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Earth Energy Imbalance (EEI) results from a net positive radiative flux at the top of atmosphere. Over 90% of this excess energy is stored as heat in the ocean causing present day ocean heat content (OHC) change. This in turn leads to volumetric or steric expansion of the water column and sea level rise. Utilizing observed bias-corrected short- and long-wave energy fluxes from the CERES project, it is possible to estimate EEI at the top of atmosphere. However, bias corrections rely on reanalysis OHC, potentially resulting in overestimation of ocean heat uptake (OHU).Combining GRACE(-FO) and altimetry observations and constructing global sea level budgets allows to derive (thermo-)steric sea level change and convert this to OHU; the latter is generally achieved considering a literatute-based ocean-mean expansion efficiency of 0.52 [W/m^2 / mm/yr]. Nonetheless, this approach is valid for global mean steric sea level change only and it is unclear to what extent one can use it for investigating regional OHU.Here, we develop a novel approach for deriving global and regional observation based OHC and OHU, which consists of three steps. (1) Fitting mass and steric spatial patterns, so called fingerprints, to GRACE(-FO) and altimetry data in a joint least-squares inversion. (2) Projecting reanalysis OHC onto the same spatial patterns that we use to explain steric variability. (3) Rescaling reanalysis OHC based on the observed steric sea level changes and reconstruction of spatial maps of OHC. These can then be further analyzed in order to derive global and regional OHU.Based on preliminary results for years 2005-01 till 2015-12, we find ~1.2 mm/yr (thermo-)steric sea level change. Global-mean OHU of 0.62 [W/m^2] can be derived from the literature expansion efficiency above, while we find 0.63 [W/m^2] from the novel rescaling approach and 0.87 [W/m^2] based on ORAS5 ocean model data only. Regionally analyzing these results regarding individual ocean contributions reveals that the ocean model seems to significantly overestimate the uptake of the Atlantic and Pacific oceans, while slightly underestimating the Indian ocean contribution.

Higher sea levels can affect the position of a coastline by increased inundation and more erosion through higher wave energy. Other morphological processes like sediment transport by currents or river discharge and sediment accumulation by plants or coastal engineering structures may enhance or counteract coastline retreat. Additionally, vertical land motions caused e.g. by extraction of gas, water or oil change the relative sea level with similar effects on the coastline as absolute sea level changes. In order to be able to assess the severity of future sea level rise and the effects on coastlines for local populations and industries, we first need to separate the effect of sea level changes on the coastline positions from the effects of vertical land motions and of morphodynamics. Here, we approach this problem by combining vertical sea surface heights from satellite altimetry measurements with horizontal coastline positions extracted from optical remote sensing images.In this case study for the barrier island of Terschelling in the Dutch part of the Wadden Sea, we quantify the different parts of the coastal geometry using geodetic and Earth observations covering a maximum time span of 30 years. For the vertical part, we show timeseries of sea surface height anomalies derived from satellite radar altimetry and compare them to recordings of two nearby tide gauges combined with vertical land motions from the available GNSS station. For the horizontal part, we show tidally corrected timeseries of cross-shore changes extracted from Landsat and Sentinel-2 imagery. A yearly Digital Elevation Model for the Netherlands from LiDAR and bathymetry observations (JARKUS) is used to test the sensitivity of the coastline position to sea level height and beach slope. In the future, the combined evaluation of sea surface and topographic heights together with the horizontal coastline positions will increase our understanding of climate change impacts on the coast. The methods designed in this case study serve as the basis for studies at other coasts.

In a warming climate, atmospheric water vapour will increase, intensifying the global water cycle. However, this ”wet-get-wetter” and ”dry-get-drier” paradigm does not hold on regional scales and models seem to contradict observations. Furthermore, it is unknown whether modelled atmospheric moisture fluxes, entering and leaving the watersheds, are mass consistent with river discharge and sinks and sources such as aquifers, soil layers and surface waters. Consequently, observational evidence of the changing water cycle components is crucial for scrutinizing models. It is also essential to assess climatic water cycle trends which have far reaching ecological and socio-economic consequences, through the occurrence of heat waves, flooding, forest fires and water availability.In this contribution, we introduce a 5 year research project, which was recently funded through the Vidi talent scheme programme of the Dutch Research Council. We will explain how we plan to use satellite gravimetry, radar altimetry, in a joint inversion scheme, to estimate water fluxes in and out of the watersheds of the North Sea region, and those of the Greater Horn of Africa. Furthermore, we’ll show how regional sea level change and vertical land motion will be consistently accounted for in the proposed estimation scheme.

Increased Greenland ice sheet melting has an impact on global mean and regional sea level rise and the ocean circulation. In this study, we explore whether Greenland melting signatures found in ocean model simulations are visible in observations from radar altimetry, satellite gravimetry and Argo floats. We have included Greenland freshwater flux (GF) in the global Finite-Element-Sea ice-Ocean Model (FESOM) for the years 1993–2016. The reference run is computed by excluding Greenland freshwater input. These experiments are performed on a low resolution (ca. 24 km) and a high resolution (ca. 6 km) eddy-permitting mesh. For comparison with the model experiments, we use different observational data, such as Argo floats, satellite observations, and reanalyses. We find that surface GF maps into signatures in temperature and salinity down to about 100 m in the surroundings of Greenland. The simulated melting signatures are particularly visible in steric heights in Baffin Bay and Davis Strait. Here, we find an improvement of the mean square error of up to 30% when including GF. For the Nordic part of the Nordic Seas, however, we find no improvement when including GF. We compare steric heights with reanalysis data and a new setup of the inversion method from gravimetric and altimetric satellite data. We cannot confirm that the GF signatures on variables such as temperature and salinity are visible in the observations on the time scales considered. However, we find that increased model resolution often causes larger improvements than occur due to including the simulated melting effect.

