3.1. Surface Elevation Change in Models and Observations
The relatively short period of observations, compared with the long timescales of ice sheet dynamics makes for challenging evaluation of ice sheet surface elevation change due to ice dynamics. In Figure 5
five year means of observed surface elevation change (SEC) in the upper panel are compared with the change in modelled SMB output from the HIRHAM5 regional climate model. The model includes firn processes such as refreezing and densification and is therefore equivalent to the observed surface elevation change. The lower panel shows the PISM modelled change in surface elevation driven by the same SMB product from HIRHAM. In this way the relative contributions of surface and dynamical processes to changes in SEC are decomposed with the help of the models. The upper panel of Figure 5
shows the 5-year running mean estimates, where especially the later part of the time series shows negative elevation change on the Greenland ice sheet, in particularly at the margins and in agreement with the literature [69
The observations show an initial small increase in elevation over much of the ice sheet in the early part of the record but over the full period there has been an absolute decline in surface elevation, demonstrating the importance of long-term observations. There are some exceptions in the east and south where the trend to overall decrease in elevation is reversed through the period of observations. The decrease in surface elevation is particularly marked around the margins of the ice sheet [71
] especially on the western side and around the basins of significant active calving glaciers, for example Jakobshavn Isbrae in the west and Helheim and Kangerlussuaq glacier basins in the east where surface elevation changes greater than 1 m per year are observed. In these locations, ice dynamics from fast flowing glaciers (see Figure 1
) are likely to contribute to significant elevation change. Comparison between the SEC observed from radar altimetry (upper panel) with the modelled SMB (middle panel) and modelled SEC from the ISM (lower panel) suggests that surface mass processes of precipitation and melt dominate the observed SEC over the vast majority of the interior of the ice sheet. This supports analysis by [7
] who also found SMB processes dominate the recent ice sheet mass budget. Around the margins of the ice sheet the modelled SMB from the RCM and SEC observations show a similar pattern of elevation change both in sign and in spatial extent. However, it is also noteworthy that the majority of the ice sheet interior shows a small surface increase in all four periods from observations; this is not reflected in the modelled SMB model, where the RCM may have a dry precipitation bias [5
]. The observed surface elevation increase in this region may also result either from biases in the correction of snow density or from ice sheet dynamic processes related to colder, stiffer glacial period ice, as suggested by Colgan et al. [72
]. The ice sheet dynamical model also does not capture this surface increase, though this may be due to uncertainties in the initialisation of the model as shown by Adalgeirsdottir et al. [14
In the regions of fast flowing outlet glaciers that show a surface lowering much greater than derived from the SMB modelling, the role of ice dynamics is likely to be much more important. However, while the PISM model results also show the strong influence of the surface mass balance forcing from HIRHAM the match between model surface elevation change and observed in some of these regions is less apparent. The ice sheet model under-predicts the SEC in some of these areas and in some cases even has the wrong sign, for example at the terminus of Jakobshavn glacier. This is likely to be at least in part a result of the model resolution inadequately capturing basal topography [65
] though may also reflect process parameter uncertainty that gives lower ice sheet velocities than observed in some locations as discussed in the following section. The lack of a dynamic calving parameterisation, a long-standing problem in ice sheet modelling [27
], may also contribute to this underestimate in SEC as the model underestimates the increase in ice velocity gradients that lead to dynamic thinning [73
] as calving rates increase. Work by [74
] also indicates that increased basal and frontal melting at outlet glaciers can lead to enhanced dynamic thinning at glaciers with termini grounded in deep water. This process is not yet included in the PISM ice sheet model version used in this study and may thus also explain the mismatch between elevation change from the model and the satellite observations.
