The Greenland Ice Sheet (GrIS) is currently losing ice mass. In order to
accurately predict future sea level rise, the mechanisms driving the observed
mass loss must be better understood. Here, we combine data from the satellite
gravimetry mission Gravity Recovery and Climate Experiment (GRACE), surface
mass balance (SMB) output of the Regional Atmospheric Climate Model v. 2
(RACMO2), and ice discharge estimates to analyze the mass budget of Greenland
at various temporal and spatial scales. We find that the mean rate of mass
variations in Greenland observed by GRACE was between

During the last decade (2006–2015), the Greenland Ice Sheet (GrIS) has been
rapidly losing mass, contributing on average 0.9 mm yr

The quantities in Eq. (

The analysis of GrIS mass variations at the seasonal timescale is still
limited. This is largely because (i) the accuracy and spatial resolution of
GRACE monthly solutions is relatively poor, as compared to long-term trend
estimates, and (ii) ice velocity data at this timescale are scarce
(typically, only a few estimates per year are available, often spanning only
a few years). A first attempt to combine GRACE data and SMB modeling in
order to evaluate an ice dynamics model of the GrIS at the monthly timescale
was made by

GrIS mass balance also depends on supra-, en-, and subglacial meltwater
storage. An example is the abundance of supraglacial lakes primarily in west
Greenland, which store water during the melt season

In this study, we analyze the individual mass variation contributors (see
Eq.

In Sect. 2, we discuss the methods and data utilized. The results are presented and analyzed in Sect. 3. Finally, the conclusions are presented in Sect. 4.

The 28-mascon parameterization of Greenland used in this study for GRACE data processing. For the purpose of further analysis, these patches are merged into five drainage systems (N, NE, SE, SW, and NW). Nine mascons (filled in blue) outside Greenland are added to absorb signals from the surrounding areas. Fifty-five glaciers utilized to compute seasonal ice discharge variations are marked in red.

We use the fifth release of GRACE monthly gravity field solutions from the
Center for Space Research (CSR) at the University of Texas as input to
compute total mass variations. Each solution is provided as a set of
spherical harmonic coefficients up to degree/order
96 and supplied with a full error covariance matrix.
For the sake of consistency with previous GRACE-based estimates, we limit the
considered time interval to January 2003–December 2013. Since data for
9 months are missing, 123 months in total are used. Furthermore, a reduced
time interval (January 2003–December 2012) is also considered in order to
make the obtained estimates consistent with ice discharge data from

To estimate mass variations over Greenland at a regional scale, we make use
of a novel data processing methodology

A further description of the adopted GRACE data processing methodology is
provided in the Appendix A. In order to investigate
the robustness of GRACE-based mass anomalies, we estimate them using
different processing parameters. This leads to multiple sets of GRACE
solutions: two primary ones (estimated with and without applying data
weighting) and alternative ones. We also consider the estimates produced by
other research teams: the Jet Propulsion Laboratory (JPL) mascon
solutions by

Similar to

SMB values over 2003–2013 from three models (i.e., RACMO2.3, SNOWPACK, and
MAR3.9) are analyzed. The SMB estimates are obtained as the sum of individual
SMB components:

Time series of mass anomalies over the period 2003–2013 for the entire GrIS: total mass anomalies from GRACE produced with and without data weighting (solid blue and dashed black, respectively), cumulative SMB anomalies from RACMO2.3 (green), the difference between them, the “total–SMB” residuals (solid red and dashed pink: with and without data weighting, respectively), and cumulative ice discharge (cyan).

RACMO2.3 was developed by the Royal Netherlands Meteorological Institute
(KNMI) and Institute for Marine and Atmospheric Research (IMAU), which is a
part of Utrecht University in the Netherlands

In addition to the daily SMB provided by RACMO2.3, we use SMB output from
SNOWPACK

The MAR3.9 model was developed by the Laboratory of Climatology at the
Department of Geography, University of Liège

In this study, we integrate SMB outputs from RACMO2.3, SNOWPACK, or MAR3.9 in
time, which results in cumulative values that can be interpreted as daily SMB
mass anomalies. These values are averaged over monthly intervals for the sake
of temporal consistency with the GRACE solutions. In order to make the SMB
outputs (11 km resolution for RACMO2.3 and SNOWPACK, or 5 km in the case of
MAR3.9) spatially match the GRACE resolution (around 300 km), we process
them consistently with the GRACE data. This scheme is similar to the
GRACE-like processing of SMB data by

