Anomalous acceleration of mass loss in the Greenland ice sheet 
drainage basins and its contribution to the sea level fingerprints 
during 2010–2012

Abstract. The sea level rise contributed from ice sheet melting has been accelerating due to global warming. Continuous melting of the Greenland ice sheet (GrIS) is a major contributor to sea level rise, which impacts directly on the surface mass balance and the instantaneous elastic response of the solid Earth. To study the sea level fingerprints (SLF) caused by the anomalous acceleration of the mass loss in GrIS can help us to understand drivers of sea level changes due to global warming and the frequently abnormal climate events. In this study, we focus on the anomalous acceleration of the mass loss in GrIS at the drainage basins from 2010 to 2012 and on its contributions to SLF and relative sea level (RSL) changes based on self-attraction and loading effects. Using GRACE monthly gravity fields and surface mass balance (SMB) data spanning 13 years between 2003 and 2015, the spatial and temporal distribution of the ice sheet balance in Greenland is estimated by mascons fitting based on six extended drainage basins and matrix scaling factors. Then the SLF spatial variations are computed by solving the sea level equation. Our results indicate that the total ice sheet mass loss is contributed from few regions only in Greenland, i.e., from the northwest, central west, southwestern and southeastern parts. Especially along the north-west coast and the south-east coast, ice was melting significantly during 2010–2012. The total mass loss rates during 2003–2015 are −288±7 Gt/yr and −275±1 Gt/yr as derived from scaled GRACE data and SMB respectively; and the magnitude of the trend increased to −456±30 Gt/yr and to −464±38 Gt/yr correspondingly over the period 2010–2012. The residuals obtained by GRACE after removing SMB show a good agreement with the surface elevation change rates derived from pervious ICESat results, which reflect a contribution from glacial dynamics to the total ice mass changes. Melting of GrIS results in decreased RSL in Scandinavia and North Europe, up to about −0.6 cm/yr. The far-field peak increase is less dependent on the precise pattern of self-attraction and loading; and the average global RSL was raised by 0.07 cm/yr only. Greenland contributes about 31 % of the total terrestrial water storage transferring to the sea level rise from 2003 to 2015. We also found that variations of the GrIS contribution to sea level have an opposite V shape (i.e., from rising to falling) during 2010–2012, while a clear global mean sea level drop also took place (i.e., from falling to rising).



Introduction
The sea level rise due to melting of ice sheets, glaciers and ice caps has been accelerating in consequence of global warming.The mass change of polar ice sheets is a major global concern, especially due to its direct impact to global sea level rise (Forsberg et al., 2017).Estimation of the global ice balance has been obviously improved in recent years based on available satellite observations, model simulations and the development of data processing technologies, e.g., using the Gravity Recovery and Climate Experiment (GRACE) (Rodell et al., 2009;Jacob et al., 2012;Velicogna et al., 2014) and the Ice, Cloud, and land Elevation Satellite (ICESat) (Zwally et al., 2011;Shepherd et al., 2012;Gardner et al., 2013).In the last decade, most studies have confirmed that significant mass loss takes place in the ice sheets of Greenland and Antarctica, which corresponds to approximately 7 m and 57 m of the sea level rise respectively when the mass is completely melted (Bamber et al., 2001;Lythe et al., 2001).Therefore, there is a high demand to monitor the trend in mass balance changes over Greenland and Antarctica to better understand global climate change and associated sea level rise.
Due to global warming, frequency and intensity of extreme weather events (i.e., snowstorms, cold currents, torrential rains, heat waves, etc.) are increasing globally.
Since the early 1990s, satellite data show that the global mean sea level has been rising by about 3 mm/yr.Numerous scientific papers on ice sheet changes and their contribution to sea level rise have been published based on satellite observations over the last decade, but we still need to focus on the continental ice mass balance caused during La Niña is related to water temporarily moved from the oceans to the land, when precipitation increased over Australia, northern South America, and Southeast Asia, while it decreased over the oceans.Increased precipitation in Australia is proven to be the dominant contributor to the global total sea level change in 2011 (Boening et al., 2012;Fasullo et al., 2013).(Rignot et al., 2011).White dots show ice caps in Greenland and surrounding areas.
It is well known that the Greenland ice sheet (GrIS) plays an important role in Earth system dynamics, which not only affects sea level but also contributes to the elastic response of the solid Earth.Here, we present detailed mass balance results for the GrIS drainage basins by estimating the anomalous acceleration of the mass loss and its contributions to sea level fingerprints (SLF).Figure 1 shows Greenland ice drainage units, named Rignot Basins from IMBIE 2016 (Ice Sheet Mass Balance Intercomparison Experiment), which are based on historical usage (Rignot et al., 2011).The GrIS is divided into six regions based on the glacier regime.Central west The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.and northwest have a clear basin boundary near Rinks.Central west to southwest mark the transition from tidewater to land-terminating.Southeast vs northeast chiefly represents a transition in the surface mass balance (SMB) with a well-defined divide inland.We use GRACE monthly gravity fields and the monthly cumulative SMB from the Regional Atmospheric Climate Model (RACMO) to estimate the spatial distribution of the ice mass balance.The time series of mass changes were estimated by a mascon fitting method described by Jacob et al. (2012).The relative sea level (RSL) spatial variations were computed by solving the sea level equation with self-attraction and loading effects.Based on the above results, we further discuss the sensitivity kernels and rescaled GrIS time series due to the limitation of exact-defined basin mask and GRACE resolution; we also analyze spatial variations of the abnormal melting in glaciers, near-surface air temperature over Greenland and contributions of GrIS to sea level changes.

