Bayesian optimization for re-analysis and calibration of extreme sea state events simulated with a spectral third-generation wave model

TL;DR

This paper develops a Bayesian optimization framework based on the Tree-structured Parzen Estimator to calibrate key sink terms in the ANEMOC-3 hindcast wave model, including bottom friction, depth-induced breaking, and wave-current interaction. By coupling TOMAWAC within openTELEMAC and applying PCA-driven selection of calibration buoys, the authors demonstrate that the calibrated configuration improves agreement with buoy observations during extreme storm events along the French Atlantic coast, reducing RMSE and bias relative to the default configuration. The work demonstrates the feasibility and benefits of AI-driven, automated calibration for high-dimensional, computationally expensive geophysical models and outlines avenues for multi-objective optimization and uncertainty quantification. The proposed approach is scalable, supports joint optimization of continuous parameters and discrete model choices, and has potential applications across coastal hydrodynamics and morphodynamics.

Abstract

Accurate hindcasting of extreme sea state events is essential for coastal engineering, risk assessment, and climate studies. However, the reliability of numerical wave models remains limited by uncertainties in physical parameterizations and model inputs. This study presents a novel calibration framework based on Bayesian Optimization (BO), leveraging the Tree structured Parzen Estimator (TPE) to efficiently estimate uncertain sink term parameters, specifically bottom friction dissipation, depth induced breaking, and wave dissipation from strong opposing currents, in the ANEMOC-3 hindcast wave model. The proposed method enables joint optimization of continuous parameters and discrete model structures, significantly reducing discrepancies between model outputs and observations. Applied to a one month period encompassing multiple intense storm events along the French Atlantic coast, the calibrated model demonstrates improved agreement with buoy measurements, achieving lower bias, RMSE, and scatter index relative to the default sea$-$state solver configuration. The results highlight the potential of BO to automate and enhance wave model calibration, offering a scalable and flexible approach applicable to a wide range of geophysical modeling problems. Future extensions include multi-objective optimization, uncertainty quantification, and integration of additional observational datasets.

Figures (8)

• Figure 1: ANEMOC-3: Oceanic, North Sea and Coastal domains (1979$-$2024).
• Figure 2: Bottom elevation and location of buoys considered over the ANEMOC-3 oceanic model.
• Figure 3: Significant wave height evolution during the months of January and February 2014 measured at Brittany buoy (UKMO 62163) with storm names highlighted in red.
• Figure 4: Correlation circle of the first two principal components of the PCA (explaining more than 99% of the total variance), illustrating model errors $f(\boldsymbol{\theta})$ across buoy measurement sites based on 1,000 Monte Carlo simulations using a model structure incorporating depth-induced breaking Thornton_1983 and wave dissipation due to opposing currents Westhuysen_2012.
• Figure 5: Evolution of the objective function value across trials during the optimization process. The plot shows both the objective value for each trial (•) and the best value (-) found up to that point, highlighting the convergence behavior of the optimization.