At the level of a watershed, the conservation of mass imposes that the net moisture transport through the atmospheric boundaries is balanced by the river discharge and an accumulation/depletion in terrestrial sources such as the soil, surface waters and groundwater.There are considerable uncertainties connected with modelled water balance components, especially since most models only simulate part of the system: either the atmosphere, the surface or the subsurface. Uncertainties in boundary conditions propagate as biases in the simulated results. For example, not accounting for anthropogenic groundwater extraction potentially introduces biases in arid regions, where groundwater is a non-negligible source of moisture for the atmosphere. The use of observations is therefore an important aid to evaluate model performances and to detect possible biases in water balance components.In this contribution, we compare total water storage changes derived from the Gravity Recovery Climate Experiment (GRACE) and its follow-on mission, with modelled components of the water balance. We use ERA5 reanalysis data to compute (net) atmospheric transports, and river discharge from GloFAS (Global Flood Awareness System). Furthermore, we use precipitation estimates (e.g. from GPCC) together with evapotranspiration from the Surface Energy Balance System (SEBS). We finally perform an accounting of the water balance components for the world’s largest watersheds and show to what extent we can find agreements, inconsistencies and biases in the data and models.

Sea level change affects hundreds of millions of people living in coastal regions. In addition to measuring the total sea level change via satellite altimetry, it is important to understand individual mass and steric contributors on global and regional scales. Consequently, deriving accurate global and regional sea level budgets is of key interest for understanding the underlying processes and aid in assessing future impacts of sea level rise. Furthermore, steric sea level change is related to the Earth’s Energy Imbalance and thus a key indicator of global warming.The global fingerprint inversion method (Rietbroek et al., 2016) allows to combine GRACE(-FO) gravity measurements and along-track satellite altimetry observations in order to jointly estimate the individual mass and steric changes in a consistent manner. We use an extended fingerprint approach which allows further separation of the ocean mass variations into contributions from the melting of land glaciers and the Greenland and Antarctic ice-sheets as well as terrestrial hydrology effects and changes of the internal mass transport within the ocean. Furthermore, the updated inversion presented here, aims at splitting the steric sea level change into contributions of the upper 700m and the deeper ocean.Here, we present the inversion results of a closed global sea level budget (within 0.1 mm/yr) during the GRACE era (2002-04 till 2015-12) attributing 1.68 mm/yr and 1.40 mm/yr to ocean mass and steric changes, respectively. Compared to state-of-the art studies the steric contribution is found to be in line while the mass estimates are slightly lower. We provide budgets for major ocean basins and compare our results to individually processed GRACE, altimetry and ocean re-analysis datasets as well as published estimates. Furthermore, we will show preliminary results when extending the inversion to incorporate additional GRACE-FO data. Finally, we extent our investigations to regional sea level budgets for selected regions of interest, such as the Bay of Bengal or the North Sea, which are dominated by completely different sea level components.

Understanding variations in the ocean heat content is tightly linked to understanding interactions of the global energy cycle with the regional water cycle. Mass, volume, temperature and density changes of the ocean water column can be estimated with complimentary observations of sea surface height from radar altimetry, ocean bottom pressure from Gravity Recovery and Climate Experiment (GRACE), temperature and salinity from Argo floats. These three techniques have their specific deficiencies and advantages, which can be exploited in a joint inversion framework in order to improve temporal and spatial coverage of oceanic temperature and salinity estimates as well as regionally varying sea level contributions. Solving an inverse problem for temperature and salinity, forward operators are formulated linking the satellite observations to temperature and salinity at depth. This is done by (1) parametrization of temperature and salinity profiles over the full depth of the ocean with B-splines to reduce dimensionality while keeping complexity of the data intact and (2) linearization of the integrated density from parameterized T/S curves. We apply forward operators in the East Indian Ocean to resolve for sea surface height, ocean bottom pressure, temperature and salinity, and assess the regional importance of these factors. We explore the stability of a joint inversion using these forward operators in combination with along-track radar altimetry, GRACE and temperature and salinity by exploring a closed-loop inversion.

GNSS velocities estimated by different analysts can significantly differ due to the choices made concerning the GNSS data processing (corrections applied and noise level of the series), the completeness of the series, the removed position discontinuities and the alignment to a terrestrial reference frame. The position discontinuities that populate the GNSS time series have probably the biggest impact on the error or dispersion of the velocity estimates at the same sites. Even when using exactly the same position series, different analysts may provide different velocity estimates and uncertainties mainly due to the choice of removing different position discontinuities.The IAG Joint Working Group 3.2 (2019 – 2023) aims at providing a global combined GNSS velocity field that takes into account the repeatability, the alignment and the relative weighting of the velocity estimates by different groups. We expect that this IAG’s unified GNSS velocity field will be useful for the scientific community inside, but especially outside, the geodetic community in areas such as tectonics, sea-level change and GIA modeling among others.In this contribution, we present the current status of the global combined velocity field, aligned to the recently released ITRF2020, and based on the velocity fields provided by several other groups.

Space geodetic estimates of ocean bottom pressure (OBP) derived by several analysis centres are evaluated. To this end, an array of 14 in situ bottom pressure recorders has been deployed between South Africa and Antarctica. The continuous measurement period of four years (2011 to 2014) and a recorder spacing of roughly 2.8 degrees latitude allows an in-depth analysis of bottom pressure variability.Our goal is to relate OBP from GRACE to in situ observations and detect which spatial and temporal features are reproduced. The recorders in the southern part of the transect generally tend to be in better agreement with GRACE and better reflect longer spatial scales of ocean bottom pressure. Over the vast expanse of the Antarctic Circumpolar Current annual and semi-annual cycles are weak (about 1cm equivalent water height (EWH)) and not reproduced well by GRACE. Variability in general amounts to a standard deviation of 2cm. This level is well captured and correlations on the order of 0.5 are found.Mean values and trends of OBP cannot be identified due to the instrumental setup. Close to the Agulhas Retroflection, signals of up to 30cm EWH are found, which cannot be resolved by GRACE. Our analysis reveals: GRACE OBP possesses longer space and time scales than in situ OBP and it misses eddy-scale signals. Filtering with DDK4 appears to be preferable to DDK6.

