Uncertainty analysis of a machine learning-aided ensemble forecast for coastal flood maps

While ensemble forecasts are widely used for river flooding, they are still in their infancy for marine flooding, one of the main difficulties being the high computing time cost of full process high-fidelity hydrodynamic numerical models. Over the past decade, machine learning-based metamodeling has proved to be an effective solution in many real-world coastal engineering cases to overcome this problem. However, the metamodel remains a statistical approximation of the “true” numerical model learned using a limited number of data. This raises the question of how much the uncertainty of the metamodel contributes to the uncertainty of the forecasts compared to that related to the ensemble of metoceanic conditions. To quantify the respective influence of the different uncertainties, we apply a global sensitivity analysis (GSA) based on a dependence measure, namely the Hilbert-Schmidt independence criterion (HSIC), to two coastal towns, Andernos and Gujan-Mestras located on the Arcachon lagoon (French Atlantic coast), and to two storms, which hit the lagoon in November 2023, i.e., Ciaran and Domingos storms. The ensemble forecast of the flood maps is computed through the combination of a dimension reduction (DR) method, using a deep-learning-based autoencoder model (AE), and Gaussian process (Gp) regression models. The application of the HSIC-based GSA approach to the cases considered in this study shows that: (1) the uncertainties related the combined DR-Gp method, i.e., the AE architecture, the completeness of the training set, and the Gp predictive uncertainty, remain minor compared to that related to the ensemble of metoceanic forcing conditions; (2) when the lead time is high, at least 2 days before the storm occurrence, the variability in the metoceanic conditions has the major impact at both towns with the total uncertainty explained by this source of uncertainty reaching up to 50%; (3) as the lead time decreases, the importance of applying a bias correction to the ensemble of metoceanic conditions increases with the total uncertainty explained reaching > 25%.