Ensemble forecasts of marine flood maps assisted by probabilistic machine learning techniques: Application at Arcachon Lagoon (France)

Recent advances in high performance computing have enabled numerical weather prediction systems to move from deterministic to probabilistic forecasting using Ensemble Prediction Systems (EPS). While EPS are increasingly used to predict river flows and induced floods in several countries, it is only emerging for marine flooding. Despite ongoing efforts to develop new generations of high performance hydrodynamic models accounting for complex processes, the main challenge still remains the computer power required to run multiple simulations with a chain of models of increasing resolutions (from a hundred meters for water level at the coast, to a few meters for coastal waves and marine flooding). To overcome this limitation, the machine-learning-based metamodelling approach has made great progresses in this field of application.

Through a statistical analysis of pre-calculated training databases, metamodels can predict key flooding indicators (surge, discharge, water depth, etc.) at a given spatial locations of interest within reasonable time and computing resources while preserving the accuracy of full process models. Yet, some issues remain to push this approach toward operational applications: (1) the production of spatialized indicators with metamodels such as inland water depth maps, (2) the characterization of the cascading sources of uncertainties throughout the entire chain.

To address these difficulties, we use a set of numerical simulation results of about 200 flood maps computed on the Arcachon Lagoon (Gironde, France) for a large variety of randomly-generated metoceanic forcing conditions (surge, tide, wave and wind). On this basis, a metamodeling procedure is developed by combining a non-linear dimension reduction method relying on deep-learning-based autoencoders, denoted AE (to represent the very high-dimensional spatialized output) and on Gaussian process (Gp) regression (to model the link between the metoceanic forcing conditions and the flood response). Cross validation and comparison to historical real cases (such as storms Xynthia and Klaus) show satisfying predictive capability. However, the concern is the model uncertainty that affects the different steps of the whole metamodeling procedure. To quantify it, we rely on a stochastic approach that combines conditional Gp simulations with AE random responses using Monte Carlo Dropout method. In order to discuss predictive uncertainty to support decision-making for real-time forecasts, we compare the impact of metamodelling uncertainty with that induced by the variability of metoceanic forcing conditions which are modelled on the basis of the Meteo-France ensemble named PEARP "Prévision d'Ensemble ARPege" for recent storm events, as well as for synthetic marine inundation events.