Ice Flux Research Articles

Numerical modelling of snow and ice thicknesses in Lake Vanajavesi, Finland

Snow and ice thermodynamics was simulated applying a one-dimensional model for an individual ice season 2008–2009 and for the climatological normal period 1971–2000. Meteorological data were used as the model input. The novel model features were advanced treatment of superimposed ice and turbulent heat fluxes, coupling of snow and ice layers and snow modelled from precipitation. The simulated snow, snow–ice and ice thickness showed good agreement with observations for 2008–2009. Modelled ice climatology was also reasonable, with 0.5 cm d−1 growth in December–March and 2 cm d−1 melting in April. Tuned heat flux from water to ice was 0.5 W m−2. The diurnal weather cycle gave significant impact on ice thickness in spring. Ice climatology was highly sensitive to snow conditions. Surface temperature showed strong dependency on thickness of thin ice (<0.5 m), supporting the feasibility of thermal remote sensing and showing the importance of lake ice in numerical weather prediction. The lake ice season responded strongly to air temperature: a level increase by 1 or 5°C decreased the mean length of the ice season by 13 or 78 d (from 152 d) and the thickness of ice by 6 or 22 cm (from 50 cm), respectively.

Description of a hybrid ice sheet-shelf model, and application to Antarctica

Abstract. The formulation of a 3-D ice sheet-shelf model is described. The model is designed for long-term continental-scale applications, and has been used mostly in paleoclimatic studies. It uses a hybrid combination of the scaled shallow ice and shallow shelf approximations for ice flow. Floating ice shelves and grounding-line migration are included, with parameterized ice fluxes at grounding lines that allows relatively coarse resolutions to be used. All significant components and parameterizations of the model are described in some detail. Basic results for modern Antarctica are compared with observations, and simulations over the last 5 million years are compared with previously published results. The sensitivity of ice volumes during the last deglaciation to basal sliding coefficients is discussed.

10Be exposure age constraints on the Late Weichselian ice‐sheet geometry and dynamics in inter‐ice‐stream areas, western Svalbard

The Late Weichselian ice sheet of western Svalbard was characterized by ice streams and inter‐ice‐stream areas. To reconstruct its geometry and dynamics we investigated the glacial geology of two areas on the island of Prins Karls Forland and the Mitrahalvøya peninsula. Cosmogenic 10Be surface exposure dating of glacial erratics and bedrock was used to constrain past ice thickness, providing minimum estimates in both areas. Contrary to previous studies, we found that Prins Karls Forland experienced a westward ice flux from Spitsbergen. Ice thickness reached &gt;470 m a.s.l., and warm‐based conditions occurred periodically. Local deglaciation took place between 16 and 13 ka. At Mitrahalvøya, glacier ice draining the Krossfjorden basin reached &gt;300 m a.s.l., and local deglaciation occurred at c. 13 ka. We propose the following succession of events for the last deglaciation. After the maximum glacier extent, ice streams in the cross‐shelf troughs and fjords retreated, tributary ice streams formed in Forlandsundet and Krossfjorden, and, finally, local ice caps were isolated over both Prins Karls Forland and Mitrahalvøya and their adjacent shelves.

Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP

Abstract. Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for 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 effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.

Marine ice sheet stability

AbstractWe examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.

Temperature distribution and local heat flux in the unidirectional freezing of antifreeze-protein solution