GRACE
The GRACE mission design makes it particularly useful for surface mass variations studies.GRACE was jointly launched by NASA and the German Aerospace Center (DLR) in March 2002 (Tapley et al. 2004).The Level-2 gravity products provide complete sets of spherical harmonic (Stokes) coefficients, typically up to the maximum degree/order l max =120, averaged over monthly intervals.Detection of mass change using GRACE data becomes a widely used tool for estimation of the ice sheet mass balance due to the operational difficulties of other measurements over large areas.However, interpretation of GRACE data is complicated by the intrinsic mixing of gravity signals.Glacial isostatic adjustment (GIA) can be corrected by modeling the lithospheric response to loading changes (Velicogna and Wahr, 2006) 2013) are used to remove the GIA effect.

SMB
In several studies RACMO and the Firn Densification Model (FDM) have been applied for Greenland using different models at different resolutions and with various forcing at the boundaries.To further compare and validate the GRACE-derived mass changes, we use monthly SMB fields to simulate GrIS mass balance from RACMO version 2.3 (RACMO2.3),which are provided on a grid of about 40 vertical layers and a horizontal resolution of ~11×11 km 2 for the period January 1958-December 2015 (Noël et al., 2015).Then we analyze the spatial and temporal patterns of glacial dynamics components combining GRACE and SMB data.The latest version of RACMO2.3 has been specifically developed to simulate SMB of glaciated regions as an updated version of RACMO2.1 (Ettema et al., 2009;Van Angelen et al., 2014).Figure 2  In this study, we first used the GrIS mask as prescribed in RACMO2.3 to remove effects of the ice caps from entire SMB in Greenland and integrated them over time to get accumulated SMB values.Because SMB represents the sum of mass fluxes inside and away from ice sheets, the mass balance of the grounded ice sheet is governed by the difference between SMB and the solid ice discharge across the grounding line.
Thus, the ice discharge must be subtracted from the accumulated SMB (SMB minus ice discharge) to be compared with GRACE (van den Broeke et al., 2016).After removing the temporal average of the accumulation rates at each point, we convert SMB data to the spectral domain and truncate them to degree 60, i.e., the limit of the GRACE data.

Other datasets
Initially, we employed the Noah land hydrology model (version 2) in the Global Land Data Assimilation System (GLDAS-2) to remove continental water mass contributions, but we found that there is a large error in the results.The global GLDAS/Noah, which possesses monthly intervals with a spatial resolution of 1.0 degree, provides a total amount of the water stored in all layers, snow, and canopy, but The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.
does not include the groundwater and water storage changes in rivers or lakes (Rodell et al., 2004).It also excludes the water storage estimates from the GrIS and permafrost areas (Liu et al., 2016).Likely, the abnormally large snow values obtained for Greenland are a result of unreliable forcing data.We simulated mass changes from the soil moisture component and found that the soil moisture from GLDAS is dominated by the annual cycle and the annual amplitudes are much smaller than the GrIS change.Finally, we ignored the terrestrial water storage (e.g., mainly presented as seasonal changes, no obvious long-term trend) impacts on the mass change in Greenland and assumed that the mass balance revealed by GRACE data is mainly due to ice sheet changes.
A previous study based on satellite-derived ice-surface temperature has confirmed a positive trend of the near surface temperature of GrIS and two major melt events from 2000 to present (Hall et al., 2013).Therefore, we chose the temperature data from the averaged over 2-months intervals.The GIA correction has been applied to the data (Beckley et al., 2017).To estimate steric sea level anomalies, we used time series of 3-month total steric sea level anomaly data, which is a contribution of the changes in the global ocean heat storage for the 0-700 m and 0-2000 m layers (the total steric sea level anomaly data was downloaded from NOAA, available at: https://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/basin_fsl_data.html).

