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Despite the increasing accuracies of GRACE (Gravity Recovery and Climate Experiment)/GRACE-FO (GRACE Follow-On) gravity field models through worldwide endeavours, the temporal aliasing effect caused by the imperfect background models used in gravity field modelling is still a crucial factor that degrades the quality of gravity field solutions. Since the important role of temporal resolution of atmospheric de-aliasing models, this paper specifically investigates the influence of temporal resolution on gravity field modelling from the perspectives of frequency, spectral and spatial domains. To this end, we introduced the gravitational acceleration and geoid height derived from the static gravity field GOCO06s in the inner integral. The introduction of the static gravity field has a comparable impact on LRI (Laser Ranging Interferometers) range-rate residuals as the accuracy of the LRI range-rate data, despite its magnitude of being less than 0.1 mm in the spatial domain. This finding also highlights the significance of error level in existing de-aliasing products as a crucial factor that restricts the current accuracy of gravity field solutions. Further analyses show that increasing the temporal resolution from 3 to 1 hr has an insignificant impact on the gravity solutions in both the frequency and spectral domains, which is also smaller than that caused by using different atmospheric data sets. However, in the spatial domain, LRI range-rate residuals can be effectively mitigated in certain regions of the Southern Hemisphere at mid- and high-latitudes by increasing the temporal resolution. Particularly, the discrepancies of mass change estimates brought about by enhancing temporal resolution have distinct characteristics, especially in the Congo River and the Amazon River Basins. The mass changes in terms of equivalent water height derived by using P4M6 filtering show that the maximum root mean square value of spatial differences caused by improving the temporal resolution of the atmospheric de-aliasing models can reach ∼13.4 mm in the subregion of the Congo River Basin. However, using different atmospheric data sets can lead to a maximum difference of ∼16.5 mm. For the Amazon River Basin, the corresponding maximum discrepancy is ∼18.1 mm, and that caused by improving temporal resolution is ∼9.4 mm. We further divide the Congo River Basin into several subregions using a lat-lon regular grid with a spatial resolution of 3°. The subsequent time-series results of mass changes reveal that the maximum contribution of temporal resolution and changes in the atmospheric data sets can reach 11.09 and 21.24 per cent, respectively. This suggests that it is necessary to consider the temporal resolution of de-aliasing products when studying mass changes at a regional scale. [ABSTRACT FROM AUTHOR]

The joint ESA/NASA Mass-change And Geosciences International Constellation (MAGIC) has the objective to extend time-series from previous gravity missions, including an improvement of accuracy and spatio-temporal resolution. The long-term monitoring of Earth's gravity field carries information on mass change induced by water cycle, climate change and mass transport processes between atmosphere, cryosphere, oceans and solid Earth. MAGIC will be composed of two satellite pairs flying in different orbit planes. The NASA/DLR-led first pair (P1) is expected to be in a near-polar orbit around 500 km of altitude; while the second ESA-led pair (P2) is expected to be in an inclined orbit of 65°–70° at approximately 400 km altitude. The ESA-led pair P2 Next Generation Gravity Mission shall be launched after P1 in a staggered manner to form the MAGIC constellation. The addition of an inclined pair shall lead to reduction of temporal aliasing effects and consequently of reliance on de-aliasing models and post-processing. The main novelty of the MAGIC constellation is the delivery of mass-change products at higher spatial resolution, temporal (i.e. subweekly) resolution, shorter latency and higher accuracy than the Gravity Recovery and Climate Experiment (GRACE) and Gravity Recovery and Climate Experiment Follow-On (GRACE-FO). This will pave the way to new science applications and operational services. In this paper, an overview of various fields of science and service applications for hydrology, cryosphere, oceanography, solid Earth, climate change and geodesy is provided. These thematic fields and newly enabled applications and services were analysed in the frame of the initial ESA Science Support activities for MAGIC. The analyses of MAGIC scenarios for different application areas in the field of geosciences confirmed that the double-pair configuration will significantly enlarge the number of observable mass-change phenomena by resolving smaller spatial scales with an uncertainty that satisfies evolved user requirements expressed by international bodies such as IUGG. The required uncertainty levels of dedicated thematic fields met by MAGIC unfiltered Level-2 products will benefit hydrological applications by recovering more than 90 per cent of the major river basins worldwide at 260 km spatial resolution, cryosphere applications by enabling mass change signal separation in the interior of Greenland from those in the coastal zones and by resolving small-scale mass variability in challenging regions such as the Antarctic Peninsula, oceanography applications by monitoring meridional overturning circulation changes on timescales of years and decades, climate applications by detecting amplitude and phase changes of Terrestrial Water Storage after 30 yr in 64 and 56 per cent of the global land areas and solid Earth applications by lowering the Earthquake detection threshold from magnitude 8.8 to magnitude 7.4 with spatial resolution increased to 333 km. [ABSTRACT FROM AUTHOR]

