Advances in spatiotemporal storm surge emulation: database imputation and multi-mode latent space projection

Surrogate models, also known as metamodels or emulators, have emerged as a valuable tool for storm surge hazard estimation. They are developed using numerical model results from a database of synthetic storms and have the potential to provide highly-accurate and efficient surge predictions for new storms beyond those in the database. Frequently, metamodels need to provide spatiotemporal predictions for the storm surge evolution over time, across a large geographic domain represented through appropriately chosen save points (SPs). This paper focuses on a specific type of metamodel, Gaussian process (GP) emulation, that has been proven versatile in past studies for this specific application. The development of the spatiotemporal metamodel in this setting may involve: (a) an imputation step to fill in missing data, associated with instances that nearshore and onshore SPs are dry; and (b) a dimensionality reduction step for projection to a latent space to improve the computational efficiency for the metamodel calibration and predictions. Advances are established across both these aspects by treating spatiotemporal storm surge responses as a three-dimensional tensor (across storm, time, and spatial domains), and by integrating techniques designed specifically for this tensor structure. For data imputation, low-rank tensor completion (LRTC) is adopted. LRTC leverages response correlations across all tensor dimensions, leading to improved imputation performance compared to established alternatives (for example, geospatial interpolation), by ensuring time-series smoothness between the imputed data and the available data in the original database. A combination of LRTC with imputation based on geospatial interpolation is also discussed. As a dimensionality reduction technique, higher-order singular value decomposition (HOSVD) is applied to separately reduce the spatial and temporal dimensions of the database, enabling the preservation of principal information associated with response correlation separately from each dimension within the latent space. Compared to the past use of principal component analysis for the augmented spatiotemporal dimensions, the separation promoted through HOSVD improves the latent output ability to capture complex surge variations, accommodating higher prediction accuracy for the metamodels developed based on this enhanced latent output structure. To improve efficiency in the metamodel calibration, different strategies are examined for grouping the HOSVD-based latent outputs. Beyond advancements associated with the metamodel development, the improvement in accuracy of the predicted surge time-series around its peak is also considered by introducing a correction step using predictions from a supplementary metamodel developed to strictly predict the peak-surge. The proposed advances are demonstrated using the Coastal Hazards System–North Atlantic (CHS-NA) database.