Spatial Averaging and scaling factor methods
Observations of mass variability are, in particular, useful for estimates of changes of continental water storage.These water storage changes are generally addressed by constructing specific averaging functions optimized for each region (Swenson and Wahr, 2002).Note that the averaging kernel method implies a Gaussian averaging function at each point, and sums those averaging functions expressed as the finite number of harmonic degrees in the GRACE solution (e.g.l max = 60 for CSR solutions).
Thus, the optimal averaging kernel technique provides an estimate of the total mass change of the region but does not give accurate estimates of sub-regions, such as those in Figure 1, due to the spatial resolution of the GRACE data.Therefore, the effect of mass changes is spread up to several hundred kilometers outside the region.In this case, we applied an approximation mascon fitting method to GRACE and SMB data to perform a comparison at the regional level.This fitting method is based on the least squares mascon approach to calculate the averaged time series for each region (Jacob et al., 2012;Sutterley et al., 2014).To evaluate the spatial differences in the melting of GrIS at a regional scale, we divided the ice sheet into six extended mascons as shown in Figure 3, and each mascon was composed of small blocks defined on a 0.5-degree grid; a unit mass equal to 1 cm of water was distributed uniformly over the block (Farrell 1972).We applied a 150-km Gaussian smoothing function on the Stokes coefficients for the GRACE (GIA corrected), SMB and all mascon coefficients.
We simultaneously fit the extended mascon Stokes coefficients, in which GrIS is represented by a single basin, to monthly GRACE coefficients (after post-processing described in section 2.1) to obtain estimates of monthly mass variability for each mascon.The corresponding result in terms of time series of entire GrIS is shown in Figure 4.When using extended mascons, the mass loss is assumed to be uniformly distributed over mascons, which is not the case everywhere (e.g., because there is no or relatively small mass change over the oceans).Thus, it is necessary to identify a realistic scaling factor.Assuming that there is a 1 cm uniform layer over exact and extended GrIS, the total mass is 17.495 Gt and 39.303 Gt, respectively.We used the exact Greenland mascon as the input to fit the extended mascon to the input signal.In this way, the 0.537 cm uniform mass is obtained over the extended GrIS, which is equivalent to a 46% reduction in ice thickness of the input mass, which is in good agreement with previous studies based on averaging functions extended outside Greenland (Velicogna and Wahr, 2006).The final scaling factor of the mass inferred is (39.303/17.495)×0.537=1.206.Therefore, the mass changes estimated with the extended mascon are larger by a factor of 1.206 when degree and order of Stokes coefficients are limited to 60 (Figure 4).We take into account the fact that the effect of each mascon could smear into the neighboring ones.Supposing that the mass spread is uniform over the truly mascon i, we computed the Stokes coefficients from the input mass, and then fit extended mascon k to the set of Stokes coefficients.Basing on the scaling method described above, those values can be used to construct a ratio matrix A(k,j), which is the contribution of those Stokes coefficients to the result for mascon k .Time series for selected regions were calculated using the corresponding mascons to fit GRACE Stokes coefficients.If M(j) are the true mascon values, and N(k) are the values that we get from the mascon fitting, then the linear observation equations is !" = $(", ')×*(') + ,-.
. Therefore, the true mascon values may be solved in a generalized inversion by * ' = $ /. (", ')×!.This method not only estimates the total mass change but also provides time series for each sub-area after the leakage correction.
However, it is worth noting that the extended mascon increases the weight of the boundary in the sensitivity kernels and also causes external leakage in the fitting results, e.g., mass change from the external glaciers, ice caps and eustatic sea level.The sensitivity kernels and leakage effects are explained in details in Section 4.1.

Sea level fingerprint
The global SLF reflects the redistribution of ocean-land masses driven by climate change; and these load changes cause the elastic structural response of the crust and affect the viscosity and strength of the lower mantle of the Earth (Peltier and Andrews, 1976).RSL changes, for instance, caused by GIA span over a time scale of 1 to 10000 years.However, for shorter time scales (1 to 100 years), melting of ice sheets, glaciers and ice caps directly leads to increase of ocean volume and causes instantaneous elastic deformation of the solid Earth.RSL is the height of the sea surface relative to the sea floor, which is defined as the difference between the geoid and the crust.The RSL solution is often referred as the fingerprint of terrestrial mass changes.
In this study we use scaled monthly (1 degree × 1 degree) mass change grids of GrIS as input to solve the self-consistent sea level equation (Farrell and Clark, 1976;Milne et al., 1999) and calculate regional SLF due to self-attraction and loading effects (Tamisiea, 2010) of mass changes on Greenland.We use the load Love numbers given by Jentzsch (1997), which were calculated using the 1-D PREM elastic Earth model (Dziewonski and Anderson, 1981).We also consider the Earth rotation feedback but neglect changes in the coastline and effects of atmospheric and non-tidal ocean loading for short-term sea level variations during 2003 to 2015.