The Combination Service for Time-variable Gravity fields (COST-G) operationally provides combinations of monthly Earth gravity field models derived from observations of the microwave ranging instrument of the GRACE Follow-on (GRACE-FO) satellite mission, applying the quality control and combination methodology originally developed by the Horizon 2020 project European Gravity Service for Improved Emergency Management for the data of the GRACE satellites. In the frame of the follow-up Horizon 2020 project Global Gravity-based Groundwater Product (G3P), the GRACE-FO combination is used to derive global grids of groundwater storage anomalies. To meet the user requirements and achieve optimal signal-to-noise ratio, the combination has been further developed and extended to incorporate: • new time-series based on the alternative accelerometer transplant product generated in the frame of the project by the Institute of Geodesy at the Graz University of Technology, which specifically improves the estimation of the C 30 coefficient and also reduces the noise at medium to short wavelengths, and • the new time-series AIUB–GRACE-FO–RL02 of monthly GRACE-FO gravity fields, which is derived at the Astronomical Institute of the University of Bern by applying empirical noise modelling techniques. The COST-G quality control confirms the consistency of the contributing GRACE-FO time-series concerning the signal amplitude of seasonal hydrology in large river basins and the secular mass change in polar regions, but it also indicates rather diverse noise characteristics. The difference in the noise levels is taken into account in the combination process by relative weights derived by variance component estimation on the solution level. The weights are expected to be inverse proportional to the noise levels of the individual gravity field solutions. However, this expectation is violated when applying the weighting scheme as developed for the GRACE combination. The reason is found in the high-order coefficients of the gravity field, which are poorly determined from the low–low range-rate observations due to the observation geometry and suffer from aliasing due to the malfunctioning accelerometer onboard one of the GRACE-FO satellites. Hence, for the final G3P-combination a revised weighting scheme is applied where the gravity field coefficients beyond order 60 are excluded from the determination of the weights. The quality of the combined gravity fields is assessed by comparison of the noise content and the signal-to-noise ratio with the individual time-series. Independent validation is provided by the COST-G validation centre at the GFZ German Research Centre for Geosciences, where orbit fits of the low-flying Gravity and steady-state Ocean Circulation Explorer satellite are performed that confirm the high quality of the combined GRACE-FO gravity fields. By the end of the G3P project, the new combination scheme is implemented by COST-G as the new COST-G–GRACE-FO–RL02 and continued to be used for the operational GRACE-FO combination. [ABSTRACT FROM AUTHOR]

Atmospheric rivers (ARs) are efficient mechanisms for transporting atmospheric moisture from low latitudes to the Antarctic continent. AR events induce intense snowfall episodes, which increase crustal deformation. Here, we used an AR detection algorithm, via a spatial matrix operation to quantify the contribution of AR-induced snowfall in the Antarctic continent, 2010–2019. Our results reveal that the AR snowfall contribution to Antarctica primarily ranged from 9.28 to 29.73 per cent from 2010 to 2019, and there was an evident increasing trend from 2015 to 2019 (20.66 per cent in 2015 to 29.30 per cent in 2019). AR-induced snowfall is one of the factors influencing the surface deformation of the Antarctic continent, based on the hourly AR snowfall deformation calculations for the Antarctic continent, both the average and maximum crustal deformation or displacement tends to be greatest near the coastline, while the displacement is less affected by AR further inland. [ABSTRACT FROM AUTHOR]

The Mass Change and Geoscience International Constellation (MAGIC) is planned as the first realization of a double-pair low-low satellite-to-satellite (ll-sst) tracking gravity mission consisting of a polar and an inclined satellite pair. Due to the much increased spatial and temporal resolution and multidirectionality of the data to be collected by this mission, new possibilities regarding the resolvability of mass transport processes in space and time are expected. In order to maximize the scientific and societal outcome of this mission, an optimization of both the mission design as well as the methods to process the expected data is fundamental. Using numerical closed-loop simulations, we investigate the impact of several key mission design aspects on the gravity retrieval from a double-pair constellation such as the planned MAGIC mission. Specifically, we show how the choice of the second pair's inclination poses a trade-off between a reduction of retrieval errors at latitudes covered by data from both pairs and at higher latitudes, thereby requiring a compromise between the latitude-dependent accuracy requirements of different user groups. One of the key mission goals is to provide fast-track gravity products with short latency for operational service applications. Towards the estimation of such short-term gravity fields of a few days, we investigate if coordinating the polar and inclined pairs' orbits to achieve a stable ground-track coverage is necessary for obtaining a homogeneous accuracy of subsequent gravity solutions. Indeed, combining two freely drifting, uncontrolled orbits significantly degrades short-term gravity fields in time periods in which both pairs show coinciding ground track gaps. Finally, we analyse the relative performance of the two satellite pairs. Double-pair scenarios that are strongly dominated by the inclined pair's data reveal degraded gravity solutions when co-estimating daily gravity fields as de-aliasing strategy. This effect can be mitigated by choosing a more balanced double-pair configuration, for example by choosing similar orbit heights and instrument noise levels for both satellite pairs. The findings presented in our study will serve to optimize the system design of the upcoming MAGIC constellation. [ABSTRACT FROM AUTHOR]

The accuracy of polar motion forecasting has been the focus of attention in the fields of satellite navigation and deep space exploration. However, the traditional or differential methods for forecasting X or Y series based on LS and AR models are straightforward and monolithic, and cannot reduce the range of forecast errors. Therefore, this study proposes a new method (called the between-within, B–W method) that combines the X, Y and Y–X series forecasts of the traditional and differential methods in pairs according to the mathematical relationship of Y–X. This approach is one way to obtain the minimum range of forecast errors by making full use of the advantages of each method in the combination. A total of 262-hindcast experiments were conducted during 2010–2020 with strictly simulated time delays. For forecasts of 1–180 d at the x-pole, the average improvement is 10.7 per cent over Bulletin-A. For the y-pole at 1–90 d an average improvement of 11.7 per cent over Bulletin-A is achieved. In addition, further incorporation of the last 1 d IGS (International Global Navigation Satellite System Service) Ultra-rapid (IGU) data can effectively improve the MAE at 1–10 d. The 2016–2018 performance of the B–W method at the x-pole may be related to the amplitude and phase of the Chandler wobble, and the 2013–2016 performance at the y-pole may be related to El Niño climate change events. In terms of overall stability, the B–W method is superior to the IERS Bulletin-A in the medium-short-term and has potential practical application. [ABSTRACT FROM AUTHOR]

SUMMARY: The GRACE Atmosphere and Ocean Level-1B (AOD1B) product is routinely applied in the processing of satellite gravimetry data to mitigate the impact of temporal aliasing. Spurious trends, low-frequency signals or bias jumps in the background model data can, if unaccounted for, introduce biases into the global gravity solutions which might be interpreted erroneously in subsequent geophysical analyses. Here, we examine the most recent release, RL07, of AOD1B for such artefacts. A focus is placed on the transition from the atmospheric re-analysis ERA5 to operational weather model data, in January 2018, which coincides with the gap between the missions GRACE and GRACE-FO. We find that linear trends computed from 1975 to 2020 are well below 30 Pa a–1 for all components of RL07. The assessment of 3-hourly tendencies gives no indication of bias jumps and shows that the transition in atmospheric data does not have an adverse effect on the consistency of RL07. We conclude with a comparison of the variability of both AOD1B RL06 and RL07 in the context of their application in satellite gravimetry. [ABSTRACT FROM AUTHOR]

Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the covariance matrix of pseudo measurements should be calculated and used to appropriately weigh the parameter estimation. In this work, we propose a statistically optimal point-mass inversion scheme by directly using the SH coefficients as measurements. We prove the equivalence between this direct approach and the conventional indirect approaches. We also demonstrated their comparable performance through both simulation and real GRACE data processing. Choosing and calculating pseudo measurements, propagating covariance matrix and potentially dealing with the singularity of the covariance matrix involved in the conventional indirect approaches are avoided in the proposed direct approach. This statistically optimal direct approach can readily be employed in mascon inversion of GRACE data and other radial basis functions-based approaches in regional gravity modeling. [ABSTRACT FROM AUTHOR]

Nonlinear trends (i.e. quadratic trends, usually defined as accelerations) in Antarctic ice mass loss due primarily to the complex climate warming forcing regimes have induced large uncertainty to future sea level projection. Here, we quantify the nonlinear and spatially varying mass losses in the Antarctic ice sheet during the last two decades using the satellite gravimetry data collected by Gravity Recovery And Climate Experiment (GRACE) and its successor GRACE Follow-On. We use a regional inversion methodology to generate the mass change time-series over Antarctica. Our findings reveal that seven regions have evidenced significant nonlinear mass change. These regions are all concentrated along the coast of Antarctica and show spatially heterogeneous mass balance nonlinear trend patterns. Among them, the Amundsen Sea Embayment (ASE) and the Dronning Maud Land (DML) are found to be particularly sensitive to short-term climate variability. The GRACE-inferred nonlinear mass balance signal can be confirmed by independent Global Positioning System (GPS) observations, and the difference between the nonlinear vertical deformation trends estimated by GRACE and GPS, especially in ASE, is likely due to the imperfect correction of the glacial isostatic adjustment (GIA) effect. For Antarctic ice sheet as a whole, GRACE satellite gravimetry indicates an ice mass loss of −101.3 ± 18.0 Gt yr−1, with an accelerated loss of −6.4 ± 1.3 Gt yr−2 during 2002–2021. [ABSTRACT FROM AUTHOR]

The visco-elastic response of the solid Earth to the past glacial cycles and the present-day surface mass change (PDSMC) are detected by the geodetic observation systems such as global navigation satellite system and satellite gravimetry. Majority of the contemporary PDSMC is driven by climate change and in order to better understand them using the aforementioned geodetic observations, glacial isostatic adjustment (GIA) signal should be accounted first. The default approach is to use forward GIA models that use uncertain ice-load history and approximate Earth rheology to predict GIA, yielding large uncertainties. The proliferation of contemporary, global, geodetic observations and their coverage have therefore enabled estimation of data-driven GIA solutions. A novel framework is presented that uses geophysical relations between the vertical land motion (VLM) and geopotential anomaly due to GIA and PDSMC to express GPS VLM trends and GRACE geopotential trends as a function of either GIA or PDSMC, which can be easily solved using least-squares regression. The GIA estimates are data-driven and differ significantly from forward models over Alaska and Greenland. [ABSTRACT FROM AUTHOR]

By anatomizing the classic Liouville equation (LE), an alternative theoretical framework is established for the Earth polar motion where the turbulent time derivative of the fluid forcing, L force, is eliminated. The observed polar motion is found a lumped signal of two physical variables, one of which is the forced polar motion, m force, that balances out the fluid forcing through a simple algebraic identity. The second component is the inertial polar motion, m inert, which conserves the total angular momentum by the restoring power of the equatorial bulge. Aside from its numerical difficulties, the time derivative dL force /dt has proved to be a redundant artefact that mixes the physical signals in the solution of the LE. By an analytical appraisal, we find that for non-Chandler forced polar motions, the dL force /dt term in the excitation function of the classic LE is 100 per cent responsible for the forced term, m force, and contributes 0.3 per cent of the inertial term, m inert. The Chandler signal originates exclusively from the inertial polar motion m inert. The artefact dL force /dt perturbs the true Chandler signal from the classic LE by 0.3 per cent. Anatomy of the LE allows us to show that a linearized mechanism for the Chandler Wobble excitation is valid, since the linearized governing equation for the inertial polar motion m inert stands as part of the exact solution of the full nonlinear equation. Anatomized polar motion equations are also considered in the presence of ocean tides, under the lunisolar torque, and on an elastically deformable Earth. Inaccuracies and misinterpretations associated with the classic LE under those circumstances are clarified in formulating the anatomized polar motion equation group. [ABSTRACT FROM AUTHOR]

Most studies of sea level budget only indicate the stationary causes for the global mean sea level (GMSL) rise over the course of a time span of interest, providing limited information on temporary changes in the GMSL budget. In this contribution, we present an instantaneous budget of the GMSL for the period of 2003–2015, which offers new insights on the time evolution of the GMSL budget. We use a space-state model to compute the instantaneous rates of GMSL and their contributing sources (barystatic and steric contributions), to investigate the causes of the GMSL instantaneous budget, which accounts for and quantifies low-frequency variations in GMSL rise. Combining the barystatic GMSL instantaneous rates (estimated from satellite gravimetry) along with a particular choice of steric GMSL instantaneous rates (inferred from an Argo product) achieves closure of the GMSL instantaneous budget with a standard deviation of 0.4 mm yr−1. We find that the barystatic GMSL rate is primarily responsible for the striking fluctuations in the GMSL instantaneous rates between 2009 and 2015. For example, over only 20 months (July 2010 to February 2012), the GMSL (barystatic) rate increases from 0.32 (0.71) to 6.12 (4.55) mm yr−1. These strong fluctuations mainly result from hydrology and mountain glacier mass variations rather than mass loss in ice sheet, for instance, Australia slowed ∼1.2 mm yr−1 equivalent contribution to GMSL rise over the year 2010, which is approximately four times the linear rate of Antarctica mass loss. [ABSTRACT FROM AUTHOR]

