The Arctic is the region of the Earth experiencing the largest increase in temperature since the pre-industrial era , with consequences already perceptible on the mass evolution of the Arctic ice caps and the Greenland ice sheet . The evolution of the Greenland ice sheet (GrIS) is governed by variations of ice dynamics and surface mass balance (SMB), the latter being defined as the difference between snow accumulation that is further transformed into ice, and the ablation processes (i.e. surface melting and sublimation). While surface melting strongly depends on the surface energy balance, snowfall is primarily controlled by atmospheric conditions (wind, humidity content, cloudiness, etc.). However, various feedbacks between the atmosphere and the GrIS impact the surface characteristics such as ice extent and thickness. This has potential consequences on ice dynamics (e.g. due to changes in surface slopes) and may lead to SMB variations that can therefore affect the total ice mass. These changes may in turn alter both local and global climate. As an example, changes in near-surface temperature and surface energy balance may occur in response to changes in orography (temperature–elevation feedback) or changes in ice-covered area (planetary albedo feedback; see and ). On the other hand, topography changes may alter the atmospheric circulation patterns causing changes in heat and humidity transports.

Quantifying the balance between these different processes and feedbacks that regulate transient ice sheet change is required to understand and project more confidently the evolution of the GrIS under current and future global warming. Although numerous studies highlighted the importance of correctly representing the interactions between the GrIS topography changes and the atmosphere , only a few global or regional models have taken the GrIS topography changes into account to compute the future evolution of the SMB and energy budget over the GrIS. For example, the CMIP5 climate models unanimously represent the ice sheet component with a fixed and constant topography, even under a warm transient climate forcing.

To explore the importance of SMB–elevation feedbacks for the future GrIS evolution, used a coarse-resolution atmosphere–ocean general circulation model (AOGCM, ECHAM5.2) coupled to an ice sheet model (ISM, SICOPOLIS3.0) forced under different representative concentration pathway (RCP) scenarios (up to 2100) and their extensions (from 2100 to 2300). Compared to a control experiment in which the ISM is forced off-line by the atmospheric model run with the fixed present-day GrIS topography, they found an amplification of ice mass loss of 8 %–11 % and 24 %–31 % in 2100 and 2300, respectively, when the elevation feedbacks are taken into account (i.e. in the coupled experiment). This results from the combination of the positive elevation–SMB feedback in low-lying areas, the negative feedback related to the elevation–desertification effect in accumulation areas, and the changes of surface slopes resulting from high mass loss in ablation areas and a slight snowfall increase in the accumulation zone, enhancing the ice transport from the central regions to the ice margins. Their study is focused on the added value of incorporating the coupled processes. However, as specified in , their model is not able to accurately reproduce the observed GrIS because (1) the ice sheet model, based on the shallow-ice approximation , is not designed to properly represent fast ice flows in the outlet glaciers and (2) the resolution of the AGCM (∼3.75∘) and the ice sheet model (10 km) are too coarse to correctly capture the steep slopes at the ice margins and the atmospheric processes acting on the SMB calculation.

Using the AGCM NCAR-CAM3 run at different spatial resolutions (T21 to T85) and coupled to the SICOPOLIS ice sheet model, investigated how the atmospheric model resolution influenced the simulated ice sheets at the Last Glacial Maximum. They found that the North American and the Eurasian ice sheets were properly reproduced with the only T85 run. According to the authors, this is likely due to the inability of the atmospheric model to properly capture the temperature and precipitation fields (used to compute the SMB) at lower horizontal resolutions, as a consequence of the poorly resolved planetary waves and smooth topography. However, running high-resolution atmospheric models at the global scale requires large computing resources. To circumvent the low resolution, some authors have used the method of elevation classes and are therefore able to offer a high resolution in the direction of the slope gradient e.g..

An alternative solution consists in using regional climate models (RCMs) to produce high-resolution atmospheric fields and much more robust energy balance and SMB calculations. A number of RCMs have been developed for the polar regions such as MAR , RACMO2 , Polar MM5 or HIRHAM5 . However, the highest resolution of the RCMs is limited by the use of the hydrostatic approximation and often remains below the resolution of Greenland ice sheet models, which are generally running at a 5–10 km scale or even below e.g.. 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, developed a method to downscale each SMB MAR component (snowfall, rainfall, runoff, sublimation and evaporation) onto a finer grid as a function of elevation changes. An alternative approach to correct the SMB field from surface elevation changes is based on statistical relationships between altitude and SMB . Also derived with MAR, the approach of computes a SMB–elevation feedback gradient for regions below and above the equilibrium line altitude in the northern and southern parts of GrIS, with limited additional computing resources. However, in both parameterizations by and , the authors only consider a strict linear relationship between topography and SMB changes. Although changes in temperature can be derived from a linear vertical lapse rate, other processes governing the SMB such as those related to energy balance, precipitation 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 ice sheet margins.

