Multilevel multifidelity Monte Carlo methods for assessing uncertainty in coastal flooding

When choosing an appropriate hydrodynamic model, there is always a compromise between accuracy and computational cost, with high-fidelity models being more expensive than low-fidelity ones. However, when assessing uncertainty, we can use a multifidelity approach to take advantage of the accuracy of high-fidelity models and the computational efficiency of low-fidelity models. Here, we apply the multilevel multifidelity Monte Carlo method (MLMF) to quantify uncertainty by computing statistical estimators of key output variables with respect to uncertain input data, using the high-fidelity hydrodynamic model XBeach and the lower-fidelity coastal flooding model SFINCS (Super-Fast INundation of CoastS). The multilevel aspect opens up the further advantageous possibility of applying each of these models at multiple resolutions. This work represents the first application of MLMF in the coastal zone and one of its first applications in any field. For both idealised and real-world test cases, MLMF can significantly reduce computational cost for the same accuracy compared to both the standard Monte Carlo method and to a multilevel approach utilising only a single model (the multilevel Monte Carlo method). In particular, here we demonstrate using the case of Myrtle Beach, South Carolina, USA, that this improvement in computational efficiency allows for in-depth uncertainty analysis to be conducted in the case of real-world coastal environments – a task that would previously have been practically unfeasible. Moreover, for the first time, we show how an inverse transform sampling technique can be used to accurately estimate the cumulative distribution function (CDF) of variables from the MLMF outputs. MLMF-based estimates of the expectations and the CDFs of the variables of interest are of significant value to decision makers when assessing uncertainty in predictions

Economically optimal safety targets for riverine flood defence systems

A breach in a flood defence will affect the downstream water levels in a riverine system, and therefore the flood risk of the system. The effect of this changed flood risk is used in an economical optimization to assess if this significantly changes the economically optimal safety targets of the flood defences in a riverine system. The impact of breaches on the flood risk and the economically optimal safety targets is modelled using simplified hydrodynamic relations and a number of conceptual case studies for small systems. Significant differences were found, but are limited to cases with a relatively high chance of breaching and/or high impact breaches. These differences seem to mostly affect the optimal heights of the flood defences, which means that including the effect of breaches can result in a different-optimal investment path.Hydraulic Structures and Flood Ris

Economically optimal safety targets for riverine flood defence systems

A breach in a flood defence will affect the downstream water levels in a riverine system, and therefore the flood risk of the system. The effect of this changed flood risk is used in an economical optimization to assess if this significantly changes the economically optimal safety targets of the flood defences in a riverine system. The impact of breaches on the flood risk and the economically optimal safety targets is modelled using simplified hydrodynamic relations and a number of conceptual case studies for small systems. Significant differences were found, but are limited to cases with a relatively high chance of breaching and/or high impact breaches. These differences seem to mostly affect the optimal heights of the flood defences, which means that including the effect of breaches can result in a different-optimal investment path