3.2. Modelled and Observed Ice Velocities
In ice sheet models, numerous parameters influence the observed dynamics of the ice and comparisons between observations and model results may assist in constraining model parameters. As an example, the effect of different sliding parameters on ice velocities have been examined. In Figure 6
the mean modelled ice velocities for the winter 2014–2015 (Oct–Mar) are compared to the corresponding observed ice velocity. Figure 6
b shows the results for the low sliding case, while Figure 6
e shows the enhanced sliding case. In both cases, overall structure of the flow field looks reasonable, even though the modelled velocities are too low. Ice streams are mostly properly located, even though the North Eastern Greenland Ice Stream (NEGIS) is less well represented. This is, however, a consistent feature of many ice sheet models since NEGIS dynamics are believed to be heavily influenced by geothermal heat anomalies [75
] an effect that is currently not well accounted for in this model setup. One solution is to do an inversion with the model based on surface velocities to obtain basal friction, and then use this for the simulations. However, as it requires a consistent surface velocity covering the entire Greenland ice sheet, not just a single area, it would then be difficult to use the surface velocities as independent validation of the ice sheet model and is beyond the scope of this current study. In this set of experiments, PISM’s ice streams are generated by bedrock topography and a combination of sliding over the base and shear deformation of a thin till and ice layer at the base [60
]. When sliding is included, see Figure 6
e, the overall ice velocity increases and the individual ice streams become more focused. Figure 6
d shows the difference in the modelled velocities. From the difference plot it is evident that the overall velocity of the ice changes very little in the two cases, but the velocity in the ice streams increases significantly and focuses the flow. Using the ice velocity data to tune the sliding enhancement factor provides a better correspondence with the observed ice velocities.
3.3. Total Ice Sheet Mass Budget down to the Basin Scale
As Figure 4
showed, there has been a long-term downward trend in the total mass budget of the Greenland ice sheet, at least since the start of the GRACE era. The methods of Barletta et al. [41
] and Groh and Horwath [42
] applied to the GMB data give an average mass loss of 255 and 260 ± 15 Gt year
respectively, though the contribution of each basin to this figure varies considerably. The GMB data can be used to determine how much of the mass loss is related to surface processes and how much to ice dynamics but it can also be used to assess how different models represent mass budget processes.
To compare surface mass changes modelled by HIRHAM5 and RACMO2.3 [10
] with those observed by GRACE, cumulative SMB anomalies are calculated from the monthly SMB values of both models. Long-term signal components are removed by calculating residuals with regard to a linear model (for the SMB) and a quadratic (for the GMB) model. In this way, the impact of differing reference periods used for deriving the cumulative SMB anomalies and of ice-dynamical mass changes included in the GMB products are largely removed. Figure 7
compares residual mass changes for eight drainage basins and the whole Greenland ice sheet. The Nash-Sutcliffe model efficiency coefficient indicates the level of agreement between the GMB products and the model predictions as well as between both models.
It is important to emphasise that there are uncertainties in the GRACE-derived estimates [78
], e.g., caused by errors in the GRACE monthly solutions or by signal leakage from adjacent regions, as well as uncertainties in the SMB estimates [5
] and seasonal fluctuations in ice dynamics [79
]. These uncertainties complicate interpretation of the data. As the GMB data also accounts for ice dynamics, we would not necessarily expect a good agreement between modelled SMB and GMB data, especially in basins with high ice velocities and active calving fronts but in other basins a closer match between SMB and GMB should be expected. Overall there is good agreement between models and the GMB data for the ice sheet as a whole with some interesting regional variations as the statistics in Figure 7
confirm. The higher amplitude positive mass balance from GRACE in basins 3, 4 and 5 in eastern, south eastern and southern Greenland respectively, coincide with regions showing the highest precipitation inputs in Greenland. This suggests that the distribution of precipitation over the ice sheet is a significant source of uncertainty in both models and in terms of decomposing the GRACE land and ice signals. However, the high amplitude mass loss in the GRACE signal compared to the RCM data is especially apparent in basins 3, 4 and 5. These basins have large calving outlet glaciers and the GRACE data therefore suggests that glacier dynamics and ocean driven processes are enhancing mass loss in these regions. Basin 4 in southeast Greenland in particular has a large number of actively calving glaciers. The large mass loss recorded by the GMB from GRACE but not in the RCMs from 2005 to 2008 coincides with a period of retreat and active calving discussed further below.