One of the first requirements to improve the representation of atmosphere–GrIS feedbacks is to use a high-resolution atmospheric model to better represent the elevation gradients and therefore the steep topography near the ice margins in the ablation zone. Additionally, the use of a detailed snow model such as those implemented in MAR or RACMO2 allows a more accurate description of the surface properties (e.g. snow cover, albedo, surface melting) and therefore a better representation of the surface energy balance and hence of surface mass balance. RCMs developed for polar regions are also able to represent more atmospheric and land surface processes occurring in these regions such as bare ice albedo and katabatic winds , being also strongly dependent on topography and thus on resolution.

The second fundamental requirement to describe the interactions between atmosphere and GrIS is to represent the ice sheet topography changes in the atmospheric model by using an ISM (instead of the fixed geometry typically used) to take into account the effects of ice dynamics on the ice sheet topography changes. This can be achieved through a numerical coupling between the RCM and the ISM. More than 20 ice sheet models exist e.g. and are currently compared in the Ice Sheet Model Intercomparison Project . They represent thermodynamical and physical processes of the GrIS with different levels of complexities . They all compute the dynamical response of the GrIS to a given climate forcing such as the SMB and the near surface temperature (ST) fields computed by RCMs (or global models). However, as SMB and ST from the climate models do not take into account the GrIS evolution, the climate forcing used by the ISM could be flawed.

In order to explicitly represent the feedbacks between the GrIS and the atmosphere and to evaluate their impacts on the ice sheet evolution, we coupled the polar regional climate model MAR to the GRISLI ice sheet model . To assess the importance of an explicit representation of the surface elevation and albedo feedbacks, this coupled experiment is then compared to a one-way coupling experiment, in which the GrIS–atmosphere interactions are not taken into account, and to a third experiment where the effects of topography changes on the simulated SMB are parameterized.

A description of the atmospheric and the ice sheet models is given in Sect. . Section  describes the experimental setup of the three coupling methods considered in this study. The results are presented in Sect. . We first describe the coupled experiment in detail before comparing it to the other uncoupled experiments. These sections are followed by a discussion related to the different coupling approaches (Sect. ) and the conclusions of this study (Sect. ).

The aim of this study is to assess to what extent accounting for the atmosphere–GrIS interactions influences the GrIS evolution in terms of changes in SMB, ST, ice thickness and sea-level rise. To achieve this goal, we designed three experiments based on coupling methods of different complexities to account for the interactions between MAR and GRISLI. For all the experiments described below, the climatic forcing is designed as follows: MAR is forced at its lateral boundaries by transient MIROC5 atmospheric fields from the CMIP5 historical run (1970–2005) and RCP8.5 scenario (2006–2100). In order to extend the MAR simulation until 2150 and in the absence of a MIROC5 simulation performed under a prolonged RCP8.5 scenario (i.e. after 2100), MAR is forced from 2101 to 2150 with the 2095 MIROC5 climate. We chose the year 2095 because, averaged over the entire GrIS, the 2095 mean climate is one of the closest to the decadal 2090–2100 one. This implies that both climate changes and large-scale inter-annual variability are neglected beyond 2100.

The evolution of the GrIS and its contribution to sea-level rise presented in this study are the first ones inferred from a regional atmospheric model synchronously coupled to an ice sheet model, thus accounting for the GrIS–atmosphere feedbacks. To evaluate the added value of a coupled RCM–ISM, we explored the importance of the GrIS–atmosphere feedbacks by comparing the results of the coupled experiment to those coming from two uncoupled experiments, PF (parameterized elevation feedbacks) and NF (no feedback). We showed that the impact of taking the feedbacks into account increases over time. This study is a necessary step toward a more accurate assessment of the contribution of Greenland to future sea-level rise and of its impact on the climate system. However, future refinements can be envisaged.

