Multi‐Level Monte Carlo Models for Flood Inundation Uncertainty Quantification

Abstract

Flood events are the most commonly occurring natural disaster, with over 5 million properties at risk in the UK alone. Changes in the global climate are expected to increase the frequency and magnitude of flood events. Flood hazard assessments, using climate projections as input, guide policy decisions and engineering projects to reduce the impact of large return period events. Probabilistic flood modeling is required to take into account uncertainties in climate model projections. However, the dichotomous relationship between probabilistic modeling, computational cost and model resolution limits the applicability of such techniques. This paper examines improvements to traditional Monte Carlo methods using Latin hypercube sampling (LHS) and Multi‐level Monte Carlo (MLMC) to quantify the uncertainty in flood extent resulting from input hydrograph uncertainty. The results demonstrate that MLMC is a more efficient modeling strategy than current methods (i.e., traditional Monte Carlo) with high resolution outputs produced in less time than previously possible. The novel application of MLMC technique to three Scottish case studies, demonstrating a variety of river characteristics, domain sizes and computational costs, using a high resolution 5 m grid resulted in a 99.2% reduction in computational cost compared to traditional Monte Carlo methods and up to 2.3 times speedup over Latin Hypercube Sampling.

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

“…Informed by the analysis of the response surfaces projections in Section 2.5.2, Flood Extent is the most uncertain quantity of interest to investigate, as is usually the case with such a slowly propagating flood over rough and realistic terrains (Aitken et al., 2022; Beevers et al., 2020; Bermúdez et al., 2017). Therefore, only the 5‐dimensional response surface for Flood Extent is produced from the reference prediction to analyze its variation due to each of the five random variables—again via the plots of centerline projections included in Figure 6e.…”

“…It is the sum of the area of the computational cells with non‐zero water depth h , that is, total wet area. The Flood Extent has often been used in probabilistic flood modeling to analyze Flood Extent frequencies (Bermúdez et al., 2017; Beevers et al., 2020; Aitken et al., 2022). Average Hazard Rate (HR ave ) and Maximum Hazard Rate (HR max ).…”

“…Brute‐force SMC requires a large sample size, referred hereafter to N s , to accurately propagate the uncertainty in the input parameters, but this is not ideal for field‐scale applications where the framework would remain computationally intensive even with a fast flood physical solver such as LISFLOOD‐FP (Aitken et al., 2022; Beevers et al., 2020). This study aims to identify alternative‐to‐SMC UQ methods that use reduced N s to reproduce Flood Extent and HR‐related histograms within a maximum allowed relative difference of 10%.…”

“…Existing studies are often limited to analyze the reduction in the N s for one alternative to SMC based on the conventional statistics like the mean or the variance (for example, Fan et al., 2015; Smemoe et al., 2007). However, the use of conventional metrics may not be adequate to suggest reliable N s reductions, because such metrics permit to overlook key information that could be present in complex output histograms (e.g., with more‐than‐one statistical peaks or multimodalities (Aitken et al., 2022; Beevers et al., 2020; Shaw & Kesserwani, 2020)). Hence, the quantification of the reduction in the N s for probabilistic flood modeling would be more reliable when considering the metric of the relative histogram difference.…”

“…For an academic flow reservoir problem with one‐dimensional uncertainty space ( D = 1), Multi‐Level Monte Carlo yielded 6‐to‐18 times smaller N s against SMC for the conventional statistical metrics (Müller et al., 2013). However, the Multi‐Level Monte Carlo approach deploys many physical grids of different resolution supported by a sensitivity analysis, which is test‐specific, making this approach burdensome for probabilistic flood modeling including high dimensional uncertainty spaces ( D > 1) (Aitken et al., 2022). In contrast, the Multi‐Fidelity Monte Carlo approach fixes the grid resolution but varies the complexity in the physical solver(s), leading to 3‐to‐10 times smaller N s against SMC (Peherstorfer et al., 2016).…”