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In this paper, we have conducted a probabilistic tsunami hazard assessment (PTHA) for Hong Kong (China) and Kao Hsiung (Taiwan), considering earthquakes generated in the Manila subduction zone. The new PTHA methodology with the consideration of uncertainties of slip distribution and location of future earthquakes extends the stochastic approach of Sepúlveda et al. (2017). Using sensitivity analyses, we further investigate the uncertainties of probability properties defining the slip distribution, the location, and the occurrence of earthquakes. We demonstrate that Kao Hsiung and Hong Kong would be significantly impacted by tsunamis generated by M W > 8.5 earthquakes in the Manila subduction zone. For instance, a specific M W 9.0 earthquake scenario is capable of producing tsunami amplitudes exceeding 4.0 and 3.5 m in Kao Hsiung and Hong Kong, respectively, with a probability of 50%. Despite the significant tsunami impact, great earthquakes have long mean return periods. As a result, the PTHA shows that Kao Hsiung and Hong Kong are exposed to a relatively small tsunami hazard. For instance, maximum tsunami amplitudes in the assessed locations of Kao Hsiung and Hong Kong exceed 0.32 and 0.18 m, respectively, with a mean return period of 100 years. The inundation hazard in populated areas is small as well, with mean return periods exceeding 1,000 years. Sensitivity analyses demonstrate that the PTHA can be affected by the uncertainties of the probability properties defining the slip distribution, the location, and the occurrence of earthquakes. However, PTHA results are most sensitive to the choice of the earthquake occurrence model.

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This paper proposes a stochastic approach to model the earthquake uncertainties in terms of the rupture location and the slip distribution for a future event, with an expected earthquake magnitude. Once the statistical properties of earthquake uncertainties are described, they are then propagated into the tsunami response and the inundation at assessed coastal areas. The slip distribution is modeled as a random field within a nonrectangular rupture area. The Karhunen‐Lòeve (K‐L) expansion method is used to generate samples of the random slip, and a translation model is employed to obtain target probability properties. A strategy is developed to specify the accuracy of the random samples in terms of numbers of subfaults of the rupture area and the truncation of the K‐L expansion. The propagation of uncertainty into the tsunami response is performed by means of a Stochastic Reduced Order Model. To illustrate the methodology, we investigated a study case in north Chile. We first demonstrate that the stochastic approach generates consistent earthquake samples with respect to the target probability properties. We also show that the results obtained from SROM are more accurate than those obtained with classic Monte Carlo simulations. To validate the methodology, we compared the simulated tsunamis and the tsunami records for the 2014 Chilean earthquake. Results show that leading wave measurements fall within the tsunami sample space. At later times, however, there are mismatches between measured data and the simulated results, suggesting that other sources of uncertainties are as relevant as the uncertainty of earthquakes.