Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment

• Kriging metamodeling is considered for approximation of hurricane wave/surge responses.
• High-dimensionality of output is addressed by adopting principal component analysis.
• Application of interest is realtime risk assessment and development of standalone tools.
• Comparisons to response surface approximation are also made.
• Incorporation of the metamodeling error in the risk assessment is also addressed.

One of the important recent advances in the field of hurricane/storm modeling has been the development of high-fidelity numerical models that facilitate accurate but also computationally intensive simulations of hurricane responses. For efficient implementation in probabilistic hurricane risk assessment, that typically requires simulation of a large number of hurricane scenarios within the coastal regions of interest, combination with metamodeling approaches has been recently proposed. In this work, kriging is investigated for this purpose, focusing on implementation for real-time assessment, i.e. for evaluating risk during an incoming event (and prior to the hurricane/storm making landfall), and on facilitating the development of efficient standalone tools. An important characteristic of this application is that the model output is very high dimensional, since the hurricane response is calculated in a large coastal region and potentially at different time instances. This makes it impractical to establish a different metamodel for each different output. Considering, though, the potential –spatial and/or temporal- correlation between the different outputs combination with principal component analysis (PCA) is proposed here. This analysis extracts a much smaller number of latent outputs to approximate the initial high-dimensional output. A separate metamodel is then developed for each latent output. Comparisons between kriging with and without PCA and between kriging and moving least squares response surface approximations are discussed in terms of both computational efficiency (speed) and memory requirements. Both these are important considerations when discussing the development of standalone tools that can efficiently run in personal laptops (or even smartphones) of emergency response managers. The impact of the number of latent outputs considered is investigated in this context, and also the optimal selection of basis and correlation functions for the kriging is discussed. Finally for calculating risk the prediction error stemming from the metamodel is explicitly addressed (i.e., the assessment does not rely only on the mean kriging response). The proposed approach is demonstrated for real-time hurricane risk assessment for the Hawaiian Islands, focusing in the region around Oahu.