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Mechanisms of fast flow in Jakobshavn Isbr??, West Greenland: Part III. Measurements of ice deformation, temperature and cross-borehole conductivity in boreholes to the bedrock
Abstract
At a site on the ice sheet adjacent to the Jakobshavn ice stream in West Greenland, ice deformation rates and temperatures have been measured in boreholes to the bedrock at 830 m depth. Enhanced deformation rates were recorded just below the Holocene-Wisconsin transition at 680 m depth. A 31m layer of temperate ice and the temperature minimum of -22°C at 520 m depth were detected. The good agreement of these data with results of a two-dimensional thermomechanically coupled flow model implies that the model input is adequate. Discrepancies between modelled and measured temperature profiles on a flowline at the ice-stream centre have been attributed to effects not accounted for by the model. We have suggested that the convergent three-dimensional flow leads to a vertical extension of the basal ice entering the stream. A thick basal layer oftemperate and Wisconsin ice would explain the fast flow of this ice stream. As a test of this hypothesis, the new core-borehole conductivity (CBC) method has been used to compare conductivity sequences from the ice stream to those of the adjacent ice sheet. The correlation thus inferred suggests that the lowest 270 m of the ice sheet correspond to the lowermost 1700 m ofthe stream, and, consequently, that the lower part of the ice stream has experienced a very large vertical extension.
... This is the case for the two sites of FOXX6 and GULL1 (Ryser et al., 2014). Furthermore, five partial profiles at one site (Lüthi et al., 2002), all situated less than 25 m from one another, were also regarded as one borehole. This means that the 95 temperature profiles in the database are considered to originate from 85 unique boreholes. ...
... Overall, 71 of the 95 profiles were available as tabulated temperature measurements (Heuberger, 1954;Classen, 1977;Stauffer and Oeschger, 1979;Clarke et al., 1987;Thom- Iken et al., 1993;Hansson, 1994;Cuffey et al., 1995;Thomsen et al., 1996;Cuffey and Clow, 1997;Dahl-Jensen et al., 1998;Fischer et al., 1998;Lüthi et al., 2002;Kinnard et al., 2006;Buchardt and Dahl-Jensen, 2007;Kinnard et al., 2008;Lemark and Dahl-Jensen, 2010;Rasmussen et al., 2013;Ryser et al., 2014;Harrington et al., 2015;Hills et al., 2017;Zekollari et al., 2017;Doyle et al., 2018b;Seguinot et al., 2020;Hubbard et al., 2021a;Law et al., 2021). The remaining 24 profiles were digitized from figures (Hansen and Landauer, 1958;Davis, 1967;Paterson, 1968;Classen, 1977;Paterson et al., 1977;Colbeck and Gow, 1979;Gundestrup and Hansen, 1984;Blatter and Kappenberger, 1988;Gundestrup et al., 1993). ...
... Several process level studies of potential heat sources have been performed, which compare individual observed temperature profiles from local areas with temperature profiles modeled by a thermal, or thermomechanical, ice flow model (Iken et al., 1993;Lüthi et al., 2002;Harrington et al., 2015;Lüthi et al., 2015;Meierbachtol et al., 2015;McDowell et al., 2021;Law et al., 2021;Maguire et al., 2021). Although these studies featured different local areas, the comparisons generally showed that models tend to underestimate englacial temperatures and thus need to incorporate additional heat sources in order to reproduce the observed ice temperature profiles. ...
Here, we present a compilation of 95 ice temperature profiles from 85 boreholes from the Greenland ice sheet and peripheral ice caps, as well as local ice caps in the Canadian Arctic. Profiles from only 31 boreholes (36 %) were previously available in open-access data repositories. The remaining 54 borehole profiles (64 %) are being made digitally available here for the first time. These newly available profiles, which are associated with pre-2010 boreholes, have been submitted by community members or digitized from published graphics and/or data tables. All 95 profiles are now made available in both absolute (meters) and normalized (0 to 1 ice thickness) depth scales and are accompanied by extensive metadata. These metadata include a transparent description of data provenance. The ice temperature profiles span 70 years, with the earliest profile being from 1950 at Camp VI, West Greenland. To highlight the value of this database in evaluating ice flow simulations, we compare the ice temperature profiles from the Greenland ice sheet with an ice flow simulation by the Parallel Ice Sheet Model (PISM). We find a cold bias in modeled near-surface ice temperatures within the ablation area, a warm bias in modeled basal ice temperatures at inland cold-bedded sites, and an apparent underestimation of deformational heating in high-strain settings. These biases provide process level insight on simulated ice temperatures.
... In contrast to growing interest in Antarctica, studies on temperate ice in Greenland are extremely limited. Lüthi et al. (2002) and Harrington et al. (2015) construct separate 2D flow line models of temperate ice development for land-and marine-terminating settings respectively. Lüthi et al. (2002) Chudley et al., 2021;Hubbard et al., 2021) in the GrIS ablation zone not producing large thicknesses of surface-adjacent temperate ice probably suggests the basal-crevassing hypothesis can not fully account for the mismatch between models and observations. ...
... Lüthi et al. (2002) and Harrington et al. (2015) construct separate 2D flow line models of temperate ice development for land-and marine-terminating settings respectively. Lüthi et al. (2002) Chudley et al., 2021;Hubbard et al., 2021) in the GrIS ablation zone not producing large thicknesses of surface-adjacent temperate ice probably suggests the basal-crevassing hypothesis can not fully account for the mismatch between models and observations. Zhang et al. (2022) provide an initial 2D exploration of heat transfer from basal hydrofracture, but do not incorporate temperate ice. ...
... All of these studies use smoothly-varying basal topography, which may reduce deformation heating above the CTS -the full implications of which are comprehensively explored in chapter 4. Last, while not numerical, Krabbendam (2016) provide an excellent conceptual framework of temperate ice processes in Greenland (alongside a review) and use this to argue for the importance of temperate ice in facilitating ice streaming motion over hard bedrock in northeast Greenland. Alongside observations from chapter 3, Krabbendam (2016) provided the initial impetus to expand upon the 2D models of Lüthi et al. (2002) and Harrington et al. (2015) and investigate a wider range of processes responsible for temperate layer evolution. ...
Predictions of ice-sheet mass loss, and therefore predictions of global sea level rise, depend sensitively upon how ice-sheet motion is incorporated into numerical models. Using field observations and numerical modelling, this thesis demonstrates that two frequently overlooked processes are central to describing borehole observations of fast ice-sheet motion --- intermediate-scale (<25 m, ⪅2 km) interaction of ice motion with realistic or real bed topography, and modulation of these ice-motion patterns through a basal layer of temperate ice (much softer ice at the pressure-melting point). I first present a fibre-optic data set from a 1,043 m deep borehole drilled to the base of the fast-moving (>500 m a‾¹) marine-terminating Sermeq Kujalleq (Store Glacier) at the western margin of the Greenland Ice Sheet. This reveals hitherto unappreciated complexity in the processes behind fast ice-sheet motion. I observe substantial but isolated strain heating ~220 m beneath the surface within stiffer interglacial-phase ice where previously none was expected. Ice deformation within glacial-phase ice below 889 m is further observed to be strongly heterogeneous, with a possible high-strain interface demarcating the Last Glacial-Interglacial Transition. I also find a 73-m-thick temperate basal layer, notably thicker than the <10-m-thick temperate layer just 8.9 km away, unexplained by existing theory, and interpreted to be important for the glacier's fast motion. To disentangle this observed complexity, I then model three isolated 3D domains from the Greenland Ice Sheet's western margin --- two from Sermeq Kujalleq and one from the land-terminating Isunnguata Sermia, all centred above a central borehole observation. By incorporating high-resolution realistic geostatistically simulated topography, I demonstrate that a layer of basal temperate ice with spatially highly variable thickness forms naturally in both marine- and land-terminating settings, alongside ice-motion patterns which are far more complex than previously considered. I show that temperate ice is expected to be vertically extensive in deep troughs, but to thin over bedrock highs. I further show that basal-slip rates are interconnected with this variability, reaching >90% or <5% of surface velocity dependent on setting. Last, I apply the assembled model to real high-resolution bed topography data produced by radio-echo sounding at Thwaites Glacier, Antarctica. This reveals a distinct pattern of ice motion controlled by rough topographic highs where basal slip rates are highly variable, and the landscape is predominantly erosive, with broader topographic basins where basal slip is high and uniform, and the landscape is predominantly depositional. This work further suggests the existence of basal temperate ice layer beneath Thwaites Glacier, at least at the rougher topographic highs. Overall, this thesis advances understanding of how ice sheets move, which may ultimately lead to improved parameterisations of ice-sheet motion for predictive models.
... Other boreholes which have been logged more than once also include GISP2-50 D, GISP2-G, NGRIP-2, NGRIP-S2, NEEM-D, however, these are currently not included in the database. The database also contains five partial profiles at one site (Lüthi et al., 2002). The boreholes were all situated less than 25 m from one another, and are therefore regarded as one borehole, meaning that the 85 profiles are considered to originate from 79 unique boreholes. ...
... Last Access 3 March 2022; Rohatgi (2021)). Overall, 61 of the 85 profiles were available as tabulated temperature measurements (Heuberger, 1954;Classen, 1977;Stauffer and Oeschger, 1979;Clarke et al., 1987;Thomsen et al., 1991;Iken et al., 1993;Hansson, 1994;Cuffey et al., 1995;Thomsen et al., 1996;Cuffey and Clow, 1997;Dahl-Jensen et al., 1998;Fischer et al., 1998;Lüthi et al., 2002;Kinnard et al., 2006;Buchardt and Dahl-Jensen, 2007;Kinnard et al., 2008;Lemark and Dahl-Jensen, 2010;Rasmussen et al., 2013;Ryser et al., 2014;Harrington et al., 2015;Hills et al., 2017;Zekollari et al., 2017;Doyle et al., 2018b;Hubbard et al., 2021a;Harper and Meierbachtol, 2021;Law et al., 2021). The remaining 24 profiles were digitized from figures (Hansen and Landauer, 1958;65 Davis, 1967;Paterson, 1968;Classen, 1977;Paterson et al., 1977;Colbeck and Gow, 1979;Gundestrup and Hansen, 1984;Blatter and Kappenberger, 1988;Gundestrup et al., 1993). ...
... To help shape best practice for using the database that we present, we describe an 240 approach for evaluating a contemporary ice-sheet simulation against all observed Greenland deep ice temperature observations. Several process-level studies of potential heat sources have been performed, which compare individual observed temperature profiles from local areas with temperature profiles modeled by a thermal, or themo-mechanical, ice flow model (Iken et al., 1993;Lüthi et al., 2002;Harrington et al., 2015;Lüthi et al., 2015;Meierbachtol et al., 2015;McDowell et al., 2021;Law et al., 2021;Maguire et al., 2021). Although these studies featured different local areas, the comparisons generally showed that models tend to underestimate englacial temperatures, and thus need to incorporate additional heat sources in order to reproduce observed ice temperature profiles. ...
Here, we present a compilation of 85 ice temperature profiles from 79 boreholes from the Greenland Ice Sheet and peripheral ice caps, as well as local ice caps in the Canadian Arctic. Only 25 profiles (32 %) were previously available in open-access data repositories. The remaining 54 profiles (68 %) are being made digitally available here for the first time. These newly available profiles, which are associated with pre-2010 boreholes, have been submitted by community members or digitized from published graphics and/or data tables. All 85 profiles are now made available in both absolute (meters) and normalized (0 to 1 ice thickness) depth scales, and are accompanied by extensive metadata. This metadata includes a transparent description of data provenance. The ice temperature profiles span 70 years, with the earliest profile being from 1950 at Camp VI, West Greenland. To highlight the value of this database in evaluating ice flow simulations, we compare the ice temperature profiles from the Greenland Ice Sheet with an ice flow simulation by the Parallel Ice Sheet Model (PISM). We find a cold bias in modeled near-surface ice temperatures within the ablation area, a warm bias in modeled basal ice temperatures at inland cold-bedded sites, and an apparent underestimation of deformational heating in high-strain settings. These biases provide process-level insight on simulated ice temperatures.
... In such cases, an ad hoc strain enhancement factor is often incorporated into the preexponential term of the Glen law to account for the combined effects of grain size, impurities, fabric development, and shear heating (see Cuffey and Paterson, 2010). For example, matching velocity profiles across ice streams (e.g., Echelmeyer et al., 1994;Jackson and Kamb, 1997) and through Pleistocene ice near the base of the Greenland ice sheet (Dahl-Jensen and Gunderstrup, 1987;Shoji and Langway, 1988;Lüthi et al., 2002;Ryser et al., 2014) often requires enhancement factors in the range of 2-10. Cuffey et al. (2000) attempted to quantify the role of grain size in the enhancement factor based on deformation recorded in Meserve Glacier, Antarctica. ...
