The rarity of tsunamis impels the scientific community to rely on numerical simulation for planning and risk assessment purposes because of the low availability of actual data from historic events. Numerical models, also called simulators, typically produce time series of outputs. Due to the large computational cost of such simulators, statistical emulation is required to carry out uncertainty quantification tasks, as emulators efficiently approximate simulators. There is thus a need to create emulators that respect the nature of time series outputs. We introduce here a novel statistical emulation of the input-output dependence of these computer models. We employ the Outer Product Emulator with two enhancements. Functional registration and Functional Principal Components techniques improve the predictions of the emulator. Our phase registration method captures fine variations in amplitude. Smoothness in the time series of outputs is modelled, and we are thus able to select more representative, and more parsimonious, regression functions than a fixed basis method such as a Fourier basis. We apply this approach to the high resolution tsunami wave propagation and coastal inundation for the Cascadia region in the Pacific Northwest. The coseismic representation in this analysis is novel, and more realistic than in previous studies. With the help of the emulator, we can carry out sensitivity analysis of the maximum wave elevation with respect to the source characteristics, and we are able to propagate uncertainties from the source characteristics to wave heights in order to issue probabilistic statements about tsunami hazard for Cascadia.
"Functional emulation of high resolution tsunami modelling over Cascadia." Ann. Appl. Stat. 12 (4) 2023 - 2053, December 2018. https://doi.org/10.1214/18-AOAS1142