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High water level at the coast may be the result of different combinations of offshore hydrodynamic conditions (e.g. wave characteristics, offshore water level, etc.). Providing the contour of the "critical" set of offshore conditions leading to high water level is of primary importance either to constrain early warning networks based on hydro-meteorological forecast or observations, or for the assessment of the coastal flood hazard return period. The challenge arises from the use of computationally intensive simulators, which prevent the application of a grid approach consisting in extracting the contour through the systematic evaluation of the simulator on a fine design grid defined in the offshore conditions domain. To overcome such a computational difficulty, we propose a strategy based on the kriging meta-modelling technique combined with an adaptive sampling procedure aiming at improving the local accuracy in the regions of the offshore conditions that contribute the most to the estimate of the targeted contour. This methodology is applied to two cases using an idealized site on the Mediterranean coast (southern France): (1) a two-dimensional case to ease the visual analysis and aiming at identifying the combination of offshore water level and of significant wave height; (2) a more complex case aiming at identifying four offshore conditions (offshore water level and offshore wave characteristics: height, direction and period). By using a simulator of moderate computation time cost (a few tens of minutes), the targeted contour can be estimated using a cluster composed of a moderate number of computer units. This reference contour is then compared with the results of the meta-model-based strategy. In both cases, we show that the critical offshore conditions can be estimated with a good level of accuracy using a very limited number (of a few tens) of computationally intensive hydrodynamic simulations

A meta-modelling strategy to identify the critical offshore conditions for coastal flooding