... To illustrate this point, we model deformation within Drill Site D in fast-moving ice near Jakobshavn Isbrae in western Greenland (Iken et al., 1993;Lüthi et al., 2002). This site experiences surface velocities of ∼ 600 m yr −1 , and tiltmeter data indicate enhanced strain rates in temperate ice below the Holocene-LGM transition near the bed. ...
... This site experiences surface velocities of ∼ 600 m yr −1 , and tiltmeter data indicate enhanced strain rates in temperate ice below the Holocene-LGM transition near the bed. Lüthi et al. (2002) developed a thermomechanical model for deformation in the borehole and found that after incorporating the temperature dependence of ice viscosity, enhancement factors of 1.7-2.6 were required to match the observations in the pre-Holocene ice below 680 m. Although neither grain size nor impurity contents were measured in the Site D core, Lüthi et al. (2002) interpreted the enhanced strain rates to re- (Lüthi et al., 2002). ...
Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.
... Under such conditions, a basal temperate zone consisting of ice at the phase transition temperature may ultimately develop if strain heating exceeds the conductive heat flux away from the cold-temperate transition zone [e.g., (17,24)] or if liquid water in veins or fractures freezes and releases latent heat within the ice (24). While our observations are consistent with previous records of these processes at other sites using discrete sensors, typically spaced tens of meters apart or more [e.g., (25)(26)(27)], our continuous DTS measurements enable us to resolve both previously identified and presently undocumented thermodynamic processes in unsurpassed detail. ...
... Although Anomaly-208 is unique in resolution, local temperature anomalies that could feasibly be fitted with a shape similar to Anomaly-208 have been detected in previous borehole-based studies, albeit at a lower resolution (7,19,26,27). This suggests that anomalies such as the one described here may be widespread. ...
... and water-filled crevasses were observed to a maximum depth of 265 m in a borehole drilled 1 km away at site R29 ( Fig. 1) (20), we instead hypothesize that Anomaly-208 is a result of increased deviatoric stress below the depth of maximum crevasse propagation or a result of longitudinal and lateral stress transfer from spatially varying bed conditions [e.g., (34)]. With similar integrated differential attenuation signatures tied to other temperature anomalies at 100 to 110 and 837 m depth, we further hypothesize that strain heating can occur within Holocene ice as well as within pre-Holocene ice in which variable deformation is more commonly observed [e.g., (7,25,26)]. ...
Measurements of ice temperature provide crucial constraints on ice viscosity and the thermodynamic processes occurring within a glacier. However, such measurements are presently limited by a small number of relatively coarse-spatial-resolution borehole records, especially for ice sheets. Here, we advance our understanding of glacier thermodynamics with an exceptionally high-vertical-resolution (~0.65 m), distributed-fiber-optic temperature-sensing profile from a 1043-m borehole drilled to the base of Sermeq Kujalleq (Store Glacier), Greenland. We report substantial but isolated strain heating within interglacial-phase ice at 208 to 242 m depth together with strongly heterogeneous ice deformation in glacial-phase ice below 889 m. We also observe a high-strain interface between glacial- and interglacial-phase ice and a 73-m-thick temperate basal layer, interpreted as locally formed and important for the glacier’s fast motion. These findings demonstrate notable spatial heterogeneity, both vertically and at the catchment scale, in the conditions facilitating the fast motion of marine-terminating glaciers in Greenland.
... In Greenland, the composition of the basal substrate is known to vary significantly. There are both hard and till beds (Booth et al., 2012;Cooper et al., 2019;Dow et al., 2013;Doyle et al., 2018;Harper et al., 2017;Kulessa et al., 2017;Lindbäck and Pettersson, 2015;Lüthi et al., 2002). The exact distribution of each is unknown, but direct observations have shown that they coexist at the regional scale (Booth et al., 2012;Dow et al., 2013;Harper et al., 2017). ...
... Further, in Greenland the uncertainty of the deformation exponent, n, is large. Direct estimates of n range considerably from 2.5 to 4.5 (Bons et al., 2018;Dahl-Jensen and Gundestrup, 1987;Gillet-Chaulet et al., 2011;Lüthi et al., 2002;Ryser et al., 2014). Other aspects of ice flow such as crevasses that are common in regions of concentrated fast flow (Cavanagh et al., 2017;Lampkin et al., 2013) and in extensional regimes are not accounted for in high-order inversions but could significantly impact the relationship between the velocity field and higherorder stresses (stress gradients). ...
... In Greenland, the rheologic uncertainty and complex thermal structure make it difficult to infer a location-specific rheology to confidently calculate deformation across the ice sheet (Maier et al., 2019). However, direct measurements of basal motion collectively show the prevalence of high fractions of basal motion (0.44-0.96) across a wide range of glaciological environments in Greenland Lüthi et al., 2002;MacGregor et al., 2016;Maier et al., 2019;Ryser et al., 2014). ...
On glaciers and ice sheets, identifying the relationship between velocity and traction is critical to constrain the bed physics that controls ice flow. Yet in Greenland, these relationships remain unquantified. We determine the spatial relationship between velocity and traction in all eight major drainage catchments of Greenland. The basal traction is estimated using three different methods over large grid cells to minimize interpretation biases associated with unconstrained rheologic parameters used in numerical inversions. We find the relationships are consistent with our current understanding of basal physics in each catchment. We identify catchments that predominantly show Mohr–Coulomb-like behavior typical of deforming beds or significant cavitation, as well as catchments that predominantly show rate-strengthening behavior typical of Weertman-type hard-bed physics. Overall, the traction relationships suggest that the flow field and surface geometry of the grounded regions in Greenland is mainly dictated by Weertman-type hard-bed physics up to velocities of approximately 450 m yr-1, except within the Northeast Greenland Ice Stream and areas near floatation. Depending on the catchment, behavior of the fastest-flowing ice (∼ 1000 m yr-1) directly inland from marine-terminating outlets exhibits Weertman-type rate strengthening, Mohr–Coulomb-like behavior, or is not confidently resolved given our methodology. Given the complex basal boundary across Greenland, the relationships are captured reasonably well by simple traction laws which provide a parameterization that can be used to model ice dynamics at large scales. The results and analysis serve as a first constraint on the physics of basal motion over the grounded regions of Greenland and provide unique insight into future dynamics and vulnerabilities in a warming climate.
... Note that A is a function of temperature. We adopted a power law as below, which is comparable to that of [10] A = A 0 10 0.1(T−273) (12) where A 0 is the rate constant at 0 • C, and is a parameter that is scale-dependent. Another form of temperature-dependence takes the form of Arrhenius equation ...
... Another important observation is the vertical variation of ice mobility, as shown in Figure 17. The lower 10% of the ice sheet contributes to~60% of the horizontal surface velocity, which is in good agreement with other studies [10,40]. Figures 15 and 16 show the comparison of modeled surface ice movement with field observations. ...
... Another important observation is the vertical variation of ice mobility, as shown in Figure 17. The lower 10% of the ice sheet contributes to ~60% of the horizontal surface velocity, which is in good agreement with other studies [10,40]. The modeling results suggest a gradual transition of ice velocity from the glacier edge inland (Figure 16). ...
Past glaciation is known to have caused a substantial morphological change to high latitude regions of the northern hemisphere. In the assessment of the long-term performance of deep geological repositories for radioactive wastes, future glaciation is a critical factor to take into consideration. This study develops a thermal-mechanical model to investigate ice sheet thermal evolution and the impact on bedrock erosion. The model is based on comprehensive field data resulting from international collaborative research on the Greenland Analogue Project. The ice sheet model considers surface energy balance and basal heat flux, as well as the temperature-dependent flow of ice that follows Glen’s law. The ice-bedrock interface is treated with a mechanical contact model, which solves the relative velocity and predicts the abrasional erosion and meltwater flow erosion. The numerical model is calibrated with measured temperature profiles and surface velocities at different locations across the glacier cross-section. The erosion rate is substantially larger near the glacier edge, where channel flow erosion becomes predominant. The abrasional erosion rate is averaged at 0.006 mm/a, and peaks at regions near the ridge divide. The mean meltwater flow erosion rate in the study area is estimated to be about 0.12 mm/a for the melted base region.
... In such cases, an ad hoc strain enhancement factor is often incorporated into the pre-exponential term of the Glen law to account for the combined effects of grain size, impurities, fabric development, and shear heating (c.f., Cuffey & Paterson, 2010). For example, matching velocity profiles across ice streams (e.g., Echelmeyer et al., 1994;Jackson & Kamb, 1997) and through Pliestocene ice near the base of the Greenland ice sheet (Dahl-Jensen & Gunderstrup, 1987;Shoji & Langway, 1988;Lüthi et al., 2002;Ryser et al., 2014) often requires enhancement factors in the range of 2-10. Cuffey et 410 al. (2000) attempted to quantify the role of grain size on the enhancement factor based on deformation recorded in Meserve Glacier, Antarctica. ...
... To illustrate this point, we model deformation within Drill Site D in fast moving ice near Jakobshavn Isbrae in western Greenland (Iken et al., 1993;Lüthi et al., 2002). This site experiences surface velocities of ~600 m/yr and tiltmeter data 415 indicates enhanced strain rates in temperate ice below the Holocene-LGM transition near the bed. ...
... This site experiences surface velocities of ~600 m/yr and tiltmeter data 415 indicates enhanced strain rates in temperate ice below the Holocene-LGM transition near the bed. Lüthi et al. (2002) developed a thermo-mechanical model for deformation in the borehole and found that after incorporating the temperature-dependence of ice viscosity, enhancement factors of 1.7-2.6 were required to match the observations in the pre-Holocene ice below 680 m. ...
Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.
... Several ice sheet flow models depict that in western Greenland enough heat is eventually added to develop a fully temperate layer of basal 20 ice (e.g.; Brinkerhof et al., 2011;Lüthi et al., 2015;Meierbachtol et al., 2015), however substantial modelling uncertainty exists regarding the spatial extent and vertical dimensions of the warm basal layer. Limited borehole temperature observations have confirmed a temperate basal layer in western Greenland that is 10s of meters to well over 100 meters thick (Lüthi et al., 2002;Ryser et al., 2014;Harrington et al., 2015). This layer potentially plays a key role in deformational motion of the ice sheet. ...
... Our results are higher than the estimate by Lüthi et al. (2002) of 2 % water content at cold ice/temperate layer interface at a site in the Jakobshavn region of Greenland. The latter was based on an observationally constrained model of refreezing at the layer boundary, whereas ours are averaged over the full thickness. ...
... With a soft basal layer, partitioning of surface velocity into sliding and deformation components would attribute enhanced deformation in the temperate layer to basal sliding processes, unless the enhanced creep is explicitly accounted for. Borehole observations have attributed 44 -73 % of winter motion to basal sliding (Lüthi et al., 2002;Reyser et al., 2014), however, tilt 5 sensors do not freeze in place within the temperate layer to yield reliable readings, thus making the distinction between hig h straining of the temperate layer and other sliding processes ambiguous. ...
Liquid water content (wetness) within glacier ice is known to strongly control ice viscosity and ice deformation processes. Little is known about wetness of ice on the outer flanks of the Greenland ice sheet, where a temperate layer of basal ice exists. This study integrates borehole and radar surveys to provide direct estimates of englacial ice wetness in the ablation zone of western Greenland. We estimate electromagnetic propagation velocity of the ice body by inverting reflection traveltimes from radar data. Our inversion is constrained by ice thickness measured in boreholes and by positioning of a temperate/cold ice boundary identified in boreholes. Electromagnetic propagation velocities are consistent with a depth-averaged wetness of ~ 0.5–1.1 %. The inversion indicates that wetness within the ice varies from
... CC BY 4.0 License. range considerably from 2.5 to 4.5 (Bons et al., 2018;Dahl-Jensen and Gundestrup, 1987;Gillet-Chaulet et al., 2011;Lüthi et al., 2002;Ryser et al., 2014). Other aspects of ice flow such as crevasses that are common in regions of concentrated fast flow (Cavanagh et al., 2017;Lampkin et al., 2013) and in extensional regimes (Poinar et al., 2015), are not accounted for in high-order inversions but could significantly impact the relationship between the 70 velocity field and higher-order stresses (stress gradients). ...
... In Greenland, the rheologic uncertainty and complex thermal structure make it difficult to infer a location specific rheology to confidently calculate deformation across the ice sheet (Maier et al., 2019). However, direct measurements of basal 205 motion collectively show the prevalence of high fractions of basal motion [0.44 -0.96] across a wide range of glaciological environments in Greenland (Doyle et al., 2018;Lüthi et al., 2002;MacGregor et al., 2016;Maier et al., 2019;Ryser et al., 2014). ...
... where ( ) is a temperature dependent rate factor (calculated following Cuffey and Paterson 2010), is the flow law exponent equal to 3, and is the basal traction as dictated by the relationships in Figure 3. This corresponds to a 215 deformation fraction of 0.33 for the rate-strengthening range of the traction relationships, which is similar to that measured along the margins (Doyle et al., 2018;Lüthi et al., 2002;MacGregor et al., 2016;Maier et al., 2019;Ryser et al., 2014), and would approximate deformation where changes in flowline ice thickness are small, i.e. some troughbound outlet glaciers. We show the characteristic features of the relationship are identical as to the theoretical relationships which relate basal motion to traction. ...