The impact of Greenland freshwater on oceanic variables in the North Atlantic has been controversially discussed in the past. Within the framework of the German research project GROCE (Greenland Ice Sheet Ocean Interaction), we present a comprehensive study using ocean modelling results including and excluding the Greenland freshwater flux. The aim of this study is whether signatures of Greenland ice sheet melting found in ocean model simulations are visible in the observations. Therefore, we estimate changes in temperature, salinity, steric heights and sea level anomalies since the 1990s. The observational database includes altimetric and gravimetric satellite data as well as Argo floats. We will discuss similarities/differences between model simulations and observations for smaller regions around Greenland in the North Atlantic. As these experiments are available for two different horizontal resolutions, we will furthermore be able to assess the effects of an increased model resolution.

This study addresses mapping of Argo temperature and salinity profiles onto arbitrary positions using physically advanced statistical information from model fields, and their subsequent parametrization as function of depth. Argo suffers from spatio-temporal sampling problems, and some signals are not well captured, e.g. in the deeper ocean below 2000m, around the boundary currents, in the Arctic or in the shelf/coastal regions which are not frequently visited by floats. Mapping of Argo data into sparsely sampled areas would greatly benefit from additional physical information of coherent T/S behavior in form of covariance functions. Outputs from global general ocean circulation model FESOM1.4 provide covariance information for least squares collocation and also complement the spatially undersampled Argo data in high latitudes and in deep ocean. Additionally, model covariances are used to identify areas of strong correlation with interpolation points, so that only Argo measurements inside these areas are included in the mapping procedure. Parametrization of T/S profiles is performed with b-splines where the choice of knot locations is a trade-off between accuracy and overfitting. Proposed methodology is tested in South Atlantic, but can be extended to other regions.

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).

Understanding present day sea level changes and their drivers requires the separation of the total sea level change into individual mass and steric related contributions. Total sea level rise has been observed continuously since 1993 providing a more than 25 year long time series of global and regional sea level variations. However, direct monitoring of ocean mass change has only been done since the start of the Gravity Recovery And Climate Experiment (GRACE) mission in 2002. It ended in 2017 and was succeeded by the follow-on mission (GRACE-FO) in 2018 leaving a gap of about 1 year. In the same time period of GRACE, since the early 2000s, a global array of freely drifting Argo floats samples temperature and salinity profiles of up to 2000m depth which can be converted to steric sea level change.By combining altimetry, GRACE(-FO) and Argo data sets it is possible to derive global and regional sea level budgets. The conventional approach is to analyze at least two of the data sets and derive the residual, or compare with the third one. A more recent approach is the global joint inversion method (Rietbroek et al., 2016) which fits forward-modeled spatial fingerprints to a combination of GRACE gravity data and Jason-1/-2 satellite altimetry data. This enables us, additionally, to separate altimetric sea level change into mass contributions from terrestrial hydrology, the melting of land glaciers and the ice-sheets in Greenland and Antarctica as well as contributions from steric sea level changes due to variations in ocean temperature and salinity. It also allows to include a data weighting scheme in the analysis.Here, we present global and regional sea level budget results from an updated inversion based on multi-mission altimetry (Jason-1/-2/-3, Envisat, Cryosat-2, Sentinel-3, …) providing better spatial coverage as well as new RL06 GRACE and GRACE-FO data which enables us to extend the time series of individual components of the sea level budget beyond the GRACE era from 2002-04 till 2019-06. The presented sea level budget is closed on global scale with a residual (unexplained) contribution of about 0.1 mm/yr, globally, originating in eddy-active regions. We provide consistent validation of our results against conventionally analyzed altimetry and GRACE data sets where we find agreement on global scales to be better than 0.1 mm/yr but a larger disagreement at regional scales as well as the implications of our results for deriving ocean heat content. We will also provide first results for filling the gap in the sea level budget estimates due to the gap between the GRACE and GRACE-FO missions by additionally incorporating time-variable gravity information from the Swarm mission as well as from Satellite Laser Ranging (SLR) to 5 satellites (Lageos-1/-2, Stella, Starlette, Ajisai).

Improved estimates of temperature, salinity, and sea surface height changes are computed from radar altimetry, satellite gravimetry and Argo profiles, and validated by the in situ ocean bottom pressure measurements in a South Atlantic transect of the Antarctic Circumpolar current. Using satellite gravimetry and altimetry observations, separate contributions to the global sea level can be estimated, but a regional solution is more challenging. Furthermore, Argo derived steric sea level change suffers from spatio-temporal sampling problems, and some signals are not well captured, e.g. in the deeper ocean below 2000m, around the boundary currents, in the Arctic or in the shelf/coastal regions. Jointly processing radar altimetry, Argo and data from the Gravity Recovery and Climate Experiment (GRACE), would allow to correct the deficiencies of the individual datasets, and produce observation based estimates of consistent temperature, salinity and sea surface height changes. In order to pave the way for an advanced joint inversion scheme that additionally resolves for temperature and salinity, the observation equations are formulated which link the satellite observations to temperature and salinity at depth. Observations in the South Atlantic region are compared with simulations from the FESOM model in terms of variability and the model data is used to find the spatial coherence of the signals at the sites with the surrounding ocean. The experiment is performed in the Southern Atlantic Ocean, where the estimates can be validated using an array of in situ ocean bottom pressure observations.

For many years the satellite gravity mission Gravity Recovery And Climate Experiment (GRACE) provided important insights into a large number of hydrological processes on Earth. However, to derive observations that can be used for hydrological applications many different postprocessing steps, e.g. filtering, replacement of low-degree coefficients, correction for glacial isostatic adjustment, need to be applied. Therefore, the official analysis centers meanwhile also provide postprocessed total water storage anomalies on a grid. Unfortunately, the effect of large earthquakes is usually not reduced. The resulting biases and artefact trends then bias hydrological analysis such as the detection of droughts and their severity. For the first time, we analyze the effect of large earthquake correction on GRACE-derived Drought Severity Index (DSI) over Peninsular Malaysia in the period 2003 to 2016. For this, we perform a time series analysis based on GRACE-derived total water storage anomalies, while estimating, among others, a co-seismic and post-seismic signal using a nonlinear Bayes estimator (Einarsson et al. 2010). Our results show that the earthquake correction has a significant impact on the detected drought severity, suggesting that the earthquake correction may become a standard tool in time series analysis of GRACE and GRACE-Follow-On level-3 data.