The low surface elevation change calculated from the SMB model compared with the observed surface elevation change in the high interior of the ice sheet indicated that modelled precipitation from RCMs may be biased low over much of the interior. There is relatively little observational data for accumulation rates across Greenland. Analysis of field data collected along the Q-transect (the Qasimiut ice lobe) in southern Greenland [53
], one of the few consistent time series of observations of accumulation, demonstrates that in basin 5, both RACMO and HIRHAM5 regional climate models overestimate precipitation over the ice sheet close to the margin and underestimate precipitation further inland as a result of the bias. Hermann et al. [53
] point out that the precipitation bias has a consequent impact on the modelled melt rate. Melt at the surface of glaciers is strongly determined by the albedo. Snow has a higher albedo than bare glacier ice so the acceleration in melting that occurs when ice is exposed occurs later in the season in the models compared to the observations. The overestimate of snowfall from the models in this location leads to an underestimate in snow and ice melt during the melt season compared to that observed at stake sites on the glacier. The bias in mass loss in the RCMs compared to the GMB in this region may thus be partly explained by biases in precipitation as well as ice dynamic processes in basin 5. As some of the highest melt rates and highest snowfall rates have been recorded by automatic weather stations on the ice sheet in Greenland in basin 5, analysis of local effects as in Hermann et al. [53
], also demonstrates the value in supplementing satellite based observations and models with field measurement campaigns.
Interestingly, in basins 1 and 2, where calving and ice dynamics are not as large contributors to mass loss as in other regions, modelled SMB and GMB data products match rather well. However, there are some significant differences between the two RCMs in some years in these regions as well as in region 8 in northwestern Greenland. We hypothesise that some of the variation between modelled SMB is due to the albedo effect and differing albedo parameterisations as well as perhaps different precipitation rates in the two models in these locations as documented in Noel et al. [10
]. Northern Greenland has low precipitation rates and once darker glacier ice is exposed after fresh snow with a higher albedo melts away, large amounts of ice can be lost [80
]. A small difference in precipitation in one model compared to the other, or different albedo parametrisations that substantially vary melt and runoff between the models, can thus have a large impact in these two basins. Differences in cloud parameterisations may well also result in a similar effect [11
]. The regional scale analysis here also demonstrates that during the high mass loss year of 2012, around 25% of the mass loss came from basin 6 in western Greenland, driven by high melt rates. An underestimate in melt rates in HIRHAM5, and likely in other RCMs, particularly in the region of basin 6 during the heat wave of 2012 was identified by Fausto et al. [81
] who compared weather station data on the ice sheet from the PROMICE network with model output. Their analysis suggested that this underestimate resulted from a bias in roughness lengths leading to underestimates of sensible and latent heat fluxes. Conversely, analysis by [82
] showed relatively consistent and reliable performance by several different SMB models including HIRHAM and RACMO at a field site within this basin, suggesting that local factors can significantly influence model performance. Our analysis thus shows the value of detailed observations of mass change from field and satellite observations in interpreting and improving process understanding in Greenland and points to areas where the physical processes within regional climate modelled SMB need to be improved.
3.4. Calving Front Location and Ice Sheet Mass Budget
As the analysis of the GMB data compared with RCM data in Figure 7
shows, calving and ice-ocean interactions are an important component of the Greenland ice sheet mass budget. Since the start of the ESA-CCI project, outlet glacier retreat rates and associated increased calving rates have been a significant contribution to the observed mass loss from the Greenland ice sheet. Ref. [1
] suggest that around one third of ice lost from the Greenland ice sheet is the result of iceberg calving and related processes. Out of the 28 glaciers monitored by the CCI project, all except two underwent significant retreat during the period 1990 to 2016 (Figure 8
), though at very different rates when averaged over the long term. The time series in the calving front location (CFL) dataset are at least 20 years and in some cases almost 30 years suggesting that the consistent retreat of glaciers observed around Greenland is the result of widespread climate change in the region. While the 28 study glaciers are only a small sample, the pattern of calving front retreat is consistent with the other datasets we discuss here and with other studies in the literature (for example, [79
]) and shows that the Greenland ice sheet is retreating both due to increased melt and runoff and due to dynamically controlled and ocean driven processes.
