Marine Gravity Field Research Articles

Weighted Fusion Method of Marine Gravity Field Model Based on Water Depth Segmentation

Among the marine gravity field models derived from satellite altimetry, the Scripps Institution of Oceanography (SIO) series and Denmark Technical University (DTU) series models are the most representative and are often used to integrate global gravity field models, which were inverted by the deflection of vertical method and sea surface height method, respectively. The fusion method based on the offshore distance used in the EGM2008 model is just model stitching, which cannot realize the true fusion of the two types of marine gravity field models. In the paper, a new fusion method based on water depth segmentation is proposed, which established the Precision–Depth relationship of each model in each water depth segment in the investigated area, then constructed the FUSION model by weighted fusion based on the precision predicted from the Precision–Depth relationship at each grid in the whole region. The application in the South China Sea shows that the FUSION model built by the new fusion method has better accuracy than SIO28 and DTU17, especially in shallow water and offshore areas. Within 20 km offshore, the RMS of the FUSION model is 5.10 mGal, which is 8% and 4% better than original models, respectively. Within 100 m of shallow water, the accuracy of the FUSION model is 4.01 mGal, which is 14% and 12% higher than the original models, respectively. A further analysis shows that the fusion model is in better agreement with the seabed topography than original models. The new fusion method can blend the effective information of original models to provide a higher-precision marine gravity field.

A convolutional neural network to optimize multi-mission satellite altimeter fusion for improving the marine gravity field

Satellite altimetry is the main tool for constructing global or regional marine gravity fields. To improve the accuracy and spatial resolution, it is necessary to fuse multi-mission altimeters. How to determine the weights of multi-mission altimeters is a crucial issue, making the conventional calculation process very complex. In addition, traditional satellite inversion methods are often independent of shipborne gravity, which is used only as validation data, thus not take full advantages of high accuracy and resolution of shipborne gravity. In this study, we introduce a convolutional neural network (CNN) to merge the vertical deflections (DOVs) obtained from multi-altimeter missions to construct a marine gravity model in the South China Sea. High-accuracy shipborne gravity and a dataset comprising DOVs and geo-locations are employed as input data for neural network training. For the validation of CNN method, the gravity model is also computed by conventional Inverse Vening Meinesz (IVM) method. Independent shipborne gravity measurements and SIO V32.1, DTU17 models are used as validation data. The evaluation results show that the CNN-derived model achieves a higher level of accuracy, yielding a standard deviation (STD) of 3.21 mGal, with an improvement of 36.56% compared to IVM-derived model. More than 92% of the differences between the CNN-derived model and shipborne gravity are less than 5 mGal. In addition, spectral analysis results further show that the CNN-derived model has stronger energy at short wavelengths (less than 25 km) compared to other models. These findings reveal that CNN method is feasible for marine gravity recovery and the CNN-derived model can achieve higher accuracy. The CNN method can improve the accuracy and spectral characteristics of the constructed gravity model by taking advantage of the high accuracy and high resolution of shipborne gravity.Graphical

Performance assessment of sentinel-3/6 altimeter data for marine gravity recovery