Global-mean sea level rises (GMSLR) by 3.1-3.5 mm a-1 (1993-2017) and of which about 50 % can be attributed to changes in global-mean ocean mass due to hydrological variations, mass changes of land glaciers, and mass changes of the major ice sheets in Greenland and Antarctica. The ice-sheet contributions account for more than the half of the contemporary ocean mass change and can be observed with time-variable gravimetry by the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO). In addition, geometric surface changes due to the volume change of ice sheets is also observed by polar altimetry missions. Of particular importance here is the signal of glacial isostatic adjustment (GIA) which is superimposed with ice mass change.Conventionally, the gravimetry and ice-altimetry observations are processed independently. For ocean applications, a global fingerprint inversion (Rietbroek et al., 2016) allows to estimate individual mass and steric contributors to the sea-level budget by combining GRACE and ocean-altimetry data in a joint approach. To improve the estimates of the ice-sheet contributions to GMSLR, we present first results from additionally incorporating independent ice-altimetry data over Greenland and Antarctica into the fingerprint inversion. We examine the sensitivity of the sea-level contributions to the additional ice-altimetry data (from ERS-2, Envisat, ICESat, CryoSat-2 missions) and provide validation against independent estimates. In our standard runs, GIA is accounted for as an a-priori correction during the inversion. However, we demonstrate the potential and limitations of a regional inverse approach in which GIA is separated from ice mass change over Antarctica using GRACE and ice altimetry. In our future work, we aim to parametrise and co-estimate GIA within the global inversion framework.

Sea level change is an important indicator of global warming. In order to predict future sea level changes, it becomes more and more important to understand the complex contribution of different components (steric changes, melting of ice sheets and glaciers, hydrology,…) to the total sea level change on global and regional scales.To distinguish between steric and mass-related sea level changes, we consider (1) satellite altimetry, which measures total sea level change, and (2) Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) data to derive mass changes within the Earth system. The information of both methods can be combined in a joint inversion approach to derive the individual components of sea level change. However, there is a gap of 11 months between GRACE and GRACE-FO and there are numerous (bi-)monthly gaps since 2011, which means that there is no dedicated gravity field mission to derive ocean mass changes during these times.In this contribution, we use time-variable gravity field data from the Swarm satellite mission and Satellite Laser Ranging (SLR) as an additional source of information on mass changes within the inversion approach. Thus, we are able to derive inversion results even in times without GRACE(-FO), albeit at the expense of an inevitably lower spatial resolution. We compare results with GRACE(-FO) data to those without GRACE(-FO) data. Furthermore, we quantify the leverage of Swarm and SLR on the low-resolution mass signal at basin scale in the combined inversion approach during the GRACE(-FO) lifetime.

Measuring the spatiotemporal variation of ocean mass allows for partitioning of volumetric sea level change, sampled by radar altimeters, into mass-driven and steric parts. The latter is related to ocean heat change and the current Earth's energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided monthly snapshots of the Earth's time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps occurred during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites, i.e. extending the GRACE time series. Here we utilize data from the European Space Agency's (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. For this aim, we use the integral equation approach with short arcs (Mayer-Gürr, 2006) to compute more than 500 time-variable gravity fields with different parameterizations from kinematic orbits. We investigate the potential to bridge the gap between the GRACE and the GRACE-FO mission and to substitute missing monthly solutions with Swarm results of significantly lower resolution. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating constant, trend, annual, and semiannual (CTAS) signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our CTAS Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, when artificially removing one solution. In the case of an 18-month artificial gap, 80.0 % of all CTAS Swarm solutions were found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modeling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including satellites not dedicated to gravity field studies.

The Antarctic Ice Sheet is an important indicator of climate change and driver of sea-level rise. Here we combine satellite observations of its changing volume, flow and gravitational attraction with modelling of its surface mass balance to show that it lost 2,720 ± 1,390 billion tonnes of ice between 1992 and 2017, which corresponds to an increase in mean sea level of 7.6 ± 3.9 millimetres (errors are one standard deviation). Over this period, ocean-driven melting has caused rates of ice loss from West Antarctica to increase from 53 ± 29 billion to 159 ± 26 billion tonnes per year; ice-shelf collapse has increased the rate of ice loss from the Antarctic Peninsula from 7 ± 13 billion to 33 ± 16 billion tonnes per year. We find large variations in and among model estimates of surface mass balance and glacial isostatic adjustment for East Antarctica, with its average rate of mass gain over the period 1992–2017 (5 ± 46 billion tonnes per year) being the least certain.

We present a state-of-the-art approach of passive-ocean Modified Radial Basis Functions (MRBFs) that improves the recovery of time-variable gravity fields from GRACE. As is well known, spherical harmonics (SHs), which are commonly used to recover gravity fields, are orthogonal basis functions with global coverage. However, the chosen SH truncation involves a global compromise between data coverage and obtainable resolution, and strong localized signals may not be fully captured. Radial basis functions (RBFs) provide another representation, which has been proposed in earlier works to be better suited to retrieve regional gravity signals. In this paper, we propose a MRBF approach by embedding the known coastal geometries in the RBF parameterization and imposing global mass conservation and equilibrium behavior of the oceans. Our hypothesis is that, with this physically justified constraint, the GRACE-derived gravity signals can be more realistically partitioned into the land and ocean contributions along the coastlines. We test this new technique to invert monthly gravity fields from GRACE level-1b observations covering 2005-2010, for which the numerical results indicate that: (1) MRBF-based solutions reduce the number of parameters by approximately 10%, and allow for more flexible regularization when compared to ordinary RBF solutions; and (2) the MRBF-derived mass flux is better confined along coastal areas. The latter is particularly tested in the Southern Greenland, and our results indicate that the trend of mass loss from the MRBF solutions is approximately 11% larger than that from the SH solutions, and approximately 4% ∼ 6% larger than that of RBF solutions.

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.

