Incorporation of sea level rise in storm surge surrogate modeling

In order to accommodate the computational burden of high-fidelity storm surge numerical models, surrogate modeling (metamodeling) techniques have gained significant popularity over the past decade. Utilizing an existing database of synthetic storm simulations, these models provide a fast-to-compute mathematical approximation to the input/output relationship of the numerical model that was used to establish this database. Thus, they offer fast predictions and, when properly calibrated, can maintain the accuracy of the high-fidelity numerical model that generated the original database. This study extends the previous work of the authors and investigates different computational aspects for incorporating Sea Level Rise (SLR) explicitly as an input within such a surrogate modeling framework. Kriging, also referenced as Gaussian process regression, is specifically chosen as the surrogate modeling technique for this study. The storms utilized correspond to a database of 300 synthetic tropical cyclones recently developed by the US Army Corps of Engineers Coastal Hazards System for the Puerto Rico and US Virgin Islands region, which considers three different SLR scenarios. The development of separate surrogate models for each of the three SLR scenarios and of a single surrogate model that predicts across all SLR scenarios are compared, addressing several relevant issues like (1) the proper definition of validation metrics (2) the correct implementation of cross-validation techniques, and (3) the need for adjustment of the surrogate model hyper-parameter calibration. It is shown that proper attention is needed when the same storms have been considered across all the different SLR scenarios in the database; otherwise, the calibration of the surrogate model may be ineffective, and the validation of its accuracy will provide erroneous confidence. The proper normalization of the storm surge output to improve the surrogate model accuracy is also discussed. Finally, the proper selection of storm simulations for establishing the database for the surrogate model development is examined, emphasizing how this selection should be performed efficiently across the different SLR scenarios. It is demonstrated that high surrogate model accuracy can be accommodated with a small number of strategically chosen storm simulations. Leveraging this investigation, recommendations are offered on how to efficiently create future high-fidelity databases to support the development of surrogate models that predict across different SLR scenarios.