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Ice-sheet mass-balance estimates derived from repeat satellite-altimetry observations require accurate calculation of spatiotemporal variability in firn-air content (FAC). However, firn-compaction models remain a large source of uncertainty within mass-balance estimates. In this study, we investigate one process that is neglected in FAC estimates derived from firn-compaction models: enhanced layer thinning due to horizontal divergence. We incorporate a layer-thinning scheme into the Community Firn Model. At every time step, firn layers first densify according to a firn-compaction model and then thin further due to an imposed horizontal divergence rate without additional density changes. We find that horizontal divergence on Thwaites (THW) and Pine Island Glaciers can reduce local FAC by up to 41% and 18%, respectively. We also assess the impact of temporal variability of horizontal divergence on FAC. We find a 15% decrease in FAC between 2007 and 2016 due to horizontal divergence at a location that is characteristic of lower THW. This decrease accounts for 16% of the observed surface lowering, whereas climate variability alone causes negligible changes in FAC at this location. Omitting transient horizontal divergence in estimates of FAC leads to an overestimation of ice loss via satellite-altimetry methods in regions of dynamic ice flow.
We describe methods for measuring crystal orientation fabric with sonic waves in an ice core borehole, with special attention paid to vertical-girdle fabrics that are prevalent at the WAIS Divide. The speed of vertically propagating compressional waves in ice is influenced by vertical clustering of the ice crystal c-axes. Shear-wave speeds – particularly the speed separation between fast and slow shear polarizations – are sensitive to azimuthal anisotropy. Sonic data from the WAIS Divide complement thin-section measurements of fabric. Thin sections show a steady transition to strong girdle fabrics in the upper 2000 m of ice, followed by a transition to vertical-pole fabrics below 2500 m depth. Compressional-wave sonic data are inconclusive in the upper ice, due to noise, as well as the method's inherent insensitivity to girdle fabrics. Compared with available thin sections, sonic data provide better resolution of the transition to pole fabrics below 2500 m, notably including an abrupt increase in vertical clustering near 3000 m. Our compressional-wave measurements resolve fabric changes occurring over depth ranges of a few meters that cannot be inferred from available thin sections, but are sensitive only to zenithal anisotropy. Future logging tools should be designed to measure shear waves in addition to compressional waves, especially for logging in regions where ice flow patterns favor the development of girdle fabrics.
Evolution of cold dry snow and firn plays important roles in glaciology; however, the physical formulation of a densification law is still an active research topic. We forced eight firn-densification models and one seasonal-snow model in six different experiments by imposing step changes in temperature and accumulation-rate boundary conditions; all of the boundary conditions were chosen to simulate firn densification in cold, dry environments. While the intended application of the participating models varies, they are describing the same physical system and should in principle yield the same solutions. The firn models all produce plausible depth-density profiles, but the model outputs in both steady state and transient modes differ for quantities that are of interest in ice core and altimetry research. These differences demonstrate that firn-densification models are incorrectly or incompletely representing physical processes. We quantitatively characterize the differences among the results from the various models. For example, we find depth-integrated porosity is unlikely to be inferred with confidence from a firn model to better than 2 m in steady state at a specific site with known accumulation rate and temperature. Firn Model Intercomparison Experiment can provide a benchmark of results for future models, provide a basis to quantify model uncertainties and guide future directions of firn-densification modeling.
The 18O/16O profile of a 554-m long ice core through Taylor Dome, Antarctica, shows the climate variability of the last glacial–interglacial cycle in detail and extends at least another full cycle. Taylor Dome shares the main features of the Vostok record, including the early climatic optimum with later cool phase of the last interglacial period in Antarctica. Taylor Dome δ18O fluctuations are more abrupt and larger than those at Vostok and Byrd Station, although still less pronounced than those of the Greenland GISP2 and GRIP records. The influence of the Atlantic thermohaline circulation on regional ocean heat transport explains the partly “North Atlantic” character of this Antarctic record. Under full glacial climate (marine isotope stage 4, late stage 3, and stage 2), this marine influence diminished and Taylor Dome became more like Vostok. Varying degrees of marine influence produce climate heterogeneity within Antarctica, which may account for conflicting evidence regarding the relative phasing of Northern and Southern Hemisphere climate change.
