The satellite altimetry missions could measure high-accuracy sea surface heights (SSHs) that can be used to recover the marine gravity field. Traditional methods for estimating the marine gravity field from SSHs all rely on approximate physical correlations between SSHs and gravity, which may neglect nature’s complex nonlinearity. This work presents a new deep network-based method to recover the gravity anomaly. This new method uses a multi-channel convolutional neural network (MCCNN) architecture to capture the nolinear features between ship-borne gravity and a group of input parameters including deflections of the vertical (DOVs), submarine topography and the geo-locations. To validate the gravity, ship-borne gravity anomalies on the two independent cruises were not used in the deep learning process. For comparison, we also estimated the gravity using the traditional inverse Vening Meinesz (IVM) method. Our results indicate that the MCCNN method can derive high-quality marine gravity anomalies. The assessments using 1 mGal-accuracy ship-borne gravity anomalies show that the average accuracy for gravity from MCCNN method is higher than 3 mGal and this method achieves 0.05-0.50 mGal improvement over benchmark methods IVM. Assessed by marine gravity anomaly models with the accuracy of 1-2 mGal, the MCCNN method has shown to improve the accuracy of gravity by at least 4%. Comparisons with the IVM results show that improvements of the MCCNN method were mainly in wavelengths between 8 km and 100 km due to the using of bathymetry. The results show that our deep learning method maintains good performance and is promising for gravity recovering.

SUMMARY: The HaiYang-2A (HY-2A) satellite was launched in August 2011, filling a gap in the field of Chinese altimetry. The application of HY-2A-measured altimeter data in gravity research needs to be studied. CryoSat-2 altimetry data play an important role in constructing global marine gravity models. Based on HY-2A and CryoSat-2 altimetry data of Level-2 plus products from March 2016 to June 2020, marine gravity anomaly models on 1′ × 1′ grids were derived by the inverse Vening–Meinesz (IVM) method over the Gulf of Mexico (80–100°W, 17–32°N). The accuracy of the altimeter-derived gravity was assessed by ship-borne gravity anomalies and the SIO V30.1 global marine gravity model. Then, integrated gravity models on 1′ × 1′ grids were constructed from the altimeter-derived gravity anomaly models by the weighted modification method and the combined altimetry data by IVM method. The results show that the accuracy of altimeter-derived marine gravity anomalies is affected by the coastline and complicated submarine topography. The accuracy of gravity anomalies derived from HY-2A is slightly lower than that derived from CryoSat-2 in the offshore region and regions containing complicated submarine topography, and is consistent with that derived from CryoSat-2 in other regions. The HY-2A-measured altimetry data play a significant role in constructing integrated gravity models. To conclude, the gravity anomalies derived from HY-2A have similar accuracy to those derived from CryoSat-2 during the same period, and HY-2A altimetry data can be used to construct high-precision global/local marine gravity models.

The topography of the seafloor is highly correlated with the local gravity through intrinsically nonlinear relationships across a particular wavelength band. The purpose of this study is to compare a fully connected deep neural network (FC-DNN) and a convolutional neural network (CNN) with the gravity-geologic method (GGM) to determine whether deep learning can provide superior predictions of bathymetry. We include the short-wavelength gravity and geological models as training parameters, and assess the performance of different models and parameter combinations using various inputs. Compared with the CNN method, the FC-DNN with the short-wavelength gravity as an input reduces the standard deviation of bathymetry differences from 118.6 m to about 73.5 m. The FC-DNN with short-wavelength gravity reduces the standard deviation of bathymetry differences by up to 13.3% compared with the conventional GGM. Furthermore, we demonstrate that the addition of geological information alongside the short-wavelength gravity does not significantly enhance the accuracy. Power spectral density analysis suggests that the FC-DNN is superior for predicting wavelengths shorter than 6 km.

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.

High-resolution sea surface heights (SSHs) can be obtained from the wide-swath data of the Surface Water and Ocean Topography (SWOT) project. The distance between two points used to calculate geoid gradients from SSH data significantly influences the accuracy of these gradients. The moving method is proposed to obtain high-precision and high-resolution geoid gradients for gravity recovery, wherein gradients are calculated using SSH data from two points that are separated by a defined distance rather than relying on adjacent points. Marine gravity models around the South China Sea are derived from SWOT-measured SSHs and CryoSat-2-measured SSHs, respectively. The global marine gravity models with high international recognition are also used for comparison. Assessed by shipborne gravity data, the accuracy of SWOT-derived gravity from three-direction geoid gradients is significantly higher than that from one-direction geoid gradients along-track, but slightly higher than that from two-direction geoid gradients. The moving method enhances the precision of the SWOT-derived gravity model by approximately 4% and improves its resolution by about 10%. Compared to CryoSat-2-derived and recognized gravity models, SWOT-derived gravity models using the moving method demonstrate accuracy improvements exceeding 12% and resolution enhancements of over 20%. All these verifications show that SWOT data has advantages over traditional altimeter data in the accuracy and resolution of SSH-derived gravity. For gravity recovery from wide-swath data, it is essential to utilize both along-track and cross-track gradients together, while the inclusion of diagonal-track gradients is optional. The proposed moving method significantly enhances the accuracy and resolution of SWOT-derived gravity, showcasing its effectiveness in marine gravity recovery.

The deep learning method based on multi-channel convolutional neural network(MCCNN) can be used for gravity recovery from altimetry and bathymetry data. Compared with the traditional inverse Vening Meinesz (IVM) method, the MCCNN method enhances gravity accuracy but introduces long-wavelength gravity errors in training data-scarce areas. The Enhanced MCCNN method (EMCCNN) is proposed, which treats geo-locations in the input layer as nodes rather than channels. Evaluated by independent ship-borne data, the EMCCNN method demonstrates a gravity accuracy improvement of 0.05-0.24 mGal compared to the IVM method, maintaining consistent gravity accuracy compared to the MCCNN method. Additionally, assessed by a recognized global marine gravity model, the EMCCNN method achieves the highest accuracy. Particularly in regions with limited training data, the EMCCNN method outperforms the MCCNN method in minimizing gravity differences relative to assessment data. In the wavelengths larger than 100 km, the gravity noise for EMCCNN method can be reduced by up to about 50% compared to MCCNN method. These findings highlight EMCCNN’s effectiveness in improving gravity recovery in training data-scarce areas.