As calving rates and calving front location are controlled by multiple processes (see below and also [27
]), the total location change and retreat rate are sensitive to the start and end dates chosen. As Figure 9
shows, CFL is often at a stable position for a decade or longer, before a calving retreat that leads to a rapid change in position before establishing a new stable location. At Petermann glacier for example, the CFL gradually moves forward before a single calving event shortened the ice shelf dramatically, after which the CFL again started to move forward again. The normally episodic nature of changes in CFL emphasises the need for long-term monitoring to understand the behaviour of calving fronts and distinguish if retreat is within the bounds of natural variability or due to an external climate change forcing.
Significant outstanding research questions on calving outlet glaciers include how much of an influence surface and submarine melting of the glacier front have on calving front positions and the implementation of calving physics in ice sheet models. This is not a trivial problem and often relies on overly simplified empirical functions [73
]. New process models, however, are now capable of detailed understanding of the key processes and are helping to improve calving laws [83
] but as [84
] show, substantial uncertainty around the rate and magnitude of future mass loss from the Greenland ice sheet due to calving will persist in the next round of the coupled model intercomparison project (CMIP6). The CFL dataset therefore presents significant possibilities for future work parameterising and evaluating calving losses from ice sheet models.
Most of the calving outlet glaciers in Greenland are tidewater type, that is with usually only a short and transiently floating calving front [27
]. However, floating ice shelves similar to those found in Antarctica do exist in Greenland although typically confined within fjords [85
]. During the course of the CCI project 2 of the 5 remaining floating ice shelves, Hagen Bræ and Zachariæ Isstrøm had significant retreat rates leaving only Petermann, Ryder and 79 glaciers with large and intact floating ice shelves at the present day. These glaciers with floating ice shelves are significant because each of these glaciers drain relatively large proportions of the ice sheet. The break-up of ice shelves that stabilise the outlet glaciers can lead to accelerations in ice velocity and therefore higher rates of sea level rise [29
], but different glaciers respond in different ways to changes at the front [86
] and careful modelling studies in combination with good observational data are required to understand the important processes [87
]. For example, Rathmann et al. [21
] showed different seasonal accelerations at neighbouring glaciers Zachariæ Isstrøm and 79 glacier in response to very similar runoff rates. Part of the differences were explained by different hydrological regimes but there is also a possibility that response to a climate forcing may be delayed by other glaciological processes such as differing bed topographies, geothermal heat flux or past strain histories. Similarly, Hogg et al. [16
] showed that the grounding line at Petermann glacier has been mostly stable over the last half decade suggesting that the glacier is likely in equilibrium with the present day climate. However, more recently Rückamp et al. [88
] showed an important link between calving retreat and increases in ice velocity at Petermann glacier as well as a retreat in the grounding line location, suggesting that longer time series of data are important to assess stability of ice shelves. By combining multiple datasets including the ice velocity, grounding line and calving front location with modelled surface runoff and an ice fracture model Rosier et al. [89
], in review assess how stable the Petermann glacier ice shelf actually is (Figure 9
). We here give a short overview as a case study in using multiple data types to gain insight into glacier processes.
