Yu Sun 孙玉

We present a new approach to estimate time variations in J2. Those variations are represented as the sum of contributions from individual sources. This approach uses solely Gravity Recovery And Climate Experiment (GRACE) data and the geoid fingerprints of mass redistributions that take place both at the surface and in the interior of the solid Earth. The results agree remarkably well with those based on satellite laser ranging, while estimates of the sources explain the observed variations in J2. Seasonal variations are dominated by terrestrial water storage and by mass redistribution in the atmosphere and ocean. Trends, however, are primarily controlled by the Greenland and Antarctic ice sheets and by glacial isostatic adjustment. The positive trend from surface mass variations is larger than the negative trend due to glacial isostatic adjustment and leads to an overall rising trend during the GRACE period (2002–2017).

The focus of the study is optimizing the technique for estimating geocenter motion and variations in J2 by combining data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with output from an Ocean Bottom Pressure model and a Glacial Isostatic Adjustment (GIA) model. First, we conduct an end-to-end numerical simulation study. We generate input time-variable gravity field observations by perturbing a synthetic Earth model with realistically simulated errors. We show that it is important to avoid large errors at short wavelengths and signal leakage from land to ocean, as well as to account for self-attraction and loading effects. Second, the optimal implementation strategy is applied to real GRACE data. We show that the estimates of annual amplitude in geocenter motion are in line with estimates from other techniques, such as satellite laser ranging (SLR) and global GPS inversion. At the same time, annual amplitudes of C10 and C11 are increased by about 50% and 20%, respectively, compared to estimates based on Swenson et al. (2008). Estimates of J2 variations are by about 15% larger than SLR results in terms of annual amplitude. Linear trend estimates are dependent on the adopted GIA model but still comparable to some SLR results.

Recently, C30 coefficients of time-variable gravity field models from GRACE and GRACE-Follow On (GRACE/GRACE-FO) are reported to contain larger uncertainties when only one of the two onboard accelerometers is fully functional, which mainly concerns the GRACE-FO period and the final stage of the GRACE period. Using these problematic coefficients leads to incorrect mass change (rate) estimates, especially over Antarctic Ice-Sheet (AIS), and a replacement with those from satellite laser ranging (SLR) is currently recommended. In this study, we aim to discuss the possibility of improving the C30 coefficients by extending the GRACE-OBP approach that has previously been applied to the estimation of geocenter motion and variations in the Earth’s dynamic oblateness. Such an approach mainly relies on GRACE/GRACE-FO level 2 products and an ocean bottom pressure model, and it produces compatible coefficients with the GRACE/GRACE-FO product labeled as GSM. With a numerical experiment, we demonstrate the effectiveness of the proposed approach and identify the optimal implementation parameter setup. The resulting C30 coefficient time series is generally consistent with those based on SLR and the original solutions from the GRACE dual-accelerometer period, but with differences in the annual amplitude estimates. Then, we obtain C30 coefficients based on real data and check the AIS mass change time series with and without replacing the original ones with our solution. Our C30 solution ensures consistent linear trend estimates for the dual- and single-accelerometer periods.

This study aims to provide valuable scientific insights into various estimation techniques of geocentre motion (GCM) from the perspective of signal analysis, thereby enhancing Gravity Recovery and Climate Experiment (GRACE) users’ understanding and application of GCM. Initially, it utilizes the satellite laser ranging (SLR) technique with the network shift approach to estimate over 30 yr of weekly GCM time-series from 1994 to 2024. Subsequently, we employ two approaches to estimate three types of monthly GCM time-series spanning more than 20 yr from 2002 to 2023: combining GRACE data with an ocean bottom pressure model (GRACE-OBP approach), the fingerprint approach (FPA), and the fingerprint approach with satellite altimetry data (FPA-SA, up to 2022). The former is referred to as SLR-based GCM estimates, while the latter, which uses GRACE Earth’s gravity field models, is termed GRACE-based GCM estimates. Furthermore, this study pioneers the use of multichannel singular spectrum analysis (MSSA) for GCM analysis, especially focusing on the latest GRACE-based GCM estimates from the GRACE-OBP and FPA/FPA-SA approaches, marking the first comprehensive analysis of GCM estimated by various techniques. The results show that MSSA can effectively extract common signals from the three components of the GCM time-series. The seasonal components extracted from GRACE-based GCM estimates using MSSA are consistent with those from SLR-based GCM estimates, although the former exhibit slightly larger amplitudes of the annual and semi-annual signals. After correcting the atmosphere-ocean dealiasing, the amplitudes of the SLR-based estimates correspondingly decrease, remaining slightly larger but becoming closer to those of the GRACE-based estimates. However, a periodic signal with an approximate 160-d period is detectable in all GRACE-based GCM estimates, but it is absent in SLR-based GCM estimates. Further investigation using MSSA into higher degree spherical harmonic (SH) coefficients of the Earth’s gravity field models reveals that these SH coefficients contain a 160-d periodic signal. This finding suggests that the signal detected in GRACE-based GCM estimates originates from systematic errors in these SH coefficients, offering new insights for improving the accuracy of GRACE Earth’s gravity field solutions. Additionally, GRACE-based GCM estimates show significant secular non-zero trends, notably larger than those in SLR-based GCM estimates, which are not expected to exhibit any trends. However, the reliance of GRACE-based GCM estimates on geophysical models (e.g. glacier melting, glacial isostatic adjustment and hydrological models) limits the accuracy of their trends, underscoring the need for further validation. Overall, this study highlights new challenges regarding the accuracy of GRACE-based GCM estimates and emphasizes the necessity for further validation in mass change research.

