Parallel Ice Sheet Model Research Articles

Investigating uncertainty in the simulation of the Antarctic ice sheet during the mid‐Piacenzian

AbstractThe mid‐Piacenzian (~3 Ma) represents the most recent warm period in Earth's history on a geological time scale; it is characterized by a significant rise of global sea level. The simulation of the size and location of the ice sheets and the investigation of the uncertainty in the simulations are potentially helpful for constraining reconstructed sea level changes. In this study, we focus on the behavior of the Antarctic ice sheet (AIS) in the mid‐Piacenzian. We investigate the influence of topography correction, model parameters, climate forcings, and model resolution on the modeled AIS and explore the isolated role of atmospheric and oceanic forcings. Forced by the simulated climate changes with the Norwegian Earth System Model, the Parallel Ice Sheet Model (15 km × 15 km) produces a nearly collapsed West AIS (WAIS) in the mid‐Piacenzian, with no significant retreat of the East AIS (EAIS). The role of increased air temperature plays a key role in the mass loss of the mid‐Piacenzian AIS, while its role is comparable to the role of ocean warming on the melting of the WAIS. In terms of the range of sea level changes, the largest source of uncertainty in the modeled AIS is derived from ice sheet model parameters and climate forcings. Although the employed model parameters, topography correction factors, and model resolution affect the simulated AIS in the mid‐Piacenzian, large‐scale deglaciation of the EAIS in our sensitivity experiments may only be possible with additional warming.

Modeling the evolution of the Juneau Icefield between 1971 and 2100 using the Parallel Ice Sheet Model (PISM)

ABSTRACTWe study the evolution of the Juneau Icefield, one of the largest icefields in North America (>3700 km2), using the Parallel Ice Sheet Model (PISM). We test two climate datasets: 20 km Weather Research and Forecasting Model (WRF) output, and data from the Scenarios Network for Alaska Planning (SNAP), derived from spatial interpolation of observations. Good agreement between simulated and observed surface mass balance was achieved only after substantially adjusting WRF precipitation to account for unresolved orographic effects, while SNAP's climate pattern is incompatible with observations of surface mass balance. Using the WRF data forced with the RCP6.0 emission scenario, the model projects a decrease in ice volume by 58–68% and a 57–63% area loss by 2099 compared with 2010. If the modeled 2070–99 climate is held constant beyond 2099, the icefield is eliminated by 2200. With constant 1971–2010 climate, the icefield stabilizes at 86% of its present-day volume. Experiments started from an ice-free state indicate that steady-state volumes are largely independent of the initial ice volume when forced by identical scenarios of climate stabilization. Despite large projected volume losses, the complex high-mountain topography makes the Juneau Icefield less susceptible to climate warming than low-lying Alaskan icefields.

Collapse of the West Antarctic Ice Sheet after local destabilization of the Amundsen Basin

The future evolution of the Antarctic Ice Sheet represents the largest uncertainty in sea-level projections of this and upcoming centuries. Recently, satellite observations and high-resolution simulations have suggested the initiation of an ice-sheet instability in the Amundsen Sea sector of West Antarctica, caused by the last decades' enhanced basal ice-shelf melting. Whether this localized destabilization will yield a full discharge of marine ice from West Antarctica, associated with a global sea-level rise of more than 3 m, or whether the ice loss is limited by ice dynamics and topographic features, is unclear. Here we show that in the Parallel Ice Sheet Model, a local destabilization causes a complete disintegration of the marine ice in West Antarctica. In our simulations, at 5-km horizontal resolution, the region disequilibrates after 60 y of currently observed melt rates. Thereafter, the marine ice-sheet instability fully unfolds and is not halted by topographic features. In fact, the ice loss in Amundsen Sea sector shifts the catchment's ice divide toward the Filchner-Ronne and Ross ice shelves, which initiates grounding-line retreat there. Our simulations suggest that if a destabilization of Amundsen Sea sector has indeed been initiated, Antarctica will irrevocably contribute at least 3 m to global sea-level rise during the coming centuries to millennia.

Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model version 0.6

Abstract. We describe and test a two-horizontal-dimension subglacial hydrology model which combines till with a distributed system of water-filled, linked cavities which open through sliding and close through ice creep. The addition of this sub-model to the Parallel Ice Sheet Model (PISM) accomplishes three specific goals: (a) conservation of the mass of water, (b) simulation of spatially and temporally variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (c) convergence under grid refinement. The model is a common generalization of four others: (i) the undrained plastic bed model of Tulaczyk et al. (2000b), (ii) a standard "routing" model used for identifying locations of subglacial lakes, (iii) the lumped englacial–subglacial model of Bartholomaus et al. (2011), and (iv) the elliptic-pressure-equation model of Schoof et al. (2012). We preserve physical bounds on the pressure. In steady state a functional relationship between water amount and pressure emerges. We construct an exact solution of the coupled, steady equations and use it for verification of our explicit time stepping, parallel numerical implementation. We demonstrate the model at scale by 5 year simulations of the entire Greenland ice sheet at 2 km horizontal resolution, with one million nodes in the hydrology grid.