High-precision sea surface height is crucial for determining the marine gravity field. The Sentinel-3/6 altimetry missions, equipped with SRAL and Poseidon-4 altimeters, provide this essential data. However, there is a lack of comprehensive assessment of the Sentinel-3/6 altimeters for inverting marine gravity anomalies (MGA). In this study, we employ the inverse Venning-Meinsz method to derive nine sets of 1’×1’ MGAs in the South China Sea (SCS) and the Ross Sea (RS). Specifically, MGAs from Sentinel-3A, Sentinel-3B, Sentinel-6 SARM, Sentinel-6 LRM, HY-2A, ICESat-2, and CryoSat-2 are denoted as S3A, S3B, S6S, S6L, H2A, IS2, and CS2, respectively. MGA from the combined HY-2A, ICESat-2, and CryoSat-2 is referred to as HIC, while 3SHIC denotes the MGA from the combination of Sentinel-3/6 SARM, HY2A, ICESat-2, and CryoSat-2. We assess the performance of these MGAs using the EGM08, DTU17, SIO V32.1, and SDUST2021 gravity field models, as well as shipboard gravity across different ocean regions. Among the Sentinel-3/6 MGAs, S3B exhibits the highest accuracy in the SCS, with a root mean square error (RMSE) of 5.277 mGal, followed closely by S3A. Conversely, S3A demonstrates the highest accuracy with an RMSE of 4.635 mGal, followed by S3B in the RS. The inversion accuracy of MGAs from S6S and S6L are comparable, though S6S outperforms S6L in the open sea. The performance of MGAs from Sentinel-3/6 matches or surpasses that of other altimetry missions during the same period. In the SCS, the best-performing MGA is 3SHIC, with an RMSE of 4.585 mGal, closely matching DTU17. However, 3SHIC exhibits superior performance in the RS with an RMSE of 4.263 mGal compared to DTU17 and SDUST 2021. Furthermore, the performance of 3SHIC, which integrates Sentinel-3/6 data, improves that of HIC by 0.74% and 3.37% in the SCS and RS, respectively. These results underscore the contribution of Sentinel-3/6 altimeters to the MGA, particularly in coastal and high-latitude regions. Integration of Sentinel-3/6 data with other altimetry satellites is expected to enhance the spatial resolution and accuracy of the global marine gravity field, especially with the successful establishment of the network of Sentinel-6 in the future.

Multidimensional Evaluation of Altimetry Marine Gravity Models with Shipborne Gravity Data from a New Platform Marine Gravimeter

With the development of satellite altimetry technology and the application of new altimetry satellites, the accuracy and resolution of altimeter-derived gravity field models have improved over the last decades. Nowadays, they are close enough to shipborne gravimetry. In this paper, multi-source shipborne gravity data in the South China Sea were taken to evaluate the accuracies of two high-precision altimeter-derived marine gravity field models (SS V30.1, DTU17). In these shipborne gravity data, there are dozens of routes’ ship gravimetry data, obtained from the National Geophysical Data Center (NGDC); data were tracked from a marine survey with a commercial marine gravimeter (type KSS31M), and data were tracked from a marine gravimetry campaign that was conducted with a newly developed platform gravimeter (type JMG) in the South China Sea in September 2020. After various data filtering, processing, and calibrations, the shipborne gravity data were validated with crossover points analysis. Then, the processed shipborne data were employed to evaluate the accuracy of the altimeter-derived marine gravity field models. During this procedure, the quality of JMG shipborne gravity data was compared with the results of KSS31M and NGDC data. Analysis and evaluation results show that the crossover points verification accuracies of KSS31M and JMG are 0.70 mGal and 1.61 mGal, which are much better than the accuracy of NGDC, which is larger than 8.0 mGal. In the area where the bathymetry changes slowly, the root mean square error values between altimetry gravity models and KSS31M data are respectively 3.28 mGal and 4.54 mGal, and those of the JMG data are respectively 2.94 mGal and 2.60 mGal. According to the above results, we can conclude that the JMG has the same 1–2 mGal accuracy level as KSS31M and can meet the measurement requirements of marine gravity.

Analysing the impact of SWOT observation errors on marine gravity recovery

SUMMARY The wide-swath altimeter satellite Surface Water and Ocean Topography (SWOT) will provide high spatiotemporal resolution sea surface heights (SSHs), which is crucial for studying the impact of observation errors on marine gravity recovery. This study uses simulated SWOT data to derive deflection of the vertical (DOV) and gravity anomalies in the northern South China Sea. We quantified the impact of SWOT errors on DOV and gravity anomalies, and analysed the contributions from different directions of geoid gradient. The results show that the geoid gradient in the cross-track direction significantly improves gravity field recovery by enhancing the precision of east component of DOV. For one-cycle SWOT observations, phase errors emerge as the most impactful error affecting both DOV and gravity anomalies, followed by random errors. 2-D Gaussian filtering and the tilt correction proposed in this study could effectively mitigate their impact. Using the corrected data for DOV computation, the precision in the east and north components improves by 75.32 and 46.80 per cent, respectively, while enhancing the accuracy of the gravity field by 70.23 per cent. For 17-cycle data, phase errors and random errors remain the predominant factors affecting DOV and gravity anomalies, but their impact diminishes with an increase in SWOT observations. Our results indicate that marine gravity accuracy improves by approximately 70 per cent compared to a single cycle. Whether for single-cycle or multicycle data, the impact of phase errors is roughly twice that of random errors. These data processing strategies can serve as valuable references for wide-swath altimeter data processing, aiming to advance the precision and resolution of marine gravity field recovery.