We present a theory of modern, thermally induced deformation in a realistic Earth. The heat conduction equation is coupled with standard elastic deformation theory to construct a boundary-value problem comprised of eighth-order differential equations. The accurate and stable dual variable and position propagating matrix technique is introduced to solve the boundary-value problem. The thermal load Love numbers are defined to describe the displacements and potential changes driven by thermally induced deformation. The proposed analytical method is validated by comparing the present results with exact solutions for a homogeneous sphere, which are also derived in this paper. The analytical method is then applied to a realistic Earth model to evaluate the effects of layering and self-gravitation of the Earth on displacement and changes of potential. Furthermore, the frequency dependence in the thermal load is illustrated by invoking different thermal periodicities in the computation. Thermal anisotropy is also considered by comparing the results obtained using isotropic and transversely isotropic Earth models. Results show that, when simulating thermally induced deformation, invoking a homogeneous spherical Earth leads to results that substantially differ from those obtained using a more realistic Earth model. [ABSTRACT FROM AUTHOR]

Geodetic observations from space continuously record surface deformation and global mass redistribution with an increasing accuracy. In parallel, surficial processes (oceanic, atmospheric and hydrological loading) are more and more precisely modelled. We propose a confrontation of the geodetic Global Positioning System (GPS) and gravity-field satellite laser ranging (SLR) observations at decadal and interannual timescales, in terms of resolution, correlation and comparison with surficial loading models. We focus on the largest global scale signals of degree 2. At interannual periods, surface deformations retrieved from GPS time-series do not exceed 0.8 mm. Our analysis does not reveal the presence of a dominant signal at a specific period, except perhaps for a signal of approximately 3 yr likely connected to the loading response to El Niño/Southern Oscillations. Contrary to the results of previous studies, we do not find in GPS time-series a clear 6-yr oscillation associated with a degree-2 order-2 pattern. Interannual variations in the degree-2 Stokes coefficients of the gravity field do not exceed 2 × 10−11. We do not detect a dominant gravity signal at one specific period but instead a broad spectrum of frequencies. The comparison between the degree-2 deformations built from GPS time-series with a prediction from SLR-derived gravity variations reveals some correlations, though their differences remain important. This highlights the present day limitations of these techniques in their ability to characterize global scale interannual variations. Hydrological loading models show some correlations with both GPS and SLR signals, but we cannot firmly establish that continental hydrology is dominantly responsible for the observed variations. Given the current limits in the resolution of both gravity and surface deformation and in the modelling of surface processes, we conclude that it will be a challenge to retrieve a geodetic signal of subdecadal period originating in the Earth's core. [ABSTRACT FROM AUTHOR]

The energy changes corresponding to the axis and speed of the Earth's rotation are the polar motion energy, Δ E pm and the spinning energy, Δ E ss. Here we develop an explicit approach to compute the coseismic Δ E pm and Δ E ss based on a spherical-Earth elastic dislocation theory. We estimate the cumulative changes induced by global major earthquakes from 1976 to 2019 using the derived expression. The results show that the rate of Δ E pm and Δ E ss is 0.45 × 1012 and 0.20 × 1019 J −1, corresponding to 0.01 MW (1 MW = 106 Watt) and 0.06 TW (1 TW = 1012 Watt), respectively. The χ 2 test shows that global earthquakes tend to strongly increase the spinning energy rather than the polar motion energy. Comparing the coseismic rotational energy to the coseismic gravitational energy and the radiated seismic-wave energy induced by every single event, we found that coseismic rotational energy is distinctly at least 7.6 times larger than the radiated seismic-wave energy, demonstrating the importance of rotational energy in the energy budget of the faulting. [ABSTRACT FROM AUTHOR]

The Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry observations have been widely used in the study of glaciers. However, there is still no detailed GRACE-based study of the glaciers over the Scandinavian Mountains (SCAMs), where the glaciers are debris-covered and the effects of glacial isostatic adjustment (GIA) are significant. In this paper, GRACE observations are combined with climate data to analyse interannual mass changes in glacier and lake areas over Scandinavia during the period from 2003 to 2016. An inversion algorithm, the constrained forward modelling method, is used to recover the signals of glaciers and lakes from GRACE observations. Our results show that the total glacier mass loss rate over Scandinavia is –1.0 ± 1.1 Gt yr–1 during our study period. We find that the glacier accumulation regime in different subregions of the SCAMs may be different. The glacier mass change in the central SCAMs tends to be mainly driven by precipitation. Two rapid transitions from dry/wet years to wet/dry years in the lake area in south Scandinavia are identified by multiple data. The transitions are likely caused by changes in atmospheric circulation, that is surface wind. The mass changes of Scandinavia can be primarily explained by the influence of winds. We find that the glacier area is controlled by both the northerly and southerly winds, while the lake area is mainly driven by the southerly winds. This discrepancy leads to the different mechanisms of mass change in glacier and lake areas. We also discuss the influence of GIA, and suggest that the GRACE-derived long-term hydrology trends over Scandinavia may be unreliable and need to be verified. Our study indicates that GRACE data have potential in detecting small-scale glacier changes. [ABSTRACT FROM AUTHOR]

