Advances in Imputation Strategies Supporting Peak Storm Surge Surrogate Modeling

Surrogate models are widely recognized as effective, data-driven predictive tools for storm surge risk assessment. For such applications, surrogate models (referenced also as emulators or metamodels) are typically developed using existing databases of synthetic storm simulations, and once calibrated can provide fast-to-compute approximations of the storm surge for a variety of downstream analyses. The storm surge predictions need to be established for different geographic locations of interest, typically corresponding to the computational nodes of the original numerical model. A number of inland nodes will remain dry for some of the database storm scenarios, requiring an imputation for them to estimate the so-called pseudo-surge in support of the surrogate model development. Past work has examined the adoption of kNN (k-nearest neighbor) spatial interpolation for this imputation. The enhancement of kNN with hydraulic connectivity information, using the grid or mesh of the original numerical model, was also previously considered. In this enhancement, neighboring nodes are considered connected only if they are connected within the grid. This work revisits the imputation of peak storm surge within a surrogate modeling context and examines three distinct advancements. First, a response-based correlation concept is considered for the hydraulic connectivity, replacing the previous notion of connectivity using the numerical model grid. Second, a Gaussian Process interpolation (GPI) is examined as alternative spatial imputation strategy, integrating a recently established adaptive covariance tapering scheme for accommodating an efficient implementation for large datasets (large number of nodes). Third, a data completion approach is examined for imputation, treating dry instances as missing data and establishing imputation using probabilistic principal component analysis (PPCA). The combination of spatial imputation with PPCA is also examined. In this instance, spatial imputation is first deployed, followed by PPCA for the nodes that were misclassified in the first stage. Misclassification corresponds to the instances for which imputation provides surge estimates higher than ground elevation, creating the illusion that the node is inundated even though the original predictions correspond to the node being dry. In the illustrative case study, different imputation variants established based on the aforementioned advancements are compared, with comparison metrics corresponding to the predictive accuracy of the surrogate models developed using the imputed databases. Results show that incorporating hydraulic connectivity based on response similarity into kNN enhances the predictive performance, that GPI provides a competitive (to kNN) spatial interpolation approach, and that the combination of data completion and spatial interpolation emerges as the recommended approach.