On glaciers and ice sheets, identifying the relationship between velocity and traction is critical to constrain the bed physics that control ice flow. Yet in Greenland, these relationships remain unquantified. We determine the spatial relationship between velocity and traction in all eight drainage catchments of Greenland. The basal traction is estimated using three different methods over large grid cells to minimize interpretation biases associated with unconstrained rheologic parameters used in numerical inversions. We find the relationships are consistent with our current understanding of basal physics in each catchment. We identify catchments that predominantly show Mohr-Coulomb-like behavior typical of deforming beds or significant cavitation, as well as catchments that predominantly show rate-strengthening behavior typical of Weertman-type hard-bed physics. Overall, the traction relationships suggest that the flow field and surface geometry over the grounded regions of the Greenland ice sheet is mainly dictated by Weertman-type hard-bed physics. Given the complex basal boundary across Greenland, the relationships are captured surprisingly well by simple traction laws over the entire velocity range, including regions with velocities over 1000 m/yr, which provide a parameterization that can be used to model ice dynamics at large scales. The results and analysis serve as a fundamental constraint on the physics of basal motion in Greenland and provide unique insight into future dynamics and vulnerabilities in a warming climate.
... Borehole inclinometry is a unique means for investigating ice deformation and basal sliding simultaneously and can be achieved either by measuring changes in borehole orientation through repeated surveys (e.g., Perutz, 1949;Shreve and Sharp, 1970;Raymond, 1971;Hooke, 1973;Hooke and Hanson, 1986;Hooke et al., 1992;Harper et al., 2001;Mar-shall et al., 2002;Chandler et al., 2008) or through continuous englacial tiltmeter recordings (e.g., Gudmundsson et al., 1999;Lüthi et al., 2002;Willis et al., 2003;Amundson et al., 2006;Ryser et al., 2014;Keller and Blatter, 2012;Doyle et al., 2018;Lee et al., 2019;Maier et al., 2019Maier et al., , 2021. These observations provide deformation rate profiles that allow for in situ estimates of ice rheology and basal velocity, as well as their respective temporal variations, with basal velocity determined by integrating the deformation rate profile with depth and subtracting it from the surface velocity (Hooke et al., 1992;Maier et al., 2021). ...
... Within this layer, the derived du/dz values are expected to be strongly biased and are thus ignored in the ice rheology interpretation. With the hypothesis that du/dz dominates the flow gradient outside of the boundary layer, the internal-deformation rate (du/dz) from the temporal evolution of the tilt (θ ) is computed as follows (Lüthi et al., 2002;Ryser et al., 2014;Doyle et al., 2018;Maier et al., 2019): ...
Glacier internal deformation is usually described by Glen's flow law using two material parameters: the creep factor (A) and the flow law exponent (n). However, the values of these parameters and their spatial and temporal variability are rather uncertain due to the difficulty in quantifying internal strain and stress fields at natural scales. In this study, we combine 1-year-long continuous measurements of borehole inclinometry and surface velocity with three-dimensional full-Stokes ice flow modeling to infer ice rheologies and sliding velocities for the ablation zone of the Argentière Glacier, a temperate glacier in the French Alps. We demonstrate that the observed deformation rate profile has limited sensitivity to the flow law exponent (n) and instead mainly reflects an increase in the creep factor (A) with depth, with A departing from its surface value by up to a factor of 2.5 below 160 m depth. We interpret this creep factor enhancement as an effect of increasing interstitial water content with depth (from 0 % to 1.3 %), which results in an average value of A=148 MPa⁻³ a⁻¹. We further observe that internal ice deformation exhibits seasonal variability similar to that concerning surface velocity, indicating that the local basal sliding velocity exhibits no significant seasonal variation. We suggest that these changes in deformation rate are due to variations in the stress field, driven by contrasting changes in subglacial hydrology conditions between the sides and center of the glacier. Our study provides further evidence that borehole inclinometry, combined with full-Stokes flow modeling, allows for the constraining of both ice rheology and basal friction at scales that cannot be inferred from surface velocity measurements alone.
... Yet, the physical processes governing this transition and the scale over which it occurs remain unresolved. Clues come from borehole measurements (Doyle et al., 2018;Harrington et al., 2015;Hills et al., 2017;Law et al., 2023;Lüthi et al., 2002;Maier et al., 2019;Ryser et al., 2014) suggest a complex, depth-dependent velocity field in the ice above a topographically variable bed. Many factors may contribute to this variability, including the presence of sediments and sediment freeze-on (Carsey et al., 2002;Goodwin, 1993;Gow et al., 1979;Herron & Langway, 1979), subglacial hydrology (Doyle et al., 2018), seasonal cycles (Ryser et al., 2014), paleolithic history (Lüthi et al., 2002), and variable basal topography (Law et al., 2023). ...
... Clues come from borehole measurements (Doyle et al., 2018;Harrington et al., 2015;Hills et al., 2017;Law et al., 2023;Lüthi et al., 2002;Maier et al., 2019;Ryser et al., 2014) suggest a complex, depth-dependent velocity field in the ice above a topographically variable bed. Many factors may contribute to this variability, including the presence of sediments and sediment freeze-on (Carsey et al., 2002;Goodwin, 1993;Gow et al., 1979;Herron & Langway, 1979), subglacial hydrology (Doyle et al., 2018), seasonal cycles (Ryser et al., 2014), paleolithic history (Lüthi et al., 2002), and variable basal topography (Law et al., 2023). Here, we focus specifically on the role of variable topography as a first step toward a more complete understanding. ...
Ice surface speed increases dramatically from upstream to downstream in many ice streams and glaciers. This speed‐up is thought to be associated with a transition from internal distributed deformation to highly localized deformation or sliding at the ice‐bedrock interface. The physical processes governing this transition remain unclear. Here, we argue that highly localized deformation does not necessarily initiate at the ice‐bedrock interface, but could also take the form of an internal shear band inside the ice flow that connects topographic highs. The power‐law exponent n in the ice rheology amplifies the feedback between shear heating and shear localization, leading to the spontaneous formation of an internal shear band that can create flow separation within the ice. We model the thermomechanical ice flow over a sinusoidal basal topography by building on the high‐resolution Stokes solver FastICE v1.0. We compile a regime diagram summarizing cases in which a sinusoidal topography with a given amplitude and wavelength leads to shear band formation for a given rheology. We compare our model results to borehole measurements from Greenland and find evidence to support the existence of an internal shear band. Our study highlights the importance of re‐evaluating the degree to which internal deformation contributes to total deformation in the ice column and to the flow‐to‐sliding transition.
... These contours indicate that Coulomb conditions only occur within about 10 km of the grounding line, which is consistent with the distances over which the assumption of perfect hydrological connectivity is likely valid (Asay-Davis et al., 2016). Numerous boreholes indicate water pressures close to flotation, and thus, low (<400 kPa) effective pressure (Luthi et al., 2002;Kamb, 2001) well away from the grounding line. The widespread presence of active subglacial lakes also suggests that low effective pressures are prevalent (Gray et al., 2005;Smith et al., 2009;Fricker et al., 2007;Bell, 2008). ...
... With q=3 and m=3 in Equation (7), the result is equivalent to Weertman friction with unbounded ℎ (i.e., basal traction declines linearly with reductions in ℎ − ℎ ). The assumption, however, that a hydrologic connection to the ocean exists over the full domain such that the water pressure is equal to ocean pressure is not well supported by borehole observations of water pressure (Luthi et al., 2002;Kamb, 2001) and the widespread presence of subglacial lakes (Gray et al., 2005;Smith et al., 2009;Fricker et al., 2007;Bell, 2008). We suggest that any law that relies solely on the local height above flotation to govern 370 changes in effective pressure, and thus, basal friction over the entire domain is likely oversimplified and incorrect. ...
Pine Island and Thwaites glaciers are the two largest contributors to sea level rise from Antarctica. Here we examine the influence of basal friction and melt in determining projected losses. We examine both Weertman and Coulomb friction laws with explicit weakening as the ice thins to flotation, which many friction laws include implicitly via the effective pressure. We find relatively small differences with the choice of friction law (Weertman or Coulomb) but find losses are highly sensitive to the rate at which the basal traction is reduced as the area above the grounding line thins. Consistent with earlier work on Pine Island Glacier, we find sea level contributions from both glaciers vary linearly with the melt volume averaged over time and space, with little influence from the spatial or temporal distribution of melt. Based on recent estimates of melt from other studies, our work simulations suggest that melt-driven combined sea-level rise contribution from both glaciers is unlikely to exceed 10 cm by 2200. We do not include other factors, such as ice shelf breakup that might increase loss, nor factors such as increased accumulation and isostatic uplift that may mitigate loss.
... State-of-the-art GrIS models run with BedMachine, the most advanced gridded data product of GrIS basal topography, which is relatively smooth compared to deglaciated terrain (12,13), produce basal slip and ice deformation rates that vary smoothly and are largely independent of one another [e.g., (4,14)]. However, GrIS borehole records indicate substantial variation in ice deformation, particularly toward the ice sheet bed (15)(16)(17) and notable catchment-scale variations in the thickness of a much softer and relatively poorly understood, basal temperate layer in which ice coexists with a liquid water phase at the pressure-dependent melting point (18,19). Here, we advance upon two-dimensional (2D) models that begin to unpick this complexity (20,21) by incorporating realistic 3D geostatistically simulated bed topography ( Fig. 1) and improved temperate ice rheology in a 3D full-Stokes model ( Fig. 2A). ...
... However, we also emphasize that stochastic spatial variation in temperate layer thickness, related to local (100 s of m) topographic relief, may play an additional role in intersite variability. This local variation may further explain observations near Swiss Camp, where temperate layer thickness decreased from~40 to~20 m over 10 km along flow (16), which could reflect natural variability as indicated by individual temperate layer thickness profiles in Fig. 8. Last, our findings fully support the existence of an inferred extremely thick (>300 m) basal temperate layer in the deeply eroded basal trough of Sermeq Kujalleq (Jakobshavn Isbrae) formed largely by vertical ice extension (17) and offer further avenues to test its importance in fast ice motion. Overall, considerations from our results and from borehole records indicate that large-scale topographic variations (e.g., rises and saddles) control broad patterns of temperate layer thickness, while geostatistically simulated topography is central to the formation of temperate ice and to intermediate-scale (≥25 m, ≲4 km) variations in its thickness. ...
Uncertainty associated with ice sheet motion plagues sea level rise predictions. Much of this uncertainty arises from imperfect representations of physical processes including basal slip and internal ice deformation, with ice sheet models largely incapable of reproducing borehole-based observations. Here, we model isolated three-dimensional domains from fast-moving (Sermeq Kujalleq/Store Glacier) and slow-moving (Isunnguata Sermia) ice sheet settings in Greenland. By incorporating realistic geostatistically simulated topography, we show that a spatially highly variable layer of temperate ice (much softer ice at the pressure-melting point) forms naturally in both settings, alongside ice motion patterns which diverge substantially from those obtained using smoothly varying BedMachine topography. Temperate ice is vertically extensive (>100 meters) in deep troughs but thins notably (<5 meters) over bedrock highs, with basal slip rates reaching >90 or <5% of surface velocity dependent on topography and temperate layer thickness. Developing parameterizations of the net effect of this complex motion can improve the realism of predictive ice sheet models.
... Mechanisms of heat transfer and heat sources in Greenland's ablation zone have been investigated by comparing sparsely collected temperature profiles to output from thermomechanical models (e.g., Iken et al., 1993;Funk et al., 1994;Lüthi et al., 2002;Harrington et al., 2015;Lüthi et al., 2015;Poinar et al., 2017). When attempting to replicate the vertical temperature structure, models consistently produced ice temperatures that are lower than collected temperatures. ...
... Any interstitial water present in the ice would then be colder than the new melting temperature and would refreeze. Lüthi et al. (2002) estimated the water content of the temperate layer of ice near the bed of Jakobshavn Isbrae has a moisture content of ∼ 1 %. However, refreezing releases latent heat into the surrounding ice, resulting in warming rather than cooling. ...
Temperature sensors installed in a grid of nine full-depth boreholes drilled in the southwestern ablation zone of the Greenland Ice Sheet recorded cooling in discrete sections of ice over time within the lowest third of the ice column in most boreholes. Rates of temperature change outpace cooling expected from vertical conduction alone. Additionally, observed temperature profiles deviate significantly from the site-average thermal profile that is shaped by all thermomechanical processes upstream. These deviations imply recent, localized changes to the basal thermal state in the boreholes. Although numerous heat sources exist to add energy and warm ice as it moves from the central divide towards the margin such as strain heat from internal deformation, latent heat from refreezing meltwater, and the conduction of geothermal heat across the ice–bedrock interface, identifying heat sinks proves more difficult. After eliminating possible mechanisms that could cause cooling, we find that the observed cooling is a manifestation of previous warming in near-basal ice. Thermal decay after latent heat is released from freezing water in basal crevasses is the most likely mechanism resulting in the transient evolution of temperature and the vertical thermal structure observed at our site. We argue basal crevasses are a viable englacial heat source in the basal ice of Greenland's ablation zone and may have a controlling influence on the temperature structure of the near-basal ice.
... These values fall within the range of water contents reported in the literature (Tab. 1 in Pettersson et al. (2004)). The (indirect) determination at Sermeq Kujalleq (Jakobshavn Isbrae, Greenland Ice Sheet) indicated a likely value of 1.5 % at the CTS (Lüthi et al., 2002), which would 125 agree with our measurements of the basal ice at Glacier d'Argentière. Interestingly, earlier in-situ calorimetric determinations obtain a water content between 0.6 and 1.5 % (Duval, 1977;Cohen, 1998;Zryd, 1991;Pettersson et al., 2004). ...
Temperate glacier ice contains liquid water at different concentrations. How much exactly depends on the history of ice formation, the heat supply from dissipative deformation, and on the drainage pathways between ice crystals. The interstitial liquid water content strongly influences the ice viscosity and therefore glacier flow speed. The hydrological system of glaciers is strongly affected by the porosity of the ice matrix. Also, material properties, such as seismic velocities, electromagnetic susceptibility and dielectricity are strongly affected. This renders seismics and radar suitable to measure water content in a glacier. An independent in-situ method is a calorimetric determination by tracking an artificially induced freezing front within the material. Here, we report on two experiments from an artificial cave within a glacier and form a tunnel at the base of a glacier. In both experiments, a liquid water content of 1–2 % was found by analyzing the measured cooling rates with a detailed numerical model of the experimental setup.
... In the ablation zone, the GrIS experiences sliding and deformation, significantly impacting its mass balance by controlling ice transport to marine outlets and areas with high melt rates. While surface velocity is well-documented at dense spatial (e.g., Rignot & Kanagaratnam, 2006) and temporal (e.g., van de Wal et al., 2008) scales, the relative contributions of sliding and deformation components to motion remain uncertain and are limited to a few locations (Lüthi et al., 2002: Ryser et al., 2014. According to Maier et al., (2019), sliding predominantly governs ice flow near the margins of the GrIS during the winter season, with marginal ice fluxes comparable to observed surface velocities. ...
... The subglacial environment is difficult to access directly; few boreholes have been drilled to the bed of tidewater glaciers (Doyle et al., 2018;Iken et al., 1993;Lüthi et al., 2002). Ice flow and hydrology models, however, can provide estimates of basal stresses and water pressure under a range of conditions, rendering a process for calculating sliding velocities. ...
Two outstanding questions for the future of the Greenland Ice Sheet are (a) how enhanced meltwater draining beneath the ice will impact the behavior of large tidewater glaciers, and (b) to what extent tidewater glacier velocity is driven by changes at the terminus versus changes in sliding velocity due to meltwater. We present a two‐way coupled framework to simulate the nonlinear feedbacks of evolving subglacial hydrology and ice dynamics using the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model within the Ice‐sheet and Sea‐level System Model (ISSM). Through coupled simulations of Helheim Glacier, we find that terminus effects dominate the seasonal velocity pattern up to 15 km from the terminus, while hydrology drives the velocity response upstream. With increased melt, the hydrology influence yields seasonal acceleration of several hundred meters per year in the interior, suggesting that hydrology will play an important role in future mass balance of tidewater glaciers.
... With the hypothesis that du/dz dominates the flow gradient outside of the boundary layer, the internal deformation rate 185 du/dz from the temporal evolution of the tilt θ is computed as (Lüthi et al., 2002;Ryser et al., 2014;Doyle et al., 2018;Maier et al., 2019), ...
Glacier internal deformation is usually described by Glen's Law using two material parameters, the creep factor A and the flow law exponent n. However, the values of these parameters and their spatial and temporal variability are rather uncertain due to the difficulty of quantifying internal strain and stress fields at the natural scale. In this study, we combine 1-year long continuous measurements of borehole inclinometry and surface velocity with three-dimensional full Stokes ice flow modeling to infer ice rheology and sliding velocity in the ablation zone of the Argentière Glacier, a temperate glacier in the French Alps. We demonstrate that the observed deformation rate profile has limited sensitivity to the flow law exponent n and instead mainly reflects an increase in the creep factor A with depth, with A departing from its surface value by at least up to a factor of 2.5 below 160 m. We interpret this creep factor enhancement as an effect of increasing interstitial water content with depth from 0 % to 1.3 % which results in an average value of A = 148 MPa-3 a-1. We further observe that internal ice deformation exhibits seasonal variability similar to that in surface velocity, such that the local basal sliding velocity exhibits no significant seasonal variation. We suggest that these changes in deformation rate are due to variations in the stress field driven by contrasting changes in subglacial hydrology conditions between the side and the center of the glacier. Our study gives further evidence that borehole inclinometry combined with full-Stokes flow model allows constraining both ice rheology and basal friction at scales that cannot be inferred from surface velocity measurements alone.
... To investigate subglacial properties, borehole measurements have provided direct access to the glacier bed and have often been instrumented to monitor water pressure (e.g., Hubbard et al., 1995;Lüthi et al., 2002;Sugiyama et al., 2011;Andrews et al., 2014;Doyle et al., 2018;Sugiyama et al., 2019;Rada and Schoof, 2018;Rada Giacaman and Schoof, 2023). Studies based on numerous boreholes show the spatial and temporal heterogeneity of water pressure variations, even at small spatial scales (Murray and Clarke, 1995;Iken and Truffer, 1997;Fudge et al., 2008;Andrews et al., 2014;Rada and Schoof, 2018), indicative of reorganization of the drainage system (Gordon et al., 1998;Kavanaugh and Clarke, 2000;Schuler et al., 2002), and the presence of hydraulic isolation (e.g., Murray and Clarke, 1995;Andrews et al., 2014;Hoffman et al., 2016;Rada and Schoof, 2018). ...
The flow of glaciers is largely controlled by changes at the ice–bed interface, where basal slip and sediment deformation drive basal glacier motion. Determining subglacial conditions and their responses to hydraulic forcing remains challenging due to the difficulty of accessing the glacier bed. Here, we monitor the interplay between surface runoff and hydro-mechanical conditions at the base of the Kongsvegen glacier in Svalbard. From July 2021 to August 2022, we measured both subglacial water pressure and till strength. Additionally, we derived median values of subglacial hydraulic gradient and radius of channelized subglacial drainage system from seismic power, recorded at the glacier surface. To characterize the variations in the subglacial conditions caused by changes in surface runoff, we investigate the variations of the following hydro-mechanical properties: measured water pressure, measured sediment ploughing forces, and derived hydraulic gradient and radius, over seasonal, multi-day, and diurnal timescales. We discuss our results in light of existing theories of subglacial hydrology and till mechanics to describe subglacial conditions. We find that during the short, low-melt-rate season in 2021, the subglacial drainage system evolved at equilibrium with runoff, increasing its capacity as the melt season progressed. In contrast, during the long and high-melt-rate season in 2022, the subglacial drainage system evolved transiently to respond to the abrupt and large water supply. We suggest that in the latter configuration, the drainage capacity of the preferential drainage axis was exceeded, promoting the expansion of hydraulically connected regions and local weakening of ice–bed coupling and, hence, enhanced sliding.
... However, the situation is more opaque for slower land-terminating glaciers along Greenland's margins, where observed surface velocities could arise solely from deformation in warm, low viscosity ice, basal sliding, or a combination of both. Over the past two decades, borehole arrays equipped with inclinometers, temperature probes, and basal sensors have constrained basal motion for numerous glaciers in Greenland [92,196,219,231,232]. These studies revealed significant and spatially variable basal slip, accounting for 40% to 96% of observed surface velocities and highlighted the importance of enhanced deformation in pre-Holocene basal ice. ...
Greenland’s glaciers have been retreating, thinning and accelerating since the mid-1990s, with the mass loss from the Greenland Ice Sheet (GrIS) now being the largest contributor to global sea level rise. Monitoring changes in glacier dynamics using in-situ or remote sensing methods has been and remains therefore crucial to improve our understanding of glaciological processes and the response of glaciers to changes in climate. Over the past two decades, significant advances in technology have provided improvements in the way we observe glacier behavior and have helped to reduce uncertainties in future projections. This review focuses on advances in in-situ monitoring of glaciological processes, but also discusses novel methods in satellite remote sensing. We further highlight gaps in observing, measuring and monitoring glaciers in Greenland, which should be addressed in order to improve our understanding of glacier dynamics and to reduce in uncertainties in future sea level rise projections. In addition, we review coordination and inclusivity of science conducted in Greenland and provide suggestion that could foster increased collaboration and co-production.
... The contribution of basal sliding to overall ice transport is especially important for large fast-flowing glaciers. For example, in the largest outlet glacier of the Greenland ice sheet (Jakobshavn Isbrae), basal sliding has been found to account for 44 % to 90 % of the measured surface speed (Lüthi et al., 2002;Ryser et al., 2014b). On Antarctic ice streams, basal sliding can account on average for about 69 % of the observed surface speed (Engelhardt and Kamb, 1998). ...
The subglacial drainage system is one of the main controls on basal sliding but remains only partially understood. Here we expand the analysis of the 8-year dataset of borehole observations on a small, alpine polythermal valley glacier in the Yukon Territory. We presented this dataset in , where we described the seasonal evolution of the drainage system and underlined the importance of hydraulic isolation at the glacier bed. These borehole observations constitute a unique dataset, both due to the length of the records and the density of the observations, with up to 157 simultaneously working pressure sensors.
Now, to explore the spatial structure of the drainage system and its seasonal progression, we automatically cluster boreholes based on similarities in their water pressure records and follow their evolution through the melt season. Some of these borehole clusters show water pressure variations that suggest they are part of a drainage system connected to the surface meltwater supply, while others show features consistent with hydraulic isolation. The distribution of connected and isolated boreholes suggests that the distributed drainage system we observe comprises a network of small conduits with spacings smaller than the borehole bottom diameter (approximately 25–50 cm). Within these hydraulically connected areas, pressure phase lags, and amplitude attenuation rarely shows the behaviour expected in a diffusive system. This observation suggests that the diffusivity distribution in such areas presents a fine structure at scales smaller than our minimum borehole spacing of 15 m. However, at a glacier-wide scale, we observe that hydraulic connections are ubiquitous in some regions of the bed and permanently absent in others, suggesting large contrasts in diffusivity.
Within disconnected areas, boreholes often show small-amplitude water pressure variations associated with horizontal normal stress transfers. Such stress transfers seem to play a more important role than previously considered for controlling the effective pressure distribution at the bed.
Through the melt season, the evolution of borehole clusters suggests that the diurnal meltwater supply promotes the growth of the low-efficiency drainage systems found early in the season while stimulating the shrinkage and fragmentation of the more efficient drainage systems that appear later in the season. Therefore, an increase in drainage efficiency is associated with the growth of disconnected areas.
Our observations support the traditional view of a distributed drainage system early in the melt season that gradually evolves into a progressively more channelized system. However, the most notable difference is the highly heterogeneous distribution of diffusivity that our results suggest and the robust support for disconnected areas. The extent of disconnected areas could be an essential control of basal speed variations. It is possible that even relatively small disconnected areas could have a disproportionate effect on basal speed.
... This means that only marineterminating parts of the ice sheet are impacted by the subglacial water. According to Lüthi et al. (2002), the pore water pressure, i.e. the pressure of the subglacial water mixed with the solid part of the till, represents a fraction slightly smaller than 100 % of the ice overburden pressure. Bueler and Brown (2009) consider the pore water pressure locally at most a fixed fraction (P w = 95 %) of the ice overburden pressure ρ i gh. ...
Major uncertainties in the response of ice sheets to environmental forcing are due to subglacial processes. These processes pertain to the type of sliding or friction law as well as the spatial and temporal evolution of the effective pressure at the base of ice sheets. We evaluate the classic Weertman–Budd sliding law for different power exponents (viscous to near plastic) and for different representations of effective pressure at the base of the ice sheet, commonly used for hard and soft beds. The sensitivity of the above slip laws is evaluated for the Antarctic ice sheet in two types of experiments: (i) the ABUMIP experiments in which ice shelves are instantaneously removed, leading to rapid grounding-line retreat and ice sheet collapse, and (ii) the ISMIP6 experiments with realistic ocean and atmosphere forcings for different Representative Concentration Pathway (RCP) scenarios. Results confirm earlier work that the power in the sliding law is the most determining factor in the sensitivity of the ice sheet to climatic forcing, where a higher power in the sliding law leads to increased mass loss for a given forcing. Here we show that spatial and temporal changes in water pressure or water flux at the base modulate basal sliding for a given power, especially for high-end scenarios, such as ABUMIP. In particular, subglacial models depending on subglacial water pressure decrease effective pressure significantly near the grounding line, leading to an increased sensitivity to climatic forcing for a given power in the sliding law. This dependency is, however, less clear under realistic forcing scenarios (ISMIP6).
