Thresholds and trends in wave steepness: A data-driven study of coastal wave breaking risk

Wave steepness plays a crucial role in coastal engineering, sediment transport, and maritime safety, as steeper waves exert stronger forces on coastal structures, enhance sediment mobilization, and increase risks for vessels and swimmers. Despite its importance, previous studies have often treated wave steepness in generalized contexts, lacking region-specific evaluations or failing to account for temporal variability and localized wave dynamics. Moreover, many analyses have not sufficiently linked wave steepness to practical risk indicators such as wave breaking potential. To address these gaps, this study presents a comprehensive analysis of wave steepness and its association with breaking risk on the Gold Coast, Australia, using data collected throughout 2023. Wave steepness, a dimensionless parameter defined as the ratio of wave height to wavelength, serves as a critical indicator for assessing wave stability and potential for breaking in coastal environments. Using the formula S≈(2πH_s)/(gT_p^2 ), we analyzed 17,520 observations of significant wave height (H_s) and peak period (T_p) to categorize waves into four distinct stability classes: gentle, moderate, steep, and breaking risk. Results indicate that only 0.34% of observations exceeded the critical breaking threshold of S>0.04, with the maximum steepness of 0.0564 recorded on December 1, 2023. Significant seasonal variations were observed, with October exhibiting the highest mean steepness (0.0127) and June the lowest (0.0052). A strong negative correlation (r=-0.78) between peak period and wave steepness confirms the theoretical relationship between these parameters. The study also revealed that 69% of waves were classified as gentle (S