Shipborne gravity can be used to refine altimeter-derived gravity whose accuracy is low in shallow waters and areas with complex submarine topography. As altimeter-derived gravity only within a small radius around the shipborne data can be corrected by traditional methods, a new method based on multi-layer perceptron (MLP) neural network is proposed to refine the altimeter-derived gravity. Input variables of MLP include the positional information at observation points and geophysical information (from our own South China Sea gravity anomaly model (SCSGA) V1.0 and bathymetry model ETOPO1) at grid points around observation points. Output variables of MLP are the refined residual gravity anomalies at observation points. Training shipborne data are classified into four cases to train four MLP models, which are used to predict the refined gravity anomaly model SCSGA V1.1. Then all of the training shipborne data are used for training an MLP model to predict the refined gravity anomaly model SCSGA V1.2. Assessed by testing shipborne data, the accuracy of SCSGA V1.2 is 0.14 mGal higher than that of SCSGA V1.0, and similar to that of SCSGA V1.1. Compared with the original gravity anomaly model (SCSGA V1.0), the accuracy of the refined gravity anomaly model (SCSGA V1.2) by MLP is improved by 4.4% in areas where the training data are concentrated, and also improved by 2.2% in other areas. Therefore, the method of MLP can be used to refine the altimeter-derived gravity model by shipborne gravity, overcoming the problem of limited correction radius for traditional methods.

Mean sea surface (MSS) is an important datum for the study of sea-level changes and charting data, and its accuracy in coastal waters has always been the focus of marine geophysics and oceanography. A new MSS model with a grid of 1′ × 1′ over the Sea of Japan and its adjacent ocean (named SJAO2020) (25° N~50° N, 125° E~150° E) was established. It ingested 12 different satellites altimeter data (including TOPEX/Poseidon, Jason-1/2/3, ERS-1/2, Envisat, GFO, HaiYang-2A, SRL/Altika, Sentinel-3A, Cryosat-2) and 24 tide gauge stations’ records and joint GNSS data. The latter were used to correct the sea surface height within 10 km from the coastline by using the Gaussian inverse distance weighting method in SJAO2020. The differences among SJAO2020, CLS15, and DTU18, as well as the differences between them and the altimeter data of HY-2A, Jason-3, and Sentinel-3A were introduced. By comparing with tide gauge records, satellite altimeter data, and other models (DTU18, DTU15, CLS15, CLS11 and WHU13), it was demonstrated that SJAO2020 produces the smallest errors, and its coastal accuracy is relatively reliable.

Satellite altimetry is an important technique to derive oceanic deflections of vertical (DOV). HaiYang-2A (HY-2A) is the first Chinese altimetry satellite launched in August 2011 to observe the global marine dynamic environment. To assess the reliability of DOVs derived from HY-2A geodetic mission data, the Bay of Bengal and its adjoining area (0°–23°N, 80°–100°E) are selected as the research area, and the accuracy of HY-2A/GM-derived DOVs is compared with that of DOVs determined from CryoSat-2-measured sea surface heights (SSHs) and SARAL/AltiKa (SARAL)-measured SSHs which are in the same period as HY-2A-measured SSHs. Compared with the along-track DOVs calculated from Sentinel-3B-measured SSHs (from cycle 20 to cycle 33), the RMS of differences for HY-2A-determined DOVs is 0.1 μ rad smaller than that for SARAL-determined DOVs and CryoSat-2-determined DOVs. The differences of the along-track DOVs in the frequency domain are also analyzed by power spectral density. In addition, the XGM2019e model is adopted to evaluate the quality of the gridded DOVs model established by least-squares collocation method. Marine gravity anomaly models (SIO V30.1) and ship-borne gravity anomalies are also used to assess the accuracy of gravity anomalies derived from gridded DOVs. The whole results show that the accuracy of HY-2A-determined DOVs is coincident with that of CryoSat-2-determined DOVs and slightly lower than that of SARAL-determined DOVs. Therefore, HY-2A/GM altimetry data can be applied in establishing the global high-precision DOV model.

