Antony J. Payne

A Reconciled Estimate of Ice-Sheet Mass Balance

Warming and Melting Mass loss from the ice sheets of Greenland and Antarctica account for a large fraction of global sea-level rise. Part of this loss is because of the effects of warmer air temperatures, and another because of the rising ocean temperatures to which they are being exposed. Joughin et al. (p. 1172) review how ocean-ice interactions are impacting ice sheets and discuss the possible ways that exposure of floating ice shelves and grounded ice margins are subject to the influences of warming ocean currents. Estimates of the mass balance of the ice sheets of Greenland and Antarctica have differed greatly—in some cases, not even agreeing about whether there is a net loss or a net gain—making it more difficult to project accurately future sea-level change. Shepherd et al. (p. 1183) combined data sets produced by satellite altimetry, interferometry, and gravimetry to construct a more robust ice-sheet mass balance for the period between 1992 and 2011. All major regions of the two ice sheets appear to be losing mass, except for East Antarctica. All told, mass loss from the polar ice sheets is contributing about 0.6 millimeters per year (roughly 20% of the total) to the current rate of global sea-level rise. The mass balance of the polar ice sheets is estimated by combining the results of existing independent techniques. We combined an ensemble of satellite altimetry, interferometry, and gravimetry data sets using common geographical regions, time intervals, and models of surface mass balance and glacial isostatic adjustment to estimate the mass balance of Earth’s polar ice sheets. We find that there is good agreement between different satellite methods—especially in Greenland and West Antarctica—and that combining satellite data sets leads to greater certainty. Between 1992 and 2011, the ice sheets of Greenland, East Antarctica, West Antarctica, and the Antarctic Peninsula changed in mass by –142 ± 49, +14 ± 43, –65 ± 26, and –20 ± 14 gigatonnes year−1, respectively. Since 1992, the polar ice sheets have contributed, on average, 0.59 ± 0.20 millimeter year−1 to the rate of global sea-level rise.

Recent dramatic thinning of largest West Antarctic ice stream triggered by oceans

A growing body of observational data suggests that Pine Island Glacier (PIG) is changing on decadal or shorter timescales. These changes may have far-reaching consequences for the future of the West Antarctic ice sheet (WAIS) and global sea levels because of PIGs role as the ice sheets primary drainage portal. We test the hypothesis that these changes are triggered by the adjoining ocean. Specifically, we employ an advanced numerical ice-flow model to simulate the effects of perturbations at the grounding line on PIGs dynamics. The speed at which these changes are propagated upstream implies a tight coupling between ice-sheet interior and surrounding ocean.

Future sea-level rise from Greenland/'s main outlet glaciers in a warming climate

Over the past decade, ice loss from the Greenland Ice Sheet increased as a result of both increased surface melting and ice discharge to the ocean. The latter is controlled by the acceleration of ice flow and subsequent thinning of fast-flowing marine-terminating outlet glaciers. Quantifying the future dynamic contribution of such glaciers to sea-level rise (SLR) remains a major challenge because outlet glacier dynamics are poorly understood. Here we present a glacier flow model that includes a fully dynamic treatment of marine termini. We use this model to simulate behaviour of four major marine-terminating outlet glaciers, which collectively drain about 22 per cent of the Greenland Ice Sheet. Using atmospheric and oceanic forcing from a mid-range future warming scenario that predicts warming by 2.8 degrees Celsius by 2100, we project a contribution of 19 to 30 millimetres to SLR from these glaciers by 2200. This contribution is largely (80 per cent) dynamic in origin and is caused by several episodic retreats past overdeepenings in outlet glacier troughs. After initial increases, however, dynamic losses from these four outlets remain relatively constant and contribute to SLR individually at rates of about 0.01 to 0.06 millimetres per year. These rates correspond to ice fluxes that are less than twice those of the late 1990s, well below previous upper bounds. For a more extreme future warming scenario (warming by 4.5 degrees Celsius by 2100), the projected losses increase by more than 50 per cent, producing a cumulative SLR of 29 to 49 millimetres by 2200.

Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade

We use a three-dimensional, higher-order ice flow model and a realistic initial condition to simulate dynamic perturbations to the Greenland ice sheet during the last decade and to assess their contribution to sea level by 2100. Starting from our initial condition, we apply a time series of observationally constrained dynamic perturbations at the marine termini of Greenland’s three largest outlet glaciers, Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. The initial and long-term diffusive thinning within each glacier catchment is then integrated spatially and temporally to calculate a minimum sea-level contribution of approximately 1 ± 0.4 mm from these three glaciers by 2100. Based on scaling arguments, we extend our modeling to all of Greenland and estimate a minimum dynamic sea-level contribution of approximately 6 ± 2 mm by 2100. This estimate of committed sea-level rise is a minimum because it ignores mass loss due to future changes in ice sheet dynamics or surface mass balance. Importantly, > 75% of this value is from the long-term, diffusive response of the ice sheet, suggesting that the majority of sea-level rise from Greenland dynamics during the past decade is yet to come. Assuming similar and recurring forcing in future decades and a self-similar ice dynamical response, we estimate an upper bound of 45 mm of sea-level rise from Greenland dynamics by 2100. These estimates are constrained by recent observations of dynamic mass loss in Greenland and by realistic model behavior that accounts for both the long-term cumulative mass loss and its decay following episodic boundary forcing.

