2.1 a) Spherical cap basis used to derive sub-basin regional estimates of the massbalance of Totten and Moscow University glaciers, East Antarctica using GRACE data. Caps are inscribed in a 3-layer hexagonal grid with diameters 2.7 ◦ (dark grey), 2.9 ◦ (light grey), and 3.2 ◦ (white). Black lines show Antarc- tic drainage basins (see Rignot et al. [2011b]) Red lines show the Totten and Moscow University glacier basins. The caps used for the sub-basin estimates are labelled with bold bright green numbers. b) Sensitivity kernel for con- figuration 1-6-7 superimposed on ice velocity [Rignot et al., 2011b, Mouginot et al., 2012, Rignot et al., 2017]. Grey lines show the major Antarctic drainage basins as in a. Black lines show the contour levels of the sensitivity kernel. The zero-contour lines displays small fluctuations in the kernel throughout the icesheet which result in minimal leakage. EAIS = East Antarctica; GRACE = Gravity Recovery and Climate Experiment. . . . . . . . . . . . . . . . . . 31 2.2 Optimized GRACE time-series of the mass (in gigatons = 10 12 kg) of the
where PR represents total precipitation (snowfall plus rain), SU is surface (SU s ) plus drifting snow (SU ds ) sublimation, ER ds is drifting-snow erosion and RU is meltwater runoff, the amount of liquid water (melt and rain) that is not retained or refrozen in the snowpack. Accurate estimates of the SMB of glaciated regions are essential for assessment of their mass change and contribution to sea-level rise (e.g. Rignot and others, 2011; Shepherd and others, 2012) In remote glaciated regions such as East Antarctica, reliable SMB observations are scarce (Favier and others, 2013) and, as a result, estimates of SMB are uncertain. Remote-sensing techniques can overcome this deficiency, but pose other challenges. Mass changes from the Gravity Recovery and Climate Experiment (GRACE; Tapley and others, 2004) do not resolve small-scale features, while altimetry measure- ments need a correction for firn processes (Gunter and others, 2009) and inter-campaign biases (Borsa and others, 2014). Estimating ice-sheetmassbalance from ice discharge using synthetic aperture radar interferometry (InSAR) ice
– Thirdly, modelling results are very sensitive to the spin- up time used in the snow model. At the beginning of the summer, the icesheet and the tundra are covered by the winter snow accumulation. Either climatologic precip- itation data or reanalysis are used to initialize the snow model at the end of the spring, or the winter accumu- lation is simulated by the model itself by beginning the simulation at the end of the previous summer. Previous MAR simulations showed a very large sensitivity to the initial snow height and the snow properties above the tundra and the ablation zone given the albedo feedback (Lefebre et al., 2005). A too thick snow pack at the be- ginning of the summer above the ablation zone delays the appearance of bare ice (with a lower albedo) in the ablation zone and can considerably reduce the melting. That is why it is preferable to begin the simulation at the end of the previous summer (or several years be- fore) in order to reduce the problem of the snow model initialization. For example, let us quote the MAR model which uses a spin-up of 2–3 years while the surface in the MM5 model is reinitialised every day with a spin- up time of 6 hours due to the fact that MM5 is used in a forecast mode (Box et al., 2006). To reduce the impacts of the reinitialisation, MM5 is however driven by data (SMB measurements from the GC-Net Auto- matic Weather Stations and remotesensing derived sur- face albedo) independent of the ECMWF atmospheric analyses used to force the model at its boundaries.
Satellite-based mass estimates began in the early 1990’s with the European Remote-sensing (ERS) satellites (Zwally et al., 2005), followed by the NASA Gravity Recovery and Climate Experiment (GRACE) (Luthcke et al., 2006; Wouters et al., 2008) but a 15 yr time series cannot cap- ture long-term mass variations of the GrIS, given the large inter-annual variability observed in the massbalance and sur- face melt (Tedesco et al., 2011). Measurements from coastal weather stations managed by the Danish Meteorological In- stitute (DMI) have been available for more than a century. However, in this case, data have been collected at local spa- tial scales and therefore, cannot be assumed to be representa- tive of other places (e.g., interior of the GrIS). Nevertheless, these data can be used to quantify the inter-annual variabil- ity (Fettweis et al., 2008; Wake et al., 2009) at selected lo- cations. Results from regionalclimatemodels (RCMs) can provide estimates of GrIS surface changes over a long period at high resolution, but measurements to validate these models are limited.