One of the main uncertainties in assessing the GrIS contribution to future sea-level rise comes from the climate projections themselves. For example, using five different global climate models to force MAR at its lateral boundaries under RCP8.5 conditions, provide SMB-inferred estimates of this contribution ranging from 4.6 to 13.1 cm in 2100. This range is fully comparable to that reported by , who used MAR simulations (forced by three GCMs chosen from the sample) to force the SICOPOLIS ice sheet model. Whatever the experimental design, the large spread in SLR projections highlights the great uncertainty associated with the choice of the global climate model used to force MAR at its lateral boundaries. It raises the question of to what extent the differences between 2W and PF or NF experiments would be amplified (mitigated) with a stronger (weaker) climate forcing than that simulated by MIROC5. Another question concerns the impact of a constant MIROC5 climate used to force MAR beyond 2100. As outlined in Sect. , this results in discarding the continued change that the climate will likely undergo beyond 2100 suggesting that our SLR projections are underestimated. Another consequence is that inter-annual variability is neglected after 2100. This can lead to conservative estimates of the Greenland contribution to sea-level rise in the future due to non-linearities of the SMB. On the other hand, the imprint of the 2095 MIROC5 climate may amplify regional changes of the GrIS response. There is therefore a strong need for iterating the present study with different global climate simulations run under an extended RCP8.5 scenario, but also with different regional climate models that may have different sensitivities, to more accurately assess the impact of the different GrIS–atmosphere feedbacks and to better evaluate the uncertainty associated with the projected sea-level rise contribution from the GrIS.

Another limitation is related to the 2000-year relaxation GRISLI experiment, run at the end of the initialization procedure to reduce the model drift in terms of ice volume. This produces residual differences with the observed topography used in the MAR simulations. This has important consequences on the MAR simulated climate. In particular, the steeper slopes existing in the GRISLI topography (i.e. Sctrl) tend to produce unrealistic katabatic winds. Therefore, we have chosen in this study to use an anomaly method of the surface elevation onto which the SMB and ST fields are downscaled at the 5 km resolution grid (Eq. ). The objective of this approach was first to maintain the realism of the simulated present-day climate computed on the observed topography and, secondly, to avoid inconsistencies between the climate simulated by MAR and that which was used to force GRISLI. However, this implies that the forcing climate is not fully consistent with the GRISLI topography. This should be taken into consideration in a future work to improve the quality of our results. As an example, a reasonable compromise to avoid the use of anomaly method would be to use the topography obtained at the end of the iterative initialization process (rather than Sctrl) as initial MAR topography to keep the mismatch with the observed topography as low as possible, and to initialize and perform MAR simulations with this new topography. Moreover, the use of an anomaly method to account for the change in topography is incompatible with a conservative coupling between the ice sheet model and the climate model. This is further amplified by the fact that we use a flux correction outside the present-day ice margin to force ice removal. This methodology has been followed to limit the impact of biases from the atmospheric model and from the initialization procedure, but the imposed ice removal outside the present-day ice mask may locally bias the model response towards increased ice thinning. Since our simulations are run under the RCP8.5 forcing scenario, this probably has a negligible impact because the GrIS is likely to experience a retreat from the present-day ice margin. However, further studies with alternative scenarios and/or GCM forcing, and even more paleoclimate studies, should ideally avoid using this kind of flux correction.

In addition, difference of resolution between MAR (25 km) and GRISLI (5 km) can cause artefacts in the results, especially at the edges of the ice sheet. Indeed, in the corresponding MAR grid cells, a fraction of permanent ice cover may coexist with a non-zero fraction of tundra. Since the surface elevation changes computed in MAR from the aggregated GRISLI topography are weighted as a function of the fraction of the different surface areas, they may be underestimated as the tundra soil type is not subject to any change in altitude. This artefact has been illustrated in Sect.  with the example of the behaviour of katabatic winds that are artificially reduced in our simulation at the ice sheet margin. Moreover, since the margin regions are those experiencing the strongest changes in altitude, they are also the most sensitive to climate change. As a consequence, an improper estimation of the topography changes may induce improper SMB changes. This underlines the need for increasing the atmospheric model resolution as far as possible to avoid such artefacts and to better represent the fine-scale atmospheric-topography feedbacks impacting the SMB. Indeed, higher spatial resolution could resolve finer-scale ice sheet dynamics to better represent the ice flow in outlet glacier or better represent fine-scale atmospheric-topography feedbacks impacting the SMB in these regions. However, a compromise must be reached between the additional computing resources and the required degree of accuracy of sea-level projections.

