A non-homogeneous hidden Markov model for predicting the distribution of sea surface elevation

The prediction problem of sea state based on the field measurements of wave and meteorological factors is a topic of interest from the standpoints of navigation safety and fisheries. Various statistical methods have been considered for the prediction of the distribution of sea surface elevation. However, prediction of sea state in the transitional situation when waves are developing by blowing wind has been a difficult problem until now, because the statistical expression of the dynamic mechanism during this situation is very complicated. In this article, we consider this problem through the development of a statistical model. More precisely, we develop a model for the prediction of the time-varying distribution of sea surface elevation, taking into account a non-homogeneous hidden Markov model in which the time-varying structures are influenced by wind speed and wind direction. Our prediction experiments suggest the possibility that the proposed model contributes to an improvement of the prediction accuracy by using a homogenous hidden Markov model. Furthermore, we found that the prediction accuracy is influenced by the circular distribution of the circular hidden Markov model for the directional time series wind direction data.