The Regional Atmospheric Climate MOdel version 2 (RACMO2 hereafter; Van Meijgaard et al., 2008) com- bines the dynamical parameterizations from the HIgh Reso- lution Limited Area Model (HIRLAM) (Undén et al., 2002) with the physical schemes from the European Centre for Medium-Range Weather Forecasts model (ECMWF cycle 23r4, White, 2001). In recent years, RACMO2 has been used to estimate the SMB of Antarctica (Van de Berg et al., 2005; Lenaerts et al., 2012b) and Greenland (Ettema et al., 2009). Modeled precipitation and surface massbalance have been extensively evaluated using available in-situ observa- tions (Ettema et al., 2009). Moreover, Ettema et al. (2010b) showed that RACMO2 provides a realistic simulation of the near-surface climate of the GrIS, although several deficien- cies were detected, especially in the snow albedo scheme. To resolve this, we included a snow albedo parameteriza- tion based on the growth of snow during dry and wet meta- morphosis, so that snow albedo can be physically coupled to snow grain size (Flanner and Zender, 2006). This signif- icantly improved net shortwave radiation in RACMO2 over the Antarctic icesheet (Kuipers Munneke et al., 2011) and the length of the melt season in Greenland (Van Angelen et al., 2012). In addition, a remotesensing-derived back- ground albedo (from the Moderate Resolution Imaging Spec- troradiometer, MODIS) is prescribed for ice (Van Angelen et al., 2012) to capture the spatial variability of albedo in the ablation area when the winter snow has melted (Van den Broeke et al., 2008). Finally, the drifting snow scheme derived from Déry and Yau (1999) has been included in RACMO2. It calculates drifting snow transport and subli- mation, and accounts for interactions between the drifting snow layer with both the overlying atmosphere and the un- derlying snow surface (Lenaerts et al., 2010). Furthermore, we use an empirically derived parameterization for surface snow density. This was derived by Lenaerts et al. (2012a) for Antarctica, such that modeled drifting snow frequency and horizontal transport agree well with available in-situ and re- mote sensing observations (Lenaerts et al., 2012a).
elevation is underestimated over a large part of Svalbard and some low altitude glaciers should not even exist in our 10 km grid, causing a likely overestimation of the surface mass loss in our projection. Moreover, glaciers are typically concentrated at higher elevations, where the negative elevation bias in MAR is largest, leading to further overestimated mass loss. The topography is also fixed in our simulations, which is an acceptable approximation under the present climate but will likely introduce an underestimation of the melt increase in the future, as a result of surface lowering. On the other hand, glaciers are going to retreat in the future, and using a fixed ice mask like we do overestimates the melt, as some areas should not be covered with permanent ice under the future warmer climate. The contribution of these areas (with relatively high mass loss) to the sea level rise should be removed in our projection. As the aforementioned effects partly compensate for each other, we expect a relatively minor impact on our future projection. According to Goelzer et al. (2013), the additional SMB changes coming from topography changes are about 10 times lower than SMB changes directly induced by climate warming. Over the Greenland icesheet, those effects are projected to contribute to about only 5–10 % of the SMB anomaly by the end of the century (Fettweis et al., 2013a) and we assume their contribution to be of the same order of magnitude in Svalbard. However, only a high-resolution simulation coupled with an icesheet model could yield insight in the magnitude of this contribution. In southern Spitsbergen, given the very negative values of SMB and the fact that glaciers rather than ice caps prevail, we expect the retreat effect to be dominant and MAR RCP8.5 probably overestimates the surface mass loss in this area. On Austfonna, on the other hand, we expect the retreat to be limited only to the proximity of the margins, but the elevation decrease towards the centre of the ice cap is also expected to be limited. We therefore expect that, on Austfonna, both effects will balance each other out, or at least that none of them will be largely dominant.
