Synthetic Aperture Radar (SAR) is widely used for observing sea surfaces and retrieving two-dimensional wave spectra. However, existing methods for retrieving directional wave spectra from SAR imagettes face challenges due to the complex non-linear SAR-wave imaging relationship and the limitation of first-guess spectra. This study proposes a novel twostage machine learning strategy for retrieving two-dimensional directional wave spectra from Chinese Gaofen-3 SAR wave mode products. We achieve the generation of complete two-dimensional wave spectra and several wave parameters solely from GF-3 SAR data without necessitating any additional inputs. In the first stage, we employ the Energy Attention Conditional Generative Adversarial Network (EA-CGAN) to retrieve the normalized wave spectrum. The generator of the EA-CGAN establishes a non-linear transformation from normalized SAR cross spectra to normalized wave spectra to enhance the capabilities. In the second stage, the XGBoost model retrieves the intensity of the wave spectrum. The EA-CGAN and XGBoost models were trained on an extensive dataset that consists of about 11,000 Gaofen-3 SAR wave mode imagettes and two-dimensional wave spectra from the fifth-generation reanalysis (ERA-5) of the European Centre for Medium-Range Weather Forecasts (ECMWF). The results of the evaluation using test samples reveal high consistency between the retrieved wave spectra and ERA-5 wave spectra in terms of spectral similarity, peak period, peak direction, significant wave height, and mean wave periods. Compared to the traditional methods, our approach offers enhanced effectiveness, demonstrating the potential of advanced deep learning in highprecision SAR wave spectrum inversion.

We present a semi-automated image processing method, the continuous maximum gradient (CMG) method, for identifying the air–water interface in side-view digital images of unidirectional water waves in a glass-walled laboratory wave flume. In a manner similar to Canny edge detection, CMG exploits gradients in pixel intensity to identify the free surface, but also enforces an additional streamline constraint. This latter step is necessary to exclude signals from other features, such as wave gauges and water droplets on the glass, which also exhibit large intensity gradients. To demonstrate the performance and accuracy of CMG, we first compare its detection results with independent wave gauge measurements. The maximum difference in total spectral variance was found to be approximately 4%, while quantitative error metrics from a regression analysis yielded an $R^{2}$ value of 0.997 for the surface elevation time-series. We also compare the CMG detection results with imagery data from existing literature where excellent visual agreement is observed, confirming the broad applicability of the CMG method. The employment of CMG facilitates free surface measurements at a very high resolution (order of millimeters) which is essential for capturing the spatio-temporal wave-field evolution and obtaining instantaneous measurement of local wave shape.

Optical (OPT) and Synthetic Aperture Radar (SAR) cross-modal remote sensing image retrieval is a key technique for all-weather Earth observation. The enhancement of SAR image resolution has driven the development from conventional scene-level retrieval to object-level retrieval. Inter-class similarity, intra-class variability, and cross-modal discrepancies are general challenges in cross-modal image retrieval. Although existing methods have attempted to address them at the scene level, these challenges persist in object-level tasks due to inherent limitations of the methods, such as detail loss caused by global pooling and insufficient local discrimination. To address this gap, a novel FGHN is proposed to enhance the retrieval accuracy. First, a focus-aware residual network is designed to highlight discriminative local features, facilitating the extraction of semantic details. Second, an intra-class feature aggregation loss is introduced to improve intra-class compactness, reinforcing the consistency of fine-grained representations. Finally, a distance enhanced weighting strategy is incorporated into the hash learning loss to promote similarity among hash codes of the same class. To support fine-grained OPT-SAR retrieval, we construct a High-Resolution OPT-SAR dataset, termed HROS. It is worth noting that the SAR images in HROS were collected by our team. Extensive experiments are conducted to evaluate both FGHN and HROS. The experimental results demonstrate that HROS exhibits high resolution, strong robustness, and superior differentiation, establishing it as a promising benchmark for OPT-SAR retrieval. FGHN achieves state-of-the-art performance on HROS, obtaining 89.80% mAP and 93.95% P@10 for OPT image retrieval with SAR queries at 32 bits hash code. Its strong generalization capability is further validated on the public CBRSIR VS dataset. Ablation studies confirm the effectiveness of the three innovative modules. Moreover, FGHN proves potential for large-scale remote sensing image retrieval applications.

