Sampling-Based Methods for Uncertainty Propagation in Flood Modeling Under Multiple Uncertain Inputs: Finding Out the Most Efficient Choice

Abstract

In probabilistic flood modeling, uncertainty manifests in frequency of occurrence, or histograms, for quantities of interest, including the Flood Extent and hazard rating (HR). Such modeling at the field-scale requires the identification of a more efficient alternative to the Standard Monte Carlo (SMC) method that can reproduce comparable output probability distributions with a relatively reduced sample size, including detailed histograms of quantities of interest. Latin hypercube sampling (LHS) is the most evaluated alternative for fluvial floods but yields no considerable sample size reduction. Potentially better alternatives include adaptive stratified sampling (ASS), Quasi Monte Carlo (QMC) and Haar-wavelet expansion (HWE), which are yet unevaluated for probabilistic flood modeling. To fulfill this gap, LHS, ASS, QMC, and HWE are compared to quantify sample size reduction to reproduce output detailed histograms—for Flood Extent, and average and maximum HR—while keeping the difference below 10% to the reference SMC prediction. The comparison is done for two test cases with two (i.e., inflow discharge and Manning's coefficient) and three (i.e., further including the ground elevation) input random variables, and a real case with five input random variables. With two input random variables, all four alternatives yield sample size reductions, with QMC and HWE considerably outperforming the others; with three and more input random variables, HWE becomes inflexible and LHS underperforms. Still, QMC is a better choice than ASS to boost sample size reduction for the real case and shall be preferred in probabilistic flood modeling. Accompanying research codes are openly available online.