Bayesian calibration of a 2D hydraulic model using a CNN-based surrogate emulator under data-scarce conditions

Two-dimensional (2D) hydraulic models are essential tools for flood hazard assessment, yet their calibration remains computationally demanding and strongly constrained by data availability. This study presents a Bayesian calibration framework that integrates a convolutional neural network (CNN) surrogate model to efficiently infer spatially distributed Manning’s roughness coefficients while explicitly accounting for model structural uncertainty.

The approach is applied to a reach of the Lower Piura River (Peru), a flood-prone basin characterized by limited in situ observations. An ensemble of TELEMAC-2D simulations is generated using Latin Hypercube Sampling over multiple roughness configurations, and a CNN is trained to emulate spatial water depth fields with high fidelity. To focus learning on hydraulically relevant regions, a weighted loss function based on roughness–depth sensitivity is employed.

The trained emulator is embedded within a Bayesian inference scheme that incorporates a Gaussian Process discrepancy term to represent systematic model–reality deviations. Posterior distributions of Manning’s coefficients and uncertainty parameters are estimated using Markov Chain Monte Carlo sampling. Synthetic experiments demonstrate accurate parameter recovery in hydraulically sensitive areas, while a real-case application based on optical satellite imagery confirms the method’s ability to reproduce observed flood depth patterns under data scarcity.

The proposed framework significantly reduces computational cost compared to conventional calibration approaches and provides a probabilistic characterization of parameter uncertainty. These results highlight the potential of CNN-based surrogate models as scalable tools for Bayesian inference in large-scale hydraulic modeling and flood risk assessment.