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- ItemMechanisms and time scales of glacial inception simulated with an Earth system model of intermediate complexity(München : European Geopyhsical Union, 2009) Calov, R.; Ganopolski, A.; Kubatzki, C.; Claussen, M.We investigate glacial inception and glacial thresholds in the climate-cryosphere system utilising the Earth system model of intermediate complexity CLIMBER-2, which includes modules for atmosphere, terrestrial vegetation, ocean and interactive ice sheets. The latter are described by the three-dimensional polythermal ice-sheet model SICOPOLIS. A bifurcation which represents glacial inception is analysed with two different model setups: one setup with dynamical ice-sheet model and another setup without it. The respective glacial thresholds differ in terms of maximum boreal summer insolation at 65° N (hereafter referred as Milankovitch forcing (MF)). The glacial threshold of the configuration without ice-sheet dynamics corresponds to a much lower value of MF compared to the full model. If MF attains values only slightly below the aforementioned threshold there is fast transient response. Depending on the value of MF relative to the glacial threshold, the transient response time of inland-ice volume in the model configuration with ice-sheet dynamics ranges from 10 000 to 100 000 years. Due to these long response times, a glacial threshold obtained in an equilibrium simulation is not directly applicable to the transient response of the climate-cryosphere system to time-dependent orbital forcing. It is demonstrated that in transient simulations just crossing of the glacial threshold does not imply large-scale glaciation of the Northern Hemisphere. We found that in transient simulations MF has to drop well below the glacial threshold determined in an equilibrium simulation to initiate glacial inception. Finally, we show that the asynchronous coupling between climate and inland-ice components allows one sufficient realistic simulation of glacial inception and, at the same time, a considerable reduction of computational costs.
- ItemThe role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles(München : European Geopyhsical Union, 2011) Ganopolski, A.; Calov, R.The origin of the 100 kyr cyclicity, which dominates ice volume variations and other climate records over the past million years, remains debatable. Here, using a comprehensive Earth system model of intermediate complexity, we demonstrate that both strong 100 kyr periodicity in the ice volume variations and the timing of glacial terminations during past 800 kyr can be successfully simulated as direct, strongly nonlinear responses of the climate-cryosphere system to orbital forcing alone, if the atmospheric CO2 concentration stays below its typical interglacial value. The existence of long glacial cycles is primarily attributed to the North American ice sheet and requires the presence of a large continental area with exposed rocks. We show that the sharp, 100 kyr peak in the power spectrum of ice volume results from the long glacial cycles being synchronized with the Earth's orbital eccentricity. Although 100 kyr cyclicity can be simulated with a constant CO2 concentration, temporal variability in the CO2 concentration plays an important role in the amplification of the 100 kyr cycles.
- 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.
- 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.