... While GBaTSv2 continues to be reported on a 5 km grid, it is increasingly clear that the basal thermal state can vary at scales finer than that (e.g., Chu et al., 2018). Further, englacial thermal structure can be quite variable at finer scales than 5 km (e.g., Lüthi et al., 2002;Harrington et al., 2015;Maier et al., 2019). Colgan et al. (2021) recently highlighted the role of bed topography in influencing geothermal flux at kilometer scales, a likely primary control on basal thermal state. ...
The basal thermal state (frozen or thawed) of the Greenland Ice Sheet is under-constrained due to few direct measurements, yet knowledge of this state is becoming increasingly important to interpret modern changes in ice flow. The first synthesis of this state relied on inferences from widespread airborne and satellite observations and numerical models, for which most of the underlying datasets have since been updated. Further, new and independent constraints on the basal thermal state have been developed from analysis of basal and englacial reflections observed by airborne radar sounding. Here we synthesize constraints on the Greenland Ice Sheet's basal thermal state from boreholes, thermomechanical ice-flow models that participated in the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6; Coupled Model Intercomparison Project Phase 6), IceBridge BedMachine Greenland v4 bed topography, Making Earth Science Data Records for Use in Research Environments (MEaSUREs) Multi-Year Greenland Ice Sheet Velocity Mosaic v1 and multiple inferences of a thawed bed from airborne radar sounding. Most constraints can only identify where the bed is likely thawed rather than where it is frozen. This revised synthesis of the Greenland likely Basal Thermal State version 2 (GBaTSv2) indicates that 33 % of the ice sheet's bed is likely thawed, 40 % is likely frozen and the remainder (28 %) is too uncertain to specify. The spatial pattern of GBaTSv2 is broadly similar to the previous synthesis, including a scalloped frozen core and thawed outlet-glacier systems. Although the likely basal thermal state of nearly half (46 %) of the ice sheet changed designation, the assigned state changed from likely frozen to likely thawed (or vice versa) for less than 6 % of the ice sheet. This revised synthesis suggests that more of northern Greenland is likely thawed at its bed and conversely that more of southern Greenland is likely frozen, both of which influence interpretation of the ice sheet's present subglacial hydrology and models of its future evolution. The GBaTSv2 dataset, including both code that performed the analysis and the resulting datasets, is freely available at 10.5281/zenodo.6759384 (MacGregor, 2022).
... Submarine iceberg melting is simulated using the IceBerg package within MITgcm , with an ice temperature of −10 • C (Inall et al., 2014;Luthi et al., 2002;Sciascia et al., 2013;Sutherland and Straneo, 2012). This package uses the velocity-dependent 3-equation melt rate parameterisation (Hellmer and Olbers, 1989;Holland and Jenkins, 1999;Xu et al., 2012). ...
The rate of ocean-driven retreat of Greenland's tidewater glaciers remains highly uncertain in predictions of future sea level rise, in part due to poorly constrained glacier-adjacent water properties. Icebergs and their meltwater contributions are likely important modifiers of fjord water properties, yet their effect is poorly understood. Here, we use a 3-D ocean circulation model, coupled to a submarine iceberg melt module, to investigate the effect of submarine iceberg melting on glacier-adjacent water properties in a range of idealised settings. Submarine iceberg melting can modify glacier-adjacent water properties in three principal ways: (1) substantial cooling and modest freshening in the upper ∼50 m of the water column; (2) warming of Polar Water at intermediate depths due to iceberg melt-induced upwelling of warm Atlantic Water and; (3) warming of the deeper Atlantic Water layer when vertical temperature gradients through this layer are steep (due to vertical mixing of warm water at depth) but cooling of the Atlantic Water layer when vertical temperature gradients are shallow. The overall effect of iceberg melt is to make glacier-adjacent water properties more uniform with depth. When icebergs extend to, or below, the depth of a sill at the fjord mouth, they can cause cooling throughout the entire water column. All of these effects are more pronounced in fjords with higher iceberg concentrations and deeper iceberg keel depths. These iceberg melt-induced changes to glacier-adjacent water properties will reduce rates of glacier submarine melting near the surface, increase them in the Polar Water layer, and cause typically modest impacts in the Atlantic Water layer. These results characterise the important role of submarine iceberg melting in modifying ice sheet-ocean interaction and highlight the need to improve representations of fjord processes in ice sheet scale models.
... This means that only marine terminated parts of the ice sheet are impacted by the subglacial water. According to Lüthi et al. (2002), the pore water pressure, i.e., the pressure of the subglacial water mixed with the solid part of the till, represents a fraction slightly smaller than 100% of the ice overburden pressure. Bueler and Brown (2009) consider the pore water pressure locally as at most a fixed fraction (P w = 95%) of the ice overburden pressure ρ i gh. ...
Major uncertainties in the response of ice sheets to environmental forcing are due to subglacial processes. These processes pertain to the type of sliding or friction law as well as the spatial and temporal evolution of the effective pressure at the base of ice sheets. We evaluate the classical Weertman/Budd sliding law for different power exponents (viscous to near plastic) and for different representations of effective pressure at the base of the ice sheet, commonly used for hard and soft beds. The sensitivity of above slip laws is evaluated for the Antarctic ice sheet in two types of experiments, i.e., (i) the ABUMIP experiments in which ice shelves are instantaneously removed, leading to rapid grounding line retreat and ice sheet collapse, and (ii) the ISMIP6 experiments with realistic ocean and atmosphere forcings for different RCP scenarios. Results confirm earlier work that the power in the sliding law is the most determining factor in the sensitivity of the ice sheet, where a higher power in the sliding law leads to increased mass loss for a given forcing. Here we show that spatial and temporal changes in water pressure or water flux at the base modulates basal sliding for a given power. In particular, subglacial models depending on subglacial water pressure decrease effective pressure significantly near the grounding line, leading to an increased sensitivity for a given power in the sliding law.
... While GBaTSv2 continues to be reported on a 5-km grid, it is increasingly clear that the basal thermal state can vary at scales finer than that (e.g., Chu et al., 2018). Further, englacial thermal structure can be quite variable at finer scales than 5 km (e.g., Lüthi et al., 2002, Harrington et al., 2015Maier et al., 2019). Colgan et al. (2021) recently highlighted the role of bed topography in influencing geothermal flux at kilometer scales, a likely primary control on basal thermal state. ...
The basal thermal state (frozen or thawed) of the Greenland Ice Sheet is under-constrained due to few direct measurements, yet knowledge of this state is becoming increasingly important to interpret modern changes in ice flow. The first synthesis of this state relied on inferences from widespread airborne and satellite observations and numerical models, for which most of the underlying datasets have since been updated. Further, new and independent constraints on the basal thermal state have been developed from analysis of basal and englacial reflections observed by airborne radar sounding. Here we synthesize constraints on the Greenland Ice Sheet’s basal thermal state from boreholes, thermomechanical ice-flow models that participated in the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), BedMachine v4 bed topography, Making Earth Science Data Records for Use in Research Environments (MEaSUREs) multi-year surface velocity mosaic v1, and multiple inferences of a thawed bed from airborne radar sounding. Most constraints can only identify where the bed is likely thawed rather than where it is frozen. This revised synthesis of the Greenland likely Basal Thermal State version 2 (GBaTSv2) indicates that 32 % of the ice sheet’s bed is likely thawed, 39 % is likely frozen, and the remainder (29 %) is too uncertain to specify. Although the spatial pattern of GBaTSv2 is broadly similar to the previous synthesis, including a scalloped frozen core and thawed outlet-glacier systems, the likely basal thermal state of nearly half (48 %) of the ice sheet has changed designation. This revised synthesis suggests that more of northern Greenland is likely thawed at its bed, and conversely that more of southern Greenland is likely frozen, both of which influence interpretation of the ice sheet’s present subglacial hydrology and models of its future evolution. The GBaTSv2 dataset, including both code that performed the analysis and the resulting raster products, is freely available at https://doi.org/10.5281/zenodo.5714527.
... The magnitude of basal ice melt in the western Greenland ablation zone has been assessed by models which are heavily dependent upon assumptions about sliding speed (e.g., Brinkerhoff et al., 2011;Meierbachtol et al., 2015). These studies suggest that ice melt rates are spatially variable and reach values on the order of 2 cm a −1 along the relatively slow-moving outer flanks of the landterminating ablation zone (10 cm a −1 adjacent to Jakobshavn Isbrae; Lüthi et al., 2002). While the water generated from basal melt is trivially small in comparison to that derived from surface melt in summer, basal ice melt may become important during the winter months, particularly when considering the accumulation of basal meltwater over time and space. ...
Basal sliding in the ablation zone of the Greenland Ice Sheet is closely associated with water from surface melt introduced to the bed in summer, yet melting of basal ice also generates subglacial water year-round. Assessments of basal melt rely on modeling with results strongly dependent upon assumptions with poor observational constraints. Here we use surface and borehole measurements to investigate the generation and fate of basal meltwater in the ablation zone of Isunnguata Sermia basin, western Greenland. The observational data are used to constrain estimates of the heat and water balances, providing insights into subglacial hydrology during the winter months when surface melt is minimal or nonexistent. Despite relatively slow ice flow speeds during winter, the basal meltwater generation from sliding friction remains manyfold greater than that due to geothermal heat flux. A steady acceleration of ice flow over the winter period at our borehole sites can cause the rate of basal water generation to increase by up to 20 %. Borehole measurements show high but steady basal water pressure rather than monotonically increasing pressure. Ice and groundwater sinks for water do not likely have sufficient capacity to accommodate the meltwater generated in winter. Analysis of basal cavity dynamics suggests that cavity opening associated with flow acceleration likely accommodates only a portion of the basal meltwater, implying that a residual is routed to the terminus through a poorly connected drainage system. A forcing from cavity expansion at high pressure may explain observations of winter acceleration in western Greenland.
... Taking into account that Jakobshavn Isbrae and Kangerlussuaq Glacier contributed to an estimated 8 mm of global sea-level rise over the last century 2 , understanding their future response is crucial. All ice discharge of the GrIS and in particular Jakobshavn Isbrae and Kangerlussuaq Glacier (Fig. 5b, d and Supplementary Fig. 13) takes place in a settings where the bed is lubricated 52 , sliding speeds are high (Fig. 5a) 53 Supplementary Fig. 12). ...
Future projections of global mean sea level change are uncertain, partly because of our limited understanding of the dynamics of Greenland’s outlet glaciers. Here we study Nioghalvfjerdsbræ, an outlet glacier of the Northeast Greenland Ice Stream that holds 1.1 m sea-level equivalent of ice. We use GPS observations and numerical modelling to investigate the role of tides as well as the elastic contribution to glacier flow. We find that ocean tides alter the basal lubrication of the glacier up to 10 km inland of the grounding line, and that their influence is best described by a viscoelastic rather than a viscous model. Further inland, sliding is the dominant mechanism of fast glacier motion, and the ice flow induces persistent elastic strain. We conclude that elastic deformation plays a role in glacier flow, particularly in areas of steep topographic changes and fast ice velocities.
... Lüthi et al. (2002) ciIcespecific heat capacity 2009 J kg −1 K −1 Aschwanden et al. (2012) cw Water specific heat capacity 4170 J kg −1 K −1 Aschwanden et al. (2012) k Ice thermal conductivity 2.10 J m −1 K −1 s −1 Aschwanden et al. (2012) L Water latent heat of fusion 3.34 × 10 5 J kg −1 K −1 Aschwanden et al. Degree-day factor for snow 3.297 × 10 −3 m K −1 day −1 Huybrechts (1998) Fi Degree-day factor for ice 8.791 × 10 −3 m K −1 day −1 Huybrechts (1998) R Refreezing fraction 0.0 -γ Air temperature lapse rate 6 × 10 −3 K m−1 - ...
The European Alps, cradle of pioneer glacial studies, are one of the regions where geological markers of past glaciations are most abundant and well-studied. Such conditions make the region ideal for testing numerical glacier models based on simplified ice flow physics against field-based reconstructions, and vice-versa. Here, we use the Parallel Ice Sheet Model (PISM) to model the entire last glacial cycle (120–0 ka) in the Alps, using horizontal resolutions of 2 and 1 km and up to 576 processors. Climate forcing is derived using present-day climate data from WorldClim and the ERA-Interim reanalysis, and time-dependent temperature offsets from multiple palaeo-climate proxies, among which only the EPICA ice core record yields glaciation during marine oxygen isotope stages 4 (69–62 ka) and 2 (34–18 ka) spatially and temporally consistent with the geological reconstructions, while the other records used result in excessive early glacial cycle ice cover and a late Last Glacial Maximum. Despite the low variability of this Antarctic-based climate forcing, our simulation depicts a highly dynamic ice sheet, showing that Alpine glaciers may have advanced many times over the foreland during the last glacial cycle. Ice flow patterns during peak glaciation are largely governed by subglacial topography but include occasional transfluences and self-sustained ice domes. Modelled maximum ice surface is 861 m higher than observed trimline elevations in the upper Rhone Valley, yet our simulation predicts little erosion at high elevation due to cold-based ice. Finally, the Last Glacial Maximum advance, often considered synchronous, is here modelled as a time-transgressive event, with some glacier lobes reaching their maximum as early as 27 ka, and some as late as 21 ka.
