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It is notoriously difficult to couple surface mass balance (SMB) results from climate models to the changing geometry of an ice sheet model. This problem is traditionally avoided by using only accumulation from a climate model, and parameterizing the meltwater run-off as a function of temperature, which is often related to surface elevation (Hs). In this study, we propose a new strategy to calculate SMB, to allow a direct adjustment of SMB to a change in ice sheet topography and/or a change in climate forcing. This method is based on elevational gradients in the SMB field as computed by a regional climate model. Separate linear relations are derived for ablation and accumulation, using pairs of Hs and SMB within a minimum search radius. The continuously adjusting SMB forcing is consistent with climate model forcing fields, also for initially non-glaciated areas in the peripheral areas of an ice sheet. When applied to an asynchronous coupled ice sheet – climate model setup, this method circumvents traditional temperature lapse rate assumptions. Here we apply it to the Greenland Ice Sheet (GrIS). Experiments using both steady-state forcing and glacial-interglacial forcing result in realistic ice sheet reconstructions.

We present a new parameterisation that relates surface mass balance (SMB: the sum of surface accumulation and surface ablation) to changes in surface elevation of the Greenland ice sheet (GrIS) for the MAR (Modèle Atmosphérique Régional: Fettweis, 2007) regional climate model. The motivation is to dynamically adjust SMB as the GrIS evolves, allowing us to force ice sheet models with SMB simulated by MAR while incorporating the SMB–elevation feedback, without the substantial technical challenges of coupling ice sheet and climate models. This also allows us to assess the effect of elevation feedback uncertainty on the GrIS contribution to sea level, using multiple global climate and ice sheet models, without the need for additional, expensive MAR simulations. We estimate this relationship separately below and above the equilibrium line altitude (ELA, separating negative and positive SMB) and for regions north and south of 77° N, from a set of MAR simulations in which we alter the ice sheet surface elevation. These give four "SMB lapse rates", gradients that relate SMB changes to elevation changes. We assess uncertainties within a Bayesian framework, estimating probability distributions for each gradient from which we present best estimates and credibility intervals (CI) that bound 95% of the probability. Below the ELA our gradient estimates are mostly positive, because SMB usually increases with elevation: 0.56 (95% CI: −0.22 to 1.33) kg m−3 a−1 for the north, and 1.91 (1.03 to 2.61) kg m−3 a−1 for the south. Above the ELA, the gradients are much smaller in magnitude: 0.09 (−0.03 to 0.23) kg m−3 a−1 in the north, and 0.07 (−0.07 to 0.59) kg m−3 a−1 in the south, because SMB can either increase or decrease in response to increased elevation. Our statistically founded approach allows us to make probabilistic assessments for the effect of elevation feedback uncertainty on sea level projections (Edwards et al., 2014).

Data collected by two automatic weather stations (AWS) on the Larsen C ice shelf, Antarctica, between 22 January 2009 and 1 February 2011 are analyzed and used as input for a model that computes the surface energy budget (SEB), which includes melt energy. The two AWSs are separated by about 70 km in the north–south direction, and both the near-surface meteorology and the SEB show similarities, although small differences in all components (most notably the melt flux) can be seen. The impact of subsurface absorption of shortwave radiation on melt and snow temperature is significant, and discussed. In winter, longwave cooling of the surface is entirely compensated by a downward turbulent transport of sensible heat. In summer, the positive net radiative flux is compensated by melt, and quite frequently by upward turbulent diffusion of heat and moisture, leading to sublimation and weak convection over the ice shelf. The month of November 2010 is highlighted, when strong westerly flow over the Antarctic Peninsula led to a dry and warm föhn wind over the ice shelf, resulting in warm and sunny conditions. Under these conditions the increase in shortwave and sensible heat fluxes is larger than the decrease of net longwave and latent heat fluxes, providing energy for significant melt.

To estimate the sea level rise (SLR) originating from changes in surface mass balance (SMB) of the Greenland ice sheet (GrIS), we present 21st century climate projections obtained with the regional climate model MAR (Modèle Atmosphérique Régional), forced by output of three CMIP5 (Coupled Model Intercomparison Project Phase 5) general circulation models (GCMs). Our results indicate that in a warmer climate, mass gain from increased winter snowfall over the GrIS does not compensate mass loss through increased meltwater run-off in summer. Despite the large spread in the projected near-surface warming, all the MAR projections show similar non-linear increase of GrIS surface melt volume because no change is projected in the general atmospheric circulation over Greenland. By coarsely estimating the GrIS SMB changes from GCM output, we show that the uncertainty from the GCM-based forcing represents about half of the projected SMB changes. In 2100, the CMIP5 ensemble mean projects a GrIS SMB decrease equivalent to a mean SLR of +4 ± 2 cm and +9 ± 4 cm for the RCP (Representative Concentration Pathways) 4.5 and RCP 8.5 scenarios respectively. These estimates do not consider the positive melt–elevation feedback, although sensitivity experiments using perturbed ice sheet topographies consistent with the projected SMB changes demonstrate that this is a significant feedback, and highlight the importance of coupling regional climate models to an ice sheet model. Such a coupling will allow the assessment of future response of both surface processes and ice-dynamic changes to rising temperatures, as well as their mutual feedbacks.

