TY - JOUR A1 - Levermann, Anders A1 - Winkelmann, Ricarda A1 - Nowicki, S. A1 - Fastook, J. L. A1 - Frieler, Katja A1 - Greve, R. A1 - Hellmer, H. H. A1 - Martin, M. A. A1 - Meinshausen, Malte A1 - Mengel, Matthias A1 - Payne, A. J. A1 - Pollard, D. A1 - Sato, T. A1 - Timmermann, R. A1 - Wang, Wei Li A1 - Bindschadler, Robert A. T1 - Projecting antarctic ice discharge using response functions from SeaRISE ice-sheet models JF - Earth system dynamics N2 - 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. Y1 - 2014 U6 - https://doi.org/10.5194/esd-5-271-2014 SN - 2190-4979 SN - 2190-4987 VL - 5 IS - 2 SP - 271 EP - 293 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Levermann, Anders A1 - Albrecht, Tanja A1 - Winkelmann, Ricarda A1 - Martin, Maria A. A1 - Haseloff, Monika A1 - Joughin, I. T1 - Kinematic first-order calving law implies potential for abrupt ice-shelf retreat JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - 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. Y1 - 2012 U6 - https://doi.org/10.5194/tc-6-273-2012 SN - 1994-0416 VL - 6 IS - 2 SP - 273 EP - 286 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Winkelmann, Ricarda A1 - Martin, Maria A. A1 - Haseloff, Monika A1 - Albrecht, Torsten A1 - Bueler, Ed A1 - Khroulev, C. A1 - Levermann, Anders T1 - The Potsdam parallel ice sheet model (PISM-PIK) - Part 1: Model description JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - 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). Y1 - 2011 U6 - https://doi.org/10.5194/tc-5-715-2011 SN - 1994-0416 VL - 5 IS - 3 SP - 715 EP - 726 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Martin, Maria A. A1 - Winkelmann, Ricarda A1 - Haseloff, M. A1 - Albrecht, Tanja A1 - Bueler, Ed A1 - Khroulev, C. A1 - Levermann, Anders T1 - The Potsdam parallel ice sheet model (PISM-PIK) - Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - 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. Y1 - 2011 U6 - https://doi.org/10.5194/tc-5-727-2011 SN - 1994-0416 VL - 5 IS - 3 SP - 727 EP - 740 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Albrecht, Tanja A1 - Martin, M. A1 - Haseloff, M. A1 - Winkelmann, Ricarda A1 - Levermann, Anders T1 - Parameterization for subgrid-scale motion of ice-shelf calving fronts JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - 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. Y1 - 2011 U6 - https://doi.org/10.5194/tc-5-35-2011 SN - 1994-0416 VL - 5 IS - 1 SP - 35 EP - 44 PB - Copernicus CY - Göttingen ER - TY - GEN A1 - Levermann, Anders A1 - Winkelmann, Ricarda T1 - A simple equation for the melt elevation feedback of ice sheets T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In 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 slow-down 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 degrees C above the threshold and 500 years for 5 degrees 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 529 KW - sea-level rise KW - mass-balance KW - climate-change KW - Greenland KW - model KW - glacier KW - projections KW - dynamics KW - impact KW - 21st-Century Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409834 SN - 1866-8372 IS - 529 ER - TY - JOUR A1 - Ueckerdt, Falko A1 - Frieler, Katja A1 - Lange, Stefan A1 - Wenz, Leonie A1 - Luderer, Gunnar A1 - Levermann, Anders T1 - The economically optimal warming limit of the planet JF - Earth system dynamics N2 - Both climate-change damages and climate-change mitigation will incur economic costs. While the risk of severe damages increases with the level of global warming (Dell et al., 2014; IPCC, 2014b, 2018; Lenton et al., 2008), mitigating costs increase steeply with more stringent warming limits (IPCC, 2014a; Luderer et al., 2013; Rogelj et al., 2015). Here, we show that the global warming limit that minimizes this century's total economic costs of climate change lies between 1.9 and 2 ∘C, if temperature changes continue to impact national economic growth rates as observed in the past and if instantaneous growth effects are neither compensated nor amplified by additional growth effects in the following years. The result is robust across a wide range of normative assumptions on the valuation of future welfare and inequality aversion. We combine estimates of climate-change impacts on economic growth for 186 countries (applying an empirical damage function from Burke et al., 2015) with mitigation costs derived from a state-of-the-art energy–economy–climate model with a wide range of highly resolved mitigation options (Kriegler et al., 2017; Luderer et al., 2013, 2015). Our purely economic assessment, even though it omits non-market damages, provides support for the international Paris Agreement on climate change. The political goal of limiting global warming to “well below 2 degrees” is thus also an economically optimal goal given above assumptions on adaptation and damage persistence. Y1 - 2019 U6 - https://doi.org/10.5194/esd-10-741-2019 SN - 2190-4979 SN - 2190-4987 VL - 10 IS - 4 SP - 741 EP - 763 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Schlemm, Tanja A1 - Levermann, Anders T1 - A simple stress-based cliff-calving law JF - The Cryosphere : TC ; an interactive open access journal of the European Geosciences Union N2 - Over large coastal regions in Greenland and Antarctica the ice sheet calves directly into the ocean. In contrast to ice-shelf calving, an increase in calving from grounded glaciers contributes directly to sea-level rise. Ice cliffs with a glacier freeboard larger than approximate to 100 m are currently not observed, but it has been shown that such ice cliffs are increasingly unstable with increasing ice thickness. This cliff calving can constitute a self-amplifying ice loss mechanism