Spatial GrIS variability
The spatial pattern of long-term mass trend, shown in Figure 5 Especially important is that during 2010-2012 a large mass loss is revealed in the 286 entire southern and western regions of Greenland (Figure 5b), which reflects a major 287 melting event that took place in this period.For example, the anomalous warm 288 summer and declined albedos associated with the north Atlantic oscillation led to 289 increased temperatures over Greenland in 2010 (Box et al., 2012).Consequently, the 290 extreme melt event took place over almost the entire surface of the GrIS in 2012 291 (Nghiem et al. 2012).

Time series of mass change
In order to obtain time series of GrIS mass changes we applied the basin estimation and scaling method described in Section 2 (Figure 7).Representing GrIS by single and extended mascons, we found that the scaled trend rate (-269 Gt/yr when l max =60 shown in Figure 4)  For GrIS drainage basins at the regional scale, the melting rate of GrIS in the southern part is significantly higher than in the northern part.The mass loss in the north and northeast was less than -31 Gt/yr for both GRACE andSMB during 2003-2015, and the mass loss of the other four basins (i.e., northwest, central west, south west and southeast) were several times larger than the ones in the two northern regions.The time series of GRACE and SMB revealed that almost all regions experienced large mass losses in 2010-2012.In the southwest and southeast, we found an anomalous acceleration of the mass loss of -118±18 Gt/yr and -112±17 Gt/yr in GRACE and -184±16 Gt/yr and -89±11 Gt/yr in SMB, respectively.The contribution of these two regions is responsible for about 50% of the total loss.In addition, we also found that the melting rate of ice sheets from SMB was greater than the estimates derived from GRACE in the southwest and northeast.This difference indicates that SMB may ).In addition, the surface ice elevation was changed by fast-flowing ice dynamics in the southwestern and northeastern areas (Hurkmans et al., 2014).Since 2013, the mass loss slowed down and recovered in the GrIS drainage basins.The agreement between GRACE and SMB results also confirm that the ice sheets returned to near-normal melt conditions, i.e., the refreezing process reduced the melt extent back to normal conditions (Nghiem et al., 2012).

Sea level fingerprints induced by GrIS
The distribution of GrIS mass changes directly affects the combined contributions of the sea level self-attraction and loading as well as of the ocean-land mass balance resulting in differences in the global sea level distribution (Figure 8).Melting of ice sheets is confirmed over entire Greenland, especially in the southern part and along the coasts (Figure 6).This mass loss of GrIS caused RSL lowering in the entire Arctic Circle, for instance, negative changes of RSL in Scandinavia and Northern Europe up to about -0.6 cm/yr (Figure 8a).It should be noted that the mass loss of Greenland mainly increases RSL in tropical and southern latitudes due to the isostatic rebound of the sea floor around Greenland (Figure 8b).  the melting of Antarctica affects the United States.These regional differences are significant if we consider the global melting of ice sheets, glaciers and ice caps.For instance, the amount of ice mass melt in the northern hemisphere is higher than in the southern hemisphere, resulting in apparent RSL rise in the South America, South Africa, and Australia, what is nearly 30% higher than the global mean sea level rise rate (Mitrovica et al., 2001;Bamber et al., 2009).In addition, induced by the mass loss of GrIS, the mean RSL trend is approximately 0.07 cm/yr extending through Alaska, Mexico and northern Africa (solid blue line in Figure 8).This pattern illustrates that the dynamic sea level change is determined by the ocean-land mass redistribution and by the instantaneous elastic response of the lithosphere.

