Using Multilevel Monte Carlo methods with XBeach to assess erosion/flood risk in the coastal zone

Abstract:

For millennia, coastal zones have been at risk from both erosion and flooding and this risk has the potential to increase due to climate change. The models used to simulate coastal zones suffer as decision support tools due to the high degree of uncertainty associated with them, both due to incomplete knowledge and natural variability in the system.

Here we show for the first time, how Multilevel Monte Carlo methods (MLMC) can be used in conjunction with one of these models (XBeach) to calculate the expected value of output variables for given uncertain parameters. MLMC develops the Monte Carlo method into a multilevel environment, which is especially beneficial when the underlying model is computationally expensive; the case for the applications considered here. We consider a variety of theoretical and real-world coastal zone case studies and show that MLMC can significantly reduce computational costs compared to the simple Monte Carlo method, whilst maintaining the same level of accuracy. Furthermore, we show how MLMC can be used to estimate cumulative distributions. This allows us to calculate the risk of variables exceeding a certain value, for example, a wave exceeding the height of a physical structure such as a seawall, which is a useful tool in decision-making.