Mass balance of the Greenland Ice Sheet from 1992 to 2018

The Greenland Ice Sheet has been a major contributor to global sea-level rise in recent decades1,2, and it is expected to continue to be so3. Although increases in glacier flow4–6 and surface melting7–9 have been driven by oceanic10–12 and atmospheric13,14 warming, the magnitude and trajectory of the ice sheet’s mass 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. The ice sheet was close to a state of balance in the 1990s, but annual losses have risen since then, peaking at 345 ± 66 billion tonnes per year in 2011. In all, Greenland lost 3,902 ± 342 billion tonnes of ice between 1992 and 2018, causing the mean sea level to rise by 10.8 ± 0.9 millimetres. Using three regional climate models, we show that the reduced surface mass balance has driven 1,964 ± 565 billion tonnes (50.3 per cent) of the ice loss owing to increased meltwater runoff. The remaining 1,938 ± 541 billion tonnes (49.7 per cent) of ice loss was due to increased glacier dynamical imbalance, which rose from 46 ± 37 billion tonnes per year in the 1990s to 87 ± 25 billion tonnes per year since then. The total rate of ice loss slowed to 222 ± 30 billion tonnes per year between 2013 and 2017, on average, as atmospheric circulation favoured cooler conditions15 and ocean temperatures fell at the terminus of Jakobshavn Isbræ16. Cumulative ice losses from Greenland as a whole have been close to the rates predicted by the Intergovernmental Panel on Climate Change for their high-end climate warming scenario17, which forecast an additional 70 to 130 millimetres of global sea-level rise by 2100 compared with their central estimate. Three techniques for estimating mass losses from the Greenland Ice Sheet produce comparable results for the period 1992–2018 that approach the trajectory of the highest rates of sea-level rise projected by the IPCC.

The Greenland Ice Sheet holds enough water to raise mean global sea level by 7.4 m (ref. 18 ). Its ice flows to the oceans through a network of glaciers and ice streams 19 , each with a substantial inland catchment 20 . Fluctuations in the mass of the Greenland Ice Sheet occur due to variations in snow accumulation, meltwater runoff, ocean-driven melting and iceberg calving. There have been marked increases in air 21 and ocean 12 temperatures and reductions in summer cloud cover 22 around Greenland in the past few decades. These changes have produced increases in surface runoff 8 , supraglacial lake formation 23 and drainage 24 , iceberg calving 25 , glacier terminus retreat 26 , submarine melting 10,11 and ice flow 6 , leading to widespread changes in the surface elevation-particularly near the margin of the ice sheet (Fig. 1).
Over recent decades, ice losses from Greenland have made a substantial contribution to global sea-level rise 2 , and model projections suggest that this imbalance will continue in a warming climate 3 . Since the early 1990s there have been comprehensive satellite observations of changing ice sheet velocity 4,6 , elevation [27][28][29] and, between 2002 and 2016, its changing gravitational attraction 30,31 , from which complete estimates of Greenland Ice Sheet mass balance are determined 1 . Before the 1990s, only partial surveys of the ice sheet elevation 32 and velocity 33 change are available. In combination with models of surface mass balance (SMB; the net difference between precipitation, sublimation and meltwater runoff) and glacial isostatic adjustment 34 , satellite measurements, reported by the 2012 Ice Sheet Mass Balance Intercomparison Exercise (IMBIE) 1 , have shown a fivefold increase in the rate of ice loss from Greenland overall, rising from 51 ± 65 Gt yr −1 in the early 1990s to 263 ± 30 Gt yr −1 between 2005 and 2010. This ice loss has been driven by changes in SMB 7,21 and ice dynamics 5,33 . There was, however, a marked reduction in ice loss between 2013 and 2018, as a consequence of cooler atmospheric conditions and increased precipitation 15 . Although the broad pattern of change across Greenland ( Fig. 1) is one of ice loss, there is considerable variability; for example, during the 2000s just four glaciers were responsible for half of the total ice loss due to increased discharge 5 , whereas many others contribute today 33 . Moreover, some neighbouring ice streams have been observed to speed up over this period while others slowed down 35 , suggesting diverse reasons for the changes that have taken place-including their geometrical configuration and basal conditions, as well as the forcing they have experienced 36 . In this study we combine satellite altimetry, gravimetry and ice velocity measurements to produce a reconciled estimate of the Greenland Ice Sheet mass balance between 1992 and 2018, we evaluate the impact of changes in SMB and uncertainty in glacial isostatic adjustment and we partition the ice sheet mass loss into signals associated with surface mass balance and ice dynamics. In doing so, we extend a previous assessment 1 to include more satellite and ancillary data and to cover the period since 2012.