Sensitivity kernels and rescaling
As an example of the averaging kernel, Figure 9 shows the sum of the sensitivity kernels for all exact and extended mascons shown in Figure 3. Ideally, the solution for mascon fitting would recover the true spatial average of the mascons' mass.When mascons are fitted for the exact-defined GrIS drainage sub-areas (Fig. 3a), the results are automatically scaled.The effective scaling factor based on the least squares mascon approach is defined assuming that surface masses are spread uniformly across any mascon.This method will give exactly the right total mass for that mascon, and will give 0 for the other mascons.However, similar to the optimal averaging kernel method, the mascon fitting based on an exact-defined basin mask (i.e., truly six drainage basins) will also cause weakening of the signal or large uncertainty (e.g., leakage and bias).This is especially the case in boundary areas, which largely contribute to the mass loss, because of the finite number of harmonic degrees in the GRACE solution.Previous studies suggest that an increasing of the number of mascons covering the anomaly might reduce leakage, so that the anomaly is almost constant across each individual mascon (Jacob et al., 2012).However, there are also indications that using more and smaller mascons can lead to the drawback that the inversion relies more on the higher harmonic degrees.
For six sub-areas of the extended mascon (Figure 9b), we assessed a potential impact of the non-uniformity over the exact mascons and external mascons.For the leakage effects, we first computed the mascon distribution between sub-regions, and then we obtained the scale factors by fitting the six extended mascons to the corresponding exact mascons (Table 1).To confirm the validity of signal recovery based on this scaling method, we also used two different regional average methods to compare the results.One method represents a data-driven approach, which is able to restore the GRACE signal loss due to filtering independent of the catchment size (Vishwakarma et al., 2016;2017).Another method implies scaled optimal averaging functions to recover unbiased mass estimates for six basins (Velicogna and Wahr, 2006).fitting in the northeast accompanied by the regional average based on the optimal averaging kernel and data-driven approach.
Exemplarily, Figure 10 shows a validation with the time series comparison between the results from the exact mascon fitting and the extended mascon fitting after rescaling in the northeast.The results confirm that the exact mascon fitting cannot accurately extract the melting contribution of glaciers close to the border (i.e., sensitivity kernel less than 1 shown in Figure 9a).Consequently, the time series from the exact mascon fitting in the northeast show an increasing trend, what is inconsistent with the actual situation and contradicts most previous studies (Velicogna et al., 2014;Sutterley et al., 2014).In addition, the time series obtained by the other two methods also confirm the mass loss trend of ice sheets in the northeast.However, the optimal averaging kernel after scaling may include leakage in other regions and a data-driven approach shows a large noise error in the time series.This is mainly due to the fact that the optimal averaging kernels were created to isolate the gravity signal of individual regions while simultaneously minimizing the effects of GRACE observational errors and contamination from dynamic changes of nearby glaciers (Swenson and Wahr, 2002).Though, this method cannot prevent leakage from adjacent areas.Therefore, there still exists large signal loss in each region due to the filtering and truncation of GRACE coefficients.A data-driven approach was developed to extract leakage information from the filtered versions of the field, but this method also suffers several limitations, e.g., it does not work with sufficient accuracy for active catchments, and both the scaling factors and the aggregated noise over catchments increase as the catchment size decreases (Vishwakarma et al., 2016).

Spatial differences of abnormal melting in glacier dynamics
If we ignore the GIA correction error, total mass changes detected by GRACE contain a component caused by changes in SMB (corrected ice discharge) and a component caused by ice dynamics.Usually, the latter can be estimated from satellite altimetry data.Thus, the residuals obtained from GRACE after removing SMB may well reflect glacial dynamics.Figure 11 shows the residuals for each drainage basin and the entire GrIS, which is used to interpret the contribution from glacial dynamics to total ice mass changes.The time series for six drainage basins are quite different and show no overall trend characteristics in GrIS.In the southeast and northwest, there is a negative trend in the difference GRACE minus SMB.Global navigational satellite system data also revealed intense Greenland melting.For example, crustal motion data show that solitary seasonal waves are associated with substantial mass transport through the Rink Glacier in 2010 and 2012 (Adhikari et al., 2017).In contrast, a The Cryosphere Discuss.positive rate of mass change is found in southwest and northeast areas.In central west, north and entire Greenland, the time series of the residuals do not have apparent trends.This spatial difference is in a good agreement with surface elevation changes derived from ICESat, GRACE and GPS data based on previous results (Howat et al., 2008;Khan et al., 2010;Hurkmans et al., 2014).Particularly, satellite observations such as the Oceansat-2 satellite, MODIS and Special Sensor Microwave Imager/Sounder reveal that melt occurred at or near the surface of GrIS across 98.6% of its surface on 12 July 2012 (Nghiem et al., 2012).Because of the combination of the modelled (SMB) and observed (GRACE) data, any uncertainty or error of the data source will appear in the residuals.Based on the mass budget method, the SMB model estimates the difference between individual mass sources (mainly snowfall) and sinks (mainly meltwater runoff and solid ice discharge) (van den Broeke et al., 2016).The accumulation/ablation zones of an ice sheet are largely driven by changes in weather conditions (Hanna et al., 2011).More importantly, glacial dynamics refer to the flow of ice from the interior of the ice sheet outward through outlet and land-terminating glaciers (Liu et al., 2016).Although this kind of ice discharge may not be accurately estimated by the SMB model, its contribution to the total mass balance cannot be ignored either.Another factor influencing the residual is the accuracy and limited resolution of GRACE data, e.g., measurement errors, GIA correction, leakage effects from outside the ice sheet and the eustatic sea level, etc.For Greenland the uncertainties in the GRACE estimates of the ice sheet mass balance have been analyzed in previous studies ( Van den Broeke et al., 2009;Bolsch et al. 2013;Velicogna and Wahr, 2013).Therefore, we will not discuss them here in detail.At the same time, we are aware that the errors come mostly from the uncertainty in the scaling factor due to partitioning of GrIS into six mascons.The difference between the non-uniform distribution of actual ice sheets and our assumption of uniform mass distribution within the basin or each mascon also leads to uncertainty of the scaling factor, which increases the uncertainty of final mass loss estimates.

