What is the most efficient sampling-based uncertainty propagation method in flood modelling?

Modelling uncertainty propagation in flood modelling manifests in frequency of occurrence, or histograms, for quantities of interest, including the flood extent and hazard rating. Such modelling 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 reduced sample size. Latin Hypercube Sampling (LHS) is the most evaluated alternative 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 modelling. In this paper, LHS, ASS, QMC and HWE are compared to quantify sample size reduction to reproduce output detailed histograms—for flood extent, and average and maximum hazard rating—while keeping the difference below 10% to the reference SMC prediction. The comparison is done a synthetic test case 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 and should be preferred.