Data and methods
We use 26 estimates of ice sheet mass balance derived from satellite altimetry (9 datasets), satellite gravimetry (14 datasets) and the inputoutput method (3 datasets) to assess changes in the Greenland Ice Sheet mass balance. The satellite data were computed using common spatial 20,37 and temporal domains, and a range of models to estimate signals associated with changes in SMB and glacial isostatic adjustment. Satellite altimetry provides direct measurements of changing ice sheet surface elevation recorded at orbit crossing points 32 , along repeated ground tracks 27 or using plane-fit solutions 28 . The ice sheet mass balance is estimated from these measurements either by prescribing the density of the elevation fluctuation 38 or by making an explicit model-based correction for changes in firn height 39 . Satellite gravimetry measures fluctuations in the Earth's gravitational field computed using either global spherical harmonic solutions 30 or using spatially discrete mass concentration units 31 . Ice sheet mass changes are determined after making model-based corrections for glacial isostatic adjustment 30 . The input-output method uses model estimates of SMB 7 (the input) and satellite observations of ice sheet velocity computed from radar 6 and optical 40 imagery combined with airborne measurements of ice thickness 33 to compute changes in marine-terminating glacier discharge into the oceans (the output). The overall mass balance is the difference between the input and output. Not all annual surveys of ice sheet discharge are complete, and sometimes regional extrapolations have to be employed to account for gaps in coverage 33 . Because they provide important ancillary data, we also assess six models of glacial isostatic adjustment and ten models of surface mass balance.
To compare and aggregate the individual satellite datasets, we first adopt a common approach to derive linear rates of ice sheet mass balance over 36-month intervals (see Methods). We then compute errorweighted averages of all altimetry, gravimetry and input-output group mass trends, and combine these into a single reconciled estimate of the ice sheet mass balance using error-weighting of the group trends. Uncertainties in the individual rates of mass change are estimated as the root sum square of the linear model misfit and their measurement error, uncertainties in the group rates are estimated as the root mean square of the contributing time-series errors and uncertainties in the reconciled rates are estimated as their root mean square error divided by the square root of the number of independent groups. Cumulative uncertainties are computed as the root sum square of annual errors, an approach that has been employed in numerous studies 1,17,33,41 and assumes that annual errors are not correlated over time. To improve on this assumption, it is necessary to consider the covariance of the systematic and random errors present in each mass balance solution (see Methods).

Intercomparison of satellite and model results
The satellite gravimetry and satellite altimetry data used in our assessment are corrected for the effects of glacial isostatic adjustment, although the correction is relatively small for altimetry as it manifests as a change in elevation and not mass. The most prominent and consistent local signals of glacial isostatic adjustment among the six models we considered are two instances of uplift peaking at about 5-6 mm yr −1 , one centred over northwest Greenland and Ellesmere Island, and one Although some models identify a 2 mm yr −1 subsidence under large parts of the central and southern parts of the ice sheet, it is absent or of lower magnitude in others, which suggests that it is less certain (Extended Data Table 1). The greatest difference among model solutions is at Kangerlussuaq Glacier in the southeast, where a study 42 has shown that models and observations agree if a localized weak Earth structure associated with overpassing the Iceland hotspot is assumed; the effect is to offset earlier estimates of mass trends associated with glacial isostatic adjustment by about 20 Gt yr −1 . Farther afield, the highest spread between modelled uplift occurs on Baffin Island and beyond due to variations in regional model predictions related to the demise of the Laurentide Ice Sheet 42 . This regional uncertainty is probably a major factor in the spread across the ice-sheet-wide estimates. Nevertheless, at −3 ± 20 Gt yr −1 , the mass signal associated with glacial isostatic adjustment in Greenland shows no coherent substantive change and is negligible relative to reported ice sheet mass trends 1 . There is generally good agreement between the models of Greenland Ice Sheet SMB that we have assessed for determining mass inputparticularly those of a similar class; for example, 70% of all model estimates of runoff and accumulation fall within 1σ of their mean (see Methods and Extended Data Table 2). The exceptions are a global reanalysis with coarse spatial resolution that tends to underestimate runoff due to its poor delineation of the ablation zone, and a snow process model that tends to underestimate precipitation and to overestimate runoff in most sectors. Among the other eight models, the average surface mass balance between 1980 and 2012 is 361 ± 40 Gt yr −1 , with a marked negative trend over time (Extended Data Fig. 4) that is mainly due to increased runoff 7 . At the regional scale, the largest differences occur in the northeast, where two regional climate models predict considerably less runoff, and in the southeast, where there is considerable spread in precipitation and runoff across all models. All models show high temporal variability in SMB components, and all models show that the southeast receives the highest net intake of mass at the surface due to high rates of snowfall originating from the Icelandic Low 43 . By contrast, the southwest, which features the widest ablation zone 7 , has experienced alternate periods of net surface mass loss and gain over recent decades, and has the lowest average SMB across the ice sheet.
