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- ItemFracture-induced softening for large-scale ice dynamics(München : European Geopyhsical Union, 2014) Albrecht, T.; Levermann, A.Floating ice shelves can exert a retentive and hence stabilizing force onto the inland ice sheet of Antarctica. However, this effect has been observed to diminish by the dynamic effects of fracture processes within the protective ice shelves, leading to accelerated ice flow and hence to a sea-level contribution. In order to account for the macroscopic effect of fracture processes on large-scale viscous ice dynamics (i.e., ice-shelf scale) we apply a continuum representation of fractures and related fracture growth into the prognostic Parallel Ice Sheet Model (PISM) and compare the results to observations. To this end we introduce a higher order accuracy advection scheme for the transport of the two-dimensional fracture density across the regular computational grid. Dynamic coupling of fractures and ice flow is attained by a reduction of effective ice viscosity proportional to the inferred fracture density. This formulation implies the possibility of non-linear threshold behavior due to self-amplified fracturing in shear regions triggered by small variations in the fracture-initiation threshold. As a result of prognostic flow simulations, sharp across-flow velocity gradients appear in fracture-weakened regions. These modeled gradients compare well in magnitude and location with those in observed flow patterns. This model framework is in principle expandable to grounded ice streams and provides simple means of investigating climate-induced effects on fracturing (e.g., hydro fracturing) and hence on the ice flow. It further constitutes a physically sound basis for an enhanced fracture-based calving parameterization.
- ItemSimulating the Greenland ice sheet under present-day and palaeo constraints including a new discharge parameterization(München : European Geopyhsical Union, 2015) Calov, R.; Robinson, A.; Perrette, M.; Ganopolski, A.In this paper, we propose a new sub-grid scale parameterization for the ice discharge into the ocean through outlet glaciers and inspect the role of different observational and palaeo constraints for the choice of an optimal set of model parameters. This parameterization was introduced into the polythermal ice-sheet model SICOPOLIS, which is coupled to the regional climate model of intermediate complexity REMBO. Using the coupled model, we performed large ensemble simulations over the last two glacial cycles by varying two major parameters: a melt parameter in the surface melt scheme of REMBO and a discharge scaling parameter in our parameterization of ice discharge. Our empirical constraints are the present-day Greenland ice sheet surface elevation, the surface mass balance partition (ratio between total ice discharge and total precipitation) and the Eemian interglacial elevation drop relative to present day in the vicinity of the NEEM ice core. We show that the ice discharge parameterization enables us to simulate both the correct ice-sheet shape and mass balance partition at the same time without explicitly resolving the Greenland outlet glaciers. For model verification, we compare the simulated total and sectoral ice discharge with other estimates. For the model versions that are consistent with the range of observational and palaeo constraints, our simulated Greenland ice sheet contribution to Eemian sea-level rise relative to present-day amounts to 1.4 m on average (in the range of 0.6 and 2.5 m).
- ItemAntarctic sub-shelf melt rates via PICO(München : European Geopyhsical Union, 2018) Reese, Ronja; Albrecht, Torsten; Mengel, Matthias; Asay-Davis, Xylar; Winkelmann, RicardaOcean-induced melting below ice shelves is one of the dominant drivers for mass loss from the Antarctic Ice Sheet at present. An appropriate representation of sub-shelf melt rates is therefore essential for model simulations of marine-based ice sheet evolution. Continental-scale ice sheet models often rely on simple melt-parameterizations, in particular for long-term simulations, when fully coupled ice–ocean interaction becomes computationally too expensive. Such parameterizations can account for the influence of the local depth of the ice-shelf draft or its slope on melting. However, they do not capture the effect of ocean circulation underneath the ice shelf. Here we present the Potsdam Ice-shelf Cavity mOdel (PICO), which simulates the vertical overturning circulation in ice-shelf cavities and thus enables the computation of sub-shelf melt rates consistent with this circulation. PICO is based on an ocean box model that coarsely resolves ice shelf cavities and uses a boundary layer melt formulation. We implement it as a module of the Parallel Ice Sheet Model (PISM) and evaluate its performance under present-day conditions of the Southern Ocean. We identify a set of parameters that yield two-dimensional melt rate fields that qualitatively reproduce the typical pattern of comparably high melting near the grounding line and lower melting or refreezing towards the calving front. PICO captures the wide range of melt rates observed for Antarctic ice shelves, with an average of about 0.1 m a−1 for cold sub-shelf cavities, for example, underneath Ross or Ronne ice shelves, to 16 m a−1 for warm cavities such as in the Amundsen Sea region. This makes PICO a computationally feasible and more physical alternative to melt parameterizations purely based on ice draft geometry.