... We assume isothermal, isotropic ice with a uniform ice viscosity A, corresponding to an ice temperature T ice ¼ À5 C (Cuffey and Paterson, 2010, p.75), consistent with present-day western Greenland (Luthi et al., 2002), an area of similar maritime climate as expected for southwestern Norway at the YDeHolocene transition. ...
Marine outlet glaciers on Greenland are retreating, yet it is unclear if the recent fast retreat will persist, and how atmosphere and ocean warming will impact future retreat. We show how a marine outlet glacier in Hardangerfjorden retreated rapidly in response to the abrupt warming following the Younger Dryas cold period (approximately 11,600 years before present). This almost 1000 m deep fjord, with several sills at 300–500 m depth, hosted a 175 km long outlet glacier at the western rim of the Scandinavian Ice Sheet. We use a dynamic ice-flow model constrained by well-dated terminal and lateral moraines to simulate the reconstructed 500-year retreat of Hardangerfjorden glacier. The model includes an idealized oceanic and atmospheric forcing based on reconstructions, but excludes the surface mass balance-elevation feedback. Our simulations show a highly episodic retreat driven by surface melt and warming fjord waters, paced by the fjord bathymetry. Warming air and ocean temperatures by 4–5 °C during the period of retreat result in a 125-km retreat of Hardangerfjorden glacier in 500 years. Retreat rates throughout the deglaciation vary by an order of magnitude from 50 to 2500 m a−1, generally close to 200 m a−1, punctuated by brief events of swift retreat exceeding 500 m a−1, each event lasting a few decades. We show that the fastest retreat rates occur in regions of the bed with the largest retrograde slopes; ice shelf length and fjord water depth is less important. Our results have implications for modern glacial fjord settings similar to Hardangerfjorden, where high retreat rates have been observed. Our findings imply that increasing air temperatures and warming subsurface waters in Greenland fjords will continue to drive extensive retreat of marine outlet glaciers. However, the recent high retreat rates are not expected to be sustained for longer than a few decades due to constraints by the fjord bathymetry.
... We convert surface strain rates derived from ice flow speeds to ice stresses using n = 3 and the temperature-dependent rate parameter, B = 324 kPa −1 yr −1/3 , that corresponds to an ice temperature of −5°C (Cuffey & Paterson, 2010). Though the depth-averaged ice temperature of most glaciers in Greenland is potentially colder than −5°C, borehole observations suggest that the ice in surface and basal regions where crevasses are expected to form near glacier termini may generally be in the range of −2 to −10°C (Iken et al., 1993;Lüthi et al., 2002). ...
Frontal ablation processes at marine‐terminating glaciers are challenging to observe and difficult to represent in numerical ice flow models, yet play critical roles in modulating ice sheet mass balance. Current ice sheet models typically rely on simple iceberg calving models to prescribe either terminus positions or iceberg calving rates, but the relative accuracies and uncertainties of these calving models remain largely unconstrained at the ice sheet scale. Here, we evaluate six published iceberg calving models against spatially and temporally diverse observations from 50 marine‐terminating outlet glaciers in Greenland. We seek the single model that best reproduces observed conditions across all glaciers, at all observation times, and with low sensitivity to calibration uncertainty. Five of six calving models can produce unbiased estimates of calving position or calving rate at the ice sheet scale. However, time series analysis reveals that, when using a single, optimized model parameter, rate‐predicting calving models frequently yield calving rate errors in excess of 10 m d⁻¹. In comparison, terminus position‐predicting calving models more accurately track observed changes in terminus position (remaining within ~1 km of the observed grounded terminus position). Overall, our results indicate that the crevasse depth calving model provides the best balance of high accuracy and low sensitivity to imperfect parameter calibration. While the crevasse depth model appears unlikely to capture the true controls on crevasse penetration, numerically, it reproduces observed terminus dynamics with high fidelity and should be considered a leading candidate for use in models of the Greenland Ice Sheet.
The response of the Antarctic ice sheet to climate change and its contribution to sea level under different emission scenarios are subject to large uncertainties. A key uncertainty is the slipperiness at the ice sheet base and how it is parameterized in glaciological projections. Alternative formulations of the sliding law exist, but very limited access to the ice base makes it difficult to select among them. Here, we use satellite observations of ice flow, inverse methods, and a theory of acoustic propagation in granular material to relate the effective pressure, which is a key control of basal sliding, to seismic observations recovered from Antarctica. Together with independent estimates of grain diameter and porosity from sediment cores, this enables a comparison of basal sliding laws within a Bayesian framework. The presented direct link between seismic observations and sliding law parameters can be readily applied to any acoustic impedance data collected in a glacial environment. For rapidly sliding tributaries of Pine Island Glacier, these calculations provide support for a Coulomb-type sliding law and widespread low effective pressures.
The Pine Island and Thwaites glaciers are the two largest contributors to sea level rise from Antarctica. Here we examine the influence of basal friction and ice shelf basal melt in determining projected losses. We examine both Weertman and Coulomb friction laws with explicit weakening as the ice thins to flotation, which many friction laws include implicitly via the effective pressure. We find relatively small differences with the choice of friction law (Weertman or Coulomb) but find losses to be highly sensitive to the rate at which the basal traction is reduced as the area upstream of the grounding line thins. Consistent with earlier work on Pine Island Glacier, we find sea level contributions from both glaciers to vary linearly with the melt volume averaged over time and space, with little influence from the spatial or temporal distribution of melt. Based on recent estimates of melt from other studies, our simulations suggest that the combined melt-driven and sea level rise contribution from both glaciers may not exceed 10 cm by 2200, although the uncertainty in model parameters allows for larger increases. We do not include other factors, such as ice shelf breakup, that might increase loss, or factors such as increased accumulation and isostatic uplift that may mitigate loss.
In the past two decades, mass loss from the Greenland ice sheet has accelerated, partly due to the speedup of glaciers. However, uncertainty in speed derived from satellite products hampers the detection of inland changes. In-situ measurements using stake surveys or GPS have lower uncertainties. To detect inland changes, we repeated in-situ measurements of ice-sheet surface velocities at 11 historical locations first measured in 1959, located upstream of Jakobshavn Isbræ, west Greenland. Here, we show ice velocities have increased by 5–15% across all deep inland sites. Several sites show a northward deflection of 3–4.5° in their flow azimuth. The recent appearance of a network of large transverse surface crevasses, bisecting historical overland traverse routes, may indicate a fundamental shift in local ice dynamics. We suggest that creep instability—a coincident warming and softening of near-bed ice layers—may explain recent acceleration and rotation, in the absence of an appreciable change in local driving stress.
Measurement of ice-sheet thermal state via microwave remote sensing techniques has the potential to provide critically needed observations on englacial temperature at the local and continental scale. Better constraints of the vertical englacial temperature structure are needed to improve understanding of thermomechanical processes, ice rheology, and basal sliding, and to reduce uncertainty in interpretations of basal conditions such as material, roughness, and thermal state. We investigate the potential to combine active and passive microwave remote sensing techniques, namely ice-penetrating radar sounding and microwave radiometry, to enable more precise, accurate, and robust measurement of ice-sheet thermal state across widely varying thermal regimes. We simulate the effects of englacial temperature profiles on the attenuation and brightness temperature and explore the performance tradeoffs for joint radar-radiometer system architectures. Our analysis shows that active and passive microwave measurements have complementary sensitivities to englacial temperature as a function of depth, and that a ground-based joint radar-radiometer system can reduce the requirements and complexity demanded of each single instrument.
Ice shelves are floating extensions of grounded ice and play a crucial role in slowing ice discharge into the ocean. Ice flows in response to stresses according to the flow law, which is essential for predicting the mass loss of ice sheet. Laboratory experiments have shown that polycrystalline ice obeys Glen’s flow law, a power-law relation between the stress and strain rate that has been applied to ice-sheet models for decades. However, it remains unclear how processes at ice-shelf scales impact the flow law, i.e. rheology, of glacial ice. Here, we reveal the rheology of glacial ice in Antarctic Ice Shelves leveraging the availability of remote-sensing data and physics-informed deep learning. We find that the rheology of ice shelves differs substantially between the compression and extension zones. In the compression zone near the grounding line the rheology of ice closely obeys power laws with exponents in the range 1 < n < 3, consistent with prior laboratory experiments. In the extension zone, which comprises most of the total ice-shelf area, the rheology deviates from laboratory findings and does not follow a clear trend. Our result highlights a need to examine the impact of ice-shelf scale processes on glacial rheology.
Ice streams are warmed by shear strain, both vertical shear near the bed and lateral shear at the margins. Warm ice deforms more easily, establishing a positive feedback loop in an ice stream where fast flow leads to warm ice and then to even faster flow. Here, we use radar attenuation measurements to show that the Siple Coast ice streams are colder than previously thought, which we hypothesize is due to along-flow advection of cold ice from upstream. We interpret the attenuation results within the context of previous ice-temperature measurements from nearby sites where hot-water boreholes were drilled. These in-situ temperatures are notably colder than model predictions, both in the ice streams and in an ice-stream shear margin. We then model ice temperature using a 1.5-dimensional numerical model which includes a parameterization for along-flow advection. Compared to analytical solutions, we find depth-averaged temperatures that are colder by 0.7°C in the Bindschadler Ice Stream, 2.7°C in the Kamb Ice Stream and 6.2–8.2°C in the Dragon Shear Margin of Whillans Ice Stream, closer to the borehole measurements at all locations. Modelled cooling corresponds to shear-margin thermal strengthening by 3–3.5 times compared to the warm-ice case, which must be compensated by some other weakening mechanism such as material damage or ice-crystal fabric anisotropy.
Glacial ripping involves glaciotectonic disintegration of rock hills and extensive removal of rock at the ice-sheet bed, triggered by hydraulic jacking caused by fluctuating water pressures. Evidence from eastern Sweden shows that glacial ripping caused significant subglacial erosion during the final deglaciation of the Fennoscandian ice sheet, distinct from abrasion and plucking (quarrying). Here we analyse the ice drag forces exerted onto rock obstacles at the base of an ice sheet, and the resisting forces of such rock obstacles: glaciotectonic disintegration requires that ice drag forces exceed the resisting forces of the rock obstacle. We consider rock obstacles of different sizes, shapes and fracture patterns, informed by natural examples from eastern Sweden. Our analysis shows that limited overpressure events, unfavourable fracture patterns, low-transmissivity fractures, slow ice and streamlined rock hamper rock hill disintegration. Conversely, under fast ice flow and fluctuating water pressures, disintegration is possible if the rock hill contains subhorizontal, transmissive fractures. Rock steps on previously smooth, abraded surfaces, caused by hydraulic jacking, also enhance drag forces and can cause disintegration of a rock hill. Glacial ripping is a physically plausible erosion mechanism, under realistic glaciological conditions prevalent near ice margins.
Iceberg calving, the process where icebergs detach from glaciers, remains poorly understood. Moreover, few parameterizations of the calving process can easily be integrated into numerical models to accurately capture observations, resulting in large uncertainties in projected sea level rise. Recent efforts have focused on estimating crevasse depths assuming tensile failure occurs when crevasses fully penetrate the glacier thickness. However, these approaches often ignore the role of advecting crevasses on calculations of crevasse depth. Here, we examine a more general crevasse depth calving model that includes crevasse advection. We apply this model to idealized prograde and retrograde bed geometries as well as a prograde geometry with a sill. Neglecting crevasse advection results in steady glacier advance and ice tongue formation for all ice temperatures, sliding law coefficients and constant slope bed geometries considered. In contrast, crevasse advection suppresses ice tongue formation and increases calving rates, leading to glacier retreat. Furthermore, crevasse advection allows a grounded calving front to stabilize on top of sills. These results suggest that crevasse advection can radically alter calving rates and hint that future parameterizations of fracture and failure need to more carefully consider the lifecycle of crevasses and the role this plays in the calving process.
