| Summary: | The objective of this study is to investigate the “inversion approach” for flood defense optimization in an inundated area. This new methodology within this engineering field consists in defining a “safety criterion” (for instance, “the water level in a given location must be lower than a given value”) and the combined analysis of all the uncertain controlled parameters (i.e., flood defense geometry, location, etc.) that ensure the safety objective for all the possible combinations of uncontrolled parameters (i.e., the flow hydrograph parameters) representing the natural phenomenon is not exceeded. To estimate this safety set, a metamodeling approach will be used which significantly reduces the number of model evaluations required. This algorithm relies on a kriging surrogate built from a few model evaluations, sequentially enriched with new numerical model evaluations as long as the remaining uncertainty of the entire safety set remains too high. Also known as “Stepwise Uncertainty Reduction,” this algorithm is embedded in the “Funz” engine (https://github.com/Funz) tasked with bridging the numerical model and any design of experiments algorithm. We applied this algorithm to a real two-dimensional numerical model of the Garonne river (France), constructed using the open-source TELEMAC-2D model. We focused our attention mainly on the maximum water depth in a given area (the “safety criterion”) when considering the influence of a simplified flood defense during a flooding event. We consider the two safety control parameters describing the slab and dyke elevations of the flood defense system, to design against the full operating range of the river in terms of possible watershed flooding. For this application case, it appears that less than 200 simulations are needed to properly evaluate the restricted zone of the design parameters (the “safety zone”) where the safety criterion is always met. This provides highly valuable data for full risk-informed management of the area requiring protection.
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