- ItemDesign and results of the ice sheet model initialisation experiments initMIP-Greenland: an ISMIP6 intercomparison(München : European Geopyhsical Union, 2018) Goelzer, Heiko; Nowicki, Sophie; Edwards, Tamsin; Beckley, Matthew; Abe-Ouchi, Ayako; Aschwanden, Andy; Calov, Reinhard; Gagliardini, Olivier; Gillet-Chaulet, Fabien; Golledge, Nicholas R.; Gregory, Jonathan; Greve, Ralf; Humbert, Angelika; Huybrechts, Philippe; Kennedy, Joseph H.; Larour, Eric; Lipscomb, William H.; Le clec'h, Sébastien; Lee, Victoria; Morlighem, Mathieu; Pattyn, Frank; Payne, Antony J.; Rodehacke, Christian; Martin Rückamp, Martin; Saito, Fuyuki; Schlegel, Nicole; Seroussi, Helene; Shepherd, Andrew; Sun, Sainan; van de Wal, Roderik; Ziemen, Florian A.Earlier large-scale Greenland ice sheet sea-level projections (e.g. those run during the ice2sea and SeaRISE initiatives) have shown that ice sheet initial conditions have a large effect on the projections and give rise to important uncertainties. The goal of this initMIP-Greenland intercomparison exercise is to compare, evaluate, and improve the initialisation techniques used in the ice sheet modelling community and to estimate the associated uncertainties in modelled mass changes. initMIP-Greenland is the first in a series of ice sheet model intercomparison activities within ISMIP6 (the Ice Sheet Model Intercomparison Project for CMIP6), which is the primary activity within the Coupled Model Intercomparison Project Phase 6 (CMIP6) focusing on the ice sheets. Two experiments for the large-scale Greenland ice sheet have been designed to allow intercomparison between participating models of (1) the initial present-day state of the ice sheet and (2) the response in two idealised forward experiments. The forward experiments serve to evaluate the initialisation in terms of model drift (forward run without additional forcing) and in response to a large perturbation (prescribed surface mass balance anomaly); they should not be interpreted as sea-level projections. We present and discuss results that highlight the diversity of data sets, boundary conditions, and initialisation techniques used in the community to generate initial states of the Greenland ice sheet. We find good agreement across the ensemble for the dynamic response to surface mass balance changes in areas where the simulated ice sheets overlap but differences arising from the initial size of the ice sheet. The model drift in the control experiment is reduced for models that participated in earlier intercomparison exercises.
- ItemA simple equation for the melt elevation feedback of ice sheets(Katlenburg-Lindau : European Geosciences Union, 2016) Levermann, Anders; Winkelmann, RicardaIn recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. The rate of ice loss is highly relevant for coastal protection worldwide. The ice loss is likely to increase under future warming. Beyond a critical temperature threshold, a meltdown of the Greenland Ice Sheet is induced by the self-enforcing feedback between its lowering surface elevation and its increasing surface mass loss: the more ice that is lost, the lower the ice surface and the warmer the surface air temperature, which fosters further melting and ice loss. The computation of this rate so far relies on complex numerical models which are the appropriate tools for capturing the complexity of the problem. By contrast we aim here at gaining a conceptual understanding by deriving a purposefully simple equation for the self-enforcing feedback which is then used to estimate the melt time for different levels of warming using three observable characteristics of the ice sheet itself and its surroundings. The analysis is purely conceptual in nature. It is missing important processes like ice dynamics for it to be useful for applications to sea-level rise on centennial timescales, but if the volume loss is dominated by the feedback, the resulting logarithmic equation unifies existing numerical simulations and shows that the melt time depends strongly on the level of warming with a critical slowdown near the threshold: the median time to lose 10 % of the present-day ice volume varies between about 3500 years for a temperature level of 0.5 °C above the threshold and 500 years for 5 °C. Unless future observations show a significantly higher melting sensitivity than currently observed, a complete meltdown is unlikely within the next 2000 years without significant ice-dynamical contributions.