Experiments have been conducted on the unidirectional freezing of dilute aqueous solutions of winter flounder antifreeze protein, which are 0.02mm thick, between two cover glasses on the stage of a microscope. The instantaneous temperature field has been obtained by measuring the intensity of near-infrared light with a near-infrared camera. In addition, the local protein concentration has been measured separately using the brightness of fluorescence emitted from molecules tagged to the protein. It is found that the temperature distribution in the ice region near the ice/water interface is similar to that predicted from the modified Neumann solution. Furthermore, the temperature measurement made using the near-infrared light with a specific wavelength is verified. In addition to this, in the case of antifreeze protein solutions, serrated interfaces are observed. The sum of the conduction heat flux of a protein solution near the front edge of the serrated interface and the heat flux for solidification is lower than the conduction heat flux of ice. On the other hand, the sum of the conduction heat flux of protein solution near the bottom edge of the serrated interface and the heat flux for solidification is higher than the conduction heat flux of ice. The balance of heat flux is obtained by taking account of heat convection due to high-concentration regions of protein. These regions move to the deepest parts of the interface and form narrow liquid regions inside the ice. The convection is maintained by the heat conduction in a direction perpendicular to the direction of ice growth. Not only protein adsorption to the interface but also the heat conduction/convection contributes to the modification of ice growth in the non-equilibrium state.

The response of Black Rapids Glacier, Alaska, to the Denali earthquake rock avalanches

We describe the impact of three simultaneous earthquake‐triggered rock avalanches on the dynamics of Black Rapids Glacier, Alaska, by using spaceborne radar imagery and numerical modeling. We determined the velocities of the glacier before and after landslide deposition in 2002 by using a combination of ERS‐1/ERS‐2 tandem, RADARSAT‐1, and ALOS PALSAR synthetic aperture radar data. Ice velocity above the debris‐covered area of the glacier increased up to 14% after the earthquake but then decreased 20% by 2005. Within the area of the debris sheets, mean glacier surface velocity increased 44% within 2 years of the landslides. At the downglacier end of the lowest landslide, where strong differential ablation produced a steep ice cliff, velocities increased by 109% over the same period. By 2007, ice velocity throughout the debris area had become more uniform, consistent with a constant ice flux resulting from drastically reduced ablation at the base of the debris. Without further analysis, we cannot prove that these changes resulted from the landslides, because Black Rapids Glacier displays large seasonal and interannual variations in velocity. However, a full Stokes numerical ice flow model of a simplified glacier geometry produced a reversal of the velocity gradient from compressional to extensional flow after 5 years, which supports our interpretation that the recent changes in the velocity field of the glacier are related to landslide‐induced mass balance changes.

Glacier longitudinal profiles in regions of active uplift

We combine a simplified equation for ice flow with several proposed glacial erosion laws to solve for longitudinal profiles of glaciers in topographic steady state based on prescribed patterns of rock uplift. The solutions produce realistic looking glaciers and are consistent with previous numerical results. Scaling relationships for the dependence of ice thickness and surface slope on rock uplift and climate (in the form of an imposed ice flux) emerge from the solutions. The general patterns of these dependencies are robust. The ice thickness is dependent upon the ice flux and inversely dependent upon the rock uplift, while the surface slope is inversely dependent upon the ice flux and dependent upon the rock uplift. Different erosion laws lead to only subtle differences in these slope and thickness dependencies. Despite the simplicity of the physics, a first-order match to an actual, over-deepened fjord profile can be obtained. The results provide a theoretical basis for understanding the shape of glacier profiles in tectonically active landscapes, can be used to benchmark numerical models of glacial erosion, and can readily be incorporated directly into simple models of orogen dynamics.

Relative contribution of surface mass-balance and ice-flux changes to the accelerated thinning of Mer de Glace, French Alps, over1979-2008

AbstractBy subtracting surface topographies from 1979, 1994, 2000 and 2008, we measured icethinning rates increasing from 1 ma-1 (1979-94) to &gt;4 ma-1 (2000-08) on the tongue of Mer de Glace, French Alps. The relative contributions of changes in surface mass balance and ice fluxes to this acceleration in the thinning are estimated using field and remote-sensing measurements. Between 1979-94 and 2000-08, surface mass balance diminished by 1.2mw.e.a-1, mainly because of atmospheric warming. Mass-balance changes induced by the growing debris-covered area and the evolving glacier hypsometry compensated each other. Meanwhile, Mer de Glace slowed down and the ice fluxes through two cross sections at 2200 and 2050ma.s.l. decreased by 60%. Between 1979-94 and 2000-08, two-thirds of the increase in the thinning rates was caused by reduced ice fluxes and one- third by rising surface ablation. However, these numbers need to be interpreted cautiously given our inability to respect mass conservation below our upper cross section. An important implication is that large errors would occur if one term of the continuity equation (e.g. surface mass balance) were deduced from the two others (e.g. elevation and ice-flux changes).