Low‐degree coefficients of time‐variable gravity field models from Gravity Recovery and ClimateExperiment(GRACE)andGRACE‐FollowOn(GRACE‐FO)capturelarge‐scalemasschangeswithin theEarthsystem.However,someofthesecoefficientsareeithermissing(e.g.,degree‐1coefficients)orpoorly determined(e.g.,C20).SuchasituationisexacerbatedparticularlyovertheGRACE‐FOperiodwhenoneofthe accelerometers carries elevated noise. In this study, we present a framework for estimating low‐degree coefficients using the fingerprint approach. Our results demonstrate that this method can reliably estimate multiple coefficients simultaneously, producing degree‐1, C20, and C30 estimates that are comparable to the currently recommended solutions, both in direct comparisons and in the context of estimating mass changes over the Antarctic Ice Sheet. This framework not only provides an alternative approach for determining low‐ degree coefficients currently identified as problematic in GRACE/GRACE‐FO gravity field models, but also showspotentialforaddressingotherdegradedlow‐degreecoefficientsthatmayemergeduringfutureGRACE‐ FO operations.

Understanding the geophysical drivers of seasonal geocentre motion (GCM) variations remains challenging due to the complexity of Earth system interactions, limited data on individual mass redistribution components and model uncertainties. This study presents a comprehensive investigation of seasonal GCM signals from April 2002 to January 2024 using the Fingerprint Approach (FPA), which enables direct quantification of contributions from distinct Earth system components. Additionally, Multichannel Singular Spectrum Analysis (MSSA) is applied to quantify the influence of terrestrial water storage (TWS), atmosphere (ATM) and ocean (OCN) variability on seasonal GCM fluctuations. Correlation and lag analyses are employed to explore their temporal relationships and underlying geophysical linkages. The results reveal that TWS, ATM and OCN jointly explain 97.9 per cent, 98.1 per cent and 90.8 per cent of the seasonal variance in the X, Y and Z components of GCM, respectively. TWS exerts as the dominant contributor in the Y (66.4 per cent) and Z (67.9 per cent) components, while ATM and OCN each contribute less than 49 per cent to all components. Further analysis indicates that ATM, OCN and TWS exhibit varying lag relationships with GCM in the X and Z components, while TWS demonstrates a notably stronger correlation with GCM in the Y component. Importantly, an approximately 120-d periodic signal identified in GCM is, for the first time, linked to global precipitation variability, providing a novel geophysical interpretation. These findings enhance our understanding of climate-driven geophysical mass redistribution and offer new insights into the processes governing seasonal GCM variations.

Phase information from vertical land motion observed by the Global Positioning System (GPS) and predicted by Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) has untapped potential for advancing hydrological and geophysical studies. After correcting for effects of glacial isostatic adjustment, non-tidal oceanic and atmospheric loading using existing models, GPS observations reflect both elastic deformation due to hydrological loading and poroelastic deformation in some aquifer regions. In contrast, GRACE(FO) data are sensitive only to mass changes and thus provide a good reference of elastic loading deformation. Over aquifer systems, discrepancies in the annual phase of vertical displacement between GPS and GRACE(FO) can therefore reveal where deformation is not explained by elastic loading alone but must also be influenced by poroelastic effects. In this study, we explore this phase difference as a diagnostic tool to identify GPS stations influenced by poroelastic deformation. By comparing the annual phases of GPS observation and GRACE(FO)-predicted elastic loading deformation, we establish a threshold-based criterion for identifying poroelastically influenced stations. We applied this method to the Central Valley of California and validated the results using in-situ well observations and a terrestrial water storage inversion based on GPS data. This phase-based identification method not only provides a simple, robust, and physically interpretable method for identifying GPS stations affected by poroelastic deformation but also highlights the broader potential of exploiting GPS and GRACE(FO) phase information in hydrological and geophysical studies.

