Author(s): Adil Siripatana; Amy L. Wilson; Lindsay Beevers

Linked Author(s): Lindsay Beevers

Keywords: Fluvial flood Uncertainty Quantification Gaussian Process Regression (GRP) Polynomial Chaos Expansion (PCE)

Abstract: Predicting the future implications of flood events is becoming increasingly challenging. The practice of running hydrodynamic models with estimates of future hydrological events to obtain flood inundation predictions is fraught with uncertainties arising from climate change, the non-stationarity of extremes, and other factors. This amplifies uncertainties in flood risk models, making it more difficult to accurately anticipate the severity and frequency of future flooding events (Andrikopoulou et al., 2021). The conventional use of deterministic methods to assess return period flood footprints is insufficient, as these approaches fail to acknowledge, quantify, and capture the cascading uncertainties inherent in flood modelling (Bates et al., 2021). With increasing computational capabilities, the implementation of statistical approaches to quantify and propagate input uncertainties through hydrological models has become feasible and crucial for capturing the full range of output scenarios, particularly for quantifying extremes, although this can still be computationally expensive (Maranzoni et al., 2022). 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 flood extents in realistic fluvial flood scenarios. Using LISFLOOD-FP, a two-dimensional flood inundation model, we analyzed two distinct modeling scenarios for the Inverurie floodplain in Scotland. In the first scenario, named the "two-input scenario, " we varied the peak inflow values of the Don and Urie river gauge hydrographs from the major 2016 flood event, reflecting uncertainties in hydrograph magnitudes for a 1-in-30-year return period. In the second scenario, called the "three-input scenario, " we introduced an additional layer of uncertainty by incorporating the time lag between the hydrograph peaks of the two rivers. In each case, 10,000 independent Full Monte Carlo (FMC) simulations were conducted, with inputs selected as follows: for the 'two-input scenario, ' flow magnitudes for the Don and Urie rivers were used; and for the 'three-input scenario, ' flow magnitudes for the Don and Urie rivers along with the time lag of the hydrograph arrival for the Urie were considered. With proper tuning, both GPR and PCE emulators, requiring only 9 model runs, provide near-perfect estimates of flood extents for the two-input scenario, with R2 values consistently exceeding 0.99 and a minimum normalized root-mean-squared error (NMRSE) of 0.006 using pseudo-spectral projection (PCE-PSP) method, compared to the FMC simulation. The violin plot (Fig. 1) and Kullback-Leibler (KL) divergences in Table 1 further confirm that, for cases where the response surface is simple and can be approximated well with low-order polynomials, PCE-PSP, where the PC coefficients are computed through direct numerical integration, can emulate FMC flood extent outputs extremely well. This can be observed from the accurate distribution shape, median, and interquartile values. 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, and 18 for the PCE-PSP method. The largest R2 of 0.66 with a NMRSE of 0.08 is obtained by the PCE-Regression method with a Halton quasi-sampling experimental design (Table 1). While PCE-PSP provides the best overall distribution shape compared to FMC, with a KL divergence value of 0.02, GPR outperforms PCE in capturing lower extreme flood extents (Fig. 2) due to its ability to model uncertainty and fine-tune variance across the input space (Gramacy, 2020). 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, the erratic patterns emerging in the true response surface of spatially integrated flood extents, due to time lag uncertainties, present significant challenges for constructing high-fidelity emulators. We anticipate that this work will serve as a foundation for exploring more advanced uncertainty quantification surrogate methods, capable of better capturing highly nonlinear response surfaces and their errors while maintaining reasonable computational costs.

DOI:

Year: 2025