With the help of the analytical expression of the vertical gravity gradient (VGG) generated by a rectangular prism, an analytical algorithm for predicting seafloor topography using the VGG data has been studied. Nevertheless, ship sounding data are an essential constraint in solving the seafloor topography. This paper combines ship sounding data with VGG anomaly to predict the seafloor topography. The main research contents include the following: Using the ship soundings and VGG data in the study area, the observation equations about sea depth are established, and the stability of the equations are studied; furthermore, considering the influence of seafloor topography outside the study area on the observation equations, these effects are divided into boundary effects and far‐field effects, and different processing methods are proposed. Finally, the method is tested on the East Pacific Rise, only using VGG anomaly and adding the mean value to fix the boundary region, the RMS error of the results is 108.8 m; SIO's model is added to the boundary region and the seven maximum absolute errors are replaced by ship sounding data, the RMS error of the results can reach 94.2 m and the accuracy improvement is 13.42%.

As high-resolution global coverage cannot easily be achieved by direct bathymetry, the use of gravity data is an alternative method to predict seafloor topography. Currently, the commonly used algorithms for predicting seafloor topography are mainly based on the approximate linear relationship between topography and gravity anomaly. In actual application, it is also necessary to process the corresponding data according to some empirical methods, which can cause uncertainty in predicting topography. In this paper, we established analytical observation equations between the gravity anomaly and topography, and obtained the corresponding iterative solving method based on the least square method after linearizing the equations. Furthermore, the regularization method and piecewise bilinear interpolation function are introduced into the observation equations to effectively suppress the high-frequency effect of the boundary sea region and the low-frequency effect of the far sea region. Finally, the seafloor topography beneath a sea region (117.25°–118.25°E, 13.85°–14.85°N) in the South China Sea is predicted as an actual application, where gravity anomaly data of the study area with a resolution of 1′ × 1′ are from the DTU17 model. Comparing the prediction results with the data of ship soundings from the National Geophysical Data Center (NGDC), the root-mean-square (RMS) error and relative error can be up to 127.4 m and approximately 3.4%, respectively.

Owing to the dependence of algorithms on the measurement of ship soundings and geophysical parameters, the accuracy and coverage of topography still need to be improved. Previous studies have mostly predicted topography using gravity or gravity gradient, However, there is a relative lack of integrated research combining or comparing gravity and gravity gradient. In this study, we develop observation equations to predict topography based on vertical gravity anomalies (VG; also called gravity anomalies) and vertical gravity gradient (VGG) anomalies generated by a rectangular prism. The sources of interference are divided into medium- to high-frequency errors and low-frequency errors, and these new methods reduce these errors through regularization and error equations. We also use numerical simulations to test the efficiency of the algorithm and error-reduction method. Statistics show that VGG anomalies are more sensitive to topographic fluctuations; however, the linear correlation between VG anomalies and topography is stronger. Additionally, we use the EIGEN-6C4 model of VG and VGG anomalies to predict topography in shallow and deep-sea areas, with maximum depths of 2 km and 5 km, respectively. In the shallow and deep-sea areas, the root mean square (RMS) errors of VGG anomalies prediction are 93.8 m and 233.8 m, and the corresponding accuracies improved by 7.3% and 2.3% compared with those of VG anomaly prediction, respectively. Furthermore, we use cubic spline interpolation to fuse ship soundings and improve the accuracy of the final topography results. We develop a novel analytical algorithm by constructing an observation equation system applicable to VG and VGG anomalies. This will provide new insights and directions to refine topography prediction based on VG and VGG anomalies.