We assessed the consistency of the satellite altimetry, gravimetry and input-output method estimates of Greenland Ice Sheet mass balance using common spatial and temporal domains (see Fig. 2 and Methods).
In general, there is close agreement between estimates determined using each approach, and the standard deviations of annual mass balance solutions from the coincident altimetry, gravimetry and inputoutput methods are 42, 31 and 23 Gt yr −1 , respectively (Extended Data Table 3). Once averages were computed for each technique, the resulting estimates of mass balance were also closely aligned (Extended Data Fig. 6). For example, over the common period 2005-2015, the average Greenland Ice Sheet mass balance is −254 ± 18 Gt yr −1 and, by comparison, the spread of the altimetry, gravimetry and input-output method estimates is just 36 Gt yr −1 (Extended Data Table 3). The estimated uncertainty of the aggregated mass balance solution (see Methods) is larger than the standard deviation of model corrections for glacial isostatic adjustment (20 Gt yr −1 for gravimetry) and for surface mass balance (40 Gt yr −1 ), which suggests that their collective impacts have been adequately compensated; it is also larger than the estimated 30 Gt yr −1 mass losses from peripheral ice caps 44 , which are not accounted for in all individual solutions. In keeping with results from Antarctica 41 , rates of mass loss determined using the input-output method are the most negative, and those determined from altimetry are the least negative. However, the spread among the three techniques is six times lower for Greenland than it is for Antarctica 41 , reflecting differences in ice sheet size, the complexity of the mass balance processes and the limitations of the various geodetic techniques.

Ice sheet mass balance
We aggregated the average mass balance estimates from gravimetry, altimetry and the input-output method to form a single, time-varying record ( Fig. 2) and then integrated these data to determine the cumulative mass lost from Greenland since 1992 (Fig. 3). Although Greenland has been losing ice throughout most of the intervening period, the rate of loss has varied considerably. The rate of ice loss progressively increased between 1992 and 2012, reaching a maximum of 345 ± 66 Gt yr −1 in 2011, ahead of the extreme summertime surface melting that occurred in the following year 14 . Since 2012, however, the trend has reversed, with a progressive reduction in the rate of mass loss during the subsequent period. By 2018-the last complete year of our survey-the annual rate of ice mass loss had reduced to 85 ± 75 Gt yr −1 . The highly variable nature of ice losses from Greenland is a consequence of the wide range of physical processes that are affecting different sectors of the ice sheet 16,28,35 , which suggests that care should be taken when extrapolating measurements that Article are sparse in space or time. Although the rates of mass loss we have computed between 1992 and 2011 are 16% less negative than those of a previous assessment, which included far fewer datasets 1 , the results are consistent given their respective uncertainties. Altogether, the Greenland Ice Sheet has lost 3,902 ± 342 Gt of ice to the ocean since 1992, with roughly half of this loss occurring during the 6-yr period between 2006 and 2012.
