Statistical Analysis of Tsunami Wave Heights Based on the Mixed Lognormal Distribution

Tsunami is an extremely destructive oceanic disaster. The Hawaiian Islands are located in the central Pacific Ocean and are highly vulnerable to tsunamis due to their unique geographical location and topography. This study focuses on assessing the potential tsunami inundation risk in the Honolulu area of Hawaii. By analyzing historical tsunami events from 1819 to 2015, a stochastic analysis approach is employed. The data is divided into four samples based on their characteristics. The occurrence frequency of tsunamis is modeled using a Poisson distribution. To address the abundance of small values in tsunami wave heights, a new method is introduced, utilizing the Poisson-Mix-Lognormal distribution to estimate tsunami wave heights at different return periods. The results show that when using shorter-term data, incorporating the maximum values of tsunami wave heights leads to slightly larger calculated return values compared to longer-term samples. These results contribute to a better understanding of tsunami risks in the Honolulu area and provide valuable insights for future tsunami risk assessments and mitigation strategies.