8 Jun 2026

Emulation of Peak Storm Surge Across Extended Spatial Domains Using Separable Gaussian Process Techniques

Abstract: Data-driven emulation of peak storm surge has emerged as a popular strategy for overcoming limitations arising from the computational burden of high-fidelity hydrodynamic numerical models used within coastal risk assessment applications. The surrogate models used for this emulation are developed using suites of synthetic storm simulations, and once calibrated, can replace the original high-fidelity model to establish predictions for new storms. These predictions pertain to the geographic domain, and therefore nodal locations, covered by the original high-fidelity simulation suite. This creates a two-dimensional space for the peak surge predictions, with one corresponding to the storm features and the other to the spatial domain. Gaussian Process techniques have emerged as a widely popular surrogate modeling technique for peak surge emulation. In all GP implementations so far, the spatial variability has been incorporated in the analysis through the metamodel output, considering a multi-output GP implementation. This approach fails to explicitly model spatial dependencies for the peak surge. To address this shortcoming, this study examines an alternative implementation that considers spatial and storm feature variability as part of the metamodel input, establishing a surrogate model that simultaneously predicts the peak storm surge across both the spatial domain and the storm features. For computational tractability, a separable covariance function is considered for the GP, establishing separate kernels for the spatial and storm feature spaces. Particularly for the spatial domain, an adaptive covariance tapering formulation, which infuses sparsity in the corresponding covariance matrix, is adopted to support applications with a large number of nodal locations. A simultaneous calibration approach for the hyperparameters of the separate kernels is further proposed to improve emulation accuracy. Comparisons of computational efficiency and accuracy of the alternative GP implementations are established utilizing the Coastal Hazards System–North Atlantic database, with those employing the adaptive covariance tapering formulation evaluated under varying sparsity levels. The case study demonstrates that the simultaneous hyperparameter calibration is beneficial for the separable GP's predictive accuracy, particularly as it relates to the worst-performing nodes in the domain, and that the imposed sparsity level impacts the separable GP's ability to model non-stationary spatial trends in the domain.