchment work performed in the framework of the RainGain project about fractal analysis of environmental data of 10 pilot sites located in Europe (Gires et al, 2017). The break at 64 m is related, according to this study, to the typical distance between two roads in urban areas.…”

“…They are widely used in several science domains including geology, medicine, meteorology and finance (Niu et al, 2016;West, 2012;Goldberger and West, 1987;Nonnenmacher et al, 2013;Turcotte and Huang, 1995;Yanshi and Kaixuan, 2002;Turcotte, 1989). In hydrology, the fractal dimension concept has been used in many studies in the past for various purposes, ranging from catchment geometrical characterization to flow analysis (Mesev et al, 1995;Wu et al, 2013;Thibault and Crews, 1995;Frankhauser, 1998;Wu and He, 2009;Sagar, 2004;Jiang et al, 2012;Gires et al, 2013;Radziejewski and Kundzewicz, 1997), but has seldom been used in urban hydrology (Gires et al, 2017).…”

Multifractal characterisation of a simulated surface flow: A case study with Multi-Hydro in Jouy-en-Josas, France

“…The similarity between both fractal dimensions (imperviousness and large scale sewers) indicates that it is a relevant way of quantifying a level of urbanisation for the area. See Gires et al (2017) for an extension of this approach to 10 areas in 5 European countries.…”

Multifractal Analysis of River Networks in an Urban Catchment on the Taihu Plain, China

“…Wang et al (2016) also established a relationship between the Hurst index of the water level and the fractal dimension, revealing that changes in a river network under urbanization have an influence on a river network's storage capacity [61]. Besides this, Gires et al (2017) applied fractal analysis to quantify how well the spatial structures of imperviousness of urban catchments performed in hydrological models [62]. All the directions of the abovementioned studies will be given more attention in future work, particularly the relationship between a flood-forming regime and the multifractal structures of the river networks in the plain's river networks area.…”