Validation of Just-Released SWOT L2 KaRIn Beta Prevalidated Data Based on Restore the Marine Gravity Field and Its Application

Validation of Just-Released SWOT L2 KaRIn Beta Prevalidated Data Based on Restore the Marine Gravity Field and Its Application

Performance evaluation of HY-2 series satellites in marine gravity field recovery

China has successfully launched four Haiyang-2 (HY-2) series altimetry satellites. HY-2A has attracted significant attention in gravity field recovery, but the performance of other HY-2 series satellites, including HY-2B/C/D, is seldom discussed. This study evaluated the performance of all the HY-2 series satellites in recovering marine gravity field. First, the crossover discrepancies in sea surface height of the four satellites, HY-2A, HY-2B, HY-2C, and HY-2D, were analyzed to assess their altimetry stability. It was found that HY-2B had the best altimetry quality, followed by HY-2D. Subsequently, different combinations of altimetry data were used to calculate vertical deflections and gravity anomalies in the South China Sea (112°E−119°E, 12°N-20°N). The results showed that combining data from HY-2B, HY-2C, and HY-2D improved the inversion accuracy of gravity anomalies by 0.3 mGal compared to using HY-2A data alone. HY-2C and HY-2D contributed to enhancing the accuracy of the east component of vertical deflections.

Analysis of the Principle and State-of-art Facilities of Mobile Atom Interferometry Gravity

With over 20 years of development, atomic interferometry gravimeters have distinguished themselves in gravity measurements by their high precision and sensitivity. To cater to the demands of field absolute gravity measurements for marine and aerial gravity field measurements, resource exploration, inertial navigation, and positioning, the miniaturization, mobility, and engineering of atomic interferometry gravimeters have become crucial areas of development. On this basis, this article elucidates the principles of atomic interferometry gravimeters, encompassing various laser cooling techniques, magneto-optical traps, and Raman light interference. As a matter of fact, it provides an overview of the principles and achieved precision benchmarks of portable, vehicular, airborne, and shipborne atomic interferometry gravimeters. Additionally, it analyzes the experimental content and results of maritime, terrestrial, and aerial experiments based on portable atomic interferometry gravimeters. The limitations of portable atomic interferometry gravimeters are discussed, along with an exploration of their application prospects. Overall, these results shed light on guiding further exploration of mobile atom interferometry gravity.

The Tikhonov-L-curve regularization method for determining the best geoid gradients from SWOT altimetry

The Surface Water and Ocean Topography (SWOT) mission generates dense altimetry data that, when used in geoid gradient component estimations through least-squares collocation (LSC), lead to an ill-conditioned problem. Such problems also arise in geodetic network designs. This study introduces the Tikhonov-L-curve regularization to effectively address this challenge. By pinpointing the maximum curvatures of the L-curve, we discern optimal regularization parameters, countering issues stemming from the dense data of SWOT and the resulting ill-conditioned covariance matrices. Our approach not only stabilizes LSC solutions but also achieves gradient accuracies at 1-microrad levels compared to theoretical values. Additionally, we experimented with a strategic removal process that selectively eliminates adjacent geoid gradients. This technique considerably improves geoid gradient component determinations, especially evident at a threshold distance of 0.755 km within an 8′× 8′ data selection window. While our findings are rooted in simulated SWOT data, they are pivotal for future research intending to employ real SWOT data, anticipated by late 2023. This work serves as a precursor for marine gravity field determinations, emphasizing the importance of stabilized LSC solutions to avoid misleading seafloor signatures due to data compactness.