At Taylor Glacier, a cold-based outlet glacier of the East Antarctic ice sheet, observed surface speeds in the terminus region are 20 times greater than those predicted using Glen’s flow law for cold (–17°C), thin (100 m) ice. Rheological properties of the clean meteoric glacier ice and the underlying deformable debris-rich basal ice can be inferred from surface-velocity and ablation-rate profiles using inverse theory. Here, with limited data, we use a two-layer flowband model to examine two end-member assumptions about the basal-ice properties: (1) uniform softness with spatially variable thickness and (2) uniform thickness with spatially variable softness. We find that the basal ice contributes 85–98% to the observed surface velocity in the terminus region. We also find that the basal-ice layer must be 10–15 m thick and 20–40 times softer than clean Holocene-age glacier ice in order to match the observations. Because significant deformation occurs in the basal ice, our inverse problem is not sensitive to variations in the softness of the meteoric ice. Our results suggest that despite low temperatures, highly deformable basal ice may dominate flow of cold-based glaciers and rheologically distinct layers should be incorporated in models of polar-glacier flow.
When 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.
We used observations and modeling of Siple Dome, West Antarctica, a ridge ice divide, to infer the importance of linear deformation mechanisms in ice-sheet flow. We determined the crossover stress (a threshold value of the effective deviatoric stress below which linear flow mechanisms dominate over nonlinear flow mechanisms) by combining measurements of ice properties with in situ deformation rate measurements and a finite-element ice flow model that accounts for the effects of viscous anisotropy induced by preferred crystal-orientation fabric. We found that a crossover stress of 0.18 bar produces the best match between predicted and observed deformation rates. For Siple Dome, this means that including a linear term in the flow law is necessary, but generally the flow is still dominated by the nonlinear (Glen; n = 3) term. The pattern of flow near the divide at Siple Dome is also strongly affected by crystal fabric. Measurements of sonic velocity, which is a proxy for vertically oriented crystal fabric, suggest that a bed-parallel shear band exists several hundred meters above the bed within the Ice Age ice.
We have developed a technique in which we use a borehole video camera and post-processing software to make a record of the optical brightness as a function of depth in polar firn. We call this method borehole optical stratigraphy. To measure firn compaction, we note the positions of optical features on the borehole wall detected by an initial ‘baseline’ log. We track the displacements of these features in subsequent logs. The result provides a measurement of the relative vertical motion and thus compaction of the firn over the survey period. We have successfully used this system at Summit, Greenland, to measure the depth distribution of firn column shortening experienced in a borehole over three 1 year periods. The uppermost 30 m of the firn at Summit is compacting as predicted by a simple steady-state model, implying that the firn density profile at Summit is at or close to steady state over the past ∼70 years.
‘Extrusion flow’ describes any velocity field where maximum horizontal velocity occurs below the surface. By 1914, viscous flow and basal sliding over rough beds were accepted concepts. Between the world wars, there was little communication between naturalists describing complicated ice sheets, and physicists studying fundamental processes controlling flow. Max Demorest brought concepts from mechanics into glaciology and glacial geology; however, his extrusion flow theory, to explain how ice flowed out of central Greenland, overlooked force imbalance. Rudolf Streiff-Becker found an apparent large imbalance between ice flux discharged through a gate and net accumulation in the upstream catchment at Claridenfirn, Switzerland. Because he underestimated uncertainty in ice depth, he had to propose a strong undercurrent (extrusion flow) to evacuate the excess mass. Reassessment of his assumptions shows that extrusion was actually unnecessary. However, confluence of two lines of evidence for extrusion flow added stature to the concept. In 1952, John Nye showed that free extrusion flow was impossible due to force imbalance. Two forms of extrusion flow survive: capped extrusion flow is possible on local scales where longitudinal stress gradients allow upper ice to move slowly, and rigid- body rotational flow can allow deeper ice to move faster without strain.
Using a Monte Carlo (MC) method, we determine the accumulation-rate profile along a flowband, the influx of ice into the upstream end of the flowband and the age of an internal layer. The data comprise the depth profile of the internal layer, a few velocity measurements at the surface and the average accumulation at one location. The data in our example were collected at Taylor Mouth, a flank site off Taylor Dome, Antarctica. We present three alternative formulations of this inverse problem. Depending on the formulation used, this particular inverse problem can have up to four solutions, each corresponding to a different spatial accumulation-rate pattern. This study demonstrates the ability of a MC method to find several solutions to this inverse problem, and how to use a Metropolis algorithm to determine the probability distribution of each of these different solutions. The only disadvantage of the MC method is that it is computationally more expensive than other inverse methods, such as the Gradient method.
