Implementation/optimization of moving least squares response surfaces for approximation of hurricane/storm surge and wave responses

One of the important recent advances in the field of hurricane/storm modelling has been the development of high-fidelity numerical simulation models for reliable and accurate prediction of wave and surge responses. The computational cost associated with these models has simultaneously created an incentive for researchers to investigate surrogate modelling (i.e. metamodeling) and interpolation/regression methodologies to efficiently approximate hurricane/storm responses exploiting existing databases of high-fidelity simulations. Moving least squares (MLS) response surfaces were recently proposed as such an approximation methodology, providing the ability to efficiently describe different responses of interest (such as surge and wave heights) in a large coastal region that may involve thousands of points for which the hurricane impact needs to be estimated. This paper discusses further implementation details and focuses on optimization characteristics of this surrogate modelling approach. The approximation of different response characteristics is considered, and special attention is given to predicting the storm surge for inland locations, for which the possibility of the location remaining dry needs to be additionally addressed. The optimal selection of the basis functions for the response surface and of the parameters of the MLS character of the approximation is discussed in detail, and the impact of the number of high-fidelity simulations informing the surrogate model is also investigated. Different normalizations of the response as well as choices for the objective function for the optimization problem are considered, and their impact on the accuracy of the resultant (under these choices) surrogate model is examined. Details for implementation of the methodology for efficient coastal risk assessment are reviewed, and the influence in the analysis of the model prediction error introduced through the surrogate modelling is discussed. A case study is provided, utilizing a recently developed database of high-fidelity simulations for the Hawaiian Islands.