Tidewater glaciers have been observed to experience instantaneous, stepwise increases in velocity during iceberg-calving events due to a loss of resistive stresses. These changes in stress can ...potentially impact tidewater glacier stability by promoting additional calving and affecting the viscous delivery of ice to the terminus. Using flow models and perturbation theory, we demonstrate that calving events and subsequent terminus readvance produce quasi-periodic, sawtooth oscillations in stress that originate at the terminus and propagate upstream. The stress perturbations travel at speeds much greater than the glacier velocities and, for laterally resisted glaciers, rapidly decay within a few ice thickness of the terminus. Consequently, because terminus fluctuations due to individual calving events tend to be much higher frequency than climate variations, individual calving events have little direct impact on the viscous delivery of ice to the terminus. This suggests that the primary mechanism by which calving events can trigger instability is by causing fluctuations in stress that weaken the ice and lead to additional calving and sustained terminus retreat. Our results further demonstrate a stronger response to calving events in simulations that include the full stress tensor, highlighting the importance of accounting for higher order stresses when developing calving parameterizations.
Marine ice-cliff instability could accelerate ice loss from Antarctica, and according to some model predictions could potentially contribute >1 m of global mean sea level rise by 2100 at current ...emission rates. Regions with over-deepening basins >1 km in depth (e.g., the West Antarctic Ice Sheet) are particularly susceptible to this instability, as retreat could expose increasingly tall cliffs that could exceed ice stability thresholds. Here, we use a suite of high-fidelity glacier models to improve understanding of the modes through which ice cliffs can structurally fail and derive a conservative ice-cliff failure retreat rate parameterization for ice-sheet models. Our results highlight the respective roles of viscous deformation, shear-band formation, and brittle-tensile failure within marine ice-cliff instability. Calving rates increase non-linearly with cliff height, but runaway ice-cliff retreat can be inhibited by viscous flow and back force from iceberg mélange.
The simple calving laws currently used in ice-sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound ...understanding of how calving actually works. Here, we develop a new strategy for formulating calving laws, using (a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and (b) the continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts. Calving driven by buoyancy and melt under-cutting is under-predicted by existing calving laws, but we show that the location and magnitude of HiDEM calving events can be predicted in Elmer/Ice from characteristic stress patterns. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum.
We review the two main approaches to estimating sea level rise over the coming century: physically plausible models of reduced complexity that exploit statistical relationships between sea level and ...climate forcing, and more complex physics‐based models of the separate elements of the sea level budget. Previously, estimates of future sea level rise from semiempirical models were considerably larger than those from process‐based models. However, we show that the most recent estimates of sea level rise by 2100 using both methods have converged, but largely through increased contributions and uncertainties in process‐based model estimates of ice sheets mass loss. Hence, we focus in this paper on ice sheet flow as this has the largest potential to contribute to sea level rise. Progress has been made in ice dynamics, ice stream flow, grounding line migration, and integration of ice sheet models with high‐resolution climate models. Calving physics remains an important and difficult modeling issue. Mountain glaciers, numbering hundreds of thousands, must be modeled by extensive statistical extrapolation from a much smaller calibration data set. Rugged topography creates problems in process‐based mass balance simulations forced by regional climate models with resolutions 10–100 times larger than the glaciers. Semiempirical models balance increasing numbers of parameters with the choice of noise model for the observations to avoid overfitting the highly autocorrelated sea level data. All models face difficulty in separating out non‐climate‐driven sea level rise (e.g., groundwater extraction) and long‐term disequilibria in the present‐day cryosphere‐sea level system.
Key Points
We review the two approaches to estimating sea level rise by 2100
We give an overview of glacier, ice sheet and semiempirical modeling
We discuss limitations of state of the art ice sheet and semiempirical models
Abstract
We investigate the physical basis of the crevasse-depth (CD) calving law by analysing relationships between glaciological stresses and calving behaviour at Sermeq Kujalleq (Store Glacier), ...Greenland. Our observations and model simulations show that the glacier has a stable position defined by a compressive arch between lateral pinning points. Ice advance beyond the arch results in calving back to the stable position; conversely, if melt-undercutting forces the ice front behind the stable position, it readvances because ice velocities exceed subaqueous melt rates. This behaviour is typical of self-organising criticality, in which the stable ice-front position acts as an attractor between unstable super-critical and sub-critical regimes. This perspective provides strong support for a ‘position-law’ approach to modelling calving at Sermeq Kujalleq, because any calving ‘rate’ is simply a by-product of how quickly ice is delivered to the critical point. The CD calving law predicts ice-front position from the penetration of surface and basal crevasse fields, and accurately simulates super-critical calving back to the compressive arch and melt-driven calving into the sub-critical zone. The CD calving law reflects the glaciological controls on calving at Sermeq Kujalleq and exhibits considerable skill in simulating its mean position and seasonal fluctuations.
Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view marine ice-sheet models. ...Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (<500 m), or subgrid interpolation of the grounding line. The latter still requires nominal grid sizes of <5 km. For larger grid spacings, appropriate parameterizations for ice flux may be imposed at the grounding line, but the short-time transient behaviour is then incorrect and different from models that do not incorporate grounding-line parameterizations. The numerical error associated with predicting grounding-line motion can be reduced significantly below the errors associated with parameter ignorance and uncertainties in future scenarios.
We investigate the temporal evolution and spatial distribution of mass balance on the glacier Midtre Lovénbreen, Svalbard. Running a diagnostic high-resolution full-stress ice flow model with ...geometries obtained from five digital elevation models (DEMs) in the period 1962–2005, we compute velocity fields and linearly interpolated volume change of the glacier. We evaluate the kinematic free surface equation using these model outputs to solve the surface mass balance (SMB). Monitoring data on Midtre Lovénbreen allows model results to be compared with point measurements from the glacier over several decades. This method allows us to estimate the mass balance over the entire glacier surface, beyond the spatially limited field measurements, and to derive past SMB over an extended time period.
Abstract
Retreat of calving glaciers worldwide has contributed substantially to sea-level rise in recent decades. Mass loss by calving contributes significantly to the uncertainty of sea-level rise ...projections. At Bowdoin Glacier, Northwest Greenland, most calving occurs by a few large events resulting from kilometre-scale fractures forming parallel to the calving front. High-resolution terrestrial radar interferometry data of such an event reveal that crevasse opening is fastest at low tide and accelerates during the final 36 h before calving. Using the ice flow model Elmer/Ice, we identify the crevasse water level as a key driver of modelled opening rates. Sea water-level variations in the range of local tidal amplitude (1 m) can reproduce observed opening rate fluctuations, provided crevasse water level is at least 4 m above the low-tide sea level. The accelerated opening rates within the final 36 h before calving can be modelled by additional meltwater input into the crevasse, enhanced ice cliff undercutting by submarine melt, ice damage increase due to tidal cyclic fatigue, crevasse deepening or a combination of these processes. Our results highlight the influence of surface meltwater and tides on crevasse opening leading to major calving events at grounded tidewater glaciers such as Bowdoin.
Iceberg calving accounts for between 30 % and 60 % of net mass loss from
the Greenland Ice Sheet, which has intensified and is now the single largest
contributor to global sea level rise in the ...cryosphere. Changes to calving
rates and the dynamics of calving glaciers represent a significant
uncertainty in projections of future sea level rise. A growing body of
observational evidence suggests that calving glaciers respond rapidly to
regional environmental change, but predictive capacity is limited by the lack
of suitable models capable of simulating calving mechanisms realistically.
Here, we use a 3-D full-Stokes calving model to investigate the environmental
sensitivity of Store Glacier, a large outlet glacier in West Greenland. We
focus on two environmental processes: undercutting by submarine melting and
buttressing by ice mélange, and our results indicate that Store Glacier
is likely to be able to withstand moderate warming perturbations in which the
former is increased by 50 % and the latter reduced by 50 %. However,
severe perturbation with a doubling of submarine melt rates or a complete
loss of ice mélange destabilises the calving front in our model runs.
Furthermore, our analysis reveals that stress and fracture patterns at
Store's terminus are complex and varied, primarily due to the influence of
basal topography. Calving style and environmental sensitivity vary greatly,
with propagation of surface crevasses significantly influencing iceberg
production in the northern side, whereas basal crevasses dominate in the
south. Any future retreat is likely to be initiated in the southern side by a
combination of increased submarine melt rates in summer and reduced
mélange strength in winter. The lateral variability, as well as the
importance of rotational and bending forces at the terminus, underlines the
importance of using the 3-D full-Stokes stress solution when modelling
Greenland's calving glaciers.
Discharge and water temperature measurements in the Skaftá river and measurements of the lowering of the ice over the subglacial lake at the western Skaftá cauldron, Vatnajökull, Iceland, were made ...during a rapidly rising glacial outburst flood (jökulhlaup) in September 2006. Outflow from the lake, flood discharge at the glacier terminus and the transient subglacial volume of floodwater during the jökulhlaup are derived from these data. The 40 km long initial subglacial path of the jökulhlaup was mainly formed by lifting and deformation of the overlying ice, induced by water pressure in excess of the ice overburden pressure. Melting of ice due to the heat of the floodwater from the subglacial lake and frictional heat generated by the dissipation of potential energy in the flow played a smaller role. Therefore this event, like other rapidly rising jökulhlaups, cannot be explained by the jökulhlaup theory of Nye (1976). Instead, our observations indicate that they can be explained by a coupled subglacial-sheet–conduit mechanism where essentially all of the initial flood path is formed as a sheet by the propagation of a subglacial pressure wave.
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