Coastal populations are impacted by relative sea level variations, which consist both of absolute sea level variations and of vertical land motions. This paper focuses on the Southwest and Central Pacific region, a recognized vulnerable region to sea level rise and where a large range of vertical land motion dynamics is observed. We analyse vertical displacement rates obtained from Global Navigation Satellite Systems (GNSS) by different analysis centres. We study the role played by modelled parameters, such as step discontinuities (due to equipment changes, earthquakes, etc.), in the position time-series analysis. We propose a new modelling approach based on a joint inversion of GNSS position time-series from different analysis centres. The final uncertainty on the vertical land motion rates is estimated as a combination of the uncertainty due to the GNSS data processing itself and the uncertainty due to the stability of the reference frame in which the GNSS data are expressed. We find that the dominant trend in the Southwest and Central Pacific is a moderate subsidence, with an average rate of −1.1 mm yr–1, but significant variations are observed, with displacement rates varying from an uplift of 1.6 ± 0.3 mm yr–1 to a subsidence of −5.4 ± 0.3 mm yr–1. Taking into account the geodynamic context, we assess, for each station, the relevance of current estimates of linear vertical displacement rate and uncertainty for forecasting future coastal sea levels. [ABSTRACT FROM AUTHOR]

Earth observation satellites yield a wealth of data for scientific, operational and commercial exploitation. However, the redistribution of mass in the system Earth is not yet part of the standard inventory of Earth Observation (EO) data products to date. It is derived from the Gravity Recovery and Climate Experiment (GRACE) mission and its Follow-On mission (GRACE-FO). Among many other applications, mass redistribution provides fundamental insights into the global water cycle. Changes in continental water storage impact the regional water budget and can, in extreme cases, result in floods and droughts that often claim a high toll on infrastructure, economy and human lives. The initiative for a European Gravity Service for Improved Emergency Management (EGSIEM) established three different prototype services to promote the unique value of mass redistribution products for Earth Observation in general and for early-warning systems in particular. The first prototype service is a scientific combination service to derive improved mass redistribution products from the combined knowledge of the European GRACE analysis centres. Second, the timeliness and reliability of such products is a primary concern for any early-warning system and therefore EGSIEM established a prototype for a near real-time service that provides dedicated gravity field information with a maximum latency of 5 d. Third, EGSIEM established a prototype of a hydrological/early warning service that derives wetness indices as indicators of hydrological extremes and assessed their potential for timely scheduling of high-resolution optical/radar satellites for follow-up observations in case of evolving hydrological extreme events. [ABSTRACT FROM AUTHOR]

Mascon solutions, one of the recent advances in Gravity Recovery and Climate Experiment (GRACE) products, are being widely used due to their significant improvement in spatial accuracy and their ability to be directly employed without post-processing. However, few studies have verified the performance of mascon solutions at different regional scales, especially those smaller than GRACE's native resolution. We investigated the consistency between mascon and spherical harmonic solutions (hereafter named mascon and SH solutions) as release-05 products from the Center for Space Research and determined whether mascon solutions had a higher resolution than SH solutions (approximately 300 km). In addition, we used ICESat, LEGOS and DAHITI observations of water levels as independent supplementary data to validate the comparison results. We considered three cases of mass signals with varying spatial scales to examine the performance of mascon solutions in specific regions: (1) the abrupt water-level change in Longyang Reservoir (an area smaller than 1° × 1°) driven by heavy rainfall, (2) mass increase in the middle and lower Yangtze River basin and (3) mass loss of Tianshan Mountain glaciers and their subregions, including Bosten Lake at the foot of the glaciers. We concluded that mascon solutions have the potential to reveal gravity signals in areas larger than 3° × 3° from mass sources of Terrestrial Water Storage Anomalies, whereas they perform poorer than gridded SH products or SH solutions with a decorrelation filter in some specific regions smaller than 3° × 3°. The results of the three different cases provide references to non-geodetic users to select suitable GRACE solutions for different applications. [ABSTRACT FROM AUTHOR]

Observations from the Gravity Recovery and Climate Experiment (GRACE) satellite mission provide quantitative estimates of the global water budget components. However, these estimates are uncertain as they show discrepancies when different parameters are used in the processing of the GRACE data. We examine trends in ocean mass, ice loss from Antarctica, Greenland, arctic islands and trends in water storage over land and glaciers from GRACE data (2005–2015) and explore the associated uncertainty. We consider variations in six different GRACE processing parameters, namely the processing centre of the raw GRACE solutions, the geocentre motion, the Earth oblateness, the filtering, the leakage correction and the glacial isostatic adjustment (GIA). Considering all possible combinations of the different processing parameters leads to an ensemble of 1500 post-processed GRACE solutions, which is assumed to cover a significant part of the uncertainty range of GRACE estimates. The ensemble-mean trend in all global water budget components agree within uncertainties with previous estimates based on different sources of observations. The uncertainty in the global water budget is ±0.27 mm yr−1 [at the 90 per cent confidence level (CL)] over 2005–2015. We find that the uncertainty in the geocentre motion and GIA corrections dominate the uncertainty in GRACE estimate of the global water budget. Their contribution to the uncertainty in GRACE estimate is respectively ±0.21 and ±0.12 mm yr−1 (90 per cent CL). This uncertainty in GRACE estimate implies an uncertainty in the net warming of the ocean and the Earth energy budget of ±0.25 W m−2 (90 per cent CL) when inferred using the sea level budget approach. [ABSTRACT FROM AUTHOR]

