A nuanced quantile random forest approach for fast prediction of a stochastic marine flooding simulator applied to a macrotidal coastal site

Abstract

Integrating full-process high resolution hydrodynamic simulations within early warning system (EWS) for marine flooding is hindered by the large computation time cost of such numerical models. This problem can be alleviated through the statistical analysis of pre-calculated simulation results to build a fast (low computation time cost) statistical predictive model (named metamodel). Despite the success of this approach, a direct application of such techniques for EWS is not straightforward in all settings, more particularly in environments where the stochastic character of waves has a significant effect on the induced flood, i.e., where overtopping is on a duration smaller than 500 times the offshore wave period. In such environments, the numerical simulator is not deterministic and provides statistical quantities of the flooding indicators. By focusing on the estimates of quantiles, the objective of the present study is to explore the applicability of random forest (RF) models for marine flooding prediction by providing two levels of information: (1) the quantile of interest via a quantile random forest regression model (qRF); (2) the flooding probability via a classification random forest (cRF). We use the macrotidal site of Gâvres (French Atlantic coast) as an application case for which ~ 2000 numerical simulations were performed (i.e. stochastic simulations given 100 different extreme-but-realistic offshore meteo-oceanic input conditions were repeated 20 times) to compute local and global flooding indicators (respectively the maximum water depth at the coast and the total volume of water entering the territory). Through an extensive repeated cross-validation procedure, we tune the qRF parameters leading to high coefficient of determination of ~ 90% for the quantiles at 25–50–75%, and we show that the qRF models outperform the commonly used Tobit regression model. The comparison with the numerical results on historical events shows very satisfactory prediction for events both leading to major flooding and to absence of impact. For low quantile level and minor-to-moderate flooding events, the second level provided by the cRF-derived flooding probability shows its added value by enabling the EWS user to nuance the qRF prediction and to tag some situations where the prediction remains unsure.