Preliminary Results of Marine Gravity Recovery by Tiangong-2 Interferometric Imaging Radar Altimeter

This paper presents for the first time the results of marine gravity recovery using the ocean observation data acquired by Tiangong-2 interferometric imaging radar altimeter (TG2 InIRA) which demonstrate not only the balanced accuracies of the north and east components of deflection of the vertical (DOV) as envisaged, but also the improved spatial resolutions of DOV compared with that by conventional altimeters (CAs). Moreover, much higher measurement efficiency owing to the wide-swath capability and the great potential in accuracy improvement of marine gravity field are also demonstrated. TG2 InIRA adopts the interferometry with short baseline and takes small incidence angles, by which wide-swath sea surface height (SSH) can be measured with high accuracy. Gravity recovery experiments in the Western Pacific area are conducted to demonstrate the performance, advantages and capability of TG2 InIRA. SSH data processing algorithms and DOV calculation have been designed by taking the wide-swath feature into account, based on which, the gravity anomalies are then calculated using the inverse Vening Meinesz formula. The derived gravity anomalies are compared with both the published gravity models and the shipborne gravity measurements. The results show that the accuracy of TG2 InIRA is equivalent to, or even a little better than, that of CAs. The fused gravity result using equal TG2 InIRA data and CAs data performs better than those using TG2 InIRA data alone or CAs data alone. Due to the signal bandwidth of TG2 InIRA is only 40 MHz which is much smaller than that of CAs, much higher accuracy can be hopefully achieved for future missions if larger signal bandwidth is used.

High spatial resolution marine gravity trend determined from multisatellite altimeter data over Bay of Bengal

SUMMARY Mass redistribution in the Earth system induce variations of the Earth's gravity field. Now, the time-varying gravity models from the Gravity Recovery and Climate Experiment (GRACE) mission can only estimate the large-scale gravity changes, so the high-resolution marine gravity trend (MGT) model is urgently required to detect small-scale Earth's mass migration. The sea level change is a significant response to marine gravity field change. Here, we propose to estimate the high-resolution MGT using the sea level trend (SLT). Firstly, the SLT model caused by marine mass change (MMC) on 5′ × 5′ grids covering the Bay of Bengal (BOB) is established based on multisatellite altimetry data and EN4 quality-controlled ocean data, named BOB_MMC_SLT. Then, the marine mass trend (MMT) is calculated using the BOB_MMC_SLT. The spherical harmonic function (SHF) method is applied to estimate MGT using the MMT, and this MGT model on 5′ × 5′ grids, named BOB_SHF_MGT, is used to study marine gravity changes and their associated geophysical processes. The results show that, the MGT mean of BOB_SHF_MGT is about 0.14 μGal yr−1, which indicates that marine gravity in BOB is rising. The earthquakes mainly occur in the southeastern BOB where MGT is obviously rising, which may be related to the increased density of the Burma Plate due to the subduction of the India Plate and the Australia Plate. BOB_SHF_MGT shows that the marine gravity rise rate is increasing from the 85°E ridge to Andaman–Nicobar ridge, with a maximum at the location where the India Plate subducts to the Burma Plate. The MGT model based on altimetry data constructed by SHF method is important for the study of small-scale mass migration near the subduction boundaries.

