Annual cycles in the geocenter motion time series are primarily driven by mass changes in the Earth’s hydrologic system, which includes land hydrology, atmosphere, and oceans. Seasonal variations of the geocenter motion have been reliably determined according to Sun et al. (J Geophys Res Solid Earth 121(11):8352–8370, 2016) by combining the Gravity Recovery And Climate Experiment (GRACE) data with an ocean model output. In this study, we reconstructed the observed seasonal geocenter motion with geophysical model predictions of mass variations in the polar ice sheets, continental glaciers, terrestrial water storage (TWS), and atmosphere and dynamic ocean (AO). The reconstructed geocenter motion time series is shown to be in close agreement with the solution based on GRACE data supporting with an ocean bottom pressure model. Over 85% of the observed geocenter motion time series, variance can be explained by the reconstructed solution, which allows a further investigation of the driving mechanisms. We then demonstrated that AO component accounts for 54, 62, and 25% of the observed geocenter motion variances in the X, Y, and Z directions, respectively. The TWS component alone explains 42, 32, and 39% of the observed variances. The net mass changes over oceans together with self-attraction and loading effects also contribute significantly (about 30%) to the seasonal geocenter motion in the X and Z directions. Other contributing sources, on the other hand, have marginal (less than 10%) impact on the seasonal variations but introduce a linear trend in the time series.

The ocean load in glacial isostatic adjustment (GIA) modelling is represented by the so-called sea level equation (SLE). The SLE describes the mass redistribution of water between ice sheets and oceans on a deforming Earth. Despite various teams independently investigating GIA, there has been no systematic intercomparison among the numerical solvers of the SLE through which the methods may be validated. The goal of this paper is to present a series of synthetic examples designed for testing and comparing the numerical implementations of the SLE in GIA modelling. The 10 numerical codes tested combine various temporal and spatial parametrizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parametrize the GIA-related field variables spatially. The surface ice-water load and solid Earth's topography are represented spatially either on an equiangular grid, a Gauss-Legendre or an equiarea grid with icosahedron-shaped spherical pixels. Comparisons aremade in a series of five benchmark examples with an increasing degree of complexity. Due to the complexity of the SLE, there is no analytical solution to it. The accuracy of the numerical implementations is therefore assessed by the differences of the individual solutions with respect to a reference solution. While the benchmark study does not result in GIA predictions for a realistic loading scenario, we establish a set of agreed-upon results that can be extended in the future by including more complex case studies, such as solutions with realistic loading scenarios, the rotational feedback in the linear-momentum equation, and by considering a 3-D viscosity structure of the Earth's mantle. The test computations performed so far show very good agreement between the individual results and their ability to capture the main features of sea-surface variation and the surface vertical displacement. The differences found can often be attributed to the different approximations inherent in the various algorithms. This shows the accuracy that can be expected from different implementations of the SLE, which helps to assess differences noted in the literature between predictions for realistic loading cases.

In this study, we develop a methodology to estimate monthly variations in degree-1 andC₂₀ coefficients by combing Gravity Recovery and Climate Experiment (GRACE) data withoceanic 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 thusproduces stochastically optimal solutions supplied with realistic error information. Numericalsimulations show that the quality of degree-1 and -2 coefficients may be increased in this wayby about 30 per cent in terms of RMS error.We also proved that the proposed approach can bereduced to the approach of Sun et al. provided that the GRACE data are noise-free and noise inoceanic data is white. Subsequently, we evaluate the quality of the resulting degree-1 and C₂₀coefficients by estimating mass anomaly time-series within carefully selected validation areas,where mass transport is small. Our validation shows that, compared to selected Satellite LaserRanging (SLR) and joint inversion degree-1 solutions, the proposed combination approachbetter complementsGRACE solutions. The annual amplitude of the SLR-based C₁₀ is probablyoverestimated by about 1 mm. The performance of the C₂₀ coefficients, on the other hand, issimilar to that of traditionally used solution from the SLR technique.

Uncertainty in the geocenter position and its subsequent motion affects positioning estimates on the surface of the Earth and downstream products such as site velocities, particularly the vertical component. The current version of the International Terrestrial Reference Frame, ITRF2014, derives its origin as the long-term averaged center of mass as sensed by satellite laser ranging (SLR), and by definition, it adopts only linear motion of the origin with uncertainty determined using a white noise process. We compare weekly SLR translations relative to the ITRF2014 origin, with network translations estimated from station displacements from surface mass transport models. We find that the proportion of variance explained in SLR translations by the model-derived translations is on average less than 10%. Time-correlated noise and nonlinear rates, particularly evident in the Y and Z components of the SLR translations with respect to the ITRF2014 origin, are not fully replicated by the model-derived translations. This suggests that translation-related uncertainties are underestimated when a white noise model is adopted and that substantial systematic errors remain in the data defining the ITRF origin. When using a white noise model, we find uncertainties in the rate of SLR X, Y, and Z translations of ±0.03, ±0.03, and ±0.06, respectively, increasing to ±0.13, ±0.17, and ±0.33 (mm/yr, 1 sigma) when a power law and white noise model is adopted.

An accurate estimation of water resources dynamics is crucial for proper management of both agriculture and the local ecology, particularly in semi-arid regions. Imperfections in model physics, uncertainties in model land parameters and meteorological data, as well as the human impact on land changes often limit the accuracy of hydrological models in estimating water storages. To mitigate this problem, this study investigated the assimilation of terrestrial water storage variation (TWSV) estimates derived from the Gravity Recovery And Climate Experiment (GRACE) data using an ensemble Kalman filter (EnKF) approach. The region considered was the Hexi Corridor in northern China. The hydrological model used for the analysis was PCR-GLOBWB, driven by satellite-based forcing data from April 2002 to December 2010. The impact of the GRACE data assimilation (DA) scheme was evaluated in terms of the TWSV, as well as the variation of individual hydrological storage estimates. The capability of GRACE DA to adjust the storage level was apparent not only for the entire TWSV but also for the groundwater component. In this study, spatially correlated errors in GRACE data were taken into account, utilizing the full error variance-covariance matrices provided as a part of the GRACE data product. The benefits of this approach were demonstrated by comparing the EnKF results obtained with and without taking into account error correlations. The results were validated against in situ groundwater data from five well sites. On average, the experiments showed that GRACE DA improved the accuracy of groundwater storage estimates by as much as 25 %. The inclusion of error correlations provided an equal or greater improvement in the estimates. In contrast, a validation against in situ streamflow data from two river gauges showed no significant benefits of GRACE DA. This is likely due to the limited spatial and temporal resolution of GRACE observations. Finally, results of the GRACE DA study were used to assess the status of water resources over the Hexi Corridor over the considered 9-year time interval. Areally averaged values revealed that TWS, soil moisture, and groundwater storages over the region decreased with an average rate of approximately 0.2, 0.1, and 0.1 cm yr^-1 in terms of equivalent water heights, respectively. A particularly rapid decline in TWS (approximately -0.4 cm yr^-1) was seen over the Shiyang River basin located in the southeastern part of Hexi Corridor. The reduction mostly occurred in the groundwater layer. An investigation of the relationship between water resources and agricultural activities suggested that groundwater consumption required to maintain crop yield in the growing season for this specific basin was likely the cause of the groundwater depletion.

The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.