^{a}and Yi Zeng

^{b}

^{a}zhangzhenhao@csust.edu.cn

^{b}294906064@qq.com

Uncertainty is a key challenge in tsunami hazards analysis. The tsunami height has obvious stochastic nature in tsunami propagation process. In this paper a stochastic model of maximum tsunami height is studied. Firstly the physical process of tsunami propagation from deep sea to shallow water is illustrated, which indicates that tsunami propagation in shallow water areas is different from that in deep water areas. The tsunami spread velocity depends on water depth in shallow water areas. Then the water depth in shallow water area is considered random, and it is assumed that the random water depth follows the Wiener process, which is reasonable according to Wiener processâ€™s irregular characteristics. And according to the energy conservation principle, tsunami wave velocity affects wave height. So the tsunami height depends on water depth, namely the submarine topographies. Based on that a stochastic model of maximum tsunami height is established. Finally the probability distribution of maximum tsunami height is calculated using the stochastic model, and it is showed that the calculation results of the mean value of maximum tsunami height is very similar to the average value of 165 actual observation values of maximum tsunami heights during the recent twenty years from 1997 to 2017.