Near-surface air temperature over the Greenland
In general, mass changes of the GrIS mainly depend on temperature variations, which cause both ice discharge and surface meltwater runoff.Near-surface temperatures can be derived from global land surface models forced with atmospheric data (e.g., Satellite-derived MODIS data in this study) (Syed et al. 2008).Figure 12

Contribution of GrIS to sea level change
It is well-known that global mean sea level variations are dominated by thermal The trend rate of the contributions of the total land (without Greenland), GrIS and steric sea level changes are 1.1 mm/yr, 0.7 mm/yr and 1.4 mm/yr, respectively.It is important to note that a V-shaped or solitary wave sea level change is observed from 2010 to 2012 (black line in Figure 13), which is mainly caused by terrestrial water storage anomalies (blue line in Figure 13) related to the 2010/2011 La Niña event (Boening et al., 2012;Fasullo et al., 2013).The GrIS is an important contributor to present-day global mean sea level rise.The average contribution rate (ratio of GrIS to the total mass change) is about 31%.Furthermore, there is a clear acceleration of i.e., the sea level changes from rising to falling.This result indicates that increased melting of GrIS partially compensated the sea level drop, which was due to a temporary shift of water from the ocean to continents.

Conclusions
In this study, the GrIS variations estimated from GRACE gravity fields and SMB data have been investigated with respect to ice melting of Greenland and its contributions to sea level changes.The spatial pattern of both long-term mass trends obtained from monthly GRACE data and SMB indicates that the ice loss appears clearly over drainage basins in different spatial scales and different time spans.Specifically during the warm period 2010 to 2012, an anomalous acceleration of mass loss occurs in the entire southern and western regions of GrIS, which reflects the major melt event due to higher near-surface temperatures.We calculated time series for six sub-regions defined by mascons using the least squares mascon fitting approach.
We found that the GrIS changes from the extended mascons solutions combined with the matrix scaling factor method are in good agreement with previous studies.The We also assessed a potential impact of the spherical harmonic truncation, spatial averaging of mascon fitting and leakages from other time-dependent signals.The sensitivity kernels for all extended mascons indicate that the sum of kernels is well-localized to their regions and increased the weight of the boundary of GrIS.This study suggests that the rescaled GrIS time series based on a uniform distribution within the basin can effectively reduce the uncertainty caused by non-uniform mass distribution of continental and oceanic areas.However, contributions of leakage effects from outside ice sheets and the eustatic sea level to the total mass errors cannot be avoided when using extended mascons.These factors likely limit the accuracy of the estimated GrIS contributions to sea level changes.
by abnormal climate fluctuations in a short term period.A solitary wave disturbance of global mean sea level has happened during 2010-2012, when the sea level decreased by 5 mm from the beginning of 2010 to mid 2011 and then rose by nearly 20 mm until the end of 2012 (NASA: SEA LEVEL CHANGE Observations from Space).This occurred along with a La Niña phase of the El Niño-Southern Oscillation (ENSO).Previous studies have shown that the change in the sea level The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 1 .
Figure 1.Greenland drainage basins.NO: north; NE: northeast; SE: southeast; SW: southwest; CW: central west and NW: northwest according to Rignot Basins from IMBIE 2016(Rignot et al., 2011).White dots show ice caps in Greenland and while other mass change contributions (e.g., terrestrial water storage) are smaller on ice sheets compared to other areas.The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.In this study, we use monthly sets of spherical harmonics from the GRACE Release 05 (RL05) gravity field solutions generated by the Center for Space Research (CSR) at the University of Texas, spanning January 2003 to December 2015.Each monthly GRACE field consists of a set of Stokes coefficients, C lm and S lm , up to degree and order (l and m) of 60.We replaced the GRACE C 20 coefficients with the results inferred from satellite laser ranging (Cheng et al. 2013), and include degree-one coefficients as calculated by Swenson et al. (2008).The Stokes coefficients from A et al. (
shows root mean square errors of accumulated SMB values in two versions for the period 1960 to 2011.Both models consist of 312 (latitude) × 306 (longitude) grid cells and include Iceland, the Svalbard archipelago and the Canadian Arctic.Overall, there is no significant difference in the cumulative root mean square (1960-2011) between the two versions of the model, but RACMO2.3 shows larger fluctuations at the boundary of GrIS.This is mainly due to the fact that RACMO2.3 is forced at the lateral boundaries by the 40-year European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) for the period January 1958-December 1979 and the ECMWF Interim Reanalysis (ERA-Interim) afterwards (van den Broeke et al., 2016).