Radar altimetry, when corrected for tides, atmospheric forcing of the sea surface, and the effects of density variations and mean and time-variable currents, provides an along-track realization of the marine geoid. In this study we investigate whether and how such an ‘altimetric-hydrodynamic’ geoid over the North Sea can serve for validating satellite-gravimetric geoids. Our results indicate that, using ERS-2 and ENVISAT along-track altimetry and water levels from the high-resolution operational circulation model BSHcmod, we do find distinct differences in RMS fits for various state-of-the art satellite-only models (beyond degree 145 for GRACE-only, and beyond degree 185 for GOCE models) and for combined geoid models, very similar as seen in GPS-levelling validations over land areas. We find that, at spectral resolution of up to about 200, an RMS fit as low as about 7 cm can be obtained for the most recent GOCE-derived models such as GOCO05S. This is slightly above what we expect from budgeting in...

Sea level rise is perceived as a major threat to the densely populated coast of the Bay of Bengal. Addressing future rise requires understanding the present-day sea level budget. Using a novel method and data from the Gravity Recovery and Climate Experiment (GRACE) satellite, we partition altimetric sea level rise (6.1 mm/a over 2002–2014) into mass and steric components. We find that current mass trends in the Bay of Bengal are slightly above global mean, while steric trends appear much larger: 2.2–3.1 mm/a if we disregard a residual required to close the budget, and 4.3–4.6 mm/a if, as an upper bound, we attribute this residual entirely to steric expansion. Our method differs from published approaches in that it explains altimetry and GRACE data in a least squares inversion, while mass anomalies are parameterized through gravitationally self-consistent fingerprints, and steric expansion through EOFs. We validate our estimates by comparing to Argo and modeling for the Indian Ocean, and by comparing total water storage change (TWSC) for the Ganges and Brahmaputra basins to the conventional GRACE approach. We find good agreement for TWSC, and reasonable agreement for steric heights, depending on the ocean region and Argo product. We ascribe differences to weaknesses of the Argo data, but we also find the inversion to be to some extent sensitive with respect to the EOFs. Finally, combining our estimates with CMIP5-simulations, we estimate that Bay of Bengal absolute sea level may rise for additional 37 cm under the RCP4.5 scenario and 40 cm under RCP8.5 until 2050, with respect to 2005.

Besides the warming of the ocean, sea level is mainly rising due to land ice mass loss of the major ice sheets in Greenland, the West Antarctic, and the Alaskan Glaciers. However, it is not clear yet how these land ice mass losses influence regional sea level. Here, we use the global Finite Element Sea-ice Ocean Model (FESOM) to simulate sea surface height (SSH) changes caused by these ice mass losses and combine it with the passive ocean response to varying surface loading using the sea level equation. We prescribe rates of fresh water inflow, not only around Greenland, but also around the West Antarctic Ice Sheet and the mountain glaciers in Alaska with approximately present-day amplitudes of 200, 100, and 50 Gt/yr, respectively. Perturbations in sea level and in freshwater distribution with respect to a reference simulation are computed for each source separately and in their combination. The ocean mass change shows an almost globally uniform behavior. In the North Atlantic and Arctic Ocean, mass is redistributed toward coastal regions. Steric sea level change varies locally in the order of several centimeters on advective time- scales of decades. Steric effects to local sea level differ significantly in different coastal locations, e.g., at North American coastal regions the steric effects may have the same order of magnitude as the mass driven effect, whereas at the European coast, steric effects remain small during the simulation period.

Measuring the spatiotemporal variation of ocean mass allows one to partition volumetric sea level change, sampled by radar altimeters, into a mass-driven and a steric part, the latter being related to ocean heat change and the current Earth’s energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission provides estimates of the Earth’s time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites; i.e. extending the GRACE time series. Here we utilize data from the European Space Agency’s (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. We investigate the potential to bridge the gap between the GRACE missions and to substitute missing monthly solutions. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating trend, annual and semiannual signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, for 80.0 % of all investigated cases of an 18-months-gap, Swarm ocean mass was found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modelling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including non-dedicated satellites.

We investigated two ‘gap-filler’ methods based on GPS-derived low-degree surface loading variations (GPS-I and GPS-C) and a more simple method (REF-S) which extends a seasonal harmonic variation into the expected Gravity Recovery and Climate Experiment (GRACE) mission gap. We simulated two mission gaps in a reference solution (REF), which is derived from a joint inversion of GRACE (RL05) data, GPS-derived surface loading and simulated ocean bottom pressure. The GPS-I and GPS-C methods both have a new type of constraint applied to mitigate the lack of GPS station network coverage over the ocean. To obtain the GPS-C solution, the GPS-I method is adjusted such that it fits the reference solution better in a 1.5 year overlapping period outside of the gap. As can be expected, the GPS-I and GPS-C solutions contain larger errors compared to the reference solution, which is heavily constrained by GRACE. Within the simulated gaps, the GPS-C solution generally fits the reference solution better compared to the GPS-I method, both in terms of spherical harmonic loading coefficients and in terms of selected basin-averaged hydrological mass variations. Depending on the basin, the RMS-error of the water storage variations (scaled for leakage effects) ranges between 1.6 cm (Yukon) and 15.3 cm (Orinoco). In terms of noise level, the seasonal gap-filler method (REF-S) even outperforms the GPS-I and GPS-C methods, which are still affected by spatial aliasing problems. However, it must be noted that the REF-S method cannot be used beyond the study of simple harmonic seasonal variations.