Analysis of the ice velocity dataset shows that velocity increases significantly in summer, likely due to melt water at the bed of the grounded part of Petermann glacier, reducing the basal pressure (Figure 10
A). Increasing melt and runoff due to climate warming is therefore a plausible mechanism that can lead to increased calving and retreat of the calving fronts. Ice velocity data is used to derive strain rates that are further used to calculate crevasse penetration depths as described in [90
] (Figure 10
B). Crevasse depth models have been implemented as a parameterisation in ice sheet models to determine calving front location and the associated dynamic feedbacks by, for example Nick et al. [73
]. The CCI ice velocity data products are therefore an ideal opportunity to derive strain rates and constrain estimates of calving activity.
Using Glen’s flow law [91
] the principle stresses are calculated from the strain rates. We then apply a linear elastic fracture mechanics formulation to calculate the penetration depth of a crevasse for the given tensile stress based on [90
]. Apart from the internal stresses, the maximum depth of a crevasse, and therefore whether calving can also occur is also controlled by the spacing between crevasses and the presence of water in crevasses as shown in Figure 10
C,D. The stress intensity factor (shown in Figure 10
C) is a quantitative measure that shows the stress state of a fracture considering the applied loading and fracture geometry. When the stress intensity factor reaches an empirically derived threshold known as fracture toughness, the fracture is considered unstable allowing it to propagate the entire thickness of the ice shelf rapidly. In Figure 10
we use a value of 100 MPa for the fracture toughness, based on analysis by [90
]. Fracture spacing, W, is important in this analysis. The closer spaced crevasses (W < 400m) penetrate to shallower depths whereas the more widely spaced crevasses (W > 450m) lead to unstable propagation through the full ice shelf thickness. The presence of water in crevasses enhances crevasse penetration and can lead to fractures propagating through the entire thickness of the ice sheet [27
]. At Petermann glacier in northern Greenland, liquid water in crevasses is present only during the summer months when there is liquid run-off present, nonetheless as Figure 10
D shows even closely spaced crevasses filled with water can penetrate the full ice shelf thickness and at lower strain rates than dry crevasses. The sensitivity of the fracture depth to water suggests that under a warming climate with greater melt water production at the surface, the ice shelf may well be vulnerable to break up as other glaciers in this region have also collapsed, for example, the retreat at C.H. Ostenfeldt glacier shown in Figure 8
and described along with other Greenland glaciers by Hill et al. [85
It follows that with increasing air temperatures, a higher density of lakes can form increasing the volume of water available for hydro fracturing and causing an increase in the ice tongue instability. However, this effect can be mitigated by drainage of excess water through surface rivers and basal channels [93
]. Figure 10
therefore only shows the potential effect increasing runoff can have on the stability of the Petermann ice shelf. Equally, higher velocities, leading to higher strain rates could lead to deeper fractures, though this effect is reduced if more crevasses open since the crevasse spacing also affects the depth of an individual fracture. The final fracture depth is dependent on the ice thickness by the ratio of crevasse depth over ice thickness. A thicker ice shelf means that the ratio is smaller and, all other things considered equal, would reduce the final fracture depth. This is however only the case in the situation where there is enough water available for hydro fracturing, in the case that no water is present the final fracture depth would increase slightly relative to the thinner ice shelf. As [95
] showed that basal melting is also important at Petermann glacier in reducing ice shelf thickness, ocean forcing that increases basal melt rates may at least initially and somewhat paradoxically help to stabilise fracture propagation via the geometric effect.
Regional climate change projections for example, [45
], show a significant increase in melt water runoff across Greenland under two different climate change scenarios, particularly in northern Greenland. This indicates that floating ice shelves like Petermann glacier are vulnerable to future retreat, a conclusion supported by Nick et al. [86
] and a possible explanation for the loss of the other ice shelves around Greenland. Extending this analysis at Petermann glacier to other outlet glaciers covered by the CCI Greenland ice sheet datasets could also give a wider indication of the potential stability of outlet glaciers. As the analysis of the GMB data in Figure 7
shows, calving and submarine processes are likely to be very important mass budget components in basins 3 and 4 in particular and to a lesser extent basins 5 and 7.