24 Mar 2022
24 Mar 2022
Status: this preprint is currently under review for the journal NHESS.

Multilevel multifidelity Monte Carlo methods for assessing coastal flood risk

Mariana C. A. Clare1, Tim W. B. Leijnse2, Robert T. McCall2, Ferdinand L. M. Diermanse2, Colin J. Cotter1, and Matthew D. Piggott1 Mariana C. A. Clare et al.
  • 1Imperial College London, UK
  • 2Deltares, NL

Abstract. 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 inputs, using the high fidelity hydrodynamic model XBeach and the lower fidelity coastal flooding model SFINCS. 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, USA, that this improvement in computational efficiency allows 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 risk.

Mariana C. A. Clare et al.

Status: open (until 05 Jun 2022)

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  • RC1: 'Comment on nhess-2022-74', Anonymous Referee #1, 18 Apr 2022 reply

Mariana C. A. Clare et al.

Mariana C. A. Clare et al.


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Short summary
Assessing risk is computationally expensive because it requires multiple runs of expensive models. We take the novel approach of assessing risk from coastal flooding using a multi-model multi-resolution method (MLMF) which combines the efficiency of less accurate models with the accuracy of more expensive models at different resolutions. This significantly reduces the computational cost of assessing uncertainty but maintains accuracy making previously unfeasible real-world risk studies possible.