Accumulation rates and their spatio-temporal variability are important boundary conditions for ice-flow models. The depths of radar-detected internal layers can be used to infer the spatial variability of accumulation rates. Here we infer accumulation rates from three radar layers (26, 35 and 41 ka old) in the Vostok Subglacial Lake region using two methods: (1) the local-layer approximation (LLA) and (2) a combination of steady-state flowband modeling and formal inverse methods. The LLA assumes that the strain-rate history of a particle traveling through the ice sheet can be approximated by the vertical strain-rate profile at the current position of the particle, which we further assume is uniform. The flowband model, however, can account for upstream strain-rate gradients. We use the LLA to map accumulation rates over a 150 km × 350 km area, and we apply the flowband model along four flowbands. The LLA accumulation-rate map shows higher values in the northwestern corner of our study area and lower values near the downstream shoreline of the lake. These features are also present but less distinct in the flowband accumulation-rate profiles. The LLA-inferred accumulation-rate patterns over the three time periods are all similar, suggesting that the regional pattern did not change significantly between the start of the Holocene and the last ~20 ka of the last Glacial Period. However, the accumulation-rate profiles inferred from the flowband model suggest changes during that period of up to 1 cma–1 or ~50% of the inferred values.
Recent observations of increased discharge through fast-flowing outlet glaciers and ice streams motivate questions concerning the inland migration of regions of fast flow, which could increase drawdown of the ice-sheet interior. To investigate one process that could lead to inland migration we conduct experiments with a two-dimensional, full-stress, transient ice-flow model. An initial steady state is perturbed by initiating a jump in sliding speed over a fraction of the model domain. As a result, longitudinal-stress gradients increase frictional melting upstream from the slow-to-fast sliding transition, and a positive feedback between longitudinal-stress gradients, basal meltwater production and basal sliding causes the sliding transition to migrate upstream over time. The distance and speed of migration depend on the magnitude of the perturbation and on the degree of non-linearity assumed in the link between basal stress and basal sliding: larger perturbations and/or higher degrees of non-linearity lead to farther and faster upstream migration. Migration of the sliding transition causes the ice sheet to thin over time and this change in geometry limits the effects of the positive feedback, ultimately serving to impede continued upstream migration.
A finite-volume model is used to simulate 9 years (1995–2003) of snow temperatures at the South Pole. The upper boundary condition is skin-surface temperature derived from routine upwelling longwave radiation measurements, while the lower boundary condition is set to the seasonal temperature gradient at 6.5 m depth, taken from prior measurements at the South Pole. We focus on statistics of temperature, heat fluxes, heating rates and vapour pressures in the top metre of snow, but present results from the full depth of the model (6.5 m). The monthly mean net heat flux into the snow agrees with results from previous studies performed at the South Pole. On shorter timescales, the heating rates and vapour pressures show large variability. The net heat flux into the snow, which is between ±5 W m−2 in the monthly mean, can be greater than ±20 W m−2 on hourly timescales. On sub-daily timescales, heating rates exceed 40 K d−1 in the top 10 cm of the snow. Subsurface temperatures, and therefore heating rates, are more variable during winter (April–September) due to increased synoptic activity and the presence of a strong, surface-based, atmospheric temperature inversion. The largest vapour pressures (60–70 Pa) and vertical gradients of vapour pressure are found in the top metre of snow during the short summer (December–January). In contrast, during the long winter, the low temperatures result in very small vapour pressures and insignificant vapour-pressure gradients. The high summertime vapour-pressure gradients may be important in altering the isotopic composition of snow and ice on the Antarctic plateau.
Knowledge of ice flow and strain rate in the vicinity of the Taylor Dome (East Antarctica) ice-core site enhances interpretation of the paleoclimate information from the ice core. We measured surface ice motion by repeated optical and GPS surveys of a network of 253 markers. We developed a robust data reduction method that uses least squares based on singular value decomposition, to simultaneously calculate positions and velocities of these markers in a geocentric coordinate system. Constrained by these surface velocities, we used a finite-element model to compute the modern ice velocity field at depth. As the geometry of Taylor Dome appears to have been steady through the Holocene, we used particle paths from a steady-state model to track ice particles to the ice core from their points of origin on the surface. By removing the effects of path-dependent vertical strain, we derived past accumulation rates at the origin points of those particle paths from measured layer thicknesses in the ice core. Comparison with accumulation rates estimated from concentrations of 10Be and SO4 in the core suggests that significant amounts of snow were lost by wind scouring during the Last Glacial Maximum and at ~50kyr BP.
The spatial pattern of accumulation rate can be inferred from internal layers in glaciers and ice sheets. Non-dimensional analysis determines where finite strain can be neglected (‘shallow-layer approximation’) or approximated with a local one-dimensional flow model (‘local-layer approximation’), and where gradients in strain rate along particle paths must be included (‘deep layers’). We develop a general geophysical inverse procedure to infer the spatial pattern of accumulation rate along a steady-state flowband, using measured topography of the ice-sheet surface, bed and a ‘deep layer’. A variety of thermomechanical ice-flow models can be used in the forward problem to calculate surface topography and ice velocity, which are used to calculate particle paths and internal-layer shapes. An objective tolerance criterion prevents over-fitting the data. After making site-specific simplifications in the thermomechanical flow algorithm, we find the accumulation rate along a flowband through Taylor Mouth, a flank site on Taylor Dome, Antarctica, using a layer at approximately 100 m depth, or 20% of the ice thickness. Accumulation rate correlates with ice-surface curvature. At this site, gradients along flow paths critically impact inference of both the accumulation pattern, and the depth-age relation in a 100 m core.