that may significantly alter sea-level projections both of Greenland and Antarctica. Here we seek to derive a minimalist stress-based parametrization for cliff calving from grounded glaciers whose freeboards exceed the 100m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs. To this end we compute the stress field for a glacier with a simplified two-dimensional geometry from the two-dimensional Stokes equation. First we assume a constant yield stress to derive the failure region at the glacier front from the stress field within the glacier. Secondly, we assume a constant response time of ice failure due to exceedance of the yield stress. With this strongly constraining but very simple set of assumptions we propose a cliff-calving law where the calving rate follows a power-law dependence on the freeboard of the ice with exponents between 2 and 3, depending on the relative water depth at the calving front. The critical freeboard below which the ice front is stable decreases with increasing relative water depth of the calving front. For a dry water front it is, for example, 75 m. The purpose of this study is not to provide a comprehensive calving law but to derive a particularly simple equation with a transparent and minimalist set of assumptions. Y1 - 2019 U6 - https://doi.org/10.5194/tc-13-2475-2019 SN - 1994-0416 SN - 1994-0424 VL - 13 IS - 9 SP - 2475 EP - 2488 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Menon, Arathy A1 - Levermann, Anders A1 - Schewe, Jacob A1 - Lehmann, J. A1 - Frieler, Katja T1 - Consistent increase in Indian monsoon rainfall and its variability across CMIP-5 models JF - Earth system dynamics N2 - The possibility of an impact of global warming on the Indian monsoon is of critical importance for the large population of this region. Future projections within the Coupled Model Intercomparison Project Phase 3 (CMIP-3) showed a wide range of trends with varying magnitude and sign across models. Here the Indian summer monsoon rainfall is evaluated in 20 CMIP-5 models for the period 1850 to 2100. In the new generation of climate models, a consistent increase in seasonal mean rainfall during the summer monsoon periods arises. All models simulate stronger seasonal mean rainfall in the future compared to the historic period under the strongest warming scenario RCP-8.5. Increase in seasonal mean rainfall is the largest for the RCP-8.5 scenario compared to other RCPs. Most of the models show a northward shift in monsoon circulation by the end of the 21st century compared to the historic period under the RCP-8.5 scenario. The interannual variability of the Indian monsoon rainfall also shows a consistent positive trend under unabated global warming. Since both the long-term increase in monsoon rainfall as well as the increase in interannual variability in the future is robust across a wide range of models, some confidence can be attributed to these projected trends. Y1 - 2013 U6 - https://doi.org/10.5194/esd-4-287-2013 SN - 2190-4979 SN - 2190-4987 VL - 4 IS - 2 SP - 287 EP - 300 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Schneider von Deimling, Thomas A1 - Meinshausen, Malte A1 - Levermann, Anders A1 - Huber, Veronika A1 - Frieler, Katja A1 - Lawrence, D. M. A1 - Brovkin, Victor T1 - Estimating the near-surface permafrost-carbon feedback on global warming JF - Biogeosciences N2 - Thawing of permafrost and the associated release of carbon constitutes a positive feedback in the climate system, elevating the effect of anthropogenic GHG emissions on global-mean temperatures. Multiple factors have hindered the quantification of this feedback, which was not included in climate carbon-cycle models which participated in recent model intercomparisons (such as the Coupled Carbon Cycle Climate Model Intercomparison Project - (CMIP)-M-4). There are considerable uncertainties in the rate and extent of permafrost thaw, the hydrological and vegetation response to permafrost thaw, the decomposition timescales of freshly thawed organic material, the proportion of soil carbon that might be emitted as carbon dioxide via aerobic decomposition or as methane via anaerobic decomposition, and in the magnitude of the high latitude amplification of global warming that will drive permafrost degradation. Additionally, there are extensive and poorly characterized regional heterogeneities in soil properties, carbon content, and hydrology. Here, we couple a new permafrost module to a reduced complexity carbon-cycle climate model, which allows us to perform a large ensemble of simulations. The ensemble is designed to span the uncertainties listed above and thereby the results provide an estimate of the potential strength of the feedback from newly thawed permafrost carbon. For the high CO2 concentration scenario (RCP8.5), 33-114 GtC (giga tons of Carbon) are released by 2100 (68% uncertainty range). This leads to an additional warming of 0.04-0.23 degrees C. Though projected 21st century permafrost carbon emissions are relatively modest, ongoing permafrost thaw and slow but steady soil carbon decomposition means that, by 2300, about half of the potentially vulnerable permafrost carbon stock in the upper 3 m of soil layer (600-1000 GtC) could be released as CO2, with an extra 1-4% being released as methane. Our results also suggest that mitigation action in line with the lower scenario RCP3-PD could contain Arctic temperature increase sufficiently that thawing of the permafrost area is limited to 9-23% and the permafrost-carbon induced temperature increase does not exceed 0.04-0.16 degrees C by 2300. Y1 - 2012 U6 - https://doi.org/10.5194/bg-9-649-2012 SN - 1726-4170 SN - 1726-4189 VL - 9 IS - 2 SP - 649 EP - 665 PB - Copernicus CY - Göttingen ER -