Uncertainty Quantification for Multi-Input Fluvial Flood Inundation Using GPR- and PCE-Based Surrogates

Abstract

With increasing computational capabilities, the implementation of statistical approaches to quantify and propagate input uncertainties through hydrodynamic models has become increasingly feasible and crucial to capture the full range of output scenarios. However, full robust uncertainty quantification remains computationally expensive and out of reach for general purposes. In this study, we demonstrate that by utilizing advanced response surface surrogate modeling techniques, specifically Gaussian Process Regression (GPR) and Polynomial Chaos Expansion (PCE), we have developed efficient and high-fidelity emulators for capturing the uncertainty in flood extents of realistic fluvial flood scenarios. With proper tuning, both emulators requiring only 9 model evaluations, provide near-perfect estimates where we have two uncertain flow magnitudes being modeled. In the more complex three-inputs scenario, where a time lag between river flow peaks is introduced, accurate flood extent emulation becomes more challenging. The computational cost required to build one surrogate for acceptable estimation accuracy increases to 27 full model runs for GPR and PCE-Regression methods. The largest (Formula presented.) of 0.66 was obtained by the PCE-Regression method with a Halton quasi-sampling experimental design. GPR outperforms PCE in capturing lower extreme flood extents due to its ability to model uncertainty and fine-tune variance across the input space. Our findings highlight the effectiveness of both GPR and PCE in capturing broad trends and extremes within response surfaces, offering substantial computational savings compared to the exponentially more expensive FMC simulations. However, when the hydrodynamic response becomes more complex, we have identified significant challenges in constructing high-fidelity emulators.