Statistical Emulation, Sensitivity Analysis and Uncertainty Quantification of Tsunami Models: the Example of Tsunamis Generated by Earthquakes at the Cascadia Subduction Zone

Abstract:

An extensive investigation on tsunami generation and the resulting coastal inundation due to coseismic seabed displacements has been performed for the Cascadia Subduction Zone. We have adopted a new approach to represent coseismic seabed deformation in giant earthquakes, which avoids artefacts generated at the edges of block deformations. We represent the deformation with arbitrary shaped 4-sided polygons in which subsidences and uplifts are represented as quadratic curves. The arbitrary shapes of these polygons allow the realistic representation of the deformed seabed as a continuous surface except at the trench, where the fault breaks the surface. Experimental Design is used to select combinations of three source characteristics generating different event scenarios amongst Cascadia whole-margin ruptures; further work on other event types is in progress. Following that, the numerical model VOLNA has been run for the different scenarios, obtaining the induced tsunami waves propagation and coastal inundation. Statistical emulation has been applied to the wave elevation time series evaluations for many locations. Statistical emulators approximate expensive computer models: they are powerful tools for analyses that require many model evaluations since they can give accurate and fast probabilistic predictions. Registration and Functional Principal Components techniques are applied to the emulation process leading to further improvement in predictions. Leave-one-out diagnostics are used to validate the emulator, showing excellent agreement in predictions and model evaluations. The statistical emulation is also used for sensitivity and uncertainty analyses. These two analyses require a large number of evaluations and hence cannot be carried out with the expensive computer model. Our approach can be applied to provide uncertainty estimates both in operational tsunami warnings and in tsunami risk modeling, and can be used with many different numerical models.