To determine the proportion of mass lost due to surface and ice dynamical processes, we computed the contemporaneous trend in Greenland Ice Sheet surface mass balance-the net balance between precipitation and ablation 7 , which is controlled by interactions with the atmosphere (Fig. 3). In Greenland, recent trends in surface mass balance have been largely driven by meltwater runoff 43 , which has increased as the regional climate has warmed 13 . As direct observations of ice sheet surface mass balance are too scarce to provide full temporal and spatial coverage 45 , regional estimates are usually taken from atmospheric models that are evaluated with existing observations. Our evaluation (see Methods) shows that the finer-spatial-resolution regional climate models produce consistent results, probably due to their ability to capture local changes in melting and precipitation associated with atmospheric forcing, and to resolve the full extent of the ablation zone 46 . We therefore compare and combine estimates of Greenland SMB derived from three regional climate models: RACMO2.3p2 46 , MARv3.6 21 and HIRHAM 9 . To assess the surface mass change across the Greenland Ice Sheet between 1980 and 2018, we accumulate SMB anomalies from each of the regional climate models (Extended Data Fig. 7) and average them into a single estimate (Fig. 3). These SMB anomalies are computed with respect to the average between 1980 and 1990, which corresponds to a period of approximate balance 8 and is common to all models. In this comparison, all three models show that the Greenland Ice Sheet entered abruptly into a period of anomalously low SMB in the late 1990s and, when combined, they show that the ice sheet lost 1,964 ± 565 Gt of its mass due to meteorological processes between 1992 and 2018 (Table 1).
Just over half (50.3%) of all mass losses from Greenland-and much of their short-term variability-have been due to variations in the ice sheet's SMB and its indirect impacts on firn processes. For example, between 2007 and 2012, 70% of the total ice loss (193 ± 37 Gt yr −1 ) was due to SMB, compared with 27% (22 ± 20 Gt yr −1 ) over the preceding 15 years and 57% (139 ± 38 Gt yr −1 ) since then ( Table 1). The rise in the total rate of ice loss during the late 2000s coincided with warmer atmospheric conditions, which promoted several episodes of widespread melting and runoff 14 . The reduction in surface mass loss since then is associated with a shift of the North Atlantic Oscillation, which brought about cooler atmospheric conditions and increased precipitation along the southeastern coast 15 . Trends in the total ice sheet mass balance are not entirely due to surface mass balance, however, and by calculating the difference between these two signals, we can estimate the total change in mass loss due to ice dynamical imbalance-that is, the integrated net mass loss from those glaciers whose velocity does not equal their long-term mean (Fig. 3). Although this approach is indirect, it makes use of all the satellite observations and regional climate models included in our study, overcoming limitations in the spatial and temporal sampling of ice discharge estimates derived from ice velocity and thickness data. Our estimate shows that, between 1992 and 2018, Greenland lost 1,938 ± 541 Gt of ice due to the dynamical imbalance of glaciers relative to their steady state, accounting for 49.7% of the total imbalance (Table 1). Losses due to increased ice discharge rose    Total rates were determined from all satellite measurements over the various epochs, rates of surface mass change were determined from three regional climate models and rates of dynamical mass change were determined as the difference between the two. The period 1992-2011 is included for comparison with a previous assessment 1 , which reported a mass balance estimate of −142 ± 49 Gt yr −1 based on far fewer data. The small differences in our updated estimate are due to our inclusion of more data and an updated aggregation scheme (see Methods). Errors are 1σ.
sharply in the early 2000s when Jakobshavn Isbrae 10 and several other outlet glaciers in the southeast 47 sped up, and the discharge losses are now four times higher than in the 1990s. For the period between 2002 and 2007, ice dynamical imbalance was the major source of ice loss from the ice sheet as a whole, although the situation has since returned to being dominated by surface mass losses as several glaciers have slowed down 16 . Despite a reduction in the overall rate of ice loss from Greenland between 2013 and 2018 (Fig. 2), the ice sheet mass balance remained negative, adding 10.8 ± 0.9 mm to global sea level since 1992. Although the average sea level contribution is 0.42 ± 0.04 mm yr −1 , the 5-yr average rate varied by a factor of 5 over the 25-yr period, peaking at 0.76 ± 0.08 mm yr −1 between 2007 and 2012. The variability in ice loss from Greenland illustrates the importance of accounting for annual fluctuations when attempting to close the global sea-level budget 2 . Satellite records of ice sheet mass balance are also an important tool for evaluating numerical models of ice sheet evolution 48 . In their 2013 assessment, the Intergovernmental Panel on Climate Change (IPCC) predicted ice losses from Greenland due to SMB and glacier dynamics under a range of scenarios, beginning in 2007 17 (Fig. 4). Although ice losses from Greenland have fluctuated considerably during the 12-yr period of overlap between the IPCC predictions and our reconciled time series, the total change and average rate (0.70 mm yr −1 ) are close to the upper range of predictions (0.72 mm yr − ), which implies 70-130 mm of sea-level rise by 2100 above central estimates. The drop in ice losses between 2013 and 2018, however, shifted rates towards the lower end of projections, and a longer period of comparison is required to establish whether the upper trajectory will continue to be followed. Even greater sea-level contributions cannot be ruled out if feedbacks between the ice sheet and other elements of the climate system are underestimated by current ice sheet models 3 . Although the volume of ice stored in Greenland is a small fraction of that in Antarctica (12%), its recent losses have been ~38% higher 41 as a consequence of the relatively strong atmospheric 13,14 and oceanic 10,11 warming that has occurred in its vicinity, and it is expected to continue to be a major source of sea-level rise 3,17 .