Greenland mean annual cycle of total mass anomalies from GRACE
produced with data weighting (dark-blue), cumulative SMB anomalies (green),
and the difference between them (brown) for the period 2003–2013. The latter
curve reflects the cumulative sum of seasonal ice discharge variations and
meltwater storage, as well as GRACE errors and SMB model bias. The shaded
strips show the 1

Previous studies on the sources of current GrIS mass loss used

We examine ice discharge from two different data sets. The first set was
presented in

In addition, we produce the second data set, which is used to examine monthly
variations of ice discharge. It covers 55 marine-terminating glaciers with
sub-annual resolution for 2009–2013. The exploited ice flow velocities were
obtained from TerraSAR-X images delivered by DLR

First, we examine multi-year mass trends and accelerations in terms of the total mass balance and the contributions thereto from SMB and ice discharge. For more details about the estimation of multi-year trend and accelerations, please refer to Appendix B.

Our estimate of the total-mass linear trend, which is based on the primary
GRACE data time series produced with optimal data weighting, is

Similar to Fig.

We also examine the SMB and ice discharge contributions to the total mass
trend. In this case, we consider the reduced time interval, 2003–2012, in
order to be consistent with the ice discharge record, which ends in 2012
(Table

Mean monthly meltwater production per calendar month (gigatonnes)
for the entirety of Greenland

Next, we present the results of a similar analysis for the individual
drainage systems. The greatest total mass losses are observed by GRACE in
drainage systems NW and SE (cf. Fig.

Estimates of seasonal meltwater storage, obtained as the monthly
deviations from the April–May and September–November linear fit of
“total–SMB” residuals (brown line in Fig.

The long-term trends of total–SMB residuals in the drainage systems of NW,
NE, and SW are consistent with the ice discharge estimates from

Monthly ice discharge estimates from 55 major marine-terminating
glaciers for the glaciers in the NW drainage system

Average accelerations of mass change anomalies over the period 2003–2012 are
also estimated using Eq. (

Linear mass change rates over the period 2003–2012 for individual
drainage systems and the entirety of Greenland: total, SMB-related, and total–SMB
residuals (GRACE–SMB), as well as ice discharge (Gt yr

We analyze the mean annual cycles of total (GRACE) and cumulative SMB
(RACMO2.3) mass anomalies over the period 2003–2013 (Fig.

Similar to Fig.

The whole-Greenland mean annual cycles of total and cumulative SMB mass
anomalies present smooth month-to-month variations (Fig.

Similar to Fig.

The total–SMB residuals show some periods of almost null variations (nearly
flat segments in Fig.

Monthly variations of ice discharge of Jakobshavn Glacier over the
period 2009–2013 (Gt yr

Hereafter, we propose a simple method with which to elucidate and quantify short-term
meltwater storage. According to RACMO2.3, meltwater is mostly produced
between May and September, and peaks in July (cf. Fig.

In order to estimate the instantaneous amount of meltwater subject to runoff,
we first fit the total–SMB residuals in two periods, before and after the
flat feature (i.e., in April–May and September–November), with a linear
function. This function can be interpreted as an empirical estimation of the
mean combined effect of ice discharge and the difference between the modeled
meltwater refreezing and the actual one. Then, we force the mass budget at
the beginning and the end of the melt season to be closed by subtracting the
obtained linear function from the total–SMB residuals (Fig.

Estimates of non-SMB mass anomalies could reflect the delayed release of
meltwater into the ocean and the variability of ice discharge. We test the
effects of ice discharge variability using a monthly resolved data set of ice
discharge for 55 glaciers in Greenland (See Fig.

Finally, we examine individual drainage systems (cf.
Figs.

In terms of the total mass, the largest meltwater accumulation takes place in
the NW and SE regions: the contribution of each region may reach around
40 Gt in July–August (cf. Figs.

As for the increase in ice discharge during the melt season, we find that it
is relatively minor for both NW and SE drainage systems (less than 20 % and
10 %, respectively; see Fig.

Note that the meltwater storage signal at the drainage system scale is present in all GRACE mascon solutions but shows some discrepancies in the timing and amplitude. This means that further effort is still needed to improve the accuracy of GRACE-based estimates.