- ItemThe Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet(München : European Geopyhsical Union, 2011) Martin, M.A.; Winkelmann, R.; Haseloff, M.; Albrecht, T.; Bueler, E.; Khroulev, C.; Levermann, A.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.
- ItemInteraction of marine ice-sheet instabilities in two drainage basins: Simple scaling of geometry and transition time(München : European Geopyhsical Union, 2015) Feldmann, J.; Levermann, A.The initiation of a marine ice-sheet instability (MISI) is generally discussed from the ocean side of the ice sheet. It has been shown that the reduction in ice-shelf buttressing and softening of the coastal ice can destabilize a marine ice sheet if the bedrock is sloping upward towards the ocean. Using a conceptional flow-line geometry, we investigate the possibility of whether a MISI can be triggered from the direction of the ice divide as opposed to coastal forcing and explore the interaction between connected basins. We find that the initiation of a MISI in one basin can induce a destabilization in the other. The underlying mechanism of basin interaction is based on dynamic thinning and a consecutive motion of the ice divide which induces a thinning in the adjacent basin and a successive initiation of the instability. Our simplified and symmetric topographic setup allows scaling both the geometry and the transition time between both instabilities. We find that the ice profile follows a universal shape that is scaled with the horizontal extent of the ice sheet and that the same exponent of 1/2 applies for the scaling relation between central surface elevation and horizontal extent as in the pure shallow ice approximation (Vialov profile). Altering the central bed elevation, we find that the extent of grounding-line retreat in one basin determines the degree of interaction with the other. Different scenarios of basin interaction are discussed based on our modeling results as well as on a conceptual flux-balance analysis. We conclude that for the three-dimensional case, the possibility of drainage basin interaction on timescales on the order of 1 kyr or larger cannot be excluded and hence needs further investigation.
- ItemCommitted sea-level rise under the Paris Agreement and the legacy of delayed mitigation action(London : Nature Publishing Group, 2018) Mengel, M.; Nauels, A.; Rogelj, J.; Schleussner, C.-F.Sea-level rise is a major consequence of climate change that will continue long after emissions of greenhouse gases have stopped. The 2015 Paris Agreement aims at reducing climate-related risks by reducing greenhouse gas emissions to net zero and limiting global-mean temperature increase. Here we quantify the effect of these constraints on global sea-level rise until 2300, including Antarctic ice-sheet instabilities. We estimate median sea-level rise between 0.7 and 1.2 m, if net-zero greenhouse gas emissions are sustained until 2300, varying with the pathway of emissions during this century. Temperature stabilization below 2 °C is insufficient to hold median sea-level rise until 2300 below 1.5 m. We find that each 5-year delay in near-term peaking of CO2 emissions increases median year 2300 sea-level rise estimates by ca. 0.2 m, and extreme sea-level rise estimates at the 95th percentile by up to 1 m. Our results underline the importance of near-term mitigation action for limiting long-term sea-level rise risks.
- ItemThe Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 1: Model description(München : European Geopyhsical Union, 2011) Winkelmann, R.; Martin, M.A.; Haseloff, M.; Albrecht, T.; Bueler, E.; Khroulev, C.; Levermann, A.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).
- ItemSimilitude of ice dynamics against scaling of geometry and physical parameters(München : European Geopyhsical Union, 2016) Feldmann, Johannes; Levermann, AndersThe concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations.