Frank Pattyn

A new three‐dimensional higher‐order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes

[1] A new three-dimensional thermomechanically coupled ice sheet model is developed. Contrary to the majority of three-dimensional ice sheet models (shallow ice approximation), higher-order stress gradients (longitudinal and transverse) are accounted for in the force balance equations. The horizontal velocity field is determined from the force balance equations in their ‘‘derivative form’’ (elliptical equation) using the method presented by Pattyn [2000, 2002a]. The model is solved on a regular grid in the horizontal and an irregular grid in the vertical and is numerically stable. Basic experiments include the European Ice Sheet Modeling Initiative (EISMINT) benchmarks for largescale ice sheet models and a comparison with the Saito-Blatter ice sheet model including higher-order stress gradients [Saito et al., 2003]. Detailed calculations of ice flow over three-dimensional bedrock perturbations showed the validity of the higher-order solution. The model is capable of simulating the evolution of an ice stream within the ice sheet and shows important aspects of observed ice stream features, such as the surface flattening and the importance of side drag. The simulation of the ice flow over a subglacial lake results in a flattening of the surface, a local velocity increase over the lake, and a deviation of the ice flow from the main flow direction, features which are also observed at Lake Vostok, Antarctica. INDEX TERMS: 1827 Hydrology: Glaciology (1863); 1863 Hydrology: Snow and ice (1827); 3230 Mathematical Geophysics: Numerical solutions; KEYWORDS: higher-order, ice sheet model, thermomechanical, ice stream, subglacial lake Citation: Pattyn, F., A new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes, J. Geophys. Res., 108(B8), 2382, doi:10.1029/2002JB002329, 2003.

Ice-sheet mass balance and climate change

Since the 2007 Intergovernmental Panel on Climate Change Fourth Assessment Report, new observations of ice-sheet mass balance and improved computer simulations of ice-sheet response to continuing climate change have been published. Whereas Greenland is losing ice mass at an increasing pace, current Antarctic ice loss is likely to be less than some recently published estimates. It remains unclear whether East Antarctica has been gaining or losing ice mass over the past 20 years, and uncertainties in ice-mass change for West Antarctica and the Antarctic Peninsula remain large. We discuss the past six years of progress and examine the key problems that remain.

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.

Investigating the stability of subglacial lakes with a full Stokes ice-sheet model

Despite the large amount of subglacial lakes present underneath the East Antarctic ice sheet and the melt processes involved, the hydrology beneath the ice sheet is poorly understood. Changes in subglacial potential gradients may lead to subglacial lake outbursts, discharging excess water through a subglacial drainage system underneath the ice sheet. Such processes can eventually lead to an increase in ice flow. In this paper, a full Stokes numerical ice-sheet model was employed which takes into account the ice flow over subglacial water bodies in hydrostatic equilibrium with the overlying ice. Sensitivity experiments were carried out for small perturbations in ice flow and basal melt rate as a function of ice thickness, general surface slope, ice viscosity and lake size, in order to investigate their influence on the subglacial potential gradient and the impact on subglacial lake drainage. Experiments clearly demonstrate that small changes in surface slope are sufficient to start and sustain episodic subglacial drainage events. Lake drainage can therefore be regarded as a common feature of the subglacial hydrological system and may influence, to a large extent, the present and future behavior of large ice sheets.

Results From the Ice-Sheet Model Intercomparison Project-Heinrich Event INtercOmparison (ISMIP HEINO)

Results from the Heinrich Event INtercOmparison (HEINO) topic of the Ice-Sheet Model Intercomparison Project (ISMIP) are presented. ISMIP HEINO was designed to explore internal large- scale ice-sheet instabilities in different contemporary ice-sheet models. These instabilities are of interest because they are a possible cause of Heinrich events. A simplified geometry experiment reproduces the main characteristics of the Laurentide ice sheet, including the sedimented region over Hudson Bay and Hudson Strait. The model experiments include a standard run plus seven variations. Nine dynamic/thermodynamic ice-sheet models were investigated; one of these models contains a combination of the shallow-shelf (SSA) and shallow-ice approximation (SIA), while the remaining eight models are of SIA type only. Seven models, including the SIA-SSA model, exhibit oscillatory surges with a period of ∼1000 years for a broad range of parameters, while two models remain in a permanent state of streaming for most parameter settings. In a number of models, the oscillations disappear for high surface temperatures, strong snowfall and small sediment sliding parameters. In turn, low surface temperatures and low snowfall are favourable for the ice-surge cycles. We conclude that further improvement of ice-sheet models is crucial for adequate, robust simulations of cyclic large-scale instabilities.

