Keywords: hurricane risk, coastal hazard, response surface approximations, moving least squares, model prediction error.

A probabilistic framework, frequently referenced as the joint probability method (JPM), is gradually emerging as the standard tool for hurricane risk assessment [1,2]. The framework relies on a simplified description of hurricane scenarios through a small number of model parameters, such as landfall location, central pressure or radius of maximum winds [1]. Characterization of the uncertainty in these parameters, through appropriate probability models, and propagation of this uncertainty to the hurricane impact leads then to a probabilistic characterization for the hurricane risk. This is ultimately expressed as a probabilistic integral and its estimation entails numerical evaluation of the hurricane impact for a significant number of scenarios resulting from the adopted probabilistic description for the hurricane model parameters [2].

One of the greater recent advances in this field has been the development and adoption of high-fidelity numerical simulation models for reliable and accurate prediction of surge responses for a specific hurricane event [1]. These models permit a detailed representation of the hydrodynamic processes, albeit at the cost of greatly increased computational effort. This development increases significantly the computational cost for estimating the hurricane risk, since the latter involves analysis of a large number of hurricane scenarios. For alleviating this problem a systematic implementation of response surface surrogate modeling is discussed in this work. Based on information from a small number of high-fidelity numerical simulations, a moving least squares response surface approximation is proposed for efficient estimation of the impact for any other hurricane scenario. This response surface is then utilized for all evaluations required in the risk estimation. The optimal selection of the basis functions for the response surface and of the parameters of the moving least squares character of the approximation are discussed. The explicit incorporation in the risk quantification of the model prediction error, introduced through the surrogate modelling, is also addressed.

As an illustrative example of these concepts, application to the Hawaiian Island is discussed, adopting the formulation and results of the study [2]. Hurricane risk is characterised in terms of the significant wave height (either expected value or probability of exceeding specific thresholds). It is illustrated in this example that the explicit optimization of the response surface characteristics provides a significant improvement in the accuracy of the surrogate modelling. The proposed approach is also demonstrated to facilitate a highly efficient estimation of hurricane risk, and to provide information that can be very useful for emergency managers as well as for the design of protective systems against hurricanes.

1

D. Resio, J. Irish, M. Cialone, "A surge response function approach to coastal hazard assessment - part 1: basic concepts", Natural Hazards, 51(1), 163-182, 2009. doi:10.1007/s11069-009-9379-y

2

A.A. Taflanidis, A.B. Kennedy, J.J. Westerink, M. Hope, S. Tanaka, J. Smith, K.F. Cheung, "A comprehensive approach for online fast hurricane-risk prediction", in 11th International Conference on Applications of Statistics and Probability in Civil Engineering, Zurich, Switzerland, 2011. doi:10.1201/b11332-130

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