We present the first fully coupled 3D full-Stokes model of a tidewater glacier, incorporating ice flow, subglacial hydrology, plume-induced frontal melting and calving. We apply the model to Store Glacier ( Sermeq Kujalleq ) in west Greenland to simulate a year of high melt (2012) and one of low melt (2017). In terms of modelled hydrology, we find perennial channels extending 5 km inland from the terminus and up to 41 and 29 km inland in summer 2012 and 2017, respectively. We also report a hydrodynamic feedback that suppresses channel growth under thicker ice inland and allows water to be stored in the distributed system. At the terminus, we find hydrodynamic feedbacks exert a major control on calving through their impact on velocity. We show that 2012 marked a year in which Store Glacier developed a fully channelised drainage system, unlike 2017, where it remained only partially developed. This contrast in modelled behaviour indicates that tidewater glaciers can experience a strong hydrological, as well as oceanic, control, which is consistent with observations showing glaciers switching between types of behaviour. The fully coupled nature of the model allows us to demonstrate the likely lack of any hydrological or ice-dynamic memory at Store Glacier.
Modeling of the climate system including, but not limited to, atmospheric dynamics, ocean dynamics, and ice dynamics, is one of the crucial scientific problems of the 21st century. This work focuses on modeling of iceberg calving, the process by which high stresses within ice cause fractures and eventual detachment of icebergs from glaciers. Iceberg calving causes approximately half of mass loss of the world's glaciers, but remains poorly understood and implemented in climate models. Existing model implementations of calving exist at a wide range of spatial and temporal scales, ranging from models that seek to resolve crevasse propagation on the scale of seconds or minutes to broad parameterizations of calving implemented in ice sheet scale climate models. In this work, we seek to develop an intermediate model that can run for year to decade timescales and determines calving based on the internal stresses within the ice. We first focus on crevasse advection, the memory of previously formed crevasses within the ice and their impact on calving behavior. Second, we implement the possibility for mixed mode calving, where ice can fail either via high tensile stresses, high shear stresses, or a combination of the two. Lastly, we include submarine melt to see the combined effect of melt and mixed mode calving on glacier stability. This model is developed using the highly flexible Python finite element library FEniCS and LEoPart, a particle tracking library developed for use with FEniCS. Our novel use of particles to track previously crevassed ice provides a computationally efficient method to track glacier parameters that does not diffuse over time. In initial model development, we identified a key numerical consideration related to the buoyant boundary condition on ice that can create unphysical results if not careful managed in a calving model. Once this issue was documented and addressed through a simple addition to the glacier momentum balance, including crevasse advection in the model, which should increase calving rates, reduces overall rate of glacier advance but is incapable of causing retreat in most cases. This indicates that other mass loss mechanisms, such as shear calving and submarine melt, are crucial to mass balance and should be included in future models whenever possible. When mixed-mode calving is included, we find that glacier behavior is highly unstable with regards to the shear strength of ice. Sharp transitions exists at shear strengths where the ice transitions from slow advance or retreat to rapid, catastrophic collapse. Including submarine melt causes further steady mass loss, but does not significantly alter the shear strength threshold necessary for rapid collapse. This shows that if models seek to model potential catastrophic glacier collapse, which is a point of current scientific contention, mixed mode failure including shear localization should be a key focus of modeling efforts.
Aquatic environments under the Antarctic ice sheet have drawn attention since the discovery of subglacial hydrological systems consisted of lakes and water channels. The ice sheet base is an important boundary, where basal sliding, geothermal heating, erosion and deposition processes take place. Further, basal melting and subshelf ocean circulation are the keys to understand recent mass loss of the ice sheet. Despite its importance, however, in-situ observation of the subglacial environment is difficult because of the ice cover with a thickness ranging from several hundred meters to several kilometers. Hot-water drilling and borehole measurement techniques are the solutions for the direct observation. In this contribution, we review hot-water drilling and subglacial measurements previously performed in Antarctica. We also introduce our project at Langhovde Glacier as an example of hot-water drilling on an Antarctic outlet glacier, and discuss the future of subglacial exploration of the ice sheet.
The Amery Ice Shelf (AIS), East Antarctica, has a layered structure, due to the presence of both meteoric and marine ice. In this study, the thermal structure of the AIS and its spatial pattern are evaluated and analysed through borehole observations and numerical simulations. In the area with marine ice, a near-isothermal basal layer up to 120 m thick is observed, which closely conforms to the pressure-dependent freezing temperature of seawater. In the area experiencing basal melting, large temperature gradients, up to −0.36 °C m−1, are observed at the base. Three-dimensional (3-D) steady-state temperature simulations with four different basal mass balance datasets reveal a high sensitivity of ice-shelf thermal structure to the distribution of basal mass balance. We also construct a one-dimensional (1-D) temperature column model to simulate the process of ice columns moving along flowlines with time-evolving boundary conditions, which achieves slightly better agreement with borehole observations than the 3-D simulations. Our simulations reveal internal cold ice advected from higher elevations by the AIS’s tributary glaciers, warming downstream along the ice flow, and we suggest the thermal structures dominated by the cold core ice may commonly exist among Antarctic ice shelves. For the marine ice, the porous structure of its lower layer and interactions with ocean below determine the local thermal regime and give rise to the near-isothermal phenomenon. The limitations in our simulations identify the need for ice shelf/ocean coupled models with improved thermodynamics and more comprehensive evaluation of boundary conditions. Given the temperature dependence of ice rheology, the depth-averaged ice stiffness factor B(Th) derived from the simulated temperature field is presented to quantify the influence of the temperature distribution on ice shelf dynamics. The full 3-D field of this factor will assist as an input to future modelling studies.
The influence of surface melt on the flow of Greenland's largest outlet glaciers remains poorly known and in situ observations are few. We use field observations to link surface meltwater forcing to glacier-wide diurnal velocity variations on East Greenland's Helheim Glacier over two summer melt seasons. We observe diurnal variations in glacier speed that peak ~6.5 h after daily maximum insolation and extend from the terminus region to the equilibrium line. Both the amplitude of the diurnal speed variation and its sensitivity to daily melt are largest at the glacier terminus and decrease up-glacier, suggesting that the magnitude of the response is controlled not only by melt input volume and temporal variability, but also by background effective pressure, which approaches zero at the terminus. Our results provide evidence that basal lubrication by meltwater drives diurnal velocity variations at Greenland's marine-terminating glaciers in a similar manner to alpine glaciers and Greenland's land-terminating outlet glaciers.
The potential of capillary forces to retain water in pores is an important property of snow and firn at glaciers. Meltwater suspended in pores does not contribute to runoff and may refreeze during winter, which can affect the climatic mass balance and the subsurface density and temperature. However, measurement of firn water content is challenging and few values have been reported in the literature. Here, we use subsurface temperature and density measured at the accumulation zone of Lomonosovfonna (1200 m a.s.l.), Svalbard, to derive water content of the firn profiles after the 2014 and 2015 melt seasons. We do this by comparing measured and simulated rates of freezing front propagation. The calculated volumetric water content of firn is ~1.0–2.5 vol.% above the depth of 5 m and <0.5 vol.% below. Results derived using different thermistor strings suggest a prominent lateral variability in firn water content. Reported values are considerably lower than those commonly used in snow/firn models. This is interpreted as a result of preferential water flow in firn leaving dry volumes within wetted firn. This suggests that the implementation of irreducible water content values below 0.5 vol.% within snow/firn models should be considered at the initial phase of water infiltration.
The evolution of the landscape and the behavior of the groundwater system are key concerns for the long-term management of radioactive waste in deep geological repositories. At timescales relevant to repository safety assessments (i.e., 1 Ma), future ice ages are an important external perturbation that may influence repository integrity in mid- and northern latitudes. Ice ages result in the alteration of the landscape by glacial erosion and sedimentation; lead to the formation of periglacial permafrost; and impose significant transient hydraulic, mechanical, thermal, and chemical changes that can influence groundwater flow and radionuclide mobility. Four case studies are presented: (1) detailing the results of a field and modeling-based investigation of thermal and hydrological conditions beneath the Greenland Ice Sheet; (2) discussing the processes involved in the formation of deeply incised troughs and overdeepened valleys in the Swiss Plateau; (3) outlining the occurrence and dimensions of tunnel valleys in Germany and their impact on repository host rocks; and (4) illustrating the integration of techniques and geoscientific evidence, as applied in assessing the stability and resilience of a deep-seated groundwater system in the Great Lakes Basin of North America.
Temperature sensors installed in a grid of 9 full-depth boreholes drilled in the southwestern ablation zone of the Greenland Ice Sheet consistently record cooling over time within the lowest third of the ice column. Rates of temperature change outpace cooling expected from vertical conduction alone. Additionally, observed static temperature profiles deviate significantly from modeled purely diffusional thermal profiles, implying strong non-conductive heat transfer processes within the lowest portion of the ice column. Although numerous heat sources exist to add energy and warm ice as it moves from the central divide towards the margin such as strain heat from internal deformation, latent heat from refreezing meltwater, and the conduction of geothermal heat across the ice-bedrock interface, identifying heat sinks proves more difficult. After eliminating possible mechanisms that could cause cooling, we find that the observed cooling is a manifestation of previous warming in basal ice. Thermal decay after latent heat is released from freezing water in basal crevasses is the most likely mechanism resulting in the temporal evolution of temperature and the vertical thermal structure observed at our site. Basal crevasses are a viable englacial heat source in the basal ice of Greenland's ablation zone and may have a controlling influence on the temperature structure of the near basal ice.
Force variations on a "ploughmeter" and fluctuations in subglacial water pressure have been measured in the same borehole at Storglaciaren, Sweden, to investigate hydraulic properties of the basal till layer. A strong inverse correlation of the pressure and force records, in conjunction with a significant lime lag between the two signals, suggests that pore-water pressures directly affect the strength of the till. Variations in sub-glacial water pressure result in potential gradients across the water till interlace at the bottom of the borehole that drive pressure waves downwards through the till layer when the borehole water level is high and back upwards when the water level is low. Analysis of the propagation velocity of this pressure wave indicates that the hydraulic diffusivity of Storglaciaren till is in the range 1.9−3.6 x 10−6m2s−1,in good agreement with estimates obtained in the laboratory. Hydraulic conductivity values associated with these difrusivities are between 10−9 and 10−8ms−1 and thus are well within the range of values for other glacial tills.
Pressure and tracer measurements in boreholes drilled to the bottom of Ice Stream B, West Antarctica, are used to obtain information about the basal water conduit system in which high water pressures are developed.These high pressures presumably make possible the rapid movement of the ice stream. Pressure in the system is indicated by the borehole water level once connection to the conduit system is made. On initial connection, here also called “breakthrough” to the basal water system, the water level drops in a few minutes to an initial depth in the range 96–117 m below the surface. These water levels are near but mostly somewhat deeper than the floation level of about 100 m depth (water level at which basal water pressure and ice overburden pressure are equal), which is calculated from depth-density profiles and is measured in one borehole. The conduit system can be modelled as a continuous or somewhat discontinuous gap between ice and bed; the thickness of the gap δ has to be about 2 mm to account for the water-level drop on breakthrough, and about 4 mm to fit the results of a salt-tracer experiment indicating downstream transport at a speed of 7.5 mm s−1. The above gap-conduit model is, however, ruled out by the way a pressure pulse injected into the basal water system at breakthrough propagates outward from the injection hole, and also by the large hole-to-hole variation in measured basal pressure, which if present in a gap-conduit system with δ = 2 or 4 mm would result in unacceptably large local water fluxes. An alternative model that avoids these objections, called the “gap opening” model, involves opening a gap as injection proceeds: starting with a thin film, the injection of water under pressure lifts the ice mass around the borehole, creating a gap 3 or 4mm wide at the ice/bed interface. Evaluated quantitatively, the gap-opening model accounts for the volume of water that the basal water system accepts on breakthrough, which obviates the gap-conduit model. In order to transport basal meltwater from upstream it is then necessary for the complete hydraulic model to contain also a network of relatively large conduits, of which the most promising type is the “canal” conduit proposed theoretically by Walder and Fowler (1994): flat, low conduits incised into the till, ∼0.1 m deep and perhaps ∼1 m wide, with a flat ice roof. The basal water-pressure data suggest that the canals are spaced ∼50–300 m apart, much closer than R-tunnels would be. The deepest observed water level, 117 m, is the most likely to reflect the actual water pressure in the canals, corresponding to a basal effective pressure of 1.6 bar. In this interpretation, the shallower water levels are affected by loss of hydraulic head in the narrow passageway (s) that connect along the bed from borehole to canal(s). Once a borehole has frozen up and any passageways connecting with canals have become closed, a pressure sensor in contact with the unfrozen till that underlies the ice will measure the pore pressure in the till, given enough time for pressure equilibration. This pressure varies considerably with time, over the equivalent water-level range from 100 to 113 m. Basal pressure sensors 500 m apart report uncorrelated variations, whereas sensors in boreholes 25 m араrt report mostly (but not entirely) well-correlated variations, of unknown origin. In part of the record, remarkable anticorrelated variations are interspersed with positively correlated ones, and there are rare, abrupt excursions to extreme water levels as deep as 125 m and as shallow as 74 m. A diurnal pressure fluctuation, intermittently observed, may possibly be caused by the ocean tide in the Ross Sea. The lack of any observed variation in ice-stream motion, when large percentagewise variations in basal effective pressure were occurring according to our data, suggests that the observed pressure variations are sufficiently local, and so randomly variable from place to place, that they are averaged out in the process by which the basal motion of the ice stream is determined by an integration over a large area of the bed.