Extracting large scale water storage (WS) patterns is essential for understanding the hydrological cycle and improving the water resource management of Iran, a country that is facing challenges of limited water resources. The Gravity Recovery and Climate Experiment (GRACE) mission offers a unique possibility of monitoring total water storage (TWS) changes. An accurate estimation of terrestrial and surface WS changes from GRACE-TWS products, however, requires a proper signal separation procedure. To perform this separation, this study proposes a statistical approach that uses a priori spatial patterns of terrestrial and surface WS changes from a hydrological model and altimetry data. The patterns are then adjusted to GRACE-TWS products using a least squares adjustment (LSA) procedure, thereby making the best use of the available data. For the period of October 2002 to March 2011, monthly GRACE-TWS changes were derived over a broad region encompassing Iran. A priori patterns were derived by decomposing the following auxiliary data into statistically independent components: (i) terrestrial WS change outputs of the Global Land Data Assimilation System (GLDAS); (ii) steric-corrected surface WS changes of the Caspian Sea; (iii) that of the Persian and Oman Gulfs; (iv) WS changes of the Aral Sea; and (v) that of small lakes of the selected region. Finally, the patterns of (i) to (v) were adjusted to GRACE-TWS maps so that their contributions were estimated and GRACE-TWS signals separated. After separation, our results indicated that the annual amplitude of WS changes over the Caspian Sea was 152 mm, 101 mm over both the Persian and Oman Gulfs, and 71 mm for the Aral Sea. Since January 2005, terrestrial WS in most parts of Iran, specifically over the center and northwestern parts, exhibited a mass decrease with an average linear rate of ~ 15 mm/yr. The estimated linear trends of groundwater storage for the drought period of 2005 to March 2011, corresponding to the six main basins of Iran: Khazar, Persian and Oman Gulfs, Urmia, Markazi, Hamoon, and Srakhs were − 6.7, − 6.1, − 11.2, − 9.1, − 3.1, and − 4.2 mm/yr, respectively. The estimated results after separation agree fairly well with 256 in-situ piezometric observations.

[1] We investigate the effect of water storage changes in the world's major hydrological catchment basins on global and regional sea level change at seasonal and long-term time scales. In a joint inversion using GRACE and Jason-1 data, we estimate the time-dependent sea level contributions of 124 spatial patterns (“fingerprints”) including glacier and ice sheet melting, thermal expansion, changes in the terrestrial hydrological cycle, and glacial isostatic adjustment. Particularly, for hydrological storage changes, we derive fingerprints of the 33 world's largest catchment basins, assuming mass distributions derived from the leading EOFs of total water storage in the WaterGap Global Hydrological Model (WGHM). From our inversion, we estimate a contribution of terrestrial hydrological cycle changes to global mean sea level of − 0.20 ± 0.04 mm/yr with an annual amplitude of 6.6 ± 0.5 mm for August 2002 to July 2009. Using only GRACE data in the inversion and comparing to hydrological changes derived from GRACE data directly using a basin averaging method shows a good agreement on a global scale, but considerable differences are found for individual catchment basins (up to 180%). Hydrological storage change estimates in 33 basins from the GRACE/Jason fingerprint inversion indicate a trend 46% smaller and an annual amplitude 43% bigger compared to WGHM-derived storage changes. Mapping the hydrological trends to regional sea level reveals the strongest sea level rise along the coastlines of South America (max 0.9 mm/yr) and West Africa (max 0.4 mm/yr), whereas around Alaska and Australia, we find the hydrological component of sea level falling (min −2.0 mm/yr and −0.9 mm/yr).

The mass-induced sea level variability and the net mass transport between Mediterranean Sea and Black Sea are derived for the interval between August 2002 and July 2008 from satellite-based observations and from model data. We construct in each basin two time series representing the basin mean mass signal in terms of equivalent water height. The first series is obtained from steric-corrected altimetry while the other is deduced from GRACE data corrected for the contamination by continental hydrology. The series show a good agreement in terms of annual and inter-annual signals, which is in line with earlier works, although different model corrections influence the consistency in terms of seasonal signal and trend. In the Mediterranean Sea, we obtain the best agreement using a steric correction from the regional oceanographic model MFSTEP and a continental hydrological leakage correction derived from the global continental hydrological model WaterGAP2. The inter-annual time series show a correlation of 0.85 and a root mean square (RMS) difference of 15 mm. The two estimates have similar accuracy and their annual amplitude and phase agree within 3 mm and 23 days respectively. The GRACE-derived mass-induced sea level variability yields an annual amplitude of 27 ± 5 mm peaking in December and a trend of 5.3 ± 1.9 mm/yr, which deviates within 3 mm/yr from the altimetry-derived estimate. In the Black Sea, the series are less consistent, with lower accuracy of the GRACE-derived estimate, but still show a promising agreement considering the smaller size of the basin. The best agreement is realized choosing the corrections from WaterGAP2 and from the regional oceanographic model NEMO. The inter-annual time series have a correlation and RMS differences of 0.68 and 55 mm, their annual amplitude and phase agree within 4 mm and 6 days respectively. The GRACE-derived seawater mass signal has an annual amplitude of 32 ± 4 mm peaking in April. On inter-annual time scales, the mass-induced sea level variability is stronger than in the Mediterranean Sea, with an increase from 2003 to 2005 followed by a decrease from 2006 to 2008. Based on mass conservation, the mass-induced sea level variations, river runoff and precipitation minus evaporation are combined to derive the strait flows between the basins and with the Atlantic Ocean. At the Gibraltar strait, the net inflow varies annually with an amplitude of 52 ± 10 × 10 −3 Sv peaking end of September (1 Sv = 10 6 m 3 s −1 ). The inflow through the Bosphorus strait displays an annual amplitude of 13 ± 3 ×10 −3 Sv peaking in the middle of March. Additionally, an increase of the Gibraltar net inflow (3.4 ± 0.8 × 10 −3 Sv/yr) is detected.