Marine gravity modelling from SARAL/AltiKA data using the Least Square Collocation for the Red Sea

Marine gravity has been modeled using satellite radar altimetry for more than two decades. However, the accuracy of the predicted gravity field is constrained by the range precision and spatial coverage of the altimetry observations. The objective of this research is to enhance the gravity field over the Red Sea by utilizing the Least Square Collocation (LSC) algorithm with SARAL/AltiKA mission observations. The marine gravity field in the Red Sea was determined by using observed Sea Surface Heights (SSHs) obtained from the SARAL/AltiKA mission. The Remove-Compute-Restore (RCR) technique, the Residual Terrain Modelling (RTM) reduction method, and the LSC technique are used to estimate the marine gravity. To evaluate the accuracy of the SARAL/AltiKA predicted model, it was compared against two global altimetry gravity models (DTU21 and SSv29.1) using 42331 shipborne gravity measurements over the Red Sea. The SARAL/AltiKA predicted model showed the best results, with root mean square error and standard deviation values of 6.29 and 5.93 mGal, respectively. The impact of bathymetry depths on the SARAL/AltiKA predicted gravity model accuracy was also investigated. The SARAL/AltiKA predicted gravity model produced better results for water depths up to 1000 m when compared with shipborne data, while the SSv29.1 model performed better for depths between 1000 and 3000 m due to the performance of the residual slopes of the SSH estimation technique used in the deep areas.

Calibration of the Instrumental Errors on Marine Gravity Recovery from SWOT Altimeter

The wide-swath altimetry mission, Surface Water and Ocean Topography (SWOT), makes it possible to further break through the accuracy and resolution of marine gravity field recovery. However, as its main payload, the Ka-band radar interferometer (KaRIN) is easy to be affected by the spacecraft attitude, mechanical deformations and dual antenna signal reception status, which generates instrumental errors including roll errors, phase errors, baseline dilation errors, timing errors, and KaRIN noise. Together with ocean temporal variations, the instrumental errors have large effects on the SWOT Sea Surface Height (SSH) observations and hence the marine gravity field recovery. Here, taking the sea area around Japan as an example, we investigated the calibrations of instrumental errors and ocean temporal variations on the recovery of the marine gravity field. The SSH observations of SWOT are first simulated by Mean Sea Surface (MSS), Absolute Dynamic Topography (ADT), Mean Dynamic Topography (MDT) and instrumental errors. Next, the influence of instrumental errors on determining vertical deflection within single-cycle data was analyzed. Then, three calibration methods (KaRIN/KaRIN cross-calibration, Representative KaRIN/KaRIN cross-calibration, and KaRIN/Nadir cross-calibration) are used to reduce the instrumental errors; the experimental results show KaRIN/KaRIN cross-calibration is the optimal one. Last, for the multi-cycle observations containing ocean temporal variations, crossover calibration is done in single cycle and then followed by collinear adjustment in multi-cycles. This approach is verified by considering 18 simulated cycles that cover almost 1 year. Our result indicates an improvement in the accuracy of marine gravity anomaly by about 45% compared to that of one cycle. The calibration strategy of instrumental errors and ocean temporal variations can be used for high-precision marine gravity field recovery with abundant SWOT observations in the near future.

An improved triple collocation-based integration of multiple gravity anomaly grids from satellite altimetry: Contribution of ICESat-2

Satellite altimetry has been widely used to determine the marine gravity fields. Different altimeter missions lead to different gravity grids with varying spatial resolutions and accuracies. Marine gravity accuracy in offshore waters is often low. Integrating marine gravity anomalies (MGA) derived from various altimeter missions are key to obtaining high-precision and high-resolution global marine gravity fields. Here an improved triple collocation (ITC) method is first proposed to establish a new 1´×1′ marine gravity anomaly in the South China Sea (SCS), named MGAITC, by merging the grids of MGA from the Haiyang-2A (HY-2A), CryoSat-2, and ICESat-2 altimeter measurements. A combined MGA (MGACOM) is also constructed by using the least squares collocation (LSC) method from three sets of altimeter-derived geoid gradients. The qualities of MGAITC, MGACOM and each altimeter-derived MGA grids are assessed using shipborne gravity and different global gravity models over waters of varying depths and distances from the coastline. The accuracy of the MGAITC gravity against the shipborne gravity is 5.52 mGal, which represents improvements of 7%, 9%, 13%, and 3% relative to the gravity grids derived only from ICESat-2, CryoSat-2, HY-2A and from MGACOM. In all assessments involving different sub-regions, seafloors, and distances from the coastline, MGAITC performs the best, and ICESat-2 yields the best single-mission MGA grid, especially in offshore waters. We find that ICESat-2 has a high potential to improve shallow-water gravity accuracy and the global marine gravity field can be improved by integrating gravity grids from different altimetry missions using ITC.