To improve the density of in situ observations and to monitor the near-surface climate and massbalance of the GrIS, automatic weather stations (AWS) are increasingly being used . In addition, numerous ice cores have been drilled, each yielding a local accumulation rate for a certain time period; however this has not led to a suﬃciently dense grid of in-situ observations to allow for an accurate determination of the SMB ﬁeld by interpolation alone. The data in Fig. 1, mainly based on , only give a general impression of a wetter southern and western icesheet and a drier north-eastern icesheet, with some suggestion of increasing accumulation towards the extreme south and south-eastern icesheet.
transport events using a conventional AR identification algorithm as well as a self-organizing map (SOM) classification applied to MERRA-2 data. We then analyze AR effects on the GrIS using melt data from passive microwave satellite observations and regionalclimate model output. Results show that anomalously strong moisture transport by ARs clearly contributed to increased GrIS mass loss in recent years. AR activity over Greenland was above normal throughout the 2000s and early 2010s, and recent melting seasons with above- average GrIS melt feature positive moisture transport anomalies over Greenland. Analysis of individual AR impacts shows a pronounced increase in GrIS surface melt after strong AR events. AR effects on SMB are more complex, as strong summer ARs cause sharp SMB losses in the ablation zone that exceed moderate SMB gains induced by ARs in the accumulation zone during summer and in all areas during other seasons. Our results demonstrate the influence of the strongest ARs in controlling GrIS SMB, and we conclude that projections of future GrIS SMB should accurately capture these rare ephemeral events.
Figure 2 | Greenland IceSheetmassbalance. Rate of mass change (dM/dt) of the Greenland IceSheet as determined from the satellite-altimetry (red), input-output method (blue) and gravimetry (green) assessments included in this study. In each case, dM/dt is computed at annual intervals from time series of relative mass change using a three-year window. An average of estimates across each class of measurement technique is also shown for each year (black). The estimated 1σ, 2σ and 3σ ranges of the class average is shaded in dark, mid and light grey, respectively; 97 % of all estimates fall within the 1σ range, given their estimated individual errors. The equivalent sea level contribution of the mass change is also indicated, and the number of individual mass- balance estimates collated at each epoch is shown below each chart entry.
and Mitchell 1995). Energy balance calculations for similar warming predictions show that this would increase ablation from the Greenland icesheet, causing an estimated 60 mm sea level rise over the century, in addition to the increase from thermal expansion of the oceans (van der Wal and Oerlemans 1994). On timescales of a century or so, the loss of ice from East Antarctica is relatively insensitive to temperature increases, because temperatures are presently far below the melting point, and ice flow velocities, which determine the rate of mass loss through iceberg calving, only respond to temperature changes on timescales of many thousands of years. However, warmer temperatures would cause melting on the floating ice shelves bordering West Antarctica, perhaps precipitating their collapse. This would not affect sea level directly, because the ice shelves are already floating. However, it may cause additional losses from the inland ice if the ice shelves are currently impeding its flow (Warrick et al. 1995). Because West Antarctica rests upon bedrock below sea level it may also suffer more rapid deglaciation in response to sea level rise or increases in ocean temperatures (Huybrechts 1990).