Dividing the sea-level budget into contributions from ice sheets and glaciers, the water cycle, steric expansion, and crustal movement is challenging, especially on regional scales. Here, Gravity Recovery And Climate Experiment (GRACE) gravity observations and sea-level anomalies from altimetry are used in a joint inversion, ensuring a consistent decomposition of the global and regional sea-level rise budget. Over the years 2002-2014, we find a global mean steric trend of 1.38 ± 0.16 mm/y, compared with a total trend of 2.74 ± 0.58 mm/y. This is significantly larger than steric trends derived from in situ temperature/salinity profiles and models which range from 0.66 ± 0.2 to 0.94 ± 0.1 mm/y. Mass contributions from ice sheets and glaciers (1.37 ± 0.09 mm/y, accelerating with 0.03 ± 0.02 mm/y(2)) are offset by a negative hydrological component (-0.29 ± 0.26 mm/y). The combined mass rate (1.08 ± 0.3 mm/y) is smaller than previous GRACE estimates (up to 2 mm/y), but it is consistent with the sum of individual contributions (ice sheets, glaciers, and hydrology) found in literature. The altimetric sea-level budget is closed by coestimating a remaining component of 0.22 ± 0.26 mm/y. Well above average sea-level rise is found regionally near the Philippines (14.7 ± 4.39 mm/y) and Indonesia (8.3 ± 4.7 mm/y) which is dominated by steric components (11.2 ± 3.58 mm/y and 6.4 ± 3.18 mm/y, respectively). In contrast, in the central and Eastern part of the Pacific, negative steric trends (down to -2.8 ± 1.53 mm/y) are detected. Significant regional components are found, up to 5.3 ± 2.6 mm/y in the northwest Atlantic, which are likely due to ocean bottom pressure variations.

The purpose of this paper is to assess the mass changes of the Greenland Ice Sheet (GrIS), Ice Sheets over Antarctica, and Land glaciers and Ice Caps with a global mascon method that yields monthly mass variations at 10,242 mascons. Input for this method are level 2 data from the Gravity Recovery and Climate Experiment (GRACE) system collected between February 2003 and June 2013 to which a number of corrections are made. With glacial isostatic adjustment (GIA) corrections from an ensemble of models based on different ice histories and rheologic Earth model parameters, we find for Greenland a mass loss of −278 ± 19 Gt/yr. Whereas the mass balances for the GrIS appear to be less sensitive to GIA modeling uncertainties, this is not the case with the mass balance of Antarctica. Ice history models for Antarctica were recently improved, and updated historic ice height data sets and GPS time series have been used to generate new GIA models. We investigated the effect of two new GIA models for Antarctica and found −92 ± 26 Gt/yr which is half of what is obtained with ICE-5G-based GIA models, where the largest GIA model differences occur on East Antarctica. The mass balance of land glaciers and ice caps currently stands at −162 ± 10 Gt/yr. With the help of new GIA models for Antarctica, we assess the mass contribution to the mean sea level at 1.47 ± 0.09 mm/yr or 532 ± 34Gt/yr which is roughly half of the global sea level rise signal obtained from tide gauges and satellite altimetry.

Weekly surface loading variations are estimated from a joint least squares inversion of load-induced GPS site displacements, GRACE gravimetry and simulated ocean bottom pressure (OBP) from the finite element sea-ice ocean model (FESOM). In this study, we directly use normal equations derived from reprocessed GPS observations, where station and satellite positions are estimated simultaneously. The OBP weight of the model in the inversion is based on a new error model, obtained from 2 FESOM runs forced with different atmospheric data sets. Our findings indicate that the geocenter motion derived from the inversion is smooth, with non-seasonal RMS values of 1.4, 0.9 and 1.9 mm for the X, Y and Z directions, respectively. The absolute magnitude of the seasonal geocenter motion varies annually between 2 and 4.5 mm. Important hydrological regions such as the Amazon, Australia, South-East Asia and Europe are mostly affected by the geocenter motion, with magnitudes of up to 2 cm, when expressed in equivalent water height. The chosen solar radiation pressure model, used in the GPS processing, has only a marginal effect on the joint inversion results. Using the empirical CODE model slightly increases the annual amplitude of the Z component of the geocenter by 0.8 mm. However, in case of a GPS-only inversion, notable larger differences are found for the annual amplitude and phase estimates when applying the older physical ROCK models. Regardless of the used radiation pressure model the GPS network still exhibits maximum radial expansions in the order of 3 mm (0.45 ppb in terms of scale), which are most likely caused by remaining GPS technique errors. In an additional experiment, we have used the joint inversion solution as a background loading model in the GPS normal equations. The reduced time series, compared to those without a priori loading model, show a consistent decrease in RMS. In terms of the annual height component, 151 of the 189 stations show a reduction of at least 10% in seasonal amplitude. On the ocean floor, we find a positive overall correlation (0.51) of the inversion solution with time series from globally distributed independent bottom pressure recorders. Even after removing a seasonal fit we still find a correlation of 0.45. Furthermore, the geocenter motion has a significant effect on ocean bottom pressure as neglecting it causes the correlation to drop to 0.42.

Meltwater from the Greenland Ice Sheet (GIS) has been a major contributor to sea level change in the recent past. Global and regional sea level variations caused by melting of the GIS are investigated with the finite element sea-ice ocean model (FESOM). We consider changes of local density (steric effects), mass inflow into the ocean, redistribution of mass, and gravitational effects. Five melting scenarios are simulated, where mass losses of 100, 200, 500, and 1000 Gt/yr are converted to a continuous volume flux that is homogeneously distributed along the coast of Greenland south of 75°N. In addition, a scenario of regional melt rates is calculated from daily ice melt characteristics. The global mean sea level modeled with FESOM increases by about 0.3 mm/yr if 100 Gt/yr of ice melts, which includes eustatic and steric sea level change. In the global mean the steric contribution is one order of magnitude smaller than the eustatic contribution. Regionally, especially in the North Atlantic, the steric contribution leads to strong deviations from the global mean sea level change. The modeled pattern mainly reflects the structure of temperature and salinity change in the upper ocean. Additionally, small steric variations occur due to local variability in the heat exchange between the atmosphere and the ocean. The mass loss has also affects on the gravitational attraction by the ice sheet, causing spatially varying sea level change mainly near the GIS, but also at greater distances. This effect is accounted for by using Green's functions.

