Combining uncertain machine learning predictions and numerical simulation results for the extreme value analysis of cyclone-induced wave heights – Application in Guadeloupe

Abstract

Assessing return level RL (with return period typically ranging from 100 to 500 years) for extreme waves in cyclone-prone regions is often made problematic by the lack of sufficient representative samples to properly fit the extreme value probability distributions. Motivated by the Guadeloupe context (French West Indies), we address this problem when the wave numerical model is too expensive to be run a large number of times. A possible option is to use a machine learning (ML) model in place of the long-running numerical mode. By construction, ML predictions are however uncertain, because they are learned from a limited number of pre-calculated wave simulation results. We propose to account for this type of error along the inference of the parameters of the extreme value probability distribution within an Approximate Bayesian Computation (ABC) scheme. Using a subset of the database of numerically computed HS for Guadeloupe (for approximately 700 synthetic cyclones representative of 1000 years of cyclonic activity), we train a random forest (RF) regression model to relate the cyclone characteristics (radius, atmospheric pressure, distance to cyclone eye) to HS. The quantile RF model is then used to model the prediction error within the ABC scheme. By comparison to the 100-year and 500-year RL reference solutions (calculated using the entire database), we show that the ML-based approach achieves low bias and high reliability of the RL estimates at locations both along Guadeloupe coasts and in deep ocean environments for low sample size (down to ∼70). Provided that the prediction error is low-to-moderate, integrating this type of uncertainty improves the performance of the ML-based approach, and decreases the computational burden of the return level estimation.