Conclusions
We combine 26 satellite estimates of ice sheet mass balance and assess 10 models of ice sheet SMB and 6 models of glacial isostatic adjustment to show that the Greenland Ice Sheet lost 3,902 ± 342 Gt of ice between 1992 and 2018. During the common period 2005-2015, the spread of mass balance estimates derived from three techniques is 36 Gt yr −1 , or 14% of the estimated rate of imbalance. The rate of ice loss has generally increased over time, rising from 26 ± 27 Gt yr −1 between 1992 and 1997, peaking at 275 ± 28 Gt yr −1 between 2007 and 2012, and reducing to 244 ± 28 Gt yr −1 between 2012 and 2017. Just over half (1,964 ± 565 Gt, or 50.3%) of the ice losses are due to reduced SMB (mostly meltwater runoff) associated with changing atmospheric conditions 13,14 , and these changes have also driven the shorter-term temporal variability in ice sheet mass balance. Despite variations in the imbalance of individual glaciers 4,5,33 , ice losses due to increasing discharge from the ice sheet as a whole have risen steadily from 46 ± 37 Gt yr −1 in the 1990s to 87 ± 25 Gt yr −1 since then, and account for just under half of all losses (49.7%) over the survey period.
Our assessment shows that estimates of Greenland Ice Sheet mass balance derived from satellite altimetry, gravimetry and the inputoutput method agree to within 20 Gt yr −1 , that model estimates of SMB agree to within 40 Gt yr −1 and that model estimates of glacial isostatic adjustment agree to within 20 Gt yr −1 . These differences represent a small fraction (13%) of the Greenland Ice Sheet mass imbalance and are comparable to its estimated uncertainty (13 Gt yr −1 ). Nevertheless, there is still disagreement among models of glacial isostatic adjustment in northern Greenland. Spatial resolution is a key factor in the degree to which models of SMB can represent ablation and precipitation at local scales, and estimates of ice sheet mass balance determined from satellite altimetry and the input-output method continue to be positively and negatively biased, respectively, compared with those based on satellite gravimetry (albeit by small amounts). More satellite estimates of ice sheet mass balance at the start (1990s) and end (2010s) of our record would help to reduce the dependence on fewer data during those periods; although new missions 49,50 will no doubt address the latter period, further analysis of historical satellite data are required to address the paucity of data during the early years.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-019-1855-2.

Data
In this assessment, we analyse five groups of data: estimates of ice sheet mass-balance determined from three distinct classes of satellite observations (altimetry, gravimetry and the input-output method (IOM)) and model estimates of SMB) and glacial isostatic adjustment (GIA). Each dataset is computed following previously reported methods (based on refs. 28,33,38, and detailed in Supplementary Table 1) and, for consistency, they are aggregated within common spatial and temporal domains. Altogether, 26 separate ice sheet mass balance datasets were used-9 derived from satellite altimetry, 3 from the IOM and 14 from satellite gravimetry-with a combined period running from 1992 to 2018 (Extended Data Fig. 1). We also assess six model estimates of GIA (Extended Data Table 1) and ten model estimates of SMB (Extended Data Table 2).

Drainage basins
We analyse mass trends using two ice sheet drainage basin sets (Extended Data Fig. 2) for consistency with those used in the first IMBIE assessment 1 and to evaluate an updated definition tailored towards mass budget assessments. The first set comprises 19 drainage basins delineated using surface elevation maps derived from ICESat-1 with a total area of 1,703,625 km 2 (ref. 20 ). The second drainage basin set is an updated definition that considers other factors such as the direction of ice flow and includes 6 basins with a combined area of 1,723,300 km 2 (ref. 37 ). The two drainage basin sets differ by 1% in area at the scale of the Greenland Ice Sheet, and this has a negligible impact on mass trends when compared to the estimated uncertainty of individual techniques.