We have studied the ability of the GRACE gravimetry mission and Jason-1 altimetry to resolve ice and glacier induced contributions to sea level rise, by means of a fingerprint method. Here, the signals from ice sheet and land glacier changes, steric changes, glacial isostatic adjustment and terrestrial hydrology are assumed to have fixed spatial patterns. In a joint inversion using GRACE and Jason-1 data the unknown temporal components can then be estimated by least-squares. In total, we estimate temporal components for up to ∼ 80 individual patterns. From a propagation of the full error-covariance from GRACE and a diagonal error-covariance from Jason-1 altimetry we find that: (1) GRACE almost entirely explains the mass related parameters in the joint inversion, (2) an inversion using only Jason-1 data has a marginal ability to estimate the mass related parameters, while the steric parameters have much better formal accuracy. In terms of mean sea level rise the steric patterns have a maximum formal accuracy of 0.01 mm for an 11 week running mean. In general, strong negative error correlations ( ρ Z direction. Total geocenter motion rates are found to be −0.28, 0.43, −1.08 mm/year for the X , Y and Z components, respectively. The inversion results have been propagated to the Jason-1 along-track measurements. Over the time period considered, we see that a large part of the variability in the Pacific, Atlantic and Indian ocean can be explained by our inversion results. The applied inversion method therefore seems a feasible way to separate steric from mass induced sea level changes. At the same time, the joint inversion would benefit from more advanced parameterizations, which may aid in fitting remaining signal from altimetry.

In an effort to learn more about the sub-monthly variations in the global mass transport processes of the Earth, a study has been performed in which the feasibility of using weekly GRACE gravity solutions, in combination with GPS displacement data and ocean bottom pressure (OBP) models, is examined. A sensitivity study was conducted in which a range of solutions using different combinations of these three data sets were compared to each other, and with the time span of each combination ranging from 1 to 4 weeks. Data sets included weekly GFZ RL04 GRACE covariance matrices, as well as IGS GPS solutions and a new FESOM global OBP model, developed at AWI. The results showed that the temporal resolution of the solutions could be increased, while still maintaining reasonable levels of accuracy, if either GPS or OBP data were included in the combination. In particular, a 2-week triple combination of GRACE, GPS and OBP data was found to have approximately the same accuracy over land as a standard monthly GRACE solution, up to degree and order 30. These results provide encouraging support for future work involving real-data combinations.

[1] We derive changes in ocean bottom pressure (OBP) and ocean mass by combining modeled ocean bottom pressure, weekly GRACE-derived models of gravity change, and large-scale deformation patterns sensed by a global network of GPS stations in a joint least squares inversion. The weekly combination allows a consistent estimation of geocenter motion, loading mass harmonics up to degree 30, and a spatially uniform mass correction term, which serves as a correction for forcing of the ocean model. We provide maps and time series of ocean mass and bottom pressure variations. Furthermore, we discuss the estimated geocenter motion and the estimated model correction. Our results indicate that the total ocean mass change is predominantly annual, with a maximum amplitude corresponding to 7.4 mm in October, which is in line with earlier work. The mean ocean bottom pressure (i.e., ocean plus atmospheric mass) shows an annual amplitude of 8.7 mm and is shifted forward by about 1.5 months. In addition, the solution exhibits typical autocorrelation times of about 2 weeks. A comparison with in situ bottom pressure time series in the southern Indian Ocean shows a good agreement, with correlations of 0.7-0.8. Based on these comparisons, we see that our results monitor realistic submonthly variations, which are strongest at high latitudes. The addition of GRACE data in the inversion is found to improve these high-latitude variations and enables better separability of the geocenter motion from other unknowns. Increasing the OBP model error from 3 cm to 4.8 cm affects mainly the higher-degree coefficients.

We have analyzed recent gravity recovery and climate experiment (GRACE) RL04 monthly gravity solutions, using a new decorrelating post-processing approach. We find very good agreement with mass anomalies derived from a global hydrological model. The post-processed GRACE solutions exhibit only little amplitude damping and an almost negligible phase shift and period distortion for relevant hydrological basins. Furthermore, these post-processed GRACE solutions have been inspected in terms of data fit with respect to the original inter-satellite ranging and to SLR and GPS observations. This kind of comparison is new. We find variations of the data fit due to solution post-processing only within very narrow limits. This confirms our suspicion that GRACE data do not firmly ‘pinpoint’ the standard unconstrained solutions. Regarding the original Kusche (J Geod 81:733–749, 2007) decorrelation and smoothing method, a simplified (order-convolution) approach has been developed. This simplified approach allows to realize a higher resolution—as necessary, e.g., for generating computed GRACE observations—and needs far less coefficients to be stored.

ArticlePublished: 10 December 2019This is an unedited manuscript that has been accepted for publication. Nature Research are providing this early version of the manuscript as a service to our customers. The manuscript will undergo copyediting, typesetting and a proof review before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers apply.Mass balance of the Greenland Ice Sheet from 1992 to 2018The IMBIE TeamNature (2019)Cite this article6914 Accesses1410 AltmetricMetricsdetailsAbstractIn recent decades, the Greenland Ice Sheet has been a major contributor to global sea-level rise1,2, and it is expected to be so in the future3. Although increases in glacier flow4–6 and surface melting7–9 have been driven by oceanic10–12 and atmospheric13,14 warming, the degree and trajectory of today’s imbalance remain uncertain. Here we compare and combine 26 individual satellite measurements of changes in the ice sheet’s volume, flow and gravitational potential to produce a reconciled estimate of its mass balance. Although the ice sheet was close to a state of balance in the 1990s, annual losses have risen since then, peaking at 335 ± 62 billion tonnes per year in 2011. In all, Greenland lost 3,800 ± 339 billion tonnes of ice between 1992 and 2018, causing the mean sea level to rise by 10.6 ± 0.9 millimetres. Using three regional climate models, we show that reduced surface mass balance has driven 1,971 ± 555 billion tonnes (52%) of the ice loss owing to increased meltwater runoff. The remaining 1,827 ± 538 billion tonnes (48%) of ice loss was due to increased glacier discharge, which rose from 41 ± 37 billion tonnes per year in the 1990s to 87 ± 25 billion tonnes per year since then. Between 2013 and 2017, the total rate of ice loss slowed to 217 ± 32 billion tonnes per year, on average, as atmospheric circulation favoured cooler conditions15 and as ocean temperatures fell at the terminus of Jakobshavn Isbræ16. Cumulative ice losses from Greenland as a whole have been close to the IPCC’s predicted rates for their high-end climate warming scenario17, which forecast an additional 50 to 120 millimetres of global sea-level rise by 2100 when compared to their central estimate.