Spatially extensive probabilistic tsunami inundation hazard assessment - Translating offshore hazards and uncertainties onshore with multiple importance sampling.

Probabilistic tsunami hazard assessment (PTHA) is widely used to quantify earthquake-tsunami hazards and their uncertainties, informing the design of evacuation zones and vertical evacuation structures. Inundation hazard studies typically leverage an "offshore" PTHA to model the tsunami sources, their uncertain occurrence rates, and the resulting deep-water tsunami wave heights. Inundation models are then used to translate the offshore PTHA onshore, but this is difficult to do rigorously because offshore PTHAs include many scenarios (e.g.10^5-10^7) and inundation models are computationally expensive. Monte Carlo sampling provides a practical solution, enabling the inundation hazard to be estimated rigorously from a sample of scenarios (typically hundreds or thousands). Recent studies show the efficiency can be greatly increased by using information from the offshore PTHA to prioritize sampling of scenarios with hazardous waves offshore the site of interest. These techniques are statistically unbiased and allow epistemic uncertainties in the offshore PTHA to be translated onshore. However, to date they have employed a single offshore site to guide the sampling, which can become less effective in regions covering hundreds or thousands of kilometres. The current study addresses this limitation using multiple importance sampling, which rigorously combines distinct Monte Carlo samples, each tailored to a different part of the study area. Information from the offshore PTHA can be used to determine how to weight each sample throughout the model domain, and reduce the chance that samples poorly tailored to some parts of the model domain will contaminate results in those areas. The approach is illustrated with a tsunami inundation hazard assessment for the entire state of New South Wales in southeast Australia, spanning 10 degrees latitude (> 1000 km). Inundation hazards are modelled uniformly at about 30 m resolution over the entire coast, using three Monte Carlo samples of 360 scenarios each from the 2018 Australian PTHA. The results demonstrate the feasibility of spatially extensive inundation hazard assessments that maintain rigorous consistency with the offshore PTHA.