The Regional Atmospheric Climate Model (RACMO2) is developed and maintained at the Royal Netherlands Mete- orological Institute (KNMI) (Van Meijgaard et al., 2008). RACMO2 adopts the atmospheric physics module from the European Centre for Medium-Range Weather Forecasts In- tegrated Forecast System (ECMWF-IFS) and the dynamical core of the High Resolution Limited Area Model (HIRLAM) (Undèn et al., 2002). The polar version of RACMO2 was developed by the Institute for Marine and Atmospheric Re- search (IMAU), Utrecht University, to specifically represent the SMB evolution over the ice sheets of Greenland, Antarc- tica and other glaciated regions. To that end, the atmosphere model has been interactively coupled to a multilayer snow model that simulates meltwater percolation, refreezing and runoff (Ettema et al., 2010). It includes an albedo scheme with prognostic snow grain size (Kuipers Munneke et al., 2011) and a drifting snow routine that simulates interactions
For over thirty years, earth observing satellites sensitive to visible, infrared, and microwave electromagnetic radiation, together with gravimetry, have documented the patterns of change on the GrIS ablation zone surface. Satellite remotesensing data show an ablation zone expanded in size, its albedo and surface elevation lower in response to enhanced melting, and an icesheet transition from steady state to negative massbalance that now represents the largest land ice contributor to global sea level rise. Already, some 78–85% of the total liquid runoff produced from surface melting is generated in the bare ice ablation zone, despite it covering ~22% of the ice sheet’s total surface area, up from ~15% in the early 1960s [20,30,33–35]. Although often conceptualized as a uniform surface of solid ice, the ablation zone is a dynamic region with widely varying electromagnetic properties controlled by diverse physical, biological, and hydrologic processes. Future progress in remotesensing the ablation zone will likely benefit most from methods that directly address this complexity, for example using multi-sensor, multi-wavelength, and cross-platform datasets. Examples include fusing radar and laser altimetry with optical stereophotogrammetry to discriminate and diagnose causes of surface elevation change , or fusing radar and laser backscatter with optical imagery to discriminate snow, ice, liquid water, and refrozen meltwater in sensitive areas near the equilibrium line altitude [312,313]. Other areas of opportunity recommended for future research include spaceborne detection of subsurface refrozen meltwater and its effects on radar backscatter, which requires additional in-situ validation [115,116], the partitioning of ablation zone thinning into ice dynamic and surface massbalance components , cross-validation of ice surface elevation change from altimetry with modeled surface massbalance  and modeled ice dynamic motion , spaceborne diagnosis of changing bare ice albedo  and grain size , and monitoring the inland migration of snowlines, surface melt extent, and surface hydrologic features including lakes, streams, and moulins [26,56].
Inclusion of ice sheets in coupled models complicates this traditional ocean-limited preindustrial spin-up approach, for the basic reason that ice sheets reach quasi-equilibrium on average deepice residence and lithospheric relaxation timescales, i.e., ∼ 10 4 –10 5 years (i.e., 1–2 orders of mag- nitude slower than the ocean). This long equilibration time means that the present-day Greenland and Antarctic ice sheets (GrIS/AIS) are not in full equilibrium with preindus- trial (i.e., recent Holocene) climate. Rather, they contain a remnant thermal and dynamic memory of past glacial peri- ods that is reflected in present-day icesheet conditions and potentially in long-term future icesheet projections. Compu- tationally efficient stand-alone icesheet model simulations forced with simple and highly parameterized climate repre- sentations driven by various paleoclimate time series are able to simulate the 10 4 –10 5 years necessary to capture this mem- ory (e.g., Huybrechts, 2002; Applegate et al., 2012). How- ever, an analogous synchronous fully coupled spin-up with a computationally expensive fully coupled icesheet/climate model is simply not possible. Several approaches have been introduced to circumvent this computational barrier to gen- erating preindustrial coupled icesheet/climate initial condi- tions. However, each method displays significant shortcom- ings:
There are a number of demands on computer and human resources (Fig. 6). A variety of independent models, differing significantly in their underlying physics and numerics, are required to provide assessments of the range of possible climate change. Models are also being developed that contain ever more complete representations of the climate system, including processes such as biogeochemical cycles, atmospheric chemistry and aerosols, clouds and convection, land processes and ice sheets. Process-oriented experiments are needed to better understand model behaviour, including internal variability and the response to various radiative forcing. The following factors increase demands on computational resources: First, internal variability has a very strong imprint on climate trends even on time scales as long as several decades and spatial scales as large as continents 81 . This calls for large ensemble simulations 96 . Second, when spatial resolution is high (25-50 km), many phenomena are reasonably well simulated in GCMs 97 , including tropical cyclones 63,91 and extratropical weather regimes such as blocking 98,99 . This makes higher resolution desirable.