Glacial isostatic adjustment GIA (the delayed response of Earth's interior to temporal changes in ice loading) affects estimates of ice sheet mass balance determined from satellite gravimetry and, to a lesser extent, satellite altimetry 93 .
Here, we compare six independent models of GIA in the vicinity of the Greenland Ice Sheet (Extended Data Table 1). The GIA model solutions we considered differ for a variety of reasons, including differences in their physics, in their computational approach, in their prescriptions of solid Earth unloading during the last glacial cycle and their Earth rheology, and in the datasets against which they are evaluated. Although alternative ice histories (for example, ref. 94 ) and mantle viscosities (for example, ref. 95 ) are available, we restricted our comparison to those that contributed to our assessment. No approach is generally accepted as optimal, and so we evaluate the models by computing the mean and standard deviation of their predicted uplift rates (Extended Data Fig. 3). We also estimate the contribution of each model to gravimetric mass trends using a common processing approach 41 that puts special emphasis on the treatment of low spherical harmonic degrees in the GIA-related trends in the gravitational field. The highest rates of GIA-related uplift occur in northern Greenland, although this region also exhibits marked variability among the solutions, as does the area around Kangerlussuaq Glacier to the southeast. Even though the model spread is high in northern Greenland, the signal in this sector is also consistently high in most solutions. However, none of the GIA models considered here fully captures all areas of high uplift present in the models, and so it is possible there is a bias towards low values in the average field across the ice sheet overall. The models yield an average adjustment for GRACE estimates of the Greenland Ice Sheet mass balance of −3 Gt yr −1 , with a standard deviation of around 20 Gt yr −1 . The spread is probably due, in part, to differences in the way each model accounts for GIA in North America (which is ongoing and impacts western Greenland), and so care must be taken when estimating mass balance at the basin scale. Local misrepresentation of the solid Earth response can also have a relatively large impact stemming especially from lateral variations of solid Earth properties 42,51 , and revisions of the current state of knowledge can be expected 34 .

SMB
Here, ice-sheet SMB is defined as total precipitation minus sublimation, evaporation and meltwater runoff; that is, the interaction of the atmosphere and the superficial snow and firn layers, for example through mass exchanges via precipitation, sublimation and runoff, and through mass redistribution by snowdrift, melting and refreezing. We compare ten estimates of Greenland Ice Sheet SMB derived using a range of alternative approaches; four regional climate models (RCMs), two downscaled RCMs, a global reanalysis, two downscaled model reanalyses of climate data and one gridded model of snow processes driven by climate model output (Extended Data Table 2).
Although SMB models of similar classes tend to produce similar results, there are larger differences between classes-most notably the global reanalysis and the process model-which lead to estimates of SMB that are substantially higher and lower than all other solutions, respectively. The regional climate model solutions agree well at the scale of individual drainage sectors, with the largest differences occurring in northeast Greenland (Extended Data Fig. 4). The snow process model tends to underestimate SMB when compared with the other solutions that we have considered in various sectors of the ice sheet, at times even yielding negative SMB, while the global reanalysis tends to overestimate it.
Across all models, the average SMB of the Greenland Ice Sheet between 1980 and 2012 is 351 Gt yr −1 and the standard deviation is 98 Gt yr −1 . However, the spread among the 8 RCM and downscaled reanalyses is considerably smaller; these solutions lead to an average Greenland Ice Sheet SMB of 361 Gt yr −1 with a standard deviation of 40 Gt yr −1 over the same period. By comparison, the global reanalysis and process model lead to ice-sheet-wide estimates of SMB that are considerably larger (504 Gt yr −1 ) and smaller (125 Gt yr −1 ) than this range, respectively. Model resolution is an important factor when estimating SMB and its components, as respective contributions where only the spatial resolution differed yield regional differences. The underlying model domains were also identified as a source of discrepancy in the case of the Greenland Ice Sheet, as some products would allocate the ablation area outside the given mask.