The mascon approach is a well-known technique to estimate mass anomalies in Greenland using Gravity Recovery and Climate Experiment (GRACE) satellite gravity data. It partitions the area of interest into laterally homogeneous patches (mascons). An important aspect of the mascon approach is the chosen geometry of mascons. So far, its impact has not been fully understood. In this study, we use a full-scale numerical study and real data analysis to identify the optimal strategy (primarily, the size of the mascons) for the extraction of mass anomalies over the Greenland drainage systems from GRACE monthly solutions. We use ordinary and weighted least-squares techniques to estimate the mascon parameters. The weighted least-squares estimator uses the full noise covariance matrices of monthly GRACE models, that is, designed to suppress random noise in the estimates. In addition, the zero-order Tikhonov regularization is applied. Four types of quantities of interest, which are associated with different temporal scales, are investigated in this study: monthly mass anomalies, mean mass anomalies per calendar month, interannual mass variations and long-term linear trends. We show that the dominant error sources are random errors and parametrization (model) errors (PEs), as well as the bias introduced by the regularization. Errors in long-term linear trend estimates are dominated by PEs, whereas the role of random errors increases with the decreasing temporal scale. The best solutions are obtained when the territory of Greenland is split into at least 23 mascons (the area of each one being ∼90 000 km2). The usage of smaller mascons does not worsen the solutions in most cases, which is explained by the application of the regularization. Usage of larger mascons leads in most cases to inferior results due to the impact of PEs. The application of the weighted least-squares estimator noticeably improves the quality of the solutions, with the exception of long-term linear trends estimated at the drainage system scale. In addition, we considered the long-term linear trend estimates integrated over entire Greenland. It is shown that the best results are obtained in that case when no regularization is applied. The results of real GRACE data processing are consistent with those obtained in the numerical study. [ABSTRACT FROM AUTHOR]

Monthly ocean bottom pressure solutions from the Gravity Recovery and Climate Experiment (GRACE), derived using surface spherical cap mass concentration (MC) blocks and spherical harmonics (SH) basis functions, are compared to tide gauge (TG) monthly averaged sea level data over 2003–2015 to evaluate improved gravimetric data processing methods near the coast. MC solutions can explain ≳ 42 per cent of the monthly variance in TG time-series over broad shelf regions and in semi-enclosed marginal seas. MC solutions also generally explain ~ 5–32 per cent more TG data variance than SH estimates. Applying a coastline resolution improvement algorithm in the GRACE data processing leads to ~ 31 per cent more variance in TG records explained by the MC solution on average compared to not using this algorithm. Synthetic observations sampled from an ocean general circulation model exhibit similar patterns of correspondence between modelled TG and MC time-series and differences between MC and SH time-series in terms of their relationship with TG time-series, suggesting that observational results here are generally consistent with expectations from ocean dynamics. This work demonstrates the improved quality of recent MC solutions compared to earlier SH estimates over the coastal ocean, and suggests that the MC solutions could be a useful tool for understanding contemporary coastal sea level variability and change. [ABSTRACT FROM AUTHOR]

Different observations regarding glacier mass balance on the Tibetan Plateau remain at odds with one another. Combining satellite gravity data with laser altimetry, we estimated consistent interannual changes in glacier mass in theNyenchen Tanglha (NT),Himalaya (HM)and Pamir-Karakoram (PK) ranges. Reconciled mass budgets and their one standard deviation errors are presented for each subregion. The total for NT, HM and PK is -23 ± 5 Gt yr-1 based on satellite gravity and -20 ± 6 Gt yr-1 based on laser altimetry over the period 2003-2008. Over a longer temporal span (2003-2015), the rates of glacier mass loss decreased towards the northwest, with values of -0.89 ± 0.15, -0.78 ± 0.11 and -0.11 ± 0.05 mwe yr-1 (metre water-equivalent change) for the NT, HM and PK, respectively. However, at shorter time intervals there have also been periods of accumulation. For example, the PK glaciers gained mass over 2003-2005 and 2009-2011, mainly owing to high precipitation. Glaciers in the HM and NT had more severe mass losses than those in the PK, especially in 2009 and 2012. Owing, perhaps, to their unique glacier accumulation regimes, only if low temperature and high precipitation occur in the same year do glaciers in the HM and NT gain mass or even stop losing mass. These interannual fluctuations and accelerating losses in the PK and HM glaciers suggest that mass changes are not well described by rate alone. [ABSTRACT FROM AUTHOR]

The empirical orthogonal function (EOF) reconstruction (EOFR) combines the dense observations, for example, satellite altimetry data or model output covering a short period, and sparse tide gauge records (TGRs) spanning a long period to infer the past sea level variability (SLV). Given that the number of the TGRs reduces significantly backward over time, it is necessary to assess how the sparse TGRs affect the reconstructed SLV. Meanwhile, EOFR involves two techniques, that is, using error matrix or not, which has not yet been fully assessed. We find that error matrix plays an important role in the EOFR. Using error matrix produces better reconstructed SLV than those without error matrix, especially when the TGRs are sparse (e.g. <100). If the error matrix is not included, the SLV reconstructed with sparse TGRs tends to be seriously overestimated. It is also found that global mean sea level variability reconstructed with sparse TGRs is not reliable even the error matrix is used. However, the recovery of first EOF pattern is shown to be robust through the entire 20th century (correlation >0.7). Since the first EOF is highly related to El Niño--Southern Oscillation (ENSO), this suggests that EOFR is useful for revealing the evolution of ENSO variability. [ABSTRACT FROM AUTHOR]

Short records of sea level measurements by the Ordnance Survey at 31 locations in 1859-1860, together with recent Mean Sea Level (MSL) information from the UK tide gauge network, have been used to estimate the average rates of sea level change around the coast of Great Britain since the mid-19th century. Rates are found to be approximately 1 mm yr-1 in excess of those expected for the present day based on geological information, providing evidence for a climate-change related component of the increase in UK sea level. In turn, the rates of change of MSL for the past 60 yr are estimated to be ~1 mm yr-1 in excess of the long-term rates since 1859, suggesting an acceleration in the rate of sea level rise between the 19th and 20th/21st centuries. Although the historical records are very short (approximately a fortnight), this exercise in 'data archaeology' shows how valuable to research even the shortest records can be, as long as the measurements were made by competent people and the datums of the measurements were fully documented. [ABSTRACT FROM AUTHOR]

