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We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid-scale representation of calving front motion (Albrecht et al., 2011) and a physically-motivated calving law based on horizontal spreading rates. The model is tested in experiments from the Marine Ice Sheet Model Intercomparison Project (MISMIP). A dynamic equilibrium simulation of Antarctica under present-day conditions is presented in Martin et al. (2011).
We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.
A parameterization for the motion of ice-shelf fronts on a Cartesian grid in finite-difference land-ice models is presented. The scheme prevents artificial thinning of the ice shelf at its edge, which occurs due to the finite resolution of the model. The intuitive numerical implementation diminishes numerical dispersion at the ice front and enables the application of physical boundary conditions to improve the calculation of stress and velocity fields throughout the ice-sheet-shelf system. Numerical properties of this subgrid modification are assessed in the Potsdam Parallel Ice Sheet Model (PISM-PIK) for different geometries in one and two horizontal dimensions and are verified against an analytical solution in a flow-line setup.
Anthropogenic climate change is likely to cause continuing global sea level rise(1), but some processes within the Earth system may mitigate the magnitude of the projected effect. Regional and global climate models simulate enhanced snowfall over Antarctica, which would provide a direct offset of the future contribution to global sea level rise from cryospheric mass loss(2,3) and ocean expansion(4). Uncertainties exist in modelled snowfall(5), but even larger uncertainties exist in the potential changes of dynamic ice discharge from Antarctica(1,6) and thus in the ultimate fate of the precipitation-deposited ice mass. Here we show that snowfall and discharge are not independent, but that future ice discharge will increase by up to three times as a result of additional snowfall under global warming. Our results, based on an ice-sheet model(7) forced by climate simulations through to the end of 2500 (ref. 8), show that the enhanced discharge effect exceeds the effect of surface warming as well as that of basal ice-shelf melting, and is due to the difference in surface elevation change caused by snowfall on grounded versus floating ice. Although different underlying forcings drive ice loss from basal melting versus increased snowfall, similar ice dynamical processes are nonetheless at work in both; therefore results are relatively independent of the specific representation of the transition zone. In an ensemble of simulations designed to capture ice-physics uncertainty, the additional dynamic ice loss along the coastline compensates between 30 and 65 per cent of the ice gain due to enhanced snowfall over the entire continent. This results in a dynamic ice loss of up to 1.25 metres in the year 2500 for the strongest warming scenario. The reported effect thus strongly counters a potential negative contribution to global sea level by the Antarctic Ice Sheet.
Recently observed large-scale disintegration of Antarctic ice shelves has moved their fronts closer towards grounded ice. In response, ice-sheet discharge into the ocean has accelerated, contributing to global sea-level rise and emphasizing the importance of calving-front dynamics. The position of the ice front strongly influences the stress field within the entire sheet-shelf-system and thereby the mass flow across the grounding line. While theories for an advance of the ice-front are readily available, no general rule exists for its retreat, making it difficult to incorporate the retreat in predictive models. Here we extract the first-order large-scale kinematic contribution to calving which is consistent with large-scale observation. We emphasize that the proposed equation does not constitute a comprehensive calving law but represents the first-order kinematic contribution which can and should be complemented by higher order contributions as well as the influence of potentially heterogeneous material properties of the ice. When applied as a calving law, the equation naturally incorporates the stabilizing effect of pinning points and inhibits ice shelf growth outside of embayments. It depends only on local ice properties which are, however, determined by the full topography of the ice shelf. In numerical simulations the parameterization reproduces multiple stable fronts as observed for the Larsen A and B Ice Shelves including abrupt transitions between them which may be caused by localized ice weaknesses. We also find multiple stable states of the Ross Ice Shelf at the gateway of the West Antarctic Ice Sheet with back stresses onto the sheet reduced by up to 90 % compared to the present state.