Figure 3 .
Figure 3. Mascons for the GrIS drainage basins (a).Each colored region represents a single mascon.(b) similar to Figure 3a but for the extended mask of six mascons.

Figure 4 .
Figure 4. Time series for the entire GrIS from the exact and extended mascons to fit monthly GRACE coefficients.Red crosses are scaled extended mascon fitting results due to change of the scale factor for different degree (l).
, was obtained from the monthly GRACE mass solutions for Greenland from 2003 to 2009 (a), 2010 to 2012 (b), 2013 to 2015 (c) and 2003 to 2015 (d).A clear negative trend was identified across the entire ice sheet except in high altitude areas (>2000 m) in the central part.During 2003-2015, the mass loss increased in northwest, central west, south west and southeast, especially along the north-west coast and the south-east coast.In the north The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.and northeast, the mass melted relatively slowly compared to the other four areas.The 284 ice mass loss increased in 2010-2012 and 2013-2015 relative to 2003-2009.285
Figure6shows spatial patterns of ice mass changes from SMB data.In 2003-2015, the SMB results indicate that ice mass loss and thinning was concentrated in the entire coastline as well as in western and southeast basins of Greenland.In 2010-2012, mass loss and thinning were stronger in the northwest, central west, south west and southeast; and this spatial and temporal distribution is very consistent with the GRACE-derived mass loss.However, the trend magnitude of SMB is smaller than of the GRACE results.Additionally, we shall keep in mind that the GRACE-derived results reflect mass changes of both SMB and ice discharge, e.g., beginning at 1995, SMB decreased while ice discharge increased, due to acceleration of the ice melting in several large outlet glaciers in the southeast and northwest, which leading to a quasi-persistent negative mass balance (van denBroeke et al., 2016).Moreover, because of large runoff and surface mass fluxes (i.e., meltwater and snowfalls) at the boundary of the GrIS, the current horizontal resolution of RACMO2.3 (11 km) is insufficient to resolve individual, low-lying outlet glaciers of the GrIS(Noël et al., 2016), which leads to potentially large errors and uncertainties in accumulated SMB values (Figure2).
from 2003 to 2015 in the whole GrIS region is in good agreement with that reported by -270 Gt/yr during 2003-2012(Schrama et al., 2014) and -270    Gt/yr during 2003-2014 (van den Broeke et al., 2016).When the GrIS is represented by six extended basins, the results also show a continuous decrease both before and after scaling (top and bottom left in Figure7) from 2003 to 2015; since 2010, the rate of this decrease suddenly accelerated towards the end of 2012.The rate of the mass loss obtained by scaled GRACE and SMB is also similar, -288±7 Gt/yr in GRACE and -275±1 Gt/yr in SMB from 2003 to 2015.The magnitude of the trend increased significantly over the period 2010-2012, about -456±30 Gt/yr in GRACE and -464±38 Gt/yr in SMB.The errors here represent fitting uncertainties, while the real uncertainties are mainly due to the GIA correction, leakage of signal from outside ice sheet, and GRACE measurement errors.Those effects in the trends were estimated to be 20 Gt/yr in both time series(Van den Broeke et al., 2009).Our estimates are in good agreement with the magnitude of the fitted linear trend both from GRACE and SMB over the period2003 -2014  (van den Broeke et al., 2016) )  but slightly larger than the reported GRACE-derived mass loss rate fromSutterley et al. (2014),Velicogna et    al. (2014) andForsberg (2017).It should be noted that the overestimation of our results likely comes from the leakage effect of glaciers and ice caps due to the fact that we used extended mascons to fit the GRACE and SMB data.The impact of this part may reach about 20~80 Gt/yr(Bolsch et al. 2013;Velicogna et al., 2013).The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 7 .
Figure 7. Ice mass change in gigatons (gtons) for GrIS, the top part of the figure from left to right is from the exact mascons of GrIS, extended mascons (after scaled) of NO, NE and SE, respectively.The lower part of the figure from left to right is from the extended mascons (scaled) of GrIS, SW, CW and NW, respectively.GRACE time series for January 2003 to December 2015 (red), time series of cumulative SMB anomaly for January 2003 to December 2015 (blue).Light blue bands represent the time span from January 2010 to December 2012.