Seafloor topography prediction can fill in sea areas without ship sounding data. However, the dependence of various topographic prediction algorithms on ship soundings varies significantly. Hence, this study explores the impact of the number and distributions of ship soundings on topographic prediction using the gravity–geologic method (GGM) and an analytical algorithm. Firstly, this study investigates the influence of ship sounding coverage on the two algorithms. The simulation results demonstrate that increasing coverage from 5.40% to 31.80%, coupled with more uniform distributions across the study area, substantially reduces the RMS error of the GGM. Specifically, the RMS error decreases from 238.68 m to 42.90 m, an improvement of 82.03%. The analytical algorithm maintains a consistent RMS error of 40.39 m because it does not depend on ship soundings. Furthermore, we select a 1° × 1° sea area (134.8°–135.8°E, 30.0°–31.0°N), and the ship soundings are divided into two control groups, Part I and Part II, with coverages of 8.19% and 33.19%, respectively. When Part II is used for calculation, the RMS error of the GGM decreases from 204.17 m to 126.95 m compared to when Part I is used, while the analytical algorithm exhibits an RMS error of 167.94 m. The findings indicate that the prediction accuracy of the GGM is significantly affected by ship soundings, whereas the analytical algorithm is more stable and independent of ship soundings. Based on simulation experiments and realistic examples, when the effective ship soundings coverage exceeds 30%, the GGM may have more advantages. Conversely, the analytical algorithm may be better. This suggests that effectively combining and utilizing different algorithms based on the ship sounding coverage can improve the accuracy of topographic prediction. This will provide a basis for integrating multiple algorithms to construct a global seafloor topography model.

Glaciers, primarily distributed in high mountainous and high-latitude regions globally, play a critical role in the global water cycle, serve as a significant part of the Earth’s climate system. There are still discrepancies in the gravimetry-based glacier mass balance due to differences in data processing by various institutions, regional divisions, and inversion methods. Here, we analyzed the performance of the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) mascon solutions provided by the NASA’s CSR, JPL, and GSFC in estimating glacier mass balance and discussed the differences among these mascon solutions. The results reveal a negative trend in gravity signals over global glacier areas, with glacier mass balances of -163.7(CSR-M), -182.3(GSFC-M),-174.3 {plus minus} 11.6 Gt/yr (JPL-M) from April 2002 to September 2023. Additionally, we compared the glacier mass balance from three mascon solutions with that from CryoSat-2, DEM time series data, and GRACE spherical harmonics (SH) solutions. Our findings demonstrate that the GSFC mascon solutions exhibit superior performance across fifteen subregions of the Randolph Glacier Inventory (RGI). In High Mountains Asia and the Southern Andes, gravity variations within glacier areas are significantly affected by terrestrial water sources, including soil moisture, seismic activity, and other geophysical signals, thereby influencing glacier mass balance estimates. Consequently, meticulous consideration of these additional signals is essential when using GRACE mascon solutions for glacier mass balance studies in these regions. This study provides valuable guidance in the selection and processing of GRACE data, facilitating a more accurate understanding of global glacier mass balance.

Lake water level variation, reflecting the dynamic balance between water input and loss, is a crucial indicator of climate change and regional hydrological cycles. This is particularly significant in arid Central Asia, where lakes are vital surface water resources and key to ecosystem stability. This study systematically reconstructed water level changes of Lake Zaysan and Lake Ulungur from 2003 to 2024 using high-precision altimetry data from ICESat, CryoSat-2, and ICESat-2 satellites. Results indicate that Lake Zaysan experienced significant water level fluctuations of 5.01 m (21.01 Gt water mass change, where 1 Gt = 10⁹ metric tons) in 2010, 5.12 m (21.47 Gt) in 2013, and 3.53 m (14.80 Gt) in 2024. Lake Ulungur also exhibited notable water level changes during the same period. Our study reveals that water level variations in both lakes are primarily controlled by runoff processes. A highly significant positive correlation exists between lake level anomalies and discharge anomalies. Conversely, the low correlation between water levels and precipitation indicates a pronounced lagged effect of snowfall, as lake water level fluctuations are driven by a combination of spring snowmelt runoff and summer precipitation. Furthermore, these findings highlight the sensitive response of these Central Asian lakes to environmental changes under climate warming. Our study enriches observational data on regional lake dynamics and provides a scientific basis for water resource management and future climate adaptation strategies in arid regions.