Polycrystalline ice near an ice divide typically shows a crystal fabric (crystal preferred orientation) with c axes clustered vertically. We explore the effect of this fabric on the large-scale flow pattern near an ice divide. We incorporate an analytical formulation for anisotropy into a non-linear flow law within a finite-element ice-sheet flow model. With four different depth profiles of crystal fabric, we find that the effect of fabric is significant only when a profile has a minimum cone angle of less than ~25º. For a steady-state divide, the shape and size of the isochrone arch can depend as much on the crystal fabric as it does on the non-linearity of ice flow. A vertically oriented fabric tends to increase the size of the isochrone arch, never to reduce it. Also, non-random fabric has little effect on the ice-divide-flow pattern when ice is modeled as a linear (Newtonian) fluid. Finally, when we use a crystal-fabric profile that closely approximates the measured profile for Siple Dome, West Antarctica, the model predicts concentrated bed-parallel shearing 300 m above the bed.
Colinear-polarized 5 MHz radar profiling data were obtained on Mýrdalsjökull, a temperate glacier in Iceland. Radar transects, and therefore polarization planes, were aligned approximately parallel, transverse and oblique to the ice flow direction. Echoes from the shallower half to two-thirds of the ice were 10–20dB stronger on the oblique and longitudinal transects than those on the transverse transects. Anisotropy as a function of depth is clearly seen at the sites where the transects cross. Strong scattering on longitudinal transects apparently caused extinction of a radar-reflecting layer that was continuously profiled on the transverse transects. A radio-wave scattering model shows that scattering from a longitudinal water-filled conduit parallel to the glacier surface can explain the observed azimuthal variations of the echo. We conclude that low-frequency (~MHz) radio waves can help to characterize englacial water regimes.
Arches in stratigraphic layers directly under a flow divide (Raymond bumps) are predicted by models of steady ice-sheet flow, and have been observed in several ice domes. Here, we model the evolution of these layers when a formerly stationary divide migrates rapidly to a new position, then again becomes stationary, leaving the arched layers in a flank position. As they are then carried downstream with the flow, these abandoned arches can develop into recumbent folds. These folds can occur over a wide range of divide migration speeds. The shearing flow that produces these recumbent folds also distributes the folded layers over a wide distance downstream from the original divide location. If the divide offset is abrupt, ‘pre-cores’, or material lines comprising core-relative isochrones, can be used to quickly identify portions of an abandoned Raymond bump that would be overturned at any future ice-core site downstream. If, as appears to be the case in Greenland, the divide is never stable long enough to produce a mature arch, folds of this type would not occur. The most likely place to find such folds might be the flank of an ice ridge bounded by unsteady ice streams.
The late-Holocene trends in δ18O differ significantly in two ice cores (30 km apart) from the area of Taylor Dome, Antarctica. It is unlikely that the trend in the core from Taylor Mouth (the flank site) is due to a standard δ18O–surface temperature relationship. Assuming that the Taylor Dome (nearsummit) core records local climate variations common to both cores, we assess two leading possible causes for the observed differences: (1) Relative to Taylor Dome, Taylor Mouth may collect snow from more sources with distinct isotopic compositions. (2) Vapor motion during prolonged near-surface exposure may cause post-depositional isotope enrichment at Taylor Mouth, where the accumulation rate is low. Our model of firn pore-space vapor and sublimating ice grains suggests that post-depositional processes can modify δ18O values by several ‰. Isotopic samples from areas with significantly different accumulation rates near Taylor Mouth could differentiate between possibilities (1) and (2).
We measured vertical strain in the firn at Siple Dome, Antarctica, using two systems, both of which measure relative displacements over time of metal markers placed in an air-filled borehole. One system uses a metal-detecting tuned coil, and the other uses a video camera to locate the markers. We compare the merits of the two systems. We combine steady-state calculations and a measured density profile to estimate the true vertical-velocity profile. This allows us to calculate a depth-age scale for the firn at Siple Dome. Our steady-state depth-age scale has ages ≈10-15% younger at any given depth when compared to depth-age scales derived by layer counting in a core 40 m away. The age of a visible ash layer at 97 m in the core is 665 ± 30 years, in agreement with a similar analysis conducted at Taylor Dome, Antarctica, where the same ash is also seen, providing an additional dated tie point between the two cores.