A firn densification model (FDM) is used to assess spatial and temporal (1979–2200) variations in the depth, density and temperature of the firn layer covering the Antarctic ice sheet (AIS). A time-dependent version of the FDM is compared to more commonly used steady-state FDM results. Although the average AIS firn air content (FAC) of both models is similar (22.5 m), large spatial differences are found: in the ice-sheet interior, the steady-state model underestimates the FAC by up to 2 m, while the FAC is overestimated by 5–15 m along the ice-sheet margins, due to significant surface melt. Applying the steady-state FAC values to convert surface elevation to ice thickness (i.e., assuming flotation at the grounding line) potentially results in an underestimation of ice discharge at the grounding line, and hence an underestimation of current AIS mass loss by 23.5% (or 16.7 Gt yr−1) with regard to the reconciled estimate over the period 1992–2011. The timing of the measurement is also important, as temporal FAC variations of 1–2 m are simulated within the 33 yr period (1979–2012). Until 2200, the Antarctic FAC is projected to change due to a combination of increasing accumulation, temperature, and surface melt. The latter two result in a decrease of FAC, due to (i) more refrozen meltwater, (ii) a higher densification rate, and (iii) a faster firn-to-ice transition at the bottom of the firn layer. These effects are, however, more than compensated for by increasing snowfall, leading to a 4–14% increase in FAC. Only in melt-affected regions, future FAC is simulated to decrease, with the largest changes (−50 to −80%) on the ice shelves in the Antarctic Peninsula and Dronning Maud Land. Integrated over the AIS, the increase in precipitation results in a similar volume increase due to ice and air (both ~150 km3 yr−1 until 2100). Combined, this volume increase is equivalent to a surface elevation change of +2.1 cm yr−1, which shows that variations in firn depth remain important to consider in future mass balance studies using satellite altimetry.

Predicting the climate for the future and how it will impact ice sheet evolution requires coupling ice sheet models with climate models. However, before we attempt to develop a realistic coupled setup, we propose, in this study, to first analyse the impact of a model simulated climate on an ice sheet. We undertake this exercise for a set of regional and global climate models. Modelled near surface air temperature and precipitation are provided as upper boundary conditions to the GRISLI (GRenoble Ice Shelf and Land Ice model) hybrid ice sheet model (ISM) in its Greenland configuration. After 20 kyrs of simulation, the resulting ice sheets highlight the differences between the climate models. While modelled ice sheet sizes are generally comparable to the observed one, there are considerable deviations among the ice sheets on regional scales. These deviations can be explained by biases in temperature and precipitation near the coast. This is especially true in the case of global models. But the deviations between the climate models are also due to the differences in the atmospheric general circulation. To account for these differences in the context of coupling ice sheet models with climate models, we conclude that appropriate downscaling methods will be needed. In some cases, systematic corrections of the climatic variables at the interface may be required to obtain realistic results for the Greenland ice sheet (GIS).

The growth of frazil or granular ice is an important mode of ice formation in the cryosphere. Recent advances have improved our understanding of the microphysical processes that control the rate of ice-crystal growth when water is cooled beneath its freezing temperature. These advances suggest that crystals grow much faster than previously thought. In this paper, we consider models of a population of ice crystals with different sizes to provide insight into the treatment of frazil ice in large-scale models. We consider the role of crystal growth alongside the other physical processes that determine the dynamics of frazil ice. We apply our model to a simple mixed layer (such as at the surface of the ocean) and to a buoyant plume under a floating ice shelf. We provide numerical calculations and scaling arguments to predict the occurrence of frazil-ice explosions, which we show are controlled by crystal growth, nucleation, and gravitational removal. Faster crystal growth, higher secondary nucleation, and slower gravitational removal make frazil-ice explosions more likely. We identify steady-state crystal size distributions, which are largely insensitive to crystal growth rate but are affected by the relative importance of secondary nucleation to gravitational removal. Finally, we show that the fate of plumes underneath ice shelves is dramatically affected by frazil-ice dynamics. Differences in the parameterization of crystal growth and nucleation give rise to radically different predictions of basal accretion and plume dynamics, and can even impact whether a plume reaches the end of the ice shelf or intrudes at depth.

