Infilling missing data of binary geophysical fields using scale invariant properties through an application to imperviousness in urban areas

High-resolution modelling is needed to improve the understanding and management of storm water in cities. It requires data, which is not always available; hence the growing importance of handling missing data. Here, we use impervious areas in cities as case study. They are responsible for rapid runoff that can generate surface flooding. A methodology to handle such binary missing data relying on scale-invariant properties is presented. It uses a previous study, which showed in 10 peri-urban areas that imperviousness exhibits scale-invariant features from metres to kilometres, to generate realistic scenarios for the missing impervious data. More precisely, fractal fields are commonly simulated thanks to a simple binary multiplicative cascade process (β-model). Here we condition it to the available data. Numerical simulations are used to confirm theoretical expectations. They are then implemented to infill missing impervious data on a 3 km² catchment and the corresponding uncertainty is quantified.