We examine vertical load deformation at four continuous Global Positioning System (GPS) sites in southern Greenland relative to Gravity Recovery and Climate Experiment (GRACE) predictions of vertical deformation over the period 2002-2016.With limited spatial resolution, GRACE predictions require adjustment before they can be compared with GPS height time series. Without adjustment, both GRACE spherical harmonic (SH) and mascon solutions predict significant vertical displacement rate differences relative to GPS. We use a scaling factor method to adjust GRACE results, based on a long-term mass rate model derived from GRACE measurements, glacial geography, and ice flowdata. AdjustedGRACE estimates show significantly improved agreement with GPS, both in terms of long-term rates and interannual variations. A deceleration of mass loss is observed in southern Greenland since early 2013. The success at reconciling GPS and GRACE observations with a more detailed mass rate model demonstrates the high sensitivity to load distribution in regions surrounding GPS stations. Conversely, the value of GPS observations in constraining mass changes in surrounding regions is also demonstrated. In addition, our results are consistent with recent estimates of GIA uplift (~4.4 mm yr-1) at the KULU site. [ABSTRACT FROM AUTHOR]

For four decades, satellite laser ranging has recorded the global nature of the long-wavelength hydrological mass redistributionwithin the Earth system, which results in significant variations in the Earth's dynamical oblateness, characterized by the second degree zonal geopotential spherical harmonic J2 (or C20). Analysis of the J2 time-series has shown a significant variation related to the strong El Ni?no-Southern Oscillation events with periods of 2-6 yr. In particular, the variation related to the powerful 2015-2016 El Ni?no that peaked during 2015 November- December was one of the strongest on record, comparable with the 1982-1983 and 1997-1998 events. In this study, we investigate further the hydrological mass transfer between atmosphere- ocean-land and their signature in the decadal variations of J2 with timescales of ~10 yr. We found that the ~6.4-yr variations can be accounted for by the atmosphere and ocean mass variations based on the improved Atmosphere-Ocean De-aliasing data, and the observed decadal variation in J2 correlates well with the decadal tropical variability characterized by the 5-yr running mean of the El Ni?no-Southern Oscillation Index, although existing physical models, especially the land water storage, are limited for the purpose of further studies of the excitation. [ABSTRACT FROM AUTHOR]

A major uncertainty in determining the mass balance of the Antarctic ice sheet from measurements of satellite gravimetry, and to a lesser extent satellite altimetry, is the poorly known correction for the ongoing deformation of the solid Earth caused by glacial isostatic adjustment (GIA). Although much progress has been made in consistently modeling the ice-sheet evolution throughout the last glacial cycle, as well as the induced bedrock deformation caused by these load changes, forward models of GIA remain ambiguous due to the lack of observational constraints on the ice sheet's past extent and thickness and mantle rheology beneath the continent. As an alternative to forward-modeling GIA, we estimate GIA from multiple spacegeodetic observations: Gravity Recovery and Climate Experiment (GRACE), Envisat/ICESat and Global Positioning System (GPS). Making use of the different sensitivities of the respective satellite observations to current and past surface-mass (ice mass) change and solid Earth processes, we estimate GIA based on viscoelastic response functions to disc load forcing. We calculate and distribute the viscoelastic response functions according to estimates of the variability of lithosphere thickness and mantle viscosity in Antarctica. We compare our GIA estimate with published GIA corrections and evaluate its impact in determining the ice-mass balance in Antarctica from GRACE and satellite altimetry. Particular focus is applied to the Amundsen Sea Sector in West Antarctica, where uplift rates of several centimetres per year have been measured by GPS. We show that most of this uplift is caused by the rapid viscoelastic response to recent ice-load changes, enabled by the presence of a low-viscosity upper mantle in West Antarctica. This paper presents the second and final contributions summarizing the work carried out within a European Space Agency funded study, REGINA(www.regina-science.eu). [ABSTRACT FROM AUTHOR]

The release 06 (RL06) of the Gravity Recovery and Climate Experiment (GRACE) Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) product has been prepared for use as a timevariable background model in global gravity research. Available since the year 1976 with a temporal resolution of 3 hr, the product is provided in Stokes coefficients up to degree and order 180. RL06 separates tidal and non-tidal signals, and has an improved long-term consistency due to the introduction of a time-invariant reference orography in continental regions. Variance reduction tests performed with globally distributed in situ ocean bottom pressure recordings and sea-surface height anomalies from Jason-2 over a range of different frequency bands indicate a generally improved performance of RL06 compared to its predecessor. Orbit tests for two altimetry satellites remain inconclusive, but GRACE K-band residuals are reduced by 0.031 nm s-2 in a global average, and by more than 0.5 nm s-2 at numerous places along the Siberian shelf when applying the latest AOD1B release. We therefore recommend AOD1B RL06 for any upcoming satellite gravimetry reprocessing effort. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Geocentre motion between the centre-of-mass of the Earth system and the centre-of-figure of the solid Earth surface is a critical signature of degree-1 components of global surface mass transport process that includes sea level rise, ice mass imbalance and continental-scale hydrological change. To complement GRACE data for complete-spectrum mass transport monitoring, geocentre motion needs to be measured accurately. However, current methods of geodetic translational approach and global inversions of various combinations of geodetic deformation, simulated ocean bottom pressure and GRACE data contain substantial biases and systematic errors. Here, we demonstrate a new and more reliable unified approach to geocentre motion determination using a recently formed satellite laser ranging based geocentric displacement time-series of an expanded geodetic network of all four space geodetic techniques and GRACE gravity data. The unified approach exploits both translational and deformational signatures of the displacement data, while the addition of GRACE's near global coverage significantly reduces biases found in the translational approach and spectral aliasing errors in the inversion. [ABSTRACT FROM AUTHOR]