Ice sheet numerical modeling is an important tool to estimate the dynamic contribution of the Antarctic ice sheet to sea level rise over the coming centuries. The influence of initial conditions on ice sheet model simulations, however, is still unclear. To better understand this influence, an initial state intercomparison exercise (initMIP) has been developed to compare, evaluate, and improve initialization procedures and estimate their impact on century-scale simulations. initMIP is the first set of experiments of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity focusing on the Greenland and Antarctic ice sheets. Following initMIP-Greenland, initMIP-Antarctica has been designed to explore uncertainties associated with model initialization and spin-up and to evaluate the impact of changes in external forcings. Starting from the state of the Antarctic ice sheet at the end of the initialization procedure, three forward experiments are each run for 100 years: a control run, a run with a surface mass balance anomaly, and a run with a basal melting anomaly beneath floating ice. This study presents the results of initMIP-Antarctica from 25 simulations performed by 16 international modeling groups. The submitted results use different initial conditions and initialization methods, as well as ice flow model parameters and reference external forcings. We find a good agreement among model responses to the surface mass balance anomaly but large variations in responses to the basal melting anomaly. These variations can be attributed to differences in the extent of ice shelves and their upstream tributaries, the numerical treatment of grounding line, and the initial ocean conditions applied, suggesting that ongoing efforts to better represent ice shelves in continental-scale models should continue.

Stable isotope ratios δ18O and δD in polar ice provide a wealth of information about past climate evolution. Snow-pit studies allow us to relate observed weather and climate conditions to the measured isotope variations in the snow. They therefore offer the possibility to test our understanding of how isotope signals are formed and stored in firn and ice. As δ18O and δD in the snowfall are strongly correlated to air temperature, isotopes in the near-surface snow are thought to record the seasonal cycle at a given site. Accordingly, the number of seasonal cycles observed over a given depth should depend on the accumulation rate of snow. However, snow-pit studies from different accumulation conditions in East Antarctica reported similar isotopic variability and comparable apparent cycles in the δ18O and δD profiles with typical wavelengths of ∼ 20 cm. These observations are unexpected as the accumulation rates strongly differ between the sites, ranging from 20 to 80 mm w. e. yr−1 ( ∼ 6–21 cm of snow per year). Various mechanisms have been proposed to explain the isotopic variations individually at each site; however, none of these are consistent with the similarity of the different profiles independent of the local accumulation conditions.Here, we systematically analyse the properties and origins of δ18O and δD variations in high-resolution firn profiles from eight East Antarctic sites. First, we confirm the suggested cycle length (mean distance between peaks) of ∼ 20 cm by counting the isotopic maxima. Spectral analysis further shows a strong similarity between the sites but indicates no dominant periodic features. Furthermore, the apparent cycle length increases with depth for most East Antarctic sites, which is inconsistent with burial and compression of a regular seasonal cycle. We show that these results can be explained by isotopic diffusion acting on a noise-dominated isotope signal. The firn diffusion length is rather stable across the Antarctic Plateau and thus leads to similar power spectral densities of the isotopic variations. This in turn implies a similar distance between isotopic maxima in the firn profiles.Our results explain a large set of observations discussed in the literature, providing a simple explanation for the interpretation of apparent cycles in shallow isotope records, without invoking complex mechanisms. Finally, the results underline previous suggestions that isotope signals in single ice cores from low-accumulation regions have a small signal-to-noise ratio and thus likely do not allow the reconstruction of interannual to decadal climate variations.

Computer models are necessary for understanding and predicting marine ice sheet behaviour. However, there is uncertainty over implementation of physical processes at the ice base, both for grounded and floating glacial ice. Here we implement several sliding relations in a marine ice sheet flow-line model accounting for all stress components and demonstrate that model resolution requirements are strongly dependent on both the choice of basal sliding relation and the spatial distribution of ice shelf basal melting.Sliding relations that reduce the magnitude of the step change in basal drag from grounded ice to floating ice (where basal drag is set to zero) show reduced dependence on resolution compared to a commonly used relation, in which basal drag is purely a power law function of basal ice velocity. Sliding relations in which basal drag goes smoothly to zero as the grounding line is approached from inland (due to a physically motivated incorporation of effective pressure at the bed) provide further reduction in resolution dependence.A similar issue is found with the imposition of basal melt under the floating part of the ice shelf: melt parameterisations that reduce the abruptness of change in basal melting from grounded ice (where basal melt is set to zero) to floating ice provide improved convergence with resolution compared to parameterisations in which high melt occurs adjacent to the grounding line.Thus physical processes, such as sub-glacial outflow (which could cause high melt near the grounding line), impact on capability to simulate marine ice sheets. If there exists an abrupt change across the grounding line in either basal drag or basal melting, then high resolution will be required to solve the problem. However, the plausible combination of a physical dependency of basal drag on effective pressure, and the possibility of low ice shelf basal melt rates next to the grounding line, may mean that some marine ice sheet systems can be reliably simulated at a coarser resolution than currently thought necessary.