Regarding the ice sheet model, a 5 km horizontal resolution does not permit the capture of the complex ice flow patterns of smallest outlet glaciers, whose characteristic length scale can be less than 1 km and to accurately quantify the ice discharge at the marine front. This may have large implications in the sea-level rise estimates. Using a 3-D ice sheet model with prescribed outlet glacier retreat, found an additional SLR contribution from outlet glaciers of 0.8 to 1.8 cm in 2100 and 1.3 to 3.8 cm in 2200, with the influence of their dynamics on SLR projections decreasing with time and with the increasing importance of the atmospheric forcing. This is in line with the fact that ice flow acts to counteract ice loss from surface melting (see Sect. ), as previously outlined by several authors . However, despite the possible decreasing influence of marine terminating glaciers at the centennial timescale, it is essential to more accurately evaluate the impact of ice dynamics and to better capture the complex geometry of fjords surrounding the marine-terminating glaciers.

There is a growing amount of evidence for attributing the acceleration of outlet glaciers to the intrusion of warm waters from adjacent oceans in the fjord systems or in the cavity of floating ice tongues e.g. that can destabilize the glacier front and/or favour the ice-shelf breakup , thereby decreasing the buttressing effect and increasing the ice calving. In turn, the released freshwater flux in ocean may impact sea-surface temperatures, oceanic circulation and sea-ice cover. Moreover, atmosphere–ocean feedbacks also have an impact on the GrIS. As an example, showed that the disappearance of Arctic sea ice in summer induced by ocean warming enhances surface melting in northern Greenland through a decrease of surface albedo and the subsequent atmospheric warming. Thus, the absence of the oceanic component in our modelling setup appears as a limiting factor, although the direct impact of ocean via sub-shelf melt at the ice sheet margin will likely be limited in the future as a result of inland retreat of GrIS.

Our initialization method adjusts the basal drag coefficient in such a way that the departure between the observed and the initial GRISLI topographies is reduced. The resulting β coefficient is spatially varied but is taken constant in time. This assumption may likely be valid for short-term forward simulations but is probably overly simplistic. On the one hand, the basal drag tends to be smaller towards the margins with respect to the interior. As the ice sheet retreats inland, a reduction in basal drag for a specific location can be expected, due for example to a decreasing effective pressure. On the other hand, changing basal hydrological conditions can also alter the basal drag. This can occur as a result of rainfall or surface meltwater infiltration that can refreeze at depth or propagate all the way to the bottom of the ice sheet and increase basal lubrication . Therefore, a time constant basal drag coefficient inferred under present-day conditions may underestimate the ice flow acceleration. A few models describing the vertical inflow exist e.g. but are generally run at the regional scale and at very high spatial resolution (a few tens to a few hundred metres at most). Implementing such models in large-scale ice sheet models is currently outside the realm of possibilities. However, as there is a growing interest in performing ice sheet projections over multi-centennial timescale, large-scale ice sheet models would undoubtedly benefit from the implementation of simplified infiltration schemes e.g., so as to account for the impact of ongoing changes in surface meltwater on ice flow.

An additional limitation related to the choice of our spin-up procedure is that the glacial–interglacial signature of past climatic changes is ignored. Neglecting the climate history of the Greenland ice sheet implies ice temperatures that are too warm. This may have an impact on the future GrIS evolution and on its contribution to sea-level rise. Indeed, the basal drag coefficient inferred from the inverse method may be too high so as to compensate the errors induced by the artificial warming. However, using a higher-order ice flow model, showed that at the centennial timescale the basal conditions and the GrIS projections are only weakly sensitive to the initial vertical temperature profile but are critically dependent on atmospheric conditions.

Despite these limitations, the sea-level projections performed with GRISLI compare well with those conducted with more sophisticated ice sheet models , and the simulated surface ice velocities present a good agreement with the observed ones (Fig. S11). It appears thus as a good numerical tool to be coupled with a regional climate model with a reasonably good representation of the ice dynamics and limited computational resources.

This study is based on the first regional atmosphere–ice sheet coupled model that allows the GrIS–atmosphere feedbacks to be accounted for. Using this new model, we investigated the GrIS evolution and its contribution to sea-level rise from 2000 to 2150 under a prolonged RCP8.5 scenario (2W experiment). The importance of the GrIS–atmosphere feedbacks has been assessed through the comparison of the two-way coupled experiment with two other simulations based on simpler coupling strategies: the NF experiment in which the MAR outputs are directly used as GRISLI forcing and the PF experiment in which the elevation feedbacks are parameterized. In both NF and PF experiments, changes in topography simulated by GRISLI are not updated in the atmospheric model. The main conclusions drawn from this study as follows.

Accounting for the GrIS–atmosphere feedbacks amplifies the ice mass loss and changes in ice sheet geometry, with increased surface slopes from the central regions to margin areas, as well as consequences on Greenland ice velocities.