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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.
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.
The Atlantic meridional overturning circulation (AMOC) carries large amounts of heat into the North Atlantic influencing climate regionally as well as globally. Palaeo-records and simulations with comprehensive climate models suggest that the positive salt-advection feedback may yield a threshold behaviour of the system. That is to say that beyond a certain amount of freshwater flux into the North Atlantic, no meridional overturning circulation can be sustained. Concepts of monitoring the AMOC and identifying its vicinity to the threshold rely on the fact that the volume flux defining the AMOC will be reduced when approaching the threshold. Here we advance conceptual models that have been used in a paradigmatic way to understand the AMOC, by introducing a density-dependent parameterization for the Southern Ocean eddies. This additional degree of freedom uncovers a mechanism by which the AMOC can increase with additional freshwater flux into the North Atlantic, before it reaches the threshold and collapses: an AMOC that is mainly wind-driven will have a constant upwelling as long as the Southern Ocean winds do not change significantly. The downward transport of tracers occurs either in the northern sinking regions or through Southern Ocean eddies. If freshwater is transported, either atmospherically or via horizontal gyres, from the low to high latitudes, this would reduce the eddy transport and by continuity increase the northern sinking which defines the AMOC until a threshold is reached at which the AMOC cannot be sustained. If dominant in the real ocean this mechanism would have significant consequences for monitoring the AMOC.
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.
The 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.
Here we report on a cyclic, physical ice-discharge instability in the Parallel Ice Sheet Model, simulating the flow of a three-dimensional, inherently buttressed ice-sheet-shelf system which periodically surges on a millennial timescale. The thermomechanically coupled model on 1 km horizontal resolution includes an enthalpy-based formulation of the thermodynamics, a nonlinear stress-balance-based sliding law and a very simple subglacial hydrology. The simulated unforced surging is characterized by rapid ice streaming through a bed trough, resulting in abrupt discharge of ice across the grounding line which is eventually calved into the ocean. We visualize the central feedbacks that dominate the subsequent phases of ice buildup, surge and stabilization which emerge from the interaction between ice dynamics, thermodynamics and the subglacial till layer. Results from the variation of surface mass balance and basal roughness suggest that ice sheets of medium thickness may be more susceptible to surging than relatively thin or thick ones for which the surge feedback loop is damped. We also investigate the influence of different basal sliding laws (ranging from purely plastic to nonlinear to linear) on possible surging. The presented mechanisms underlying our simulations of self-maintained, periodic ice growth and destabilization may play a role in large-scale ice-sheet surging, such as the surging of the Laurentide Ice Sheet, which is associated with Heinrich events, and ice-stream shutdown and reactivation, such as observed in the Siple Coast region of West Antarctica.
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.
Climate change and its impacts already pose considerable challenges for societies that will further increase with global warming (IPCC, 2014a, b). Uncertainties of the climatic response to greenhouse gas emissions include the potential passing of large-scale tipping points (e.g. Lenton et al., 2008; Levermann et al., 2012; Schellnhuber, 2010) and changes in extreme meteorological events (Field et al., 2012) with complex impacts on societies (Hallegatte et al., 2013). Thus climate change mitigation is considered a necessary societal response for avoiding uncontrollable impacts (Conference of the Parties, 2010). On the other hand, large-scale climate change mitigation itself implies fundamental changes in, for example, the global energy system. The associated challenges come on top of others that derive from equally important ethical imperatives like the fulfilment of increasing food demand that may draw on the same resources. For example, ensuring food security for a growing population may require an expansion of cropland, thereby reducing natural carbon sinks or the area available for bio-energy production. So far, available studies addressing this problem have relied on individual impact models, ignoring uncertainty in crop model and biome model projections. Here, we propose a probabilistic decision framework that allows for an evaluation of agricultural management and mitigation options in a multi-impact-model setting. Based on simulations generated within the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP), we outline how cross-sectorally consistent multi-model impact simulations could be used to generate the information required for robust decision making.
Using an illustrative future land use pattern, we discuss the trade-off between potential gains in crop production and associated losses in natural carbon sinks in the new multiple crop-and biome-model setting. In addition, crop and water model simulations are combined to explore irrigation increases as one possible measure of agricultural intensification that could limit the expansion of cropland required in response to climate change and growing food demand. This example shows that current impact model uncertainties pose an important challenge to long-term mitigation planning and must not be ignored in long-term strategic decision making.
Climate change and its impacts already pose considerable challenges for societies that will further increase with global warming (IPCC, 2014a, b). Uncertainties of the climatic response to greenhouse gas emissions include the potential passing of large-scale tipping points (e.g. Lenton et al., 2008; Levermann et al., 2012; Schellnhuber, 2010) and changes in extreme meteorological events (Field et al., 2012) with complex impacts on societies (Hallegatte et al., 2013). Thus climate change mitigation is considered a necessary societal response for avoiding uncontrollable impacts (Conference of the Parties, 2010). On the other hand, large-scale climate change mitigation itself implies fundamental changes in, for example, the global energy system. The associated challenges come on top of others that derive from equally important ethical imperatives like the fulfilment of increasing food demand that may draw on the same resources. For example, ensuring food security for a growing population may require an expansion of cropland, thereby reducing natural carbon sinks or the area available for bio-energy production. So far, available studies addressing this problem have relied on individual impact models, ignoring uncertainty in crop model and biome model projections. Here, we propose a probabilistic decision framework that allows for an evaluation of agricultural management and mitigation options in a multi-impact-model setting. Based on simulations generated within the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP), we outline how cross-sectorally consistent multi-model impact simulations could be used to generate the information required for robust decision making.
Using an illustrative future land use pattern, we discuss the trade-off between potential gains in crop production and associated losses in natural carbon sinks in the new multiple crop-and biome-model setting. In addition, crop and water model simulations are combined to explore irrigation increases as one possible measure of agricultural intensification that could limit the expansion of cropland required in response to climate change and growing food demand. This example shows that current impact model uncertainties pose an important challenge to long-term mitigation planning and must not be ignored in long-term strategic decision making.
Even if greenhouse gas emissions were stopped today, sea level would continue to rise for centuries, with the long-term sea-level commitment of a 2 degrees C warmer world significantly exceeding 2 m. In view of the potential implications for coastal populations and ecosystems worldwide, we investigate, from an ice-dynamic perspective, the possibility of delaying sea-level rise by pumping ocean water onto the surface of the Antarctic ice sheet. We find that due to wave propagation ice is discharged much faster back into the ocean than would be expected from a pure advection with surface velocities. The delay time depends strongly on the distance from the coastline at which the additional mass is placed and less strongly on the rate of sea-level rise that is mitigated. A millennium-scale storage of at least 80% of the additional ice requires placing it at a distance of at least 700 km from the coastline. The pumping energy required to elevate the potential energy of ocean water to mitigate the currently observed 3 mmyr(-1) will exceed 7% of the current global primary energy supply. At the same time, the approach offers a comprehensive protection for entire coastlines particularly including regions that cannot be protected by dikes.