Multi-Level Monte Carlo Models for Flood Inundation Uncertainty Quantification

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.