The SMB anomaly projection for k = a/b =−1 as well as the cumulated sea level rises equivalent are shown in Fig. 7 and listed in Table 5. The lower SMB anomaly in the 20th century seems to have occurred in 1931 with − 300 km 3 yr −1 . This record surface mass loss rate is likely to become com- mon at the end of the 21st century. The summer will prob- ably be much warmer than previously observed during the 20th century, but a predicted increase of precipitation will most likely partly offset the SMB decrease associated with warming. With the SRESA2 experiment, the projected neg- ative SMB anomalies are higher. The sea level rise com- ing from the GrIS SMB change should reach 4 ± 0.5 cm in 2100, which is in full agreement with Huybrechts et al. (2004), Oerlemans et al. (2005) and Meehl et al. (2007). The computation was made by using an area of a world ocean area of 361 million km 2 . Finally, Table 5 and Fig. 7 show that a warming threshold higher than 2.5 K is required for a zero surface massbalance (i.e. a SMB anomaly reaching − 350 km 3 /yr in our case), as concluded by Gregory and Huy- brechts (2006).
Ice-sheet SMB is the net result of accumulation of snow, icemass loss by sublimation, surface melt and subsequent run- off. The amount of melt is a function of the surface energy balance (SEB) components, which vary widely in space and time over the icesheet. An important source of melt energy is delivered by shortwave radiation, but due to the high albedo of snow most of the incoming shortwave radiation is reflected back into space. Therefore, the snow albedo evolution exerts a strong control on the ice-sheet SEB, and thus on the SMB. In cold, dry conditions, snow albedo over ice sheets re- mains relatively high (Loth et al., 1993), although with time snow grains grow, which effectively reduces the albedo (War- ren, 1982; Gardner and Sharp, 2010). However, this process is generally slow at low temperatures. Observed broadband albedo values in the accumulation area of the GrIS are in the range 0.75–0.83 (Alexander et al., 2014). The presence of liquid water has a darkening effect on snow: water in snow strongly accelerates grain growth and fills in voids between the snow grains. Both of these effects increase the effective grain size, thus rapidly decreasing the broadband albedo of wet snow (e.g. Gardner and Sharp, 2010). Liquid water pond- ing on the glacier surface, removal of the firn layer and subse- quent melting of the bare ice are associated with broadband albedo values of ∼ 0.5 (Van de Wal and Oerlemans, 1994; Van de Wal et al., 2005; Van den Broeke et al., 2008; van den Broeke et al., 2011; Alexander et al., 2014). The accumu- lation of impurities, microorganisms, dust or debris on the glacier surface can further decrease albedo to values < 0.3 (Greuell and Genthon, 2004; Bøggild et al., 2010; Wientjes and Oerlemans, 2010; Wientjes et al., 2011). To minimize the bias introduced by uncertainty in the albedo, it can be a solution to use observed albedo (e.g. MODIS, Box et al., 2017), but this is only a solution for experiments describing the recent observational period, and not possible for palaeo and future simulations.
accumulation but vast interior of the Antarctic IceSheet, where few direct measurements of surface massbalance ex- ist and which represents one of the largest sources of uncer- tainty in icesheetmassbalance measurements. These low- accumulation polar regions are also the most difficult to mea- sure manually due to the limited precision of core samples and the lack of chronology in the upper firn. In areas with higher accumulation, the increase in noise and loss of reso- lution with depth can be mitigated by increasing the count period, so that the duration of autonomous sensor deploy- ment would be most likely limited by the instrument power and communications (e.g. the height of the tower supporting the telemetry antenna and solar panels or the battery lifes- pan). This still could be several years in the regions of very high accumulation, or decades in the case of polar deserts. Finally, additional accuracy on short timescales (< 1 week) may be obtained by deploying a local reference sensor above the surface, reducing distance-dependent uncertainty in the count correction factors.
