Using scale invariant properties of imperviousness in urban areas to handle missing data

Auguste Gires (1) , Ioulia Tchiguirinskaia (1) , Daniel Schertzer (1)

1 HM&Co - Hydrologie, Météorologie et Complexité

High resolution modelling is needed by researchers and stake holders to improve the understanding and management of storm water in urban areas. Such models require having the corresponding data (land cover, topography, soil properties...) available, which is not always possible, especially at high resolution. Hence the tricky issue of missing data. In this paper, we focus on the distribution of impervious areas which are important in cities because they are responsible of rapid run-off that can generate surface flooding. A methodology to handle such missing data relying on scale invariance properties is presented. A previous study carried out on 10 European urban and peri-urban areas has shown that imperviousness exhibits scale invariant features on scales ranging from few m to few km (Gires et al. 2017). It was possible to assess a fractal dimension which ranged from 1.6 to 2 according to the area and enabled to quantify the level of urbanisation. Such findings is used to generate realistic scenarios for the missing data. More precisely, fractal fields are commonly simulated with the help of a simple binary multiplicative cascade process (usually called a beta-model). Here we suggest to condition such model to the available data, i.e. set all the multiplicative increments needed to obtain the available data at its value, and stochastically draw the missing increments. Ensembles of realistic fields for the missing data are generated. First, the general properties of this conditional beta model will be assessed and discussed, notably its sensitivity to the proportion of missing data according to its characteristic fractal dimension. Such methodology will be discussed with regards to a comparable one developed for the fields of hydraulic conductivity in another context (Tchiguirinskaia et al. 2004). In a second step this approach is implemented on a 3 km2 semi-urbanised area of the Paris area which enables to quantify the uncertainty associated with missing data on impervious areas.

Domaines: Ingénierie de l'environnement; Dynamique Chaotique [nlin.CD]

Auguste Gires, Ioulia Tchiguirinskaia, Daniel Schertzer. Using scale invariant properties of imperviousness in urban areas to handle missing data. AGU Fall Meeting 2019, Dec 2019, San Francisco, United States. ⟨hal-03422560⟩