The classical harmonic analysis (CHA) method only can be used to obtain the harmonic constants (amplitude and phase) of ocean tide loading displacement (OTLD). In fact, there are significant seasonal variations in the harmonic constants of OTLD. A moving harmonic analysis (MHA) method is proposed, which can effectively capture the seasonal variation of OTLD parameters. Based on 5 years of kinematic coordinate time series in direction U of six Global Positioning System (GPS) stations in Hong Kong, the MHA method is used to explore the seasonal variation of the OTLD parameters of the 6 principal tidal constituents (M2, S2, N2, K1, O1, Q1). The influence of mass loading on the seasonal variation of OTLD parameters is analyzed. The results show that there are obviously seasonal variations in OTLD parameters of the 6 principal tidal constituents in Hong Kong. The OTLD’s amplitude’s changes of the 6 principal tidal constituents are around 4–25.1% and the oscillation ranges of OTLD’s phase parameters vary from 8.8° to 20.4°. Among the seasonal variations of OTLD parameters, the annual signal, the semi-annual signal, and the ter-annual signal are the most significant. By analyzing the influence of atmospheric loading on the seasonal variation of OTLD parameters, it is found that atmospheric loading has certain contribution to the seasonal variation of OTLD parameters. Hydrological loading and non-tidal ocean loading have little influence on the seasonal variation of OTLD parameters.

Altimeter waveforms are usually contaminated due to nonmarine surfaces or inhomogeneous sea state conditions. The present work aimed to present how the singular spectrum analysis (SSA) can be used to reduce the noise level in Jason-1 altimeter waveforms to obtain SSA-denoised waveforms, improving the accuracy of a mean sea surface height (MSSH) model. Comparing the retracked sea surface heights (SSHs) by a 50% threshold retracker for the SSA-denoised waveforms with those for the raw waveforms, the results indicated that SSA allowed a noise reduction on Jason-1 waveforms, improving the accuracy of retracked SSHs. The MSSH model (called Model 1) over the South China Sea with a grid of 2′ × 2′ was established from the retracked SSHs of Jason-1 by the 50% threshold retracker for the SSA-denoised waveforms. Comparing Model 1 and Model 2 (established from the retracked SSHs by the 50% threshold retracker for the raw waveforms) with the CLS15 and DTU18 models in the South China Sea, it was found that the accuracy of Model 1 was higher than that of Model 2, which indicates that using SSA to reduce noise level in Jason-1 waveforms can effectively improve the accuracy of the MSSH model.

Accurate seabed topography is crucial for marine research, resource exploration, and engineering applications. While deep learning techniques have been widely applied in seabed inversion, existing methods often overlook the multi-scale influence of gravity anomalies, particularly the critical role of short-wavelength gravity anomalies in resolving fine-scale bathymetric features. In this study, we propose a novel Fully Connected Deep Neural Network (FCDNN) approach that systematically integrates long-wavelength, short-wavelength, and residual gravity anomaly components for seabed topography inversion. Using multi-satellite altimetry-derived gravity anomaly data (SIO V32.1) and shipborne bathymetric data (NCEI), we constructed a high-resolution (1′ × 1′) seabed topography model for the South China Sea (108°E–121°E, 6°N–23°N), termed FCD_Depth_SCS. The workflow included multi-scale decomposition of gravity anomalies, linear regression-based residual calculation, and FCDNN-based nonlinear training to capture the complex relationships between gravity anomalies and water depth. The FCD_Depth_SCS model achieved a difference standard deviation (STD) of 44.755 m and a mean absolute percentage error (MAPE) of 2.903% when validated against 160,476 shipborne control points. This performance significantly outperformed existing models, including GEBCO_2024, SIOv25.1, DTU18, and GGM_Depth (derived from the Gravity–Geologic Method), whose STDs were 82.234 m, 108.241 m, 186.967 m, and 58.874 m, respectively. Notably, the inclusion of short-wavelength gravity anomalies enabled the model to capture fine-scale bathymetric variations, particularly in open-sea regions. However, challenges remain near coastlines and complex terrains, highlighting the need for further model partitioning to address localized nonlinearity. This study highlights the benefits of integrating multi-scale gravity anomaly data with a fully connected deep neural network. Employing this innovative and robust approach enables high-resolution inversion of seabed topography with enhanced precision. The proposed method provides significant advancements in accuracy and resolution, contributing valuable insights for marine environmental research, resource management, and oceanographic studies.