culated a mean value of the sea level rise associated with the 21st century SMB changes of Svalbard with a positive degree-day (PDD) model based on the outputs of an ensem- ble of 14 GCMs for the RCP8.5 scenario. Their projected SLR at the end of the century is more than twice as large as ours (15.81 mm). Marzeion et al. (2012) projected a SLR be- tween 15 and 25 mm for Svalbard for the RCP8.5 scenario, with an empirical model based on the outputs of climatolo- gies and CMIP5 GCMs. However, these values were based on large-scale temperature and precipitation changes from global models, in most of which the topography of Svalbard is not explicitly represented given their huge spatial resolu- tion. Moreover, the surface temperature of glaciated regions is limited to 0 ◦ C in MAR, damping the MAR near-surface temperature increase (Fig. 1), whereas there is no limitation in most GCMs (Goelze et al., 2013). Additionally, those stud- ies are based on empirical calculations of the energy balance while ours are physically based, which also explains part of the differences in SMB values. Finally, there is also an error in our estimation due to the use of a fixed ice mask and topog- raphy. However, we estimate this error to be small (10 % of the SMB anomaly, see discussion below) and the SLR con-
An alternative solution consists in using regionalclimatemodels (RCMs) to produce high-resolution atmospheric fields and much more robust energy balance and SMB cal- culations. A number of RCMs have been developed for the polar regions such as MAR (Fettweis et al., 2017), RACMO2 (Noël et al., 2015), Polar MM5 (Box, 2013) or HIRHAM5 (Langen et al., 2015). However, the highest resolution of the RCMs is limited by the use of the hydrostatic approxima- tion and often remains below the resolution of Greenland icesheetmodels, which are generally running at a 5–10 km scale (Bueler and Brown, 2009; Greve et al., 2011; Price et al., 2011) or even below (e.g. Gagliardini et al., 2013). This means that SMB fields must be corrected for resolution (and thus for elevation) differences between the RCM and the ISM. With the aim of investigating the influence of the MAR resolution on the computed SMB fields, Franco et al. (2012) developed a method to downscale each SMB MAR component (snowfall, rainfall, runoff, sublimation and evap- oration) onto a finer grid as a function of elevation changes. An alternative approach to correct the SMB field from sur- face elevation changes is based on statistical relationships between altitude and SMB (Edwards et al., 2014b). Also de- rived with MAR, the approach of Edwards et al. (2014b) computes a SMB–elevation feedback gradient for regions be- low and above the equilibrium line altitude in the northern and southern parts of GrIS, with limited additional comput- ing resources. However, in both parameterizations by Franco et al. (2012) and Edwards et al. (2014b), the authors only consider a strict linear relationship between topography and SMB changes. Although changes in temperature can be de- rived from a linear vertical lapse rate, other processes gov- erning the SMB such as those related to energy balance, pre- cipitation or atmospheric circulation do not follow a linear relationship with the altitude. While this approach may be valid at the local scale for small elevation changes, it may lead to a misrepresentation of the SMB–elevation feedbacks for substantial changes in altitude, especially at the icesheet margins.
GrIS SMB has been estimated through the statistical downscaling of low resolution re-analysis data Hanna et al. (2011, 2005, 2002, 2008), and low resolution global cli- mate model data (Huybrechts et al., 2004; Gregory and Huy- brechts, 2006) through regionalclimatemodels (Box et al., 2004, 2009; Ettema et al., 2010a, b; Fettweis, 2007; Fettweis et al., 2008; Lucas-Picher et al., 2012) and also through the interpolation of in situ observations from ice cores, snow pits, stake measurements and automatic weather stations (Bales et al., 2009); however, these measurements are limited in both spatial and temporal coverage and are unable to separate components of SMB. The release of high-quality and consis- tent historical weather reanalysis data has made possible the modelling of the processes controlling SMB over the whole icesheet. Temporal differences between these SMB estima- tions have been identified (Dahl-Jensen et al., 2009; Rae et al., 2012) yet remain to be explained. Here we consider four such reconstructions of GrIS SMB carried out using a com- mon forcing: re-analysis data from ECMWF.