From balance to imbalance: a shift in the dynamic behaviour of Chhota Shigri glacier, western Himalaya, India

AbstractMass-balance and dynamic behaviour of Chhota Shigri glacier, western Himalaya, India, has been investigated between 2002 and 2010 and compared to data collected in 1987-89. During the period 2002-10, the glacier experienced a negative glacier-wide mass balance of -0.67 ± 0.40 m w.e. a-1. Between 2003 and 2010, elevation and ice-flow velocities slowly decreased in the ablation area, leading to a 24-37% reduction in ice fluxes, an expected response of the glacier dynamics to its recent negative mass balances. The reduced ice fluxes are still far larger than the balance fluxes calculated from the 2002-10 average surface mass balances. Therefore, further slowdown, thinning and terminus retreat of Chhota Shigri glacier are expected over the next few years. Conversely, the 2003/04 ice fluxes are in good agreement with ice fluxes calculated assuming that the glacier-wide mass balance is zero. Given the limited velocity change between 1987−89 and 2003/04 and the small terminus change between 1988 and 2010, we suggest that the glacier has experienced a period of near-zero or slightly positive mass balance in the 1990s, before shifting to a strong imbalance in the 21st century. This result challenges the generally accepted idea that glaciers in the Western Himalaya have been shrinking rapidly for the last few decades.

Spatial and temporal variation of ice motion and ice flux from Devon Ice Cap, Nunavut, Canada

AbstractSpeckle tracking of repeat RADARSAT-2 fine-beam imagery acquired over 24 day periods in March 2009 allowed the creation of updated surface motion maps for the entire Devon Ice Cap, Canada. Error analysis indicates that speckle tracking can determine ice motion to an accuracy of ~5 ma-1. Comparisons with earlier velocity maps from the mid-1990s and 2000 reveal velocity patterns that largely agree with flow regimes described previously. However, motion determined along East5 Glacier indicates an increase in surface velocities between the studies. Additionally, Southeast2 Glacier has significantly accelerated over the past decade, with velocities greater in 2009 than in the early 1990s along almost the entire length of the glacier. This is likely indicative of a surge. Present-day total mass loss from Devon Ice Cap due to iceberg calving is calculated as 0.40 ± 0.09 Gta-1, similar to that reported by Burgess and others (2005), with Belcher Glacier accounting for ~42% of the entire loss.

Well-posed boundary conditions for limited-domain models of transient ice flow near an ice divide

AbstractWhen an ice-flow model is constrained by data that exist over only a section of an ice sheet, it is computationally advantageous to limit the model domain to only that section. For example, a limited domain near an ice-core site might cross an ice divide, and have no termini. Accurately calculating ice-sheet evolution in response to spatial and temporal variations in climate and ice flow depends on accurately calculating the transient ice flux crossing the limited-domain boundaries. In the absence of information from outside the limited domain, this is an ill-posed problem. Boundary conditions based only on information from inside the limited domain can produce ice-sheet evolution incompatible with the full ice sheet within which we suppose it to exist. We use impulse-response functions to provide boundary values that are informed by the external ice sheet, without conventionally 'nesting' the limited domain in a full ice-sheet model. Evolution within a limited domain can then be consistent with evolution of boundary conditions is designed for future use in affected the limited domain can be inferred from the full ice sheet. Our treatment of limited-domain an inverse problem in which external changes that data from within the limited domain.

Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA

AbstractInformation about glacier volume and ice thickness distribution is essential for many glaciological applications, but direct measurements of ice thickness can be difficult and costly. We present a new method that calculates ice thickness via an estimate of ice flux. We solve the familiar continuity equation between adjacent flowlines, which decreases the computational time required compared to a solution on the whole grid. We test the method on Columbia Glacier, a large tidewater glacier in Alaska, USA, and compare calculated and measured ice thicknesses, with favorable results. This shows the potential of this method for estimating ice thickness distribution of glaciers for which only surface data are available. We find that both the mean thickness and volume of Columbia Glacier were approximately halved over the period 1957–2007, from 281 m to 143 m, and from 294 km3 to 134 km3, respectively. Using bedrock slope and considering how waves of thickness change propagate through the glacier, we conduct a brief analysis of the instability of Columbia Glacier, which leads us to conclude that the rapid portion of the retreat may be nearing an end.

Response of a marine-terminating Greenland outlet glacier to abrupt cooling 8200 and 9300 years ago

Greenland’s largest outlet glacier, using 10 Be surface exposure ages and 14 C‐dated lake sediments. Our chronology of ice‐ margin change demonstrates that Jakobshavn Isbrae advanced to deposit moraines in response to abrupt cooling recorded in central Greenland ice cores ca. 8,200 and 9,300 years ago. While the rapid, dynamically aided retreat of many Greenland outlet glaciers in response to warming is well documented, these results indicate that marine‐terminating outlet glaciers are also able to respond quickly to cooling. We suggest that short lag times of high ice flux margins enable a greater magnitude response of marine‐terminating outlets to abrupt

Impact of Shelf–Basin Freshwater Transport on Deep Convection in the Western Labrador Sea

Abstract Freshwater exiting the Arctic Ocean through the Canadian Arctic Archipelago (CAA) has been shown to affect meridional overturning circulation and thereby the global climate system. However, because of constraints of spatial resolution in most global ocean models, neither the flow of low salinity water through the CAA to the Labrador Sea nor the eddy activity that may transport freshwater from the shelf to areas of open ocean convection can be directly simulated. To address these issues, this study uses a high-resolution ice–ocean model of the pan-Arctic region with a realistic CAA and forced with realistic atmospheric data. This model resolves conditions in the Arctic Ocean upstream of the Labrador Sea and is coupled to a thermodynamic–dynamic sea ice model that responds to the atmospheric forcing. The major shelf–basin exchange of liquid freshwater occurs south of Hamilton Bank, whereas the largest ice flux occurs in the northwest of the basin. Freshwater flux anomalies entering the Labrador Sea through Davis Strait do not immediately affect deep convection. Instead, eddies acting on shorter time scales can move freshwater to locations of active convection and halt the process. Convection is modulated by the position of the ice edge, highlighting the critical need for a coupled ice–ocean model. Finally, the size of eddies and the short duration of events demonstrate the need for high resolution, both spatial and temporal.

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.

Marine ice sheet dynamics. Part 2. A Stokes flow contact problem

We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line.

West Antarctic Ice Sheet elevations in the Ohio Range: Geologic constraints and ice sheet modeling prior to the last highstand