Coupled ice sheet–climate modeling under glacial and pre-industrial boundary conditions

Abstract. In the standard Paleoclimate Modelling Intercomparison Project (PMIP) experiments, the Last Glacial Maximum (LGM) is modeled in quasi-equilibrium with atmosphere–ocean–vegetation general circulation models (AOVGCMs) with prescribed ice sheets. This can lead to inconsistencies between the modeled climate and ice sheets. One way to avoid this problem would be to model the ice sheets explicitly. Here, we present the first results from coupled ice sheet–climate simulations for the pre-industrial times and the LGM. Our setup consists of the AOVGCM ECHAM5/MPIOM/LPJ bidirectionally coupled with the Parallel Ice Sheet Model (PISM) covering the Northern Hemisphere. The results of the pre-industrial and LGM simulations agree reasonably well with reconstructions and observations. This shows that the model system adequately represents large, non-linear climate perturbations. A large part of the drainage of the ice sheets occurs in ice streams. Most modeled ice stream systems show recurring surges as internal oscillations. The Hudson Strait Ice Stream surges with an ice volume equivalent to about 5 m sea level and a recurrence interval of about 7000 yr. This is in agreement with basic expectations for Heinrich events. Under LGM boundary conditions, different ice sheet configurations imply different locations of deep water formation.

The effect of climate forcing on numerical simulations of the Cordilleran ice sheet at the Last Glacial Maximum

Abstract. We present an ensemble of numerical simulations of the Cordilleran ice sheet during the Last Glacial Maximum performed with the Parallel Ice Sheet Model (PISM), applying temperature offsets to the present-day climatologies from five different data sets. Monthly mean surface air temperature and precipitation from WorldClim, the NCEP/NCAR reanalysis, the ERA-Interim reanalysis, the Climate Forecast System Reanalysis and the North American Regional Reanalysis are used to compute surface mass balance in a positive degree-day model. Modelled ice sheet outlines and volumes appear highly sensitive to the choice of climate forcing. For three of the four reanalysis data sets used, differences in precipitation are the major source for discrepancies between model results. We assess model performance against a geomorphological reconstruction of the ice margin at the Last Glacial Maximum, and suggest that part of the mismatch is due to unresolved orographic precipitation effects caused by the coarse resolution of reanalysis data. The best match between model output and the reconstructed ice margin is obtained using the high-resolution North American Regional Reanalysis, which we retain for simulations of the Cordilleran ice sheet in the future.

Fracture-induced softening for large-scale ice dynamics

Abstract. 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.

Role of model initialization for projections of 21st-century Greenland ice sheet mass loss

AbstractModel simulations of the Greenland ice sheet contribution to 21st-century sea-level rise are performed with a state-of-the-art ice-sheet model (Parallel Ice Sheet Model (PISM)). The climate-forcing fields are obtained from the European Union’s Seventh Framework Programme project ice2sea, in which three regional climate models are used to dynamically downscale two scenarios (A1B and E1) from two general circulation models (ECHAM5 and HadCM3). To assess the sensitivity of the projections to the model initial state, four initialization methods are applied. In these experiments, the simulated contribution to sea-level rise by 2100 ranges from an equivalent of 0.2 to 6.8 cm. The largest uncertainties arise from different formulations of the regional climate models (0.8–3.9 cm) and applied scenarios (0.65–1.9 cm), but an important source of uncertainty is the initialization method (0.1–0.8 cm). These model simulations do not account for the recently observed acceleration of ice streams and consequent thinning rates, the changing ice discharge that may result from the spatial and temporal variability of ocean forcing, or the feedback occurring between ice-sheet elevation changes and climate forcing. Thus the results should be considered the lower limit of Greenland ice sheet contributions to sea-level rise, until such processes have been integrated into large-scale ice-sheet models.

Resolution-dependent performance of grounding line motion in a shallow model compared with a full-Stokes model according to the MISMIP3d intercomparison

AbstractMaking confident statements about the evolution of an ice-sheet–shelf system with a numerical model requires the capability to reproduce the migration of the grounding line. Here we show that the shallow-ice approximation/shallow-shelf approximation hybrid-type Parallel Ice Sheet Model (PISM), with its recent improvements, is capable of modeling the grounding line motion in a perturbed ice-sheet–shelf system. The model is set up according to the three-dimensional Marine Ice-Sheet Model Intercomparison Project (MISMIP3d), and simulations are carried out across a broad range of spatial resolutions. Using (1) a linear interpolation of the grounding line with locally interpolated basal friction and (2) an improved driving-stress computation across the grounding line, the reversibility of the grounding line (i.e. its retreat after an advance forced by a local perturbation of basal resistance) is captured by the model even at medium and low resolutions (∆x > 10 km). The transient model response is qualitatively similar to that of higher-order models but reveals a higher initial sensitivity to perturbations on very short timescales. Our findings support the application of PISM to the Antarctic ice sheet from regional up to continental scales and on relatively low spatial resolutions.

