Flood level spatial uncertainty simulation from expert knowledge: methods, limits and impacts

International audienceFlood hydraulic simulation aims to reproduce the flood wave, i.e. the water level, the flood duration or the flow velocity at any site of the channels and floodplain. Hydraulic model outputs may later be used in studies to delineate risk areas, to characterize impacts in cost-benefit analyses of a flood prevention project, or to alert inhabitants before flood event. To support the robustness of these studies, uncertainties of hydraulic outputs over floodplain, especially a spatially explicit representation of uncertainties may be required (Saint-Geours et al., 2013). However, due to the flood data scarcity, the available observed water level data are rather used to calibrate hydraulic model parameters rather than to validate the model. Thus, epistemic uncertainties of simulated maxima flood levels over floodplain are rarely measured, except on some points along the main channel. Nevertheless, hydraulic modellers are able to deduce general rules and ranges on flood level uncertainties from modelling experiences. These rules are built up in regards with the frequencies of the modelled events and the floodplain morphology. The translation of this expert knowledge to spatial pattern models that are able to simulate spatial explicit uncertainties has thus to be addressed. In this paper, we explored the translation of the downstream Rhône river hydraulic modellers expertise in ad hoc stochastic spatial, i.e. geostatistical models. Expertise rules were only devoted to 1D floodplain modelling using a storage cells network framework. It concerned i) the magnitude of flood level errors depending on the riverbed location (floodplain or channel) of storage cells, ii) the water level measurement accuracies, iii) the spatial dependencies on errors between connected storage cells, and iv) some additional constraints on orders between flood levels on connected storage cells. Three continuous or discrete uncertainties simulation approaches were investigated using different levels of constraint: i) multi-Gaussian random fields on storage cells centroids within an anisotropic and curvilinear euclidean 2D space, ii) multi-Gaussian random fields on storage cells lattice and iii) Gaussian Markov random fields on storage cells lattice (Rue and Held, 2004). Identical spatial 2D covariance models were used in order to respect the expert rules on the water level error spatial structure in the same conditions for the three investigated approaches. The theoretical limitations of these approaches are first identified and discussed. Resulting maps of uncertainties are thus shown and discussed. Finally, in order to discuss the importance to refine spatial hydraulic uncertainty simulation methods, the measure of the impact of hydraulic un-1 certainties in a flood-risk project cost-benefit analysis is computed in addition to other sources of uncertainties (stakes uncertainties, flood frequency uncertainties, damage curve uncertainties, etc.). This latter sensitivity analysis results allows to balance the impact of flood level errors in comparison to other sources of uncertainties. Acknowledgements: This work has benefited from the support of Plan Rhône (FEDER funding)