Relationship Between Significant Wave Period and Spectral Periods in the Coastal Waters of China

The wave period is a crucial environmental parameter in the study of upper ocean dynamic processes and the design of coastal engineering. There are various definitions of wave periods in the field of oceanography, and empirical formulas are often required for conversion between different periods. This study analyzes the statistical relationship between the significant wave period (T_s), derived from zero-crossing analysis of sea surface elevation, and several commonly used spectral periods, using three sets of wave data collected from the coastal waters of China. The results show that the relationships between T_s and spectral periods are significantly influenced by wave spectral shape parameters. Specifically, the ratio of T_s to the mean wave period (T₀₂) is closely related to the Longuet-Higgins spectral bandwidth parameter, while the ratio of T_s to the peak period (T_p) is closely associated with the Goda spectral peakedness parameter. Based on these findings, this study proposes two conversion formulas between T_s and T₀₂, as well as T_p, involving spectral shape parameters. Evaluations using three sets of wave data demonstrate that the newly proposed formulas significantly outperform traditional linear fitting methods in terms of performance. The root mean square deviations for T_s and T₀₂ using linear fitting are 0.28, 0.48, and 0.28 s, while the new formulas reduce them to 0.18, 0.16, and 0.12 s, respectively. For T_s and T_p, the root mean square deviations with linear fitting are 0.90, 1.48, and 0.44 s, whereas the new formulas reduce them to 0.63, 0.80, and 0.32 s, respectively.