Probabilistic Modelling and Return-Level Estimation of Tsunami Wave Heights: A Case Study of the 2011 Tohoku Tsunami

The powerful earthquake that struck Japan on 11 March 2011 produced one of the most destructive and catastrophic tsunamis in recent times. Despite Japan’s extensive tsunami preparedness and mitigation measures, the event caused more than 18,000 fatalities and severe damage to coastal infrastructure. Accurate estimation of tsunami wave heights is therefore essential for coastal hazard assessment. In this study, time-series water-level data associated with the 2011 tsunami were obtained from NOAA for 24 tide gauges distributed across the Pacific Ocean. Several probability distributions were fitted to the observed data, with the Weibull and Generalized Extreme Value (GEV) distributions providing comparable fits. The fitted models were used to estimate maximum wave heights for return levels of 5, 10, 25, 50, and 100 years at selected coastal locations. Although the GEV distribution generally provided a better fit, the Weibull distribution was selected for further analysis because it can be applied directly to the observed data. Comparison with observed maximum wave heights showed that the conventional Weibull distribution did not consistently capture the upper tail. Therefore, a modified Weibull distribution was proposed by introducing an additional constant. Parameter sensitivity analysis demonstrated that the transformation parameter substantially increases the estimated upper-tail wave heights, indicating its potential for improved extreme tsunami-wave estimation. Further validation using independent datasets and formal statistical tests is required.