A synthetic aperture radar (SAR) provides vital global observations of ocean waves. However, the quasi-linear inversion algorithm routinely used for Sentinel-1 Level-2 Ocean Swell Wave (OSW) products suffers from inherent nonlinear imaging limitations. These include severe distortions and the inability to resolve wind-sea components under a strong azimuth cut-off effect. To address these challenges, this paper proposes a novel prior-knowledge-integrated machine learning framework to reconstruct complete and accurate directional wave spectra from Sentinel-1A SAR wave mode data. First, an extreme gradient boosting model is trained to accurately estimate wind-sea heights, which are then used to construct a theoretical JONSWAP prior spectrum. Subsequently, a U-Net architecture seamlessly integrates this physical prior knowledge with the official OSW swell spectra baseline. Independent validation demonstrates that the proposed framework significantly increases the spectral similarity against ERA5 reanalysis compared to the standard OSW. Furthermore, the derived parameters of total significant wave height, mean wave period, and mean wave direction exhibit remarkable improvements, with root mean square errors of 0.4026 m, 0.4342 s and 20.42°, respectively. The enhancement of SAR inferred two-dimensional wave spectra is also examined and discussed by three typical case studies. It is indicated that integrating physical wave knowledge with machine learning robustly mitigates the non-linear limitations of SAR imaging, providing highly reliable directional wave spectra for global ocean monitoring and forecasting.

Synthetic aperture radar (SAR) imaging of ocean waves is well understood, and valid physical models have been proposed to describe the forward mapping from ocean wave spectra to SAR image spectra. However, retrieving wave spectra from SAR spectra typically requires precise prior wave spectra, which impedes the further development of SAR-based ocean wave observations. The primary challenge lies in the fact that directly solving the inverse nonlinear mapping is mathematically infeasible due to azimuthal cutoff effects. This study developed a data-driven strategy to approximate the inverse nonlinear mapping without relying on prior information. A simulated SAR-Wave spectrum database was created based on the forward nonlinear mapping and then a deep learning model was trained on this database to approximate the inverse nonlinear mapping. Extensive evaluations on 79,371 retrieval wave spectra across weakly to strongly nonlinear SAR imaging regimes demonstrate the effectiveness of the approximated inverse nonlinear mapping. Under strongly nonlinear SAR imaging conditions, the rootmean-square errors are 0.27 m for significant wave height, 0.53 s for mean wave period, 35.78 m for peak wavelength, and 17.4 • for peak direction. Further testing on practical GF-3 SAR wave mode data shows that the SAR spectra reconstructed from the retrieved wave spectra align well with the observed SAR spectra, confirming the validity of the approximated inverse transformation. This work highlights the potential of integrating deep learning techniques with the SAR wave imaging theory to enable reliable and near-real-time SAR wave spectrum retrieval, thereby advancing the development of operational SAR ocean observation systems.

Significant wave height (SWH) is a fundamental parameter for ocean engineering, maritime safety, and climate studies. Although spaceborne synthetic aperture radar (SAR) wave mode observations provide global, all-weather coverage, accurate SWH retrieval remains challenging due to the complex ocean-to-SAR imaging mechanism. This paper presents an explainable machine learning algorithm for retrieving SWH from Sentinel-1 SAR wave mode data. To address the scarcity of high-quality collocations and the black-box nature of existing deep-learning approaches, we first correct ERA5 SWH against high-quality Spotter drifting in situ using quantile mapping (QM). The bias-corrected ERA5 data are then collocated with Sentinel-1 SAR to generate a large-scale, globally distributed, and Spotter-calibrated training dataset. Here, QM maps each quantile of the ERA5 data distribution onto the corresponding quantile of the collocated Spotter distribution, thereby adjusting the statistical distribution of the reanalysis. An eXtreme gradient boosting regression model is then trained on 32 physically interpretable features extracted from Sentinel-1 Level-2 products, including image statistics, spectral parameters, azimuth cutoff wavelength, normalized radar cross section, and wind-related variables. Comprehensive temporal-independent validations against Spotter buoys and multi-mission altimeter data throughout one year of 2021 (excluded both from the QM correction and from model training) demonstrate high accuracy, with root-mean-square errors of 0.36 m (WV1) and 0.45 (WV2) for SAR–Spotter matchups over the range 0.5–10.0 m. In addition, SHapley Additive exPlanation (SHAP) analysis is employed to quantify feature contributions and enhance model transparency. Furthermore, a compact 12-feature model selected via SHAP-based hierarchical clustering retains a nearly equivalent performance while improving interpretability. The proposed approach offers a reliable and transparent solution for global SAR-based SWH monitoring.