Numerical modelling of historical front variations and dynamic response of Sofiyskiy glacier, Altai mountains, Russia

Abstract The recent fluctuation of the central Asian climate, and its effect on the region’s glaciers, is poorly known, largely because of a lack of knowledge of the dynamic behaviour of so-called summer-accumulation-type glaciers. In this study, a one-dimensional numerical glacier model is used to simulate the dynamic response of Sofiyskiy glacier, Altai mountains, Russia, to climate forcing. A successful simulation of the observed historical front variations was accomplished by dynamic calibration. This resulted in a reconstruction of the recent mass-balance history of the glacier, showing a distinct decline in surface mass balance in the second half of the 19th century, a slightly higher mass balance at the beginning of the 20th century, followed by a steady decline towards present conditions. The future response of Sofiyskiy glacier was projected for six 21st-century climate scenarios. Under a “no-change” scenario, the glacier will retreat > 2 km by 2100. If air temperature gradually rises by > 5°C during this century, the glacier will vanish around 2100. Basic response characteristics of Sofiyskiy glacier were determined. These indicate rather low mass-balance sensitivity to temperature change, but a strong front reaction due to geometric conditions.

Ice-dynamic conditions of Shirase Glacier, Antarctica, inferred from ERS SAR interferometry

The surface velocity field of Shirase Glacier, a fast-flowing East Antarctic outlet glacier, is determined from ERS synthetic aperture radar (SAR) images by means of speckle tracking using phase correlation, a technique which matches small image kernels of two complex SAR images by maximization of the local coherence. Velocity estimates are used to calculate surface strain rates, which are then used to calculate the large-scale, vertically integrated force balance and to determine the major stress components resisting the driving stress. For the whole glacier system, the driving stress is largely balanced by the basal drag, but with contributions from lateral drag up to 15% of the driving stress at the grounding line. Longitudinal stress gradients have only local importance to the balance of forces, limited to an area of a few square kilometers near the grounding line, where they resist the driving stress. In the grounded part of the glacier, >90% of the total ice velocity is due to basal sliding. Comparison with a balance-flux distribution of the Antarctic ice sheet suggests that the glacier in the downstream part of the Shirase drainage basin is close to equilibrium, showing a slight negative imbalance.

Radar characterization of the basal interface across the grounding zone of an ice-rise promontory in East Antarctica

Abstract Radar power returned from the basal interface along a 42 km long profile over an ice-rise promontory and the adjacent Roi Baudouin ice shelf, Dronning Maud Land, East Antarctica, is analyzed to infer spatial variations in basal reflectivity and hence the basal environment. Extracting basal reflectivity from basal returned power requires an englacial attenuation model. We estimate attenuation in two ways: (1) using a temperature-dependent model with input from thermomechanical ice-flow models; and (2) using a radar method that linearly approximates the geometrically corrected returned power with ice thickness. The two methods give different results. We argue that attenuation calculated using a modeled temperature profile is more robust than the widely used radar method, especially in locations where depth-averaged attenuation varies spatially or where the patterns of basal reflectivity correlate with the patterns of the ice thickness.

Power law or power flaw

Since its introduction by Svensson in 1959, the power law curve y = ax b (where x and y are horizontal and vertical direction, respectively) has been widely used in morphological analysis of glacial trough cross-profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y = ln a+ b ln x). The value b then gives a measure for the form of the cross-section. However, over the years this form of the power law has endured a lot of criticism. This criticism is well founded, since this particular form of the power law is not suitable for cur ve fitting in morphological analyses. In this paper a general power law is proposed, of the form y- y0 = ax- x0 b (where x0, y0 are the coordinates of the origin of the cross-profile). A unique and unbiased solution for this equation is obtained with a general least-squares method, thereby minimizing the error between the cross-profile data and the curve, and not between the logarithmic transform of the data and its regression line. This provides a robust way to characterize trough cross-section forms.

Past and present accumulation rate reconstruction along the Dome Fuji-Kohnen radio-echo sounding profile, Dronning Maud Land, East Antarctica

Abstract We used internal ice layers from a radio-echo sounding profile between the Kohnen and Dome Fuji deep drilling sites to infer the spatio-temporal pattern of accumulation rate in this sector of Dronning Maud Land, East Antarctica. Continuous internal reflection horizons can be traced to about half of the ice thickness and have a maximum age of approximately 72.7 ka BP. To infer palaeo-accumulation rates from the dated layers, we derived the thinning functions from a flow calculation with a high-resolution higher-order model of Dronning Maud Land embedded into a three-dimensional thermomechanical model of the Antarctic ice sheet. The method takes into account complex ice-flow dynamics and advection effects that cannot be dealt with using traditional local approaches. We selected seven time intervals over which we determine the average accumulation rate and average surface temperature at the place and time of origin of the layer particles. Our results show lower accumulation rates along eastern parts of the profile for the late Holocene (0–5 ka BP) than are shown by existing maps, which had no surface control points. During the last glacial period we find a substantially lower accumulation rate than predicted by the usual approach linking palaeo-accumulation rates to the condensation temperature above the surface inversion layer. These findings were used to fine-tune the relation between accumulation rate and temperature.