Accurate river discharge data are essential for effective water resource management, flood forecasting, drought mitigation, and ecological sustainability. However, the global river gauge network remains sparse, outdated, and often inaccessible, particularly in developing or remote regions, limiting our ability to monitor and manage hydrological systems. In response, global hydrological models have emerged as critical tools for estimating streamflow, yet their accuracy and applicability require systematic evaluation. This study assesses the performance of three global hydrological models—Community Water Model (CWatM), PCRaster Global Water Balance (PCR-GLOBWB), and H08—at both high (5 arcmin) and low (30 arcmin) spatial resolutions. Observed discharge data from 1,707 Global Runoff Data Centre (GRDC) stations and 62 stations in Thailand were used for evaluation. Additionally, two data fusion methods—Triple Collocation (TC) and simple averaging—were employed to enhance streamflow simulations by integrating outputs from the three models. Results show that CWatM, particularly at high resolution, consistently outperforms PCR-GLOBWB and H08, while all models demonstrate stronger performance in Europe than in other regions. Both TC and averaging methods improve simulation accuracy compared to individual models, with TC offering the highest overall performance, especially when using H08 as the reference system. Resolution analysis reveals that high-resolution models yield more accurate estimates in most regions. This study highlights the value of multi-model integration and resolution optimization in enhancing global streamflow simulation. The findings provide practical guidance for model selection and data fusion strategies, particularly in improving hydrological assessments for ungauged or poorly monitored regions.

Study region: Danube River Basin; Study focus: Streamflow prediction is essential for water resources management and flood-risk mitigation. To better exploit spatial dependencies among gauging stations, we use a Graph Convolutional Network–Long Short-Term Memory (GCN–LSTM) framework for regional streamflow forecasting. The model integrates static and dynamic predictors from ERA5-Land and is evaluated at both monthly and daily temporal resolutions, with benchmarks against MLP, RNN, GRU, LSTM, and biLSTM. We further assess robustness and transferability through station-thinning experiments and cross-station validation at ungauged sites; New hydrological insights: GCN–LSTM consistently outperforms the conventional baselines and maintains strong predictive skill across station densities, indicating that high accuracy can be achieved without an extremely dense gauging network, although performance drops when fewer than ∼30 training stations are available. Daily inputs substantially improve the representation of short-term fluctuations and extreme flows, highlighting the importance of high temporal resolution for capturing rapid hydrological processes. Cross-station tests show a clear accuracy loss at ungauged locations that increases with distance from the training stations, underscoring that spatial generalization remains a key limitation in hydrologically heterogeneous regions.

In this study, we develop a methodology to estimate monthly variations in degree-1 and C20 coefficients by combing Gravity Recovery and Climate Experiment (GRACE) data with oceanic mass anomalies (combination approach). With respect to the method by Swenson et al., the proposed approach exploits noise covariance information of both input data sets and thus produces stochastically optimal solutions supplied with realistic error information. Numerical simulations show that the quality of degree-1 and -2 coefficients may be increased in this way by about 30 per cent in terms of RMS error. We also proved that the proposed approach can be reduced to the approach of Sun et al. provided that the GRACE data are noise-free and noise in oceanic data is white. Subsequently, we evaluate the quality of the resulting degree-1 and C20 coefficients by estimating mass anomaly time-series within carefully selected validation areas, where mass transport is small. Our validation shows that, compared to selected Satellite Laser Ranging (SLR) and joint inversion degree-1 solutions, the proposed combination approach better complements GRACE solutions. The annual amplitude of the SLR-based C10 is probably overestimated by about 1 mm. The performance of the C20 coefficients, on the other hand, is similar to that of traditionally used solution from the SLR technique.

A new methodology is proposed to estimate changes in the Earth’s dynamic oblateness (J2 or equivalently, -sqrt(5)C20) on a monthly basis. The algorithm uses monthly Gravity Recovery and Climate Experiment (GRACE) gravity solutions, an ocean bottom pressure model and a glacial isostatic adjustment (GIA) model. The resulting time series agree remarkably well with a solution based on satellite laser ranging (SLR) data. Seasonal variations of the obtained time series show little sensitivity to the choice of GRACE solutions. Reducing signal leakage in coastal areas when dealing with GRACE data and accounting for self-attraction and loading effects when dealing with water redistribution in the ocean is crucial in achieving close agreement with the SLR-based solution in terms of de-trended solutions. The obtained trend estimates, on the other hand, may be less accurate due to their dependence on the GIA models, which still carry large uncertainties.

The effect of glacial isostatic adjustment (GIA) on the shape and gravity of the Earth is usually described by numerical models that solve for both glacial evolution and Earth’s rheology, being mainly constrained by the geological evidence of local ice extent and globally distributed sea level data, as well as by geodetic observations of Earth’s rotation. In recent years, GPS and GRACE observations have often been used to improve those models, especially in the context of regional studies. However, consistency issues between different regional models limit their ability to answer questions from global-scale geodesy. Examples are the closure of the sea level budget, the explanation of observed changes in Earth’s rotation, and the determination of the origin of the Earth’s reference frame. Here, we present a global empirical model of present-day GIA, solely based on GRACE data and on geoid fingerprints of mass redistribution. We will show how the use of observations from a single space-borne platform, together with GIA fingerprints based on different viscosity profiles, allows us to tackle the questions from global-scale geodesy mentioned above. We find that, in the GRACE era (2003–2016), freshwater exchange between land and oceans has caused global mean sea level to rise by 1.2±0.2 mm yr−1, the geocentre to move by 0.4±0.1 mm yr−1, and the Earth’s dynamic oblateness (J2) to increase by  yr−1.