GRACE monthly solutions have been applied to systematically analyze the mass
budget in the territory of Greenland at various temporal and spatial scales.
The obtained estimate of the mean rate of mass loss produced from CSR RL05
solutions with the new variant of the mascon approach with and without data
weighting is

Our estimates of accelerations in SMB-related (

We found a remarkable seasonal cycle in the difference between monthly total and SMB cumulative mass anomalies (“total–SMB” residuals), which likely reflects significant meltwater storage in the early summer months due to an inefficiency of the subglacial channelized network. The maximum storage is observed in July: 80–120 Gt. To estimate the potential contribution of ice discharge to the observed signals, we exploited the estimates of ice discharge over 55 outlet glaciers obtained with the flux gate method. We showed that seasonality in ice discharge is on the order of a few gigatonnes; i.e., it is negligible compared with meltwater storage. We also analyzed the short-term meltwater storage per drainage system. Our results suggest that the meltwater storage is large in NW and SE drainage systems, whereas it is weak in the northern drainage system.

A comparison of estimates derived from GRACE data with different processing parameters and from different mascon products (e.g., JPL, CSR, and GSFC) revealed the presence of the short-term meltwater storage signal in all the considered solutions. At the same time, noticeable discrepancies are observed in timing and amplitude in meltwater storage estimates. These indicates that further work is needed to improve GRACE-based estimates at both Greenland-wide and drainage system scales.

Finally, this work illustrates the potential of combining multiple observational data sets and model output complemented by simple physical constraints, to better understand the contributors to GrIS mass variations at various timescales. Improving the estimates of (natural and forced) mass variations associated with individual processes is important for robust projections of future GrIS evolution and its contribution to sea level rise.

GRACE Level 2 data and the corresponding error variance–covariance matrices used in this study are provided by the Center for Space Research at the University of Texas at Austin. The mascon product estimated by the optimal data weighting scheme is available from the authors unconditionally.

Our GRACE-based estimates of total mass variations are derived using a new
variant of the mascon approach

Parameterization of the ocean area around Greenland with one

This procedure is used to produce one of the primary solutions, referred to
as the “solution obtained with data weighting”; the other primary solution,
referred as the “solution obtained without data weighting”, is produced with
the ordinary least-squares adjustment

Same as Fig.

Contribution of different error sources to the error in the total
GrIS mass trend estimated from GRACE data both with and without data
weighting (in Gt yr

The mean mass anomalies per calendar month of the total–SMB residuals over the entirety of Greenland estimated by applying different GRACE data processing schemes.

The mean mass anomalies per calendar month of the total–SMB
residuals over the entirety of Greenland estimated from different GRACE solutions.
“BW” refers to the solution of

The mean mass anomalies per calendar month of the total–SMB residuals over the entirety of Greenland estimated from different SMB outputs.

Similar to Fig.

Acceleration of mass change over the period 2003–2012 for
individual drainage systems and the entirety of Greenland: total, SMB-related, and
total–SMB residuals (GRACE minus SMB), as well as ice discharge
(Gt yr

We approximate each mass anomaly time series (cf. Fig.

In addition, we calculate the uncertainty of the trend estimate,

In this section, we investigate the robustness of total–SMB residuals with
respect to those errors. To assess a possible impact of errors in GRACE-based
mass anomalies, we try different processing schemes in our variant of the
mascon method. The following modifications of the GRACE data processing
scheme were considered: (i) retaining a different number of eigenvalues of
the noise covariance matrix

The results are depicted in
Figs.

To assess a possible impact of uncertainties in the SMB output, we analyze
the SMB mass anomalies from RACMO2.3, SNOWPACK, and MAR3.9. As shown in
Fig.

PD, RK, and JR developed the methodology for GRACE data processing; JR processed the GRACE data; PD, MV, and JR interpreted the results based on GRACE data; MV initiated their comparison with ice discharge data; JR, MV, and PD wrote the manuscript; MvdB, TM, EE, CRS, CHR, BW, XF, MZ, and LL provided additional data; BW contributed to the GRACE-intercomparison; and all authors commented on the manuscript.

The authors declare that they have no conflict of interest.

We thank the constructive and insightful comments by the editor, Joseph MacGregor, and two anonymous reviewers. Jiangjun Ran thanks his sponsor, the Chinese Scholarship Council. Jiangjun Ran has also been partly supported by the National Natural Science Foundation of China (41474063, 41431070, and 41674084), the National Key Research and Development Program of China (2018YFC1406100), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB23030100). Miren Vizcaino is funded by the Dutch Technology Fellowship. Michiel R. van den Broeke and Bert Wouters acknowledge funding from the Polar Programme of the Netherlands Organization for Scientific Research (NWO/NPP) and the Netherlands Earth System Science Centre (NESSC). Lin Liu is funded by the Hong Kong Research Grants Council (CUHK24300414). Edited by: Joseph MacGregor Reviewed by: two anonymous referees