Modelling spatial variability along drainage networks with geostatistics

Local characteristics of drainage networks such as cross-section geometry and hydraulic roughness coefficient, influence surface water transfers and must be taken into account when assessing the impact of human activities on hydrological risks. However, as these characteristics have not been available till now through remote sensing or hydrological modelling, the only available methods are interpolation or simulation based on scarce data. In this paper we propose a statistical model based on geostatistics that allows us to take account of both the spatial distribution and spatial uncertainties. To do this, we modify the geostatistical framework to suit directed tree supports corresponding to drainage network structures. The stationarity concept is specified assuming conditional independence between parts of the network; variogram fitting and modelling are then modified accordingly. A sequential multi Gaussian simulation procedure going upstream along the network is proposed. We illustrate this approach by studying the width of an 11-km long artificial drainage network in the south of France.