The
Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.overestimate ice mass changes, since the modeled surface meltwater increases strongly with decreasing elevation and latitude in the low-lying parts of the southwestern GrIS (van den Broeke et al., 2016

Figure 8
Figure 8 Trends in the sea level fingerprint (SLF) due to mass change of GrIS (a).(b) contributions from the Earth's elastic response.Trends are calculated for the time period January 2003 to December 2015.Blue contour in Figures 8a and 8b is the mean RSL or barystatic sea level equivalent.
., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.Due to ice sheet melting, the sea level along coastlines located up to 2000 kilometers away falls as a result of the isostatic uplift of the crust.The escaping seawater flows across the equator, i.e., the melting of Greenland impacts the coastline of Brazil and

Figure 9 .
Figure 9. Sensitivity kernel for the truly mask (a) and extended mask (b) of all drainage basins.

Figure 11 .
Figure 11.Residuals obtained from GRACE after removing SMB for each drainage basin and the entire GrIS.
shows the averaged near-surface air temperatures from the GLDAS forcing (i.e, MODIS) data in Greenland for the periods 2003 2015 (Figure 12a) and 2010 2012 after removing the average of 2003 2015 (Figure 12b).The spatial distribution of the temperature anomalies indicates that the increased mass loss rate from GRACE observations and SMB simulations is mainly due to relatively high surface temperature of South Greenland (i.e., mean change range from about 10 to 5 Figure 5d and Figure 6a).According to Figure 12b, there are large positive temperature anomalies over most parts of Greenland during 2010 2012, which is consistent with the acceleration of mass loss in the GrIS during the same period.The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 12 .
Figure 12.Average near-surface air temperatures from MODIS data in Greenland for the periods 2003 2015 (a) and 2010 2012 after removing the average of 2003 2015 (b).
., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.expansioncaused by heating of the global ocean, and variations of total ocean mass due to varying water mass fluxes from land to oceans.Here, we attempt to find the contribution of the GrIS to present-day global mean sea level rise.As shown in Figure13, the sum of ocean mass variations from GRACE-derived total land contributions and steric sea level from the total steric sea level anomaly data are close to the observed sea level trend of 3.3 mm/yr derived from sea surface height anomaly data.

Figure 13 .
Figure 13.Global mean sea level (GMSL) from altimetry during 2003-2015 (black line), total freshwater input from land (without Greenland) and steric sea level changes (blue line), and GrIS contribution (red line).Seasonal signals have been removed.The grey vertical bars show the contribution rate of GrIS to the total mass change (when GRACE data are available).
Total contributions of land (no Greenland)+steric: 2.5 mm/yr Total contributions of Greenland: 0.7 mm/yr Ratio of Greenland to total mass changes The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License. the proportion of melting in Greenland (grey vertical bars).It might be stressed that the contribution of GrIS experienced an opposite V-shaped change during 2010-2012, rate of the mass loss obtained by scaled GRACE and SMB is 288±7 Gt/yr and 275±1 Gt/yr, respectively, from 2003 to 2015.The magnitude of this trend increased significantly to 456±30 Gt/yr in GRACE and 464±38 Gt/yr in SMB in the period 2010-2012.The residuals obtained from GRACE after removing SMB may reflect the contribution from glacial dynamics to total ice mass changes.These spatial differences in the residuals among six drainage basins are in good agreement with the surface elevation change rates previously derived from the ICESat data.We computed SLF due to the ice mass fluxes of Greenland for the time period 2003-2015.RSL anomalies caused by dynamics of the GrIS are not uniformly distributed across the global oceans due to self-attraction and loading effects.Mass loss of the The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-142Manuscript under review for journal The Cryosphere Discussion started: 7 August 2018 c Author(s) 2018.CC BY 4.0 License.GrIS induces reduction of RSL at most coasts of Scandinavia and Northern Europe (up to about 0.6 cm/yr), In contrast, RSL rise is concentrated around South America.The contribution ratio of GrIS to total sea level rise increased and the average contribution rate was about 31% from 2003 to 2015.Although the contribution of GrIS has an opposite V-shaped change relative to the sea level changes during 2010 2012, it could not compensate completely the mass transfer from oceans to the continents.

Table 1 .
Scale factors of six basins derived with the extended fitting approach