Knowledge of the timing and extent of past West Antarctic Ice Sheet (WAIS) elevation changes provides insight to the WAIS response to sea level and climate forcing, as well as constraints for ice sheet models. Trimlines and erratics indicate that maximum ice elevation at the Ohio Range, located near the WAIS divide, was 125 m above the present ice surface and was reached at ~ 10 ka. However, 3He and 10Be exposure ages of most granitic erratics and supra-glacial boulders in adjacent blue ice areas are older than the last highstand and provide constraints on earlier interior WAIS elevation changes. Although diffusive loss of 3He occurs in quartz, an excellent correlation between 3He and 10Be concentrations in samples up to 400 ka is observed in the Ohio Range, demonstrating the utility of 3He measurements in Antarctic quartz. The correlation is used to calculate “equivalent 10Be exposure ages” from the larger 3He data set. The exposure ages occur in distinct clusters 10–20 ka, 70–80 ka, 130–140 ka and 180–190 ka that we relate to pulses in the emergence of englacial debris in localized blue ice ablation areas. A combined ice sheet/ice shelf model predicts that WAIS elevations near the Ohio Range have varied only ~ 125 m over the last 200 kyr with highstands at ~ 10 ka and ~ 130 ka, in good agreement with observations of trimlines and peaks in the exposure age distribution at the Ohio Range. In the model, interior WAIS elevations are controlled by the interaction of accumulation rates and ice dynamics related to ice sheet/ocean interactions at the grounding line. WAIS highstands occur early in interglacial periods during intervals of warmer temperatures and high accumulation rates, prior to the arrival of a wave of thinning. We hypothesize that the correspondence of rising regional WAIS elevation with debris pulses relates to increased ice (debris) flux and ablation in the local blue ice areas resulting from the warmer temperatures. The occurrence of clasts with exposure ages up to 200 ka on the WAIS surface indicates elevation changes near the Ohio Range were limited in extent during stage 5e. The geologic observations, combined with model results, place constraints on WAIS geometry during stage 5e and limit the WAIS contribution to the higher sea levels observed during the last interglacial to ~ 3 m.

Ice flux divergence anomalies on 79north Glacier, Greenland

The ice flux divergence of a glacier is an important quantity to examine because it determines the rate of temporal change of its thickness. Here, we combine high‐resolution ice surface velocity observations of Nioghalvfjerdsfjorden (79north) Glacier, a major outlet glacier in north Greenland, with a dense grid of ice thickness data collected with an airborne radar sounder in 1998, to examine its ice flux divergence. We detect large variations, up to 100 m/yr, in flux divergence on grounded ice that are incompatible with what we know of the glacier surface mass balance, basal mass balance and thinning rate. We examine the hypothesis that these anomalies are due to the three‐dimensional flow of ice around and atop bumps and hollows in basal topography by comparing the flux divergence of three‐dimensional numerical models with its surface equivalent. We find that three‐dimensional effects have only a small contribution to the observed anomalies. On the other hand, if we degrade the spatial resolution of the data to 10 km the anomalies disappear. Further analysis shows that the source of the anomalies is not the ice velocity data but the interpolation of multiple tracks of ice thickness data onto a regular grid using a scheme (here block kriging) that does not conserve mass or ice flux. This problem is not unique to 79north Glacier but is common to all conventional ice thickness surveys of glaciers and ice sheets; and fundamentally limits the application of ice thickness grids to high‐resolution numerical modeling of glacier flow.

Switching of a paleo-ice stream in northwest Svalbard

Ice streams are the fast-flowing zones of ice sheets that can discharge a large flux of ice. The glaciated western Svalbard margin consists of several cross-shelf troughs which are the former ice stream drainage pathways during the Pliocene–Pleistocene glaciations. From an integrated analysis of high-resolution multibeam swath-bathymetric data and several high-resolution two-dimensional reflection seismic profiles across the western and northwestern Svalbard margin we infer the ice stream flow directions and the deposition centres of glacial debris that the ice streams deposited on the outer margin. Our results show that the northwestern margin of Svalbard experienced a switching of a major ice stream. Based on correlation with the regional seismic stratigraphy as well as the results from ODP 911 on Yermak Plateau and ODP 986 farther south on the western margin of Spitsbergen, off Van Mijenfjord, we find that first a northwestward flowing ice stream developed during initial northern hemispheric cooling (starting ∼2.8–2.6 Ma). A switch in ice stream flow direction to the present-day Kongsfjorden cross-shelf trough took place during a glaciation at ∼1.5 Ma or probably later during an intensive major glaciation phase known as the ‘Mid-Pleistocene Revolution’ starting at ∼1.0 Ma. The seismic and bathymetric data suggest that the switch was abrupt rather than gradual and we attribute it to the reaching of a tipping point when growth of the Svalbard ice sheet had reached a critical thickness and the ice sheet could overcome a topographic barrier.