Gravity disturbance compensation for dual-axis rotary modulation inertial navigation system

Gravity disturbance compensation is an important technique for improving the positioning accuracy of high-precision inertial navigation systems (INS). Aiming at the current problems of the resolution of gravity compensation background field and the robustness of gravity compensation algorithm are insufficient for gravity compensation. In this study, the error and frequency characteristics of INS caused by gravity disturbances are investigated. The gravity disturbance with a spatial resolution of 1’ × 1’ from a high-precision satellite altimetry marine gravity field model is preliminarily introduced into the initial alignment and pure INS calculation to implement the gravity compensation of the dual-axis rotary modulation INS. Detailed calculation results show that the east gravity disturbance affects the north attitude, and the north gravity disturbance affects the east attitude in the initial alignment. In the pure INS calculation, the horizontal gravity disturbance causes a navigation error in the form of Schuler oscillation. The INS navigation error caused by horizontal gravity disturbance is mainly affected by its amplitude; however, the horizontal gravity disturbance accuracy from the satellite altimetry model for INS gravity compensation can be ignored in practice. In addition, for low-speed underwater vehicles, the influence of high-frequency gravity disturbance signals on the INS position shows an increasing trend. Finally, the effectiveness of the gravity compensation achieved by the horizontal gravity disturbance from the satellite altimeter model is confirmed by a dynamic shipborne test. The positioning accuracy of the rotary modulation INS is maximally improved by approximately 17.9% after the horizontal gravity disturbance is compensated simultaneously in the pure INS calculation and the initial alignment.

Recovering Gravity from Satellite Altimetry Data Using Deep Learning Network

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.

Inversion of Deflection of the Vertical in the South China Sea Using ICESat-2 Sea Surface Height Data

The traditional altimetry satellites based on pulse-limited radar altimeter only calculate along-track deflection of the vertical (DOV), which results in poorer precision of the prime vertical component than that of the meridian component and limits the precision of the marine gravity field inversion. We expect an improvement in the higher precision prime vertical component using the Ice, Cloud and land Elevation Satellite 2 (ICESat-2) sea surface height (SSH) data. In this paper, the 2′ × 2′ gridded DOVs derived from along-beam DOVs, cross-beam DOVs, and joint along-cross beam DOVs in the South China Sea (SCS; 0°–23°N, 103°–120°E) are calculated with the weighted least squares method, respectively. The inverse Vening–Meinesz (IVM) formula is applied to derive 2′ × 2′ gravity anomalies over the SCS from ICESat-2-derived gridded DOVs. In addition, the XGM2019e_2159-DOV and SIO V31.1-DOV models are used to assess the precision of the gridded DOVs. The XGM2019e_2159-GRA, SIO V31.1-GRA models, and ship-borne gravity anomalies are also adopted to evaluate the quality of gravity anomalies. The results show that the gridded DOVs calculated by the joint along-cross beam DOVs have the highest precision among the three gridded DOVs determined by ICESat-2. The precision of difference between gravity anomalies derived from the joint along-cross beam DOV and the above verification data are higher than those derived from the along-beam and cross-beam DOVs. We conclude that the joint along-cross beam DOV can effectively improve the precision of the gridded DOV, which is conducive to the inversion of a high-precision marine gravity field.