Results from the EISMINT model intercomparison: the effects of thermomechanical coupling

This paper discusses results from the second phase of the European Ice sheet Modelling Initiative (EISMINT). It reports the intercompartison of ten operational ice-sheet models and uses a series of experiments to examine the implications of thermomechanical coupling for model behaviour. A schematic, circular ice sheet is used in the work which investigates both steady states and the response to stepped changes in climate. The major finding is that radial symmetry implied in the experimental design can, under certain circumstances, break down with the formation of distinct, regularly spaced spokes of cold ice which extended from the interior of the ice sheet outward to the surrounding zone of basal melt. These features also manifest themselves in the thickness and velocity distributions predicted by the models. They appear to be a common feature to all of the models which took part in the intercomparison, and may stem from interactions between ice temperature, flow and surface form. The exact nature of these features varies between models, and their existence appears to be controlled by the overall thermal regimne of the ice sheet. A second result is that there is considerable agreement between the models in their predictions of global-scale response to imposed climate change.

The Glimmer community ice sheet model

[1] We present a detailed description of the Glimmer ice sheet model, comprising the physics represented in the model and the numerical techniques used. Established methods are combined with good software design to yield an adaptable and widely applicable model. A flexible framework for coupling Glimmer to global climate forcing is also described. Testing and benchmarking is of crucial importance if the outputs of numerical models are to be regarded as credible; we demonstrate that Glimmer performs very well against the well-known EISMINT benchmarks and against other analytical solutions for ice flow. Glimmer therefore represents a well-founded and flexible framework for the open-source development of ice sheet modeling.

Limit cycles in the basal thermal regime of ice sheets

This paper investigates the thermodynamic consequences of introducing basal sliding into a two-dimensional ice sheet model. The coupling of ice sheet form, flow field, and temperature evolution gives rise to limit cycles in the basal thermal regime of the ice sheet. Typical periods are 4000 to 5000 years and up to 45% of the ice sheet length can be affected. The limit cycles are caused by the switching on and off of sliding as basal ice reaches the pressure melting point. An analysis of the various heat fluxes at the ice sheet base stresses the roles of vertical diffusion and the heat generated by internal deformation and sliding in controlling the period and extent of the cycles. Limit cycles are found to persist in the face of various climatic (snow accumulation rate and air temperature) parameterizations, as well as for different basal sliding parameterizations. The type of oscillation change produced by varying accumulation rate is particularly interesting. Several distinct patterns of behavior are observed. For low accumulation rate ice sheets, a period of 6000–7000 years is dominant; for medium accumulation rate ice sheets, the 3000 to 4000 year period is dominant; while for larger accumulation rates, the oscillations become highly irregular with long (>10,000 years) periods.

Adaptive mesh, finite volume modeling of marine ice sheets

Continental scale marine ice sheets such as the present day West Antarctic Ice Sheet are strongly affected by highly localized features, presenting a challenge to numerical models. Perhaps the best known phenomenon of this kind is the migration of the grounding line - the division between ice in contact with bedrock and floating ice shelves - which needs to be treated at sub-kilometer resolution. We implement a block-structured finite volume method with adaptive mesh refinement (AMR) for three dimensional ice sheets, which allows us to discretize a narrow region around the grounding line at high resolution and the remainder of the ice sheet at low resolution. We demonstrate AMR simulations that are in agreement with uniform mesh simulations, but are computationally far cheaper, appropriately and efficiently evolving the mesh as the grounding line moves over significant distances. As an example application, we model rapid deglaciation of Pine Island Glacier in West Antarctica caused by melting beneath its ice shelf.

Deglacial rapid sea level rises caused by ice-sheet saddle collapses

The last deglaciation (21 to 7 thousand years ago) was punctuated by several abrupt meltwater pulses, which sometimes caused noticeable climate change. Around 14 thousand years ago, meltwater pulse 1A (MWP-1A), the largest of these events, produced a sea level rise of 14–18 metres over 350 years. Although this enormous surge of water certainly originated from retreating ice sheets, there is no consensus on the geographical source or underlying physical mechanisms governing the rapid sea level rise. Here we present an ice-sheet modelling simulation in which the separation of the Laurentide and Cordilleran ice sheets in North America produces a meltwater pulse corresponding to MWP-1A. Another meltwater pulse is produced when the Labrador and Baffin ice domes around Hudson Bay separate, which could be associated with the ‘8,200-year’ event, the most pronounced abrupt climate event of the past nine thousand years. For both modelled pulses, the saddle between the two ice domes becomes subject to surface melting because of a general surface lowering caused by climate warming. The melting then rapidly accelerates as the saddle between the two domes gets lower, producing nine metres of sea level rise over 500 years. This mechanism of an ice ‘saddle collapse’ probably explains MWP-1A and the 8,200-year event and sheds light on the consequences of these events on climate.

Time-step limits for stable solutions of the ice-sheet equation

Various spatial discretizations for the ice sheet are compared for accuracy against analytical solutions in one and two dimensions. The computational efficiency of various iterated and non-iterated marching schemes is compared. The stability properties of different marching schemes, with and without iterations on the non-linear equations, are compared. Newton-Raphson techniques permit the largest time steps. A new technique, which is based on the fact that the dynamics of unstable iterated maps contain information about where the unstable root lies, is shown to improve substantially the performance of Picard iteration at a negligible computational cost.