Several aspects of global climate change, e.g., the rise of sea level and water temperature anomalies, suggest the advantages of studying wave distributions. In this study, WAVEWATCH-III (WW3) (version 6.07), which is a well-known numerical wave model, was employed for simulating waves over global seas from 1993–2020. The European Centre for Medium-Range Weather Forecasts (ECMWF), Copernicus Marine Environment Monitoring Service (CMEMS), current and sea level were used as the forcing fields in the WW3 model. The validation of modelling simulations against the measurements from the National Data Buoy Center (NDBC) buoys and Haiyang-2B (HY-2B) altimeter yielded a root mean square error (RMSE) of 0.49 m and 0.63 m, with a correlation (COR) of 0.89 and 0.90, respectively. The terms calculated by WW3-simulated waves, i.e., breaking waves, nonbreaking waves, radiation stress, and Stokes drift, were included in the water temperature simulation by a numerical circulation model named the Stony Brook Parallel Ocean Model (sbPOM). The water temperature was simulated in 2005–2015 using the high-quality Simple Ocean Data Assimilation (SODA) data. The validation of sbPOM-simulated results against the measurements obtained from the Array for Real-time Geostrophic Oceanography (Argo) buoys yielded a RMSE of 1.12 °C and a COR of 0.99. By the seasonal variation, the interrelation of the currents, sea level anomaly, and significant wave heights (SWHs) were strong in the Indian Ocean. In the strong current areas, the distribution of the sea level was consistent with the SWHs. The monthly variation of SWHs, currents, sea surface elevation, and sea level anomalies revealed that the upward trends of SWHs and sea level anomalies were consistent from 1993–2015 over the global ocean. In the Indian Ocean, the SWHs were obviously influenced by the SST and sea surface wind stress. The rise of wind stress intensity and sea level enlarges the growth of waves, and the wave-induced terms strengthen the heat exchange at the air–sea layer. It was assumed that the SST oscillation had a negative response to the SWHs in the global ocean from 2005–2015. This feedback indicates that the growth of waves could slow down the amplitude of water warming.

The Chinese-French Oceanography SATellite (CFOSAT) jointly developed by the Chinese National Space Agency (CNSA) and the Centre National d’Etudes Spatiales (CNES) of France carries a wave spectrometer (Surface Waves Investigation and Monitoring, SWIM). SWIM has one nadir and five off-nadir beams to measure ocean surface waves. These near-nadir beams range from 0° to 10° at an interval of 2°. In this work, we investigated the performance of wave parameters derived from wave spectra measured by SWIM at off-nadir beams during the period 2020 to December 2022, e.g., incidence angles of 6°, 8° and 10°, which were collocated with the wave simulated by Simulating Waves Nearshore (SWAN). The validation of SWAN-simulated significant wave heights (SWHs) against National Data Buoy Center (NDBC) buoys of National Oceanic and Atmospheric Administration (NOAA) exhibited a 0.42 m root mean square error (RMSE) in the SWH. Our results revealed a RMSE of 1.02 m for the SWIM-measured SWH in the East Pacific Ocean compared with the SWH simulated by SWAN, as well as a 0.79 correlation coefficient (Cor) and a 1.17 squared error (Err) for the wave spectrum at an incidence angle of 10°, which are better than those (i.e., the RMSEs were > 1.1 m with Cors < 0.76 and Errs > 1.2) achieved at other incidence angles of SWH up to 14 m. This analysis indicates that the SWIM product is a relevant resource for wave monitoring over global seas. The collocated wave retrievals for more than 300 cases from Gaofen-3 (GF-3) synthetic aperture radar (SAR) images in China Seas were also used to verify the accuracy of SWIM-measured wave spectra. The energy of the SWIM-measured wave spectra represented by SWH was found to decrease with an increasing incidence angle in a case study. Moreover, the SWIM-measured wave spectra were most consistent with the SAR-derived wave spectra at an incidence angle of 10°, yielding a 0.77 Cor and 1.98 Err between SAR-derived and SWIM wave spectra under regular sea state conditions (SWH < 2 m). The error analysis indicates that the difference in SWH between SWIM at an incidence angle of 10° and SWAN has an increasing tendency with the growth in sea surface wind and sea state and it stabilizes to be 0.6 m at SWH > 4 m; however, the current and sea level have less influence on the uncertainties of the SWIM product.

This study introduces a new machine learning-based algorithm for the retrieving significant wave height (SWH) using synthetic aperture radar (SAR) images. This algorithm is based on the azimuthal cut-off wavelength and was developed in quad-polarized stripmap (QPS) mode in coastal waters. The collected images are collocated with a wave simulation from the numeric model, called WAVEWATCH-III (WW3), and the current speed from the HYbrid Coordinate Ocean Model (HYCOM). The sea surface wind is retrieved from the image at the vertical–vertical polarization channel, using the geophysical model function (GMF) CSARMOD-GF. The results of the algorithm were validated against the measurements obtained from the Haiyang-2B (HY-2B) scatterometer, yielding a root mean squared error (RMSE) of 1.99 m/s with a 0.82 correlation (COR) and 0.27 scatter index of wind speed. It was found that the SWH depends on the wind speed and azimuthal cut-off wavelength. However, the current speed has less of an influence on azimuthal cut-off wavelength. Following this rationale, four widely known machine learning methods were employed that take the SAR-derived azimuthal cut-off wavelength, wind speed, and radar incidence angle as inputs and then output the SWH. The validation result shows that the SAR-derived SWH by eXtreme Gradient Boosting (XGBoost) against the HY-2B altimeter products has a 0.34 m RMSE with a 0.97 COR and a 0.07 bias, which is better than the results obtained using an existing algorithm (i.e., a 1.10 m RMSE with a 0.77 COR and a 0.44 bias) and the other three machine learning methods (i.e., a >0.58 m RMSE with a <0.95 COR), i.e., convolutional neural networks (CNNs), Support Vector Regression (SVR) and the ridge regression model (RR). As a result, XGBoost is a highly efficient approach for GF-3 wave retrieval at the regular sea state.