Individual estimates of ice sheet mass balance
To standardize our comparison and aggregation of the 26 individual satellite estimates of Greenland Ice Sheet mass balance, we applied a common approach to derive rates of mass change from cumulative mass trends 41 . Rates of mass change were computed over 36-month intervals centred on regularly spaced (monthly) epochs within each cumulative mass trend time series, oversampling the individual time series where necessary. At each epoch, rates of mass change were estimated by fitting a linear trend to data within the surrounding 36-month time window using a weighted least-squares approach, with each point weighted by its measurement error. The associated mass trend uncertainties were estimated as the root sum square of the regression error and the measurement error. Time series were truncated by half the moving-average window period at the start and end of their period. The emerging rates of mass change were then averaged over calendar years to reduce the impact of seasonal cycles.
Gravimetry. We include 14 estimates of Greenland Ice Sheet ice sheet mass balance determined from GRACE satellite gravimetry that together span the period 2003-2016 (Extended Data Fig. 1). Ten of the gravimetry solutions were computed using spherical harmonic solutions to the global gravity field and four were computed using spatially defined mass concentration units (Supplementary Table 1). An unrestricted range of alternative GIA corrections were used in the formation of the gravimetry mass balance solutions based on commonly adopted model solutions and their variants 34,51-57 (Supplementary Table 1). All of the gravimetry mass balance solutions included in this study use the same degree-1 coefficients to account for geocentre motion 58 and, although an alternative set is now available 96 , the estimated improvement in certainty is small in comparison with their magnitude and spread. There was some variation in the sampling of the individual gravimetry datasets, and their collective effective (weighted mean) temporal resolution is 0.08 yr. Overall, there is good agreement between rates of Greenland Ice Sheet mass change derived from satellite gravimetry (Extended Data Fig. 5); all solutions show the ice sheet to be in a state of negative mass balance throughout their survey periods, with mass loss peaking in 2011 and reducing thereafter. During the period 2005-2015, annual rates of mass change determined from satellite gravimetry differ by 104 Gt yr −1 on average, and their average standard deviation is 31 Gt yr −1 (Extended Data Table 3).
Altimetry. We include nine estimates of Greenland Ice Sheet mass balance determined from satellite altimetry that together span the period 2004-2018 (Extended Data Fig. 1). Three of the solutions are derived from radar altimetry, four from laser altimetry and two use a combination of both (Supplementary Table 1). The altimetry mass trends are also computed using a range of approaches, including crossovers, planar fits and repeat track analyses. The laser altimetry mass trends are computed from ICESat-1 data as constant rates of mass change over their respective survey periods, whereas the radar altimetry mass trends are computed from EnviSat and/or CryoSat-2 data with a temporal resolution of between 1 and 72 months. In consequence, the altimetry solutions have an effective collective temporal resolution of 0.74 yr. Mass changes are computed after making corrections for alternative sources of surface elevation change, including glacial isostatic and elastic adjustment, and firn height changes (see Supplementary Table 1). Despite the range of input data and technical approaches, there is good overall agreement between rates of mass change determined from the various satellite altimetry solutions (Extended Data Fig. 5). All altimetry solutions show the Greenland Ice Sheet to be in a state of negative mass balance throughout their survey periods, with mass loss peaking in 2012 and reducing thereafter. During the period 2005-2015, annual rates of mass change determined from satellite altimetry differ by 121 Gt yr −1 on average, and their average standard deviation is 42 Gt yr −1 (Extended Data Table 3). The greatest variance lies among the 4 laser altimetry mass balance solutions, which range from −248 to −128 Gt yr −1 between 2004 and 2010; aside from methodological differences; possible explanations for this high spread include the relatively short period over which the mass trends are determined, the poor temporal resolution of these datasets and the rapid change in mass balance occurring during the period in question.

IOM.
We include three estimates of Greenland Ice Sheet mass balance determined from the IOM that together span the period 1992-2015 (Extended Data Fig. 1). Although there are relatively few datasets in comparison with the gravimetry and altimetry solutions, the inputoutput data provide information on the partitioning of the mass change (surface processes and/or ice dynamics) cover a considerably longer period and are therefore an important record of changes in Greenland Ice Sheet mass during the 1990s. The IOM makes use of a wide range of satellite imagery (for example, refs. 6,40,[97][98][99][100][101][102] ) combined with measurements of ice thickness (for example, ref. 103 ) for computing ice sheet discharge (output), and several alternative SMB model estimates of snow accumulation (input) and runoff (output) (see Supplementary  Table 1). Two of the IOM datasets exhibit temporal variability across their survey periods, and ywo provide only constant rates of mass changes. Although these latter records are relatively short, they are an important marker with which variances among independent estimates can be evaluated. The collective effective (weighted mean) temporal resolution of the IOM data are 0.14 yr, although it should be noted that in earlier years the satellite ice discharge component of the data are relatively sparsely sampled in time (for example, ref. 104 ).There is good overall agreement between rates of mass change determined from the input-output method solutions (Extended Data Fig. 5). During the period 2005-2015, annual rates of mass change determined from the four input-output datasets differ by up to 48 Gt yr −1 on average, and their average standard deviation is 23 Gt yr −1 (Extended Data Table 3). These differences are comparable to the estimated uncertainty of the individual techniques and are also small relative to the estimated mass balance over the period in question. In addition to showing that the Greenland Ice Sheet was in a state of negative mass balance since 2000, with mass loss peaking in 2012 and reducing thereafter, the IOM data show that the ice sheet was close to a state of balance before this period 33 .

