Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms

This paper investigates the development of a kriging surrogate model for storm surge prediction utilizing an existing database of high-fidelity, synthetic storms. This surrogate model (metamodel) provides a fast-to-compute mathematical approximation to the input/output relationship of the computationally expensive simulation model that created this database. The implementation is considered over a large coastal region composed of nearshore nodes (locations where storm surge is predicted) and further examines the ability to provide time-series forecasting. This setting creates a high-dimensional output (over a few thousand surge responses) for the surrogate model with anticipated high spatial/temporal correlation. Kriging is considered as a surrogate model, and special attention is given to the appropriate parameterization of the synthetic storms, based on the characteristics of the given database, to determine the input for the metamodel formulation. Principal component analysis (PCA) is integrated in this formulation as a dimension reduction technique to improve computational efficiency, as well as to provide accurate and continuous predictions for time-dependent outputs without the need to introduce time averaging in the time-series forecasting. This is established by leveraging the aforementioned correlation characteristics within the initial database. A range of different implementation choices is examined within the integrated kriging/PCA setting, such as the development of single or multiple metamodels for the different outputs. The metamodel accuracy for inland nodes that have remained dry in some of the storms in the initial database is also examined. The performance of the surrogate modeling approach is evaluated through a case study, utilizing a database of 446 synthetic storms for the Gulf of Mexico (Louisiana coast). The output considered includes time histories for 30 locations over a period of 45.5 h with 92 uniform time steps, as well as peak responses over a grid of 545,635 nearshore nodes. High accuracy and computational efficiency are observed for the proposed implementation, whereas including the prediction error statistics provides estimations with significant safety margins.