Seven freak wave incidents previously documented in the real ocean in combination with model hindcast simulations are used to study the variations associated with freak-wave-related parameters, such as wave steepness, directional spreading, and frequency bandwidth. Unlike the strong correlations between the freak wave parameters and freak waves' occurrence which were obtained in experimental and physical research, the correlations are not clear in the freak waves occurring in the real ocean. Wave directional spreading–steepness joint distribution is introduced and common visual features were found in the joint distribution when freak waves occur among seven “freakish” sea states. The visual features show that freak wave incidents occur when the steepness is large and directional spreading is small. Besides large steepness and small directional spreading, a long-duration, relatively rough sea state is also necessary for the freak wave generation. The joint distribution is more informative than any single statistical wave parameter. The continuous sea states of local large steepness and small directional spreading are supposed to generate freak waves, and two-dimensional distribution visualization is found to be a useful tool for freak waves' forecast. The common visual features of joint distributions supply an important cue for the theoretical and experimental research.

Seven freak wave incidents previously documented in the real ocean in combination with model hindcast simulations are used to study the variations associated with freak wave-related parameters, such as wave steepness, directional spreading, and frequency bandwidth. Unlike the strong correlations between the freak wave parameters and freak waves' occurrence which were obtained in experimental and physical research, the correlations are not clear in the freak waves occurred in the real ocean. Wave directional spreading-steepness joint distribution is introduced and common visual features were found in the joint distribution when freak waves occur among seven "freakish" sea states. The visual features show that freak wave incidents occur when the steepness is large and directional spreading is small. Besides the steepness is large and directional spreading is small, a long-duration relatively rough sea state is also necessary for the freak wave generation. The joint distribution is more informative than the sequential variation of any single statistical wave parameter. The continuous sea states of local large steepness and small directional spreading are supposed to be "freakish" sea states, and two-dimensional distribution visualization is found to be a useful tool for freak waves forecast. The common visual features of joint distributions supply an important cue for the theoretical and experimental research.

Significant wave height (SWH) is vital for maritime safety and oceanographic research. This study systematically evaluated the accuracy of the multi-mission along-track SWH product distributed by Copernicus Marine Service (CMEMS) with a focus on China’s coastal waters. Validation used 2022–2024 in situ data from 30 coastal operational buoys. A spatiotemporal collocation of 25 km and ±30 min was adopted to balance sample size and matching accuracy. The SWH product from CMEMS showed good performance with an overall bias of 0.10 m, root-mean-square error (RMSE) of 0.19 m, correlation coefficient (CC) of 0.98, and scatter index (SI) of 0.13. Spatially, errors tended to be lower in the south, offshore, and in deeper waters. All satellites systematically overestimated SWH under low sea states (SWH < 0.5 m) with a mean bias of 0.17 m, which was identified as a major contributor to the overall error. This study provides a practical reference for the validation of the multi-mission SWH product from CMEMS in China’s coastal waters, and also offers a useful reference for the fusion and assimilation of multi-source satellite wave data in complex coastal environments.

Shallow-water bathymetry is essential for coastal dynamics, navigation, engineering, and marine-resource management, especially where in situ observations are sparse. This study proposes a wave-stripe-based method for shallow-water bathymetric retrieval from Sentinel-1A VV-polarized SAR imagery. After texture-preserving denoising, multidirectional Gabor enhancement, K-means segmentation, and skeleton tracking, wave-crest centerlines are extracted and local wavelengths are measured as the normal spacing between adjacent crest lines. The dominant wave period is estimated from deep-water wavelengths, and water depth is retrieved using the linear wave dispersion relation. The method was evaluated using five Sentinel-1 acquisitions, with SAR-derived representative wave periods ranging from 12.45 to 14.96 s. Based on the mean retrieval performance across the five acquisitions, the 0–20 m depth range yielded an RMSE of 3.87 m, an MAE of 3.56 m, and r = 0.95, while the corresponding values for 0–50 m were 6.06 m, 5.02 m, and 0.97, respectively. The most stable performance occurred within the 5–20 m depth range. The method reduces fixed-window spectral averaging and improves the representation of local wavelength variability, supporting rapid bathymetric mapping along open-coast environments with clear swell-induced wave stripes, relatively gentle bathymetric slopes, and limited field observations.

This study evaluates the accuracy of ERA5 10-m wind speed and significant wave height (SWH) using one-year hourly observations from 16 buoys in the Bohai and Yellow Seas. ERA5 agrees closely with the buoys (wind: Bias 0.04 m/s, root-mean-square error (RMSE) 1.40 m/s, scatter index (SI) 0.24, correlation coefficient (r) 0.90; SWH: Bias 0.11 m, RMSE 0.23 m, SI 0.30, r 0.94). Errors decrease offshore, and the control is offshore distance rather than water depth: a 2.5-fold depth change at fixed distance alters wind RMSE by 0.02 m/s, whereas a doubling of distance at fixed depth alters it by 0.22–0.24 m/s. Wind Bias has a marked diurnal cycle whose amplitude decreases offshore and reverses seasonally; SWH Bias stays positive but weakens in summer; both variables overestimate weak and underestimate strong conditions. The absolute errors of the two variables vary out of phase, so their correlation cancels (−0.40 to 0.02), whereas the relative errors remain strongly coupled (0.59–0.80). Above 13 m/s, ERA5 underestimates wind by 11% while overestimating SWH by 6%, an inconsistency that locates the high-sea-state error in the wave model rather than in the forcing. These quantified errors constrain design-wave estimation and Bias correction in coastal engineering.