The largest uncertainty in projections of future sea-level change results from the potentially changing dynamical ice discharge from Antarctica. Basal ice-shelf melting induced by a warming ocean has been identified as a major cause for additional ice flow across the grounding line. Here we attempt to estimate the uncertainty range of future ice discharge from Antarctica by combining uncertainty in the climatic forcing, the oceanic response and the ice-sheet model response. The uncertainty in the global mean temperature increase is obtained from historically constrained emulations with the MAGICC-6.0 (Model for the Assessment of Greenhouse gas Induced Climate Change) model. The oceanic forcing is derived from scaling of the subsurface with the atmospheric warming from 19 comprehensive climate models of the Coupled Model Intercomparison Project (CMIP-5) and two ocean models from the EU-project Ice2Sea. The dynamic ice-sheet response is derived from linear response functions for basal ice-shelf melting for four different Antarctic drainage regions using experiments from the Sea-level Response to Ice Sheet Evolution (SeaRISE) intercomparison project with five different Antarctic ice-sheet models. The resulting uncertainty range for the historic Antarctic contribution to global sea-level rise from 1992 to 2011 agrees with the observed contribution for this period if we use the three ice-sheet models with an explicit representation of ice-shelf dynamics and account for the time-delayed warming of the oceanic subsurface compared to the surface air temperature. The median of the additional ice loss for the 21st century is computed to 0.07 m (66% range: 0.02-0.14 m; 90% range: 0.0-0.23 m) of global sea-level equivalent for the low-emission RCP-2.6 (Representative Concentration Pathway) scenario and 0.09 m (66% range: 0.04-0.21 m; 90% range: 0.01-0.37 m) for the strongest RCP-8.5. Assuming no time delay between the atmospheric warming and the oceanic subsurface, these values increase to 0.09 m (66% range: 0.04-0.17 m; 90% range: 0.02-0.25 m) for RCP-2.6 and 0.15 m (66% range: 0.07-0.28 m; 90% range: 0.04-0.43 m) for RCP-8.5. All probability distributions are highly skewed towards high values. The applied ice-sheet models are coarse resolution with limitations in the representation of grounding-line motion. Within the constraints of the applied methods, the uncertainty induced from different ice-sheet models is smaller than that induced by the external forcing to the ice sheets.
Projections of changes in Antarctic Ice Sheet (AIS) surface mass balance indicate a negative contribution to sea level because of the expected increase in precipitation due to the higher moisture holding capacity of warmer air(1). Observations over the past decades, however, are unable to constrain the relation between temperature and accumulation changes because both are dominated by strong natural variability(2-5). Here we derive a consistent continental-scale increase in accumulation of approximately 5 +/- 1% K-1, through the assessment of ice-core data (spanning the large temperature change during the last deglaciation, 21,000 to 10,000 years ago), in combination with palaeo-simulations, future projections by 35 general circulation models (GCMs), and one high-resolution future simulation. The ice-core data and modelling results for the last deglaciation agree, showing uniform local sensitivities of similar to 6% K-1. The palaeo-simulation allows for a continental-scale aggregation of accumulation changes reaching 4.3% K-1. Despite the different timescales, these sensitivities agree with the multi-model mean of 6.1 +/- 2.6% K-1 (GCMprojections) and the continental-scale sensitivity of 4.9% K-1 (high-resolution future simulation). Because some of the mass gain of the AIS is offset by dynamical losses induced by accumulation(6,7), we provide a response function allowing projections of sea-level fall in terms of continental-scale accumulation changes that compete with surface melting and dynamical losses induced by other mechanisms(6,8,9).
Consequences of twenty-first-century policy for multi-millennial climate
and sea-level change
(2016)
Most of the policy debate surrounding the actions needed to mitigate and adapt to anthropogenic climate change has been framed by observations of the past 150 years as well as climate and sea-level projections for the twenty-first century. The focus on this 250-year window, however, obscures some of the most profound problems associated with climate change. Here, we argue that the twentieth and twenty-first centuries, a period during which the overwhelming majority of human-caused carbon emissions are likely to occur, need to be placed into a long-term context that includes the past 20 millennia, when the last Ice Age ended and human civilization developed, and the next ten millennia, over which time the projected impacts of anthropogenic climate change will grow and persist. This long-term perspective illustrates that policy decisions made in the next few years to decades will have profound impacts on global climate, ecosystems and human societies - not just for this century, but for the next ten millennia and beyond.
The past rapid growth of Northern Hemisphere continental ice sheets, which terminated warm and stable climate periods, is generally attributed to reduced summer insolation in boreal latitudes(1-3). Yet such summer insolation is near to its minimum at present(4), and there are no signs of a new ice age(5). This challenges our understanding of the mechanisms driving glacial cycles and our ability to predict the next glacial inception(6). Here we propose a critical functional relationship between boreal summer insolation and global carbon dioxide (CO2) concentration, which explains the beginning of the past eight glacial cycles and might anticipate future periods of glacial inception. Using an ensemble of simulations generated by an Earth system model of intermediate complexity constrained by palaeoclimatic data, we suggest that glacial inception was narrowly missed before the beginning of the Industrial Revolution. The missed inception can be accounted for by the combined effect of relatively high late-Holocene CO2 concentrations and the low orbital eccentricity of the Earth(7). Additionally, our analysis suggests that even in the absence of human perturbations no substantial build-up of ice sheets would occur within the next several thousand years and that the current interglacial would probably last for another 50,000 years. However, moderate anthropogenic cumulative CO2 emissions of 1,000 to 1,500 gigatonnes of carbon will postpone the next glacial inception by at least 100,000 years(8,9). Our simulations demonstrate that under natural conditions alone the Earth system would be expected to remain in the present delicately balanced interglacial climate state, steering clear of both large-scale glaciation of the Northern Hemisphere and its complete deglaciation, for an unusually long time.