Performance of Haiyang-2 Derived Gravity Field Products in Bathymetry Inversion

Haiyang-2A (HY-2A), China’s first altimetry satellite mission, was launched more than ten years ago, and its follow-up satellites, HY-2B, HY-2C, and HY-2D, have also been launched. More attention has been paid to the evaluation of these satellite observations in marine gravity field inversion. However, this is not the case for bathymetry inversion. This study is aimed at evaluating the performance of HY-2 gravity field products in bathymetry recovery. Not only gravity anomaly, but also deflection of the vertical from the HY-2 series’ observations is also used. The results show that the bathymetry derived from the deflection of the vertical from HY-2A has a precision of around 128~130 m, and the north-south component performs better than the east-west component. Three versions of the gravity anomaly are used in bathymetry inversion, i.e., HY2ONLY_GRA, WHU16_GRA, and NSOASS22_GRA, and three bathymetry models are derived correspondingly, named as HY2ONLY_BAT, NSOASS22_BAT, and WHU16_BAT, respectively. The results show that HY2ONLY_BAT has a precision of 82.93 m, which is a little poorer than WHU16_BAT; NSOAS22_BAT has the best performance in bathymetry inversion among the three versions of the gravity anomaly. It indicates that HY-2 observations can also contribute to bathymetry inversion compared to current altimetry datasets, since the main difference between WHU16_GRA and NSOASS22_GRA is the use of HY-2 observations. According to spatial analysis results, considerable improvements appear in the west of the Pacific and Indian oceans, and most of the improvements are within 20 m. Meanwhile, the improvements are stronger in the regions with depths ranging between 2600~5500 m. Correlation analysis demonstrates that NSOASS22_BAT is very close to SIO V19.1 and DTU21BAT, which once again indicates the excellent performance of NSOASS22_BAT.

Impact of Errors in Environmental Correction on Gravity Field Recovery Using Interferometric Radar Altimeter Observations

As a new type of altimeter, interferometric radar altimeter (InRA) has significant potential in marine gravity field recovery due to its high spatial resolution. However, errors in environmental correction on gravity field recovery using InRA observations are unclear. In this study, four kinds of these errors, including wet and dry troposphere, ionosphere, and sea state bias (SSB) correction errors, are simulated. The impact of these errors on gravity field recovery are analyzed and discussed. The results show that, among the four types of errors in environmental correction, the wet troposphere and SSB have a more significant impact on the accuracy of sea surface height computing, and the wet troposphere has the most significant impact on the accuracy of gravity field recovery. The maximum error of gravity anomaly caused by the wet troposphere residual errors is nearly 2 mGal, and the relative error of the recovered gravity anomaly is around 6.42%. We can also find that SSB has a little more significant impact than dry troposphere and ionosphere, where dry troposphere and ionosphere have an almost identical impact, on DV and GA inversion accuracy.

A Review of Marine Gravity Field Recovery from Satellite Altimetry

Marine gravity field recovery relies heavily on satellite altimetry. Thanks to the evolution of altimetry missions and the improvements in altimeter data processing methods, the marine gravity field model has been prominently enhanced in accuracy and resolution. However, high-accuracy and high-resolution gravity field recovery from satellite altimeter data remains particularly challenging. We provide an overview of advances in satellite altimetry for marine gravity field recovery, focusing on the impact factors and available models of altimetric gravity field construction. Firstly, the evolution of altimetry missions and the contribution to gravity field recovery are reviewed, from the existing altimetry missions to the future altimetry missions. Secondly, because the methods of altimeter data processing are of great significance when obtaining high-quality sea surface height observations, these improved methods are summarized and analyzed, especially for coastal altimetry. In addition, the problems to be resolved in altimeter data processing are highlighted. Thirdly, the characteristics of gravity recovery methods are analyzed, including the inverse Stokes formula, the inverse Vening Meinesz formula, Laplace’s equation, and least squares collocation. Furthermore, the latest global marine gravity field models are introduced, including the use of altimeter data and processing methods. The performance of the available global gravity field model is also evaluated by shipboard gravity measurements. The root mean square of difference between the available global marine gravity model and shipboard gravity from the National Centers for Environmental Information is approximately 5.10 mGal in the low-middle latitude regions, which is better than the result in high-latitude regions. In coastal areas, the accuracy of models still needs to be further improved, particularly within 40 km from the coastline. Meanwhile, the SDUST2021GRA model derived from the Shandong University of Science and Technology team also exhibited an exciting performance. Finally, the future challenges for marine gravity field recovery from satellite altimetry are discussed.