Monthly gravity field models from the GRACE satellite mission are widely used to determine ice mass changes of large ice sheets as well as smaller glaciers and ice caps. Here, we investigate in detail the ice mass changes of the Icelandic ice caps as derived from GRACE data. The small size of the Icelandic ice caps, their location close to other rapidly changing ice covered areas and the low viscosity of the mantle below Iceland make this especially challenging. The mass balance of the ice caps is well constrained by field mass balance measurements, making this area ideal for such investigations. We find that the ice mass changes of the Icelandic ice caps derived from GRACE gravity field models are influenced by both the large gravity change signal resulting from ice mass loss in southeast Greenland and the mass redistribution within the Earth mantle due to glacial isostatic adjustment since the Little Ice Age (~1890 AD). To minimize the signal that leaks towards Iceland from Greenland, we employ an independent mass change estimate of the Greenland Ice Sheet derived from satellite laser altimetry. We also estimate the effect of post Little Ice Age glacial isostatic adjustment, from knowledge of the ice history and GPS network constrained crustal deformation data. We find that both the leakage from Greenland and the post Little Ice Age glacial isostatic adjustment are important to take into account, in order to correctly determine Iceland ice mass changes from GRACE, and when applying these an average mass balance of the Icelandic ice caps of -11.4 ± 2.2 Gt yr-1 for the period 2003-2010 is found. This number corresponds well with available mass balance measurements. [ABSTRACT FROM AUTHOR]

In the dislocation theory for a spherical Earth model, the computation of surface co-seismic deformations using straightforward numerical methods is time consuming and may encounter a series of convergence problems, especially for the near-field deformations due to shallow earthquakes. This study proposes an asymptotic method to approximate changes in the coseismic surface strain that are caused by an arbitrary point dislocation in a homogeneous sphere. The corresponding expressions are in analytical form and can overcome these difficulties without the numerical integration of differential equations and summations of infinite associated Legendre series in practical applications. Importantly, in contrast with the classical solution for a half-space Earth model, the asymptotic solution can reflect the effect of the Earth's curvature. [ABSTRACT FROM AUTHOR]

We study fluctuations in the degree-2 zonal spherical harmonic coefficient of the Earth's gravity potential, C20, over the period 2003-2015. This coefficient is related to the Earth's oblateness and studying its temporal variations,△C20, can be used to monitor large-scale mass movements between high and low latitude regions. We examine △C20 inferred from six different sources, including satellite laser ranging (SLR), GRACE and global geophysical fluids models. We further include estimates that we derive from measured variations in the length-of-day (LOD), from the inversion of global crustal displacements as measured by GPS, as well as from the combination of GRACE and the output of an ocean model as described by Sun et al. We apply a sequence of trend and seasonal moving average filters to the different time-series in order to decompose them into an interannual, a seasonal and an intraseasonal component. We then perform a comparison analysis for each component, and we further estimate the noise level contained in the different series using an extended version of the three-cornered-hat method. For the seasonal component, we generally obtain a very good agreement between the different sources, and except for the LOD-derived series, we find that over 90 per cent of the variance in the seasonal components can be explained by the sum of an annual and semiannual oscillation of constant amplitudes and phases, indicating that the seasonal pattern is stable over the considered time period. High consistency between the different estimates is also observed for the intraseasonal component, except for the solution from GRACE, which is known to be affected by a strong tide-like alias with a period of about 161 d. Estimated interannual components from the different sources are generally in agreement with each other, although estimates from GRACE and LOD present some discrepancies. Slight deviations are further observed for the estimate from the geophysical models, likely to be related to the omission of polar ice and groundwater changes in the model combination we use. On the other hand, these processes do not seem to play an important role at seasonal and shorter timescales, as the sum of modelled atmospheric, oceanic and hydrological effects effectively explains the observed C20 variations at those scales. We generally obtain very good results for the solution from SLR, and we confirm that this well-established technique accurately tracks changes in C20. Good agreement is further observed for the estimate from the GPS inversion, showing that this indirect method is successful in capturing fluctuations in C20 on scales ranging from intra- to interannual. Obtaining accurate estimates from LOD, however, remains a challenging task and more reliable models of atmospheric wind fields are needed in order to obtain high-quality △C20, in particular at the seasonal scale. The combination of GRACE data and the output of an ocean model appears to be a promising approach, particularly since corresponding △C20 is not affected by tide-like aliases, and generally gives better results than the solution from GRACE, which still seems to be of rather poor quality. [ABSTRACT FROM AUTHOR]

We evaluate the benefit of different global geophysical loading products on the internal scatter of GPS position time-series from 240 globally distributed sites. We focus on the non-tidal atmospheric pressure loading predicted from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA-NATML) and the European Center for Medium-Range Weather Forecasts operational model (ECMWF-NATML), non-tidal ocean loading predicted from the Ocean Model for Circulation and Tides model (OMCT-NTOL), and the continental water storage loading predicted from the MERRA model (MERRA-CWSL) and the GFZ's Land Surface Discharge Model (LSDM-CWSL), respectively. The result shows that the root mean square (RMS) discrepancy of different CWSL models is larger than that of NATML models in the vertical component due to the varying model parameters and input data choices. We discuss the performance of different loading models and their combination to reduce the weighted RMS of GPS up-coordinates. MERRA-NATML & OMCT-NTOL & MERRA-CWSL reduced the weighted RMS (WRMS) in 96 per cent (JPL solutions) and 86 per cent (SOPAC solutions) of the cases, and ECMWF-NATML & OMCT-NTOL & LSDM-CWSL reduced the WRMS in 95 per cent (JPL solutions) and 88 per cent (SOPAC solutions) of the cases. The result shows that local effects and technical uncertainties in GPS time-series hamper the meaningful comparison between GPS observations and mass loading models. Hence, simply using the RMS of the time-series as the assessment criteria may lead to biased comparison results. Nonetheless, we give a detailed comparison (differences in phase and amplitude at seasonal timescales) for eight representative stations located adjacent to great rivers, lakes and reservoirs. We find that LSDM can provide a complementary model to study the small-scale hydrological loading like loading extremes along river channels. However, such small-scale hydrological loading effects are still instable to be modelled in some regions with its current accuracy. Finally, we discuss the impacts of mass loading corrections on the velocity and noise estimates. The noise reductions have the consistent performance as WRMS reductions for most sites, whereas some sites have their noise increased even though GPS signal WRMS is decreased there, suggesting that our posterior correction is potentially feasible, but not sufficient. [ABSTRACT FROM AUTHOR]