Aggregate estimate of ice sheet mass balance
To produce an aggregate estimate of Greenland Ice Sheet mass balance, we combine the 14 gravimetry, 9 altimetry and 3 IOM datasets to produce a single 26-yr record spanning the period 1992-2018. First, we combine the gravimetry, altimetry and the IOM data separately into three monthly time series by forming an error-weighted average of individual monthly rates of ice sheet mass change computed using the same technique (Extended Data Fig. 6). At each epoch, we estimate the uncertainty of these time-series as the root mean square of their component time-series errors. We then combine the mass balance time series derived from gravimetry, altimetry and the IOM to produce a single aggregate (reconciled) estimate, computed as the error-weighted mean of mass trends sampled at each epoch. We estimated the uncertainty of this reconciled rate of mass balance as either the root mean square departure of the constituent mass trends from their weighted-mean or the root mean square of their uncertainties, whichever is larger. Cumulative uncertainties are computed as the root sum square of annual errors, on the assumption that annual errors are not correlated over time. This assumption has been employed in numerous mass balance studies 1,17,33,41 , and its effect is to reduce cumulative errors by a factor of 2.2 over the 5-yr periods we employ in this study (Table 1). If some sources of error are temporally correlated, the cumulative uncertainty may therefore be underestimated. In a recent study, for example, it is estimated that 30% of the annual mass balance error is systematic 105 , and in this instance the cumulative error may be 37% larger. On the other hand, the estimated annual error on aggregate mass trends reported in this study (61 Gt yr −1 ) are 70% larger than the spread of the independent estimates from which they are combined (36 Gt yr −1 ) (Extended Data  Table 3), which suggests the underlying errors may be overestimated by a similar degree. A more detailed analysis of the measurement and systematic errors is required to improve the cumulative error budget.
During the period 2004-2015, when all three satellite techniques were in operation, there is good agreement between changes in ice sheet mass balance on a variety of timescales (Extended Data Fig. 6). In Greenland, there are large annual cycles in mass superimposed on equally prominent interannual fluctuations as well as variations of intermediate (~5 yr) duration. These signals are consistent with fluctuations in SMB that have been identified in meteorological records 1,59 , and are present within the time series of mass balance emerging from all three satellite techniques, to varying degrees, according to their effective temporal resolution. For example, correlated seasonal cycles are apparent in the gravimetry and IOM mass balance time series, because their effective temporal resolutions are sufficiently short (0.08 and 0.14 yr, respectively) to resolve such changes. However, at 0.74 yr, the effective temporal resolution of the altimetry mass balance time series is too coarse to detect cycles on sub-annual timescales. Nevertheless, when the aggregated mass balance data emerging from all three experiment groups are degraded to a common temporal resolution of 36 months, the time series are well correlated (0.63 < r 2 < 0.80) and, over longer periods, all techniques identify the marked increases in Greenland Ice Sheet mass loss peaking in 2012. During the period 2005-2015, annual rates of mass change determined from all three techniques differ by up 162 Gt yr −1 on average, and their average standard deviation is 41 Gt yr −1 -a value that is small when compared with their estimated uncertainty (18 Gt yr −1 ) (Extended Data Table 3).

Data availability
The aggregated Greenland Ice Sheet mass balance data and estimated errors generated in this study are freely available at http://imbie.org and at the NERC Polar Data Centre, https://doi.org/10.5285/8D5FF221-A470-4CC1-B7C4-CBDF383554FC.

Code availability
The code used to compute and aggregate rates of ice sheet mass change and their estimated errors are freely available at https://github.com/ IMBIE.