Dimensionality reduction techniques for analyzing tsunami simulations in hazard assessment and forecasting applications

A wide selection of linear and non-linear dimensionality reduction techniques is evaluated on synthetic tsunami data that is the basis for tsunami hazard assessment and computational forecasting. The data were computed from earthquake rupture forecasts (ERFs) supplying initial generation conditions and a linear long-wave Green's function approach to efficiently calculate tsunami propagation. The dimensionality reduction techniques include various forms of principal component analysis, manifold learning, and neural networks. Both external (e.g., mutual information) and internal (silhouette) metrics are used to evaluate clustering in the reduced dimension, focusing on peak-nearshore tsunami amplitudes (PNTA) along a nearshore isobath and time-series (marigrams) at specific nearshore locations. This evaluation is intentionally scoped to cluster-based downsampling to produce probabilistic inundation maps. For our test case along the Nankai subduction zone, manifold learning methods produced the highest clustering metric scores for PNTA profiles among the examined dimensionality reduction techniques. The marigram results are less consistent, owing primarily to uncertainty in defining appropriate clusters in the original high-dimensional (ambient) space to establish a “ground truth.” A novel application of using the integrative ERF-tsunami approach is that features extracted in the reduced domain, particularly from manifold learning, can be mapped back to rupture zones along the fault. This yields targeted fault information associated with unique PNTA profiles and marigram characteristics, such as late-arriving waves. Further testing would be needed for application-specific workflows and more complex fault systems, but results from this single subduction zone case study support the consideration of non-linear techniques (e.g., manifold learning) as alternatives to linear methods.