A statistical analysis method for significant wave height and spectral peak frequency considering the random and time-varying effects based on copula function and Bayesian inference

Random and time-varying effects are important factors for statistical analysis of wave characteristic variables, including the significant wave height and spectral peak frequency. This paper proposes a statistical analysis method for the accurate statistical analysis of the state of the ocean. Several common distributions are applied as candidates for describing a specific variable, denoted as the marginal distribution. The joint distribution for the wave characteristic variables is constructed using copula functions based on the marginal distributions. The probability and unknown parameters of the marginal distributions are then determined by fully Bayesian inference. The best-fitting marginal distribution is selected based on the posterior probabilities of the candidates. Then, unknown parameters of the candidate copula functions are estimated by maximum likelihood estimation. The best-fitting copula function is selected based on Akaike information criterion, root mean squared error and Nash Sutcliffe efficiency. The proposed method is verified using the National Data Buoy Center dataset for 2019. However, this dataset, collected from a network of almost 100 moored buoys and Coastal-Marine Automated Network (CMAN) stations, contains incomplete data. The results reveal that the best-fitting marginal distribution and copula function may vary with the month. The average and maximum values of the improved RMSE using the proposed method are only 0.0064 and 0.0187, respectively. This indicates the high accuracy of the proposed method for the statistical analysis of wave states even though missing some data.