An open ocean region in Neoproterozoic glaciations would have to be narrow to allow equatorial ice sheets

A major goal of understanding Neoproterozoic glaciations and determining their effect on the evolution of life and Earth's atmosphere is establishing whether and how much open ocean there was during them. Geological evidence tells us that continental ice sheets had to flow into the ocean near the equator during these glaciations. Here we drive the Parallel Ice Sheet Model with output from four simulations of the ECHAM5/Max Planck Institute Ocean Model atmosphere‐ocean general circulation model with successively narrower open ocean regions. We find that extensive equatorial ice sheets form on marine margins if sea ice extends to within about 20° latitude of the equator or less (Jormungand‐like and hard snowball states), but do not form if there is more open ocean than this. Given uncertainty in topographical reconstruction and ice sheet ablation parameterizations, we perform extensive sensitivity tests to confirm the robustness of our main conclusions.

Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS

Abstract. We introduce a novel, higher order, finite element ice sheet model called VarGlaS (Variational Glacier Simulator), which is built on the finite element framework FEniCS. Contrary to standard procedure in ice sheet modelling, VarGlaS formulates ice sheet motion as the minimization of an energy functional, conferring advantages such as a consistent platform for making numerical approximations, a coherent relationship between motion and heat generation, and implicit boundary treatment. VarGlaS also solves the equations of enthalpy rather than temperature, avoiding the solution of a contact problem. Rather than include a lengthy model spin-up procedure, VarGlaS possesses an automated framework for model inversion. These capabilities are brought to bear on several benchmark problems in ice sheet modelling, as well as a 500 yr simulation of the Greenland ice sheet at high resolution. VarGlaS performs well in benchmarking experiments and, given a constant climate and a 100 yr relaxation period, predicts a mass evolution of the Greenland ice sheet that matches present-day observations of mass loss. VarGlaS predicts a thinning in the interior and thickening of the margins of the ice sheet.

Numerical simulations of cyclic behaviour in the Parallel Ice Sheet Model (PISM)

AbstractNumerical experiments are conducted on a synthetic topography with a three-dimensional thermomechanically coupled ice-sheet model, the Parallel Ice Sheet Model (PISM). Within the model, combined stress balances are connected to evolving thermodynamics and hydrology. The sensitivity of cyclic behaviour to changes in sliding-law parameters and the climate input is studied. Multiple types of oscillations were found, with strong variations in both amplitude and frequency. A physical description is given, in which these variations and transitions from one oscillation type to another are linked to the interplay of stresses, heat transport and hydrological processes. High-frequency oscillations (period 114-169 years), which are shown to have a major impact on ice velocities and a small effect on the ice volume, are related to variations in the water distribution at the base. Low-frequency cycles (period 1000+ years), which have a major impact on both velocities and ice volume, are linked to changes in the thermal regime. Oscillation characteristics are shown to be strongly sensitive to changes in sliding-law parameters and the prescribed surface temperature and mass balance. Incorporating a surface-height dependence of the mass balance is shown to provide an additional feedback, which may induce long- period oscillations.

An enthalpy formulation for glaciers and ice sheets

AbstractPolythermal conditions are ubiquitous among glaciers, from small valley glaciers to ice sheets. Conventional temperature-based ‘cold-ice’ models of such ice masses cannot account for that portion of the internal energy which is latent heat of liquid water within temperate ice, so such schemes are not energy-conserving when temperate ice is present. Temperature and liquid water fraction are, however, functions of a single enthalpy variable: a small enthalpy change in cold ice is a change in temperature, while a small enthalpy change in temperate ice is a change in liquid water fraction. The unified enthalpy formulation described here models the mass and energy balance for the threedimensional ice fluid, for the surface runoff layer and for the subglacial hydrology layer, together in a single energy-conserving theoretical framework. It is implemented in the Parallel Ice Sheet Model. Results for the Greenland ice sheet are compared with those from a cold-ice scheme. This paper is intended to be an accessible foundation for enthalpy formulations in glaciology.

The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description

Abstract. 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).

The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet

Abstract. 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.

Parameterization for subgrid-scale motion of ice-shelf calving fronts

Abstract. 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.

Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model

The shallow shelf approximation, a balance of membrane stresses for ice flow, is an effective “sliding law” for ice sheet modeling. Our use of it as a sliding law becomes a standard model for ice stream flow when the sliding velocity is large (100 m a−1 and faster). Following Schoof (2006a), we describe the basal resistance as plastic till for which the yield stress is given by a Mohr‐Coulomb formula. Pore water pressure is related to basal melt rate. The velocity field used in the mass continuity and conservation of energy equations is an average of velocities from the shallow shelf approximation and the nonsliding shallow ice approximation. Using this scheme, our model has realistic, time‐dependent ice streams which exhibit the range of surface velocities seen in actual ice streams. We demonstrate the model at high spatial resolution (5 km grid) over multiple millenia using its implementation in the Parallel Ice Sheet Model. Numerical experiments show that the entire scheme is stable with respect to many parameter changes. Some experiments reveal significant ice stream variability in a hypothetical steady climate, with characteristic cycles on the order of 1000 years. We believe this is the first practical whole ice sheet model with a unified treatment of vertical shear stresses and membrane stresses. It is capable of high‐resolution, thermomechanically coupled, multimillenia simulations of ice sheets containing ice streams.