Ice at depth in ice sheets can be softer in bed-parallel shear than Glen’s flow law predicts. For example, at Dye 3, Greenland, enhancement factors of 3 4 are needed in order to explain the rate of borehole tilting Previous authors have identified crystal fabric as the dominant contributor, but the role of impurities and crystal size is still incompletely resolved. Here we use two formulations of anisotropic flow laws for ice (Azuma’s and Sachs’ models) to account for the effects of anisotropy, and show that the measured anisotropy of the ice at Dye 3 cannot explain all the detailed variations in the measured strain rates, the jump in enhancement across the Holocene–Wisconsin boundary is larger than expected from the measured fabrics alone. Dust and soluble-ion concentration divided by crystal size correlates well with the residual enhancement, indicating that most of the “excess deformation” may be due to impurities or crystal size. While the major features of the deformation at Dye 3 are explained by anisotropy and temperature, results also suggest that further research into the role of impurities and crystal size is warranted.
Ice temperature measurements were taken from three shallow and five deep (to bedrock) boreholes on Hansbreen, Svalbard, in selected years between 1988 and 1994. In general, results show a subpolar, polythermal structure. The glacier accumulation zone is of warm ice within the entire vertical profile except the uppermost layer of seasonal temperature fluctuations where there is an upper cold ice layer in the ablation zone which varies in thickness and may even be absent in the western lateral part. The upper layer of cold ice thins along the glacier centre-line from the equilibrium line altitude down to the glacier front. The depth of the pressure melting, indicating the base of the cold ice layer, was defined at the borehole measurement sites but was not manifested as an internal reflection horizon using multi-frequency radar methods. The isotherm lies about 20 m above a radar internal reflecting horizon near the equilibrium line altitude and about 40 m above it in the frontal part of the glacier. The internal reflection horizon almost certainly reflects the high water content within temperate ice and not the cold/temperate ice interface. At 10 m depth, the temperatures are 2–3°C higher than the calculated mean annual air temperatures, demonstrating the importance of meltwater refreezing on the release of latent heat.
Force variations on a 'ploughmeter' and fluctuations in subglacial water pressure have been measured in the same borehole at Storglaciaren, Sweden, to investigate hydraulic properties of the basal till layer. A strong inverse correlation of the pressure and force records, in conjunction with a significant time lag between the two signals, suggests that pore-water pressures directly affect the strength of the till. Variations in sub-glacial water pressure result in potential gradients across the water-till interface at the bottom of the borehole that drive pressure waves downwards through the till layer when the borehole water level is high and back upwards when the water level is low. Analysis of the propagation velocity of this pressure wave indicates that the hydraulic diffusivity of Storglaciaren till is in the range 1.9-3.6 x 10-6 m2s-1, in good agreement with estimates obtained in the laboratory. Hydraulic conductivity values associated with these diffusivities are between 10-9 and 10-8 m s-1 and thus are well within the range of values for other glacial tills.
Jakobshavns Glacier, a floating outlet glacier on the West Greenland coast, was surveyed during July 1976. The vertical displacements of targets along two profiles perpendicular to the fjord wall bounding the north margin of the glacier were analyzed to determine the effect of flexure caused by tidal oscillations within the fjord. An analysis based on the assumption that vertical displacements of the glacier reflected pure elastic bending yielded the conclusion that the effective thickness of the ice (i.e., the thickness which remained unaffected by surface and basal cracking and which behaved as a continuum) was ~160 m 2.6 km upglacier from the calving front and ~110 m 0.6 km from the calving front. An analysis based on the more realistic assumption that observed bending reflected elastic and viscoplastic deformation yielded the conclusion that the average thickness of the ice was 316+/-74 m (~40% of the estimated 800-m total thickness) 2.6 km from the calving front and 160+/-48 m (~21% of the estimated 750-m total) 0.6 km from the calving front. A constitutive relationship appropriate for hard glide during flexure was used.
The theory applies to basal drainage systems having multiple and extensive interconnected flow paths. Within this domain it encompasses a broad range of flow regimes, from laminar Darcian flow in a thick permeable unit to turbulent sheet flow in a very thin layer. Important terms in the model are highlighted by recasting the problem in dimensionless form. This indicates that there are four free parameters in the coupled system which characterize skin friction in the borehole, and diffusion, transmissivity and turbulent transport in the subglacial flow layer. Dimensionless results show that the effects of skin friction in the borehole are negligible. Diffusion, transmissivity and especially turbulent transport in the basal layer are found to influence subglacial water flow strongly. The model is used to predict fluctuations of borehole-water levels that result from different types of disturbances. -from Authors
A model for the calculation of two-dimensional temperature fields is described and applied along the central flowline of Jakobshavns Isbræ, West Greenland, and along a flowline through the adjacent ice sheet. The model calculates the velocity-depth distribution based on Glen’s flow law and subject to the condition that the calculated velocities agree with the measured surface velocity and the estimated sliding velocity. The model allows for two-dimensional conduction and advection, for deformational energy dissipation and for the development of a basal layer of temperate ice. The results of modeling are compared to the englacial temperatures measured in boreholes reaching a depth of 1550 m which corresponds to 60% of the total depth at the center line. While there is a good agreement of the measured and modeled minimum temperatures, the shape of the temperature—depth profiles is quite different. We attribute this difference in shape to a characteristic three-dimensional ice deformation taking place in the convergent sub-surface channel of the actual ice stream. The model does not account for this three-dimensional effect. Adjustment of the modeled central temperature profile, so that its shape matches that of the measured profile, leads to an increase of thickness of the temperate basal layer by about 30%. Hence, the predicted temperate basal layer in the ice stream is likely to be about 300 m thick while the two-dimensional model suggests about 230 m. Such a thickening of the temperate basal layer by three-dimensional ice deformation may be an important mechanism of fast ice-stream flow.
Uniaxial compression tests under constant crosshead speed were carried out on 22 new specimens from the 268, 1890, 1944 and 2006 m depths of the Dye 3, Greenland, ice core. The measurements were made in a laboratory cold-room, using an Instron model 1131 apparatus. Test temperatures were held constant between −17° and −13° C, the approximate sample in-situ temperature. Specimens were prepared with various test orientations in relation to the long vertical core axis. The specimens were analyzed in terms of the content of dust, Cl−, NO3 − and SO4 2− concentrations and various other physical parameters, such as ultrasonic wave velocities, c-axis orientation patterns and grain-size. The results of the previous uniaxial compression tests show that most of the flow occurs in the Wisconsin-age ice between 1786 m and the bottom of the ice sheet. This entire depth interval is strongly anisotropic, with a vertical c-axis fabric pattern. The enhancement factor, E, which was calculated from these tests ranges from 0.03 to 17. The Wisconsin-age ice is about ten times softer (Es = 10) than artificially made laboratory ice (E = 1). The combined results of the multi-parameter correlation analyses show that E is controlled primarily by the orientation strength of c-axes and that the impurity concentration-level variations contribute to a lesser degree.
Computations over 50 000 years into steady state with Greve’s polythermal ice-sheet model and its numerical code are performed for the Greenland ice sheet with today’s climatological input (surface temperature and accumulation function) and three values of the geothermal heat flux: (42, 54.6, 29.4) mW m−2. It is shown that through the thermomechanical coupling the geometry as well as the thermal regime, in particular that close to the bed, respond surprisingly strongly to the basal thermal heat input. The most sensitive variable is the basal temperature field, but the maximum height of the summit also varies by more than ±100m. Furthermore, some intercomparison of the model outputs with the real ice sheet is carried out, showing that the model provides reasonable results for the ice-sheet geometry as well as for the englacial temperatures.
We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments ate described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model’s prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.
Annual total precipitation and the annual accumulation on the Greenland ice sheet are evaluated and presented in two maps. The maps are based on accumulation measurements of 251 pits and cores obtained from the upper accumulation zone and precipitation measurements made at 35 meteorological stations in the coastal region. To construct the accumulation map, the annual precipitation was split into solid and liquid precipitation components. Annual total precipitation exceeding 2500mmw.e. occurs on the southeastern tip of Greenland, while the minimum precipitation is estimated to occur on the northeastern slope of the ice sheet. The mean annual precipitation for all of Greenland is 340 mm w.e. The largest annual accumulation of about 1500 mm w.e. is found on the glaciers in the southeastern corner of Greenland, while the smallest accumulation is found on the northeastern slope of the ice sheet west of Danmarkshavn. The mean accumulation on the Greenland ice sheet is estimated at 310mmw.e. The regional difference in accumulation is examined with respect to the 850hPa(mbar) level circulation. The present surface topography is found to play an important role in determining regional accumulation on the ice sheet.
The University of Kansas developed a coherent radar depth sounder during the 1980s. This system was originally developed for glacial ice-thickness measurements in the -Antarctic. During the field tests in the Antarctic and Greenland, we found the system performance to be less than optimum. The field tests in Greenland were performed in 1993, as a part of the NASA Program for Arctic Climate Assessment (PARCA). We redesigned and rebuilt this system to improve the performance.
The radar uses pulse compression and coherent signal processing to obtain high sensitivity and fine along-track resolution. It operates at a center frequency of 150 MHz with a radio frequency bandwidth of about 17 MHz., which gives a range resolution of about 5m in ice. We have been operating it from a NASA P-3 aircraft for collecting ice-thickness data in conjunction with laser surface-elevation measurements over the Greenland ice sheet during the last 4years. We have demonstrated that this radar can measure the thickness of more than 3 km of cold ice and can obtain ice-thickness information over outlet glaciers and ice margins.
In this paper we provide a brief survey of radar sounding of glacial ice, followed by a description of the system and subsystem design and performance. We also show sample results from the held experiments over the Greenland ice sheet and its outlet glaciers.
The lower 80 km of the fast-moving Jakobshavns Isbræ, West Greenland, is subject to significant melting during the summer season. The melt water drains into large supraglacial rivers which pour into moulins or feed into beautiful supraglacial lakes, some of which are observed to drain periodically. Except for a few streams that drain directly off the margins of the ice sheet within the drainage basin of this glacier, the fate of this melt water is unknown. However, a localized upwelling of highly turbid water is often observed during the melt season in the fjord adjacent Io the terminal cliff of the glacier, indicating that water from some source does move along the glacier bed.
As part of an investigation on the mechanisms of rapid flow on Jakobshavns Isbræ, measurements of surface velocity at several (∼25) locations along the ice stream at and below the equilibrium line were made in order to investigate the effects of this seasonally varying input of melt water on the speed of the glacier.
No significant seasonal variation in speed was found at any location. This indicates that, unlike many other sub-polar and temperate glaciers, surface melt-water production does not affect the motion of this glacier on a seasonal basis, and, thus, does not cause a significant temporal variation in basal sliding. This finding has important ramifications on the mechanisms of flow for this ice stream.
Several holes were drilled to depths of 1500–1630 m along a profile across Jakobshavns Isbræ, 50 km upstream from the calving front. Drilling was by hot water and required approximately 20 h. The holes were rapidly closed by refreezing, but it was possible to instrument them with thermistors and tilt sensors before this occurred.
Near the margins of the ice stream the holes reached the bed and connected with the subglacial drainage system. Water-level changes recorded in these holes are discussed in terms of the basal hydraulic system. The temperature measurements show that the glacier is temperate-based. Moreover, extrapolation of a measured temperature profile and its curvature suggests that a temperate layer of substantial thickness may exist at the bed near the center of the ice stream. There is a striking difference in the shapes of temperature profiles measured at different locations: beneath the center line the temperature minimum is at a considerably smaller relative depth than near the margins, but it is nearly the same in magnitude (−22.1°C). This may indicate a disproportionately large vertical stretching of the basal ice in the center of the ice stream. Since the basal ice is warmer and much less viscous than the ice above, a thickening of that layer would cause a corresponding increase of surface velocity. We presume that this mechanism contributes to the fast flow of Jakobshavns Isbræ.
Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character.
As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored.
The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law.
When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail.
Englacial temperature measurements in Arctic valley glaciers suggest in the ablation zone the existence of a basal layer of temperate ice lying below the bulk of cold ice. For such a polythermal glacier, a mathematical model is presented that calculates the temperature in the cold part and the position of the cold-temperate transition surface (CTS). The model is based on the continuum hypothesis for ice and the ice-water mixture, and on the conservation laws for moisture and energy. Temperate ice is treated as a binary mixture of ice and water at the melting point of pure ice. Boundary and transition conditions are formulated for the free surface, the base and the intraglacial cold-temperate transition surface. The model is reduced to two dimensions (plane flow) and the shallow-ice approximation is invoked. The limit of very small moisture diffusivity is analysed by using a stationary model with further reduction to one dimension (parallel-sided slab), thus providing the means of a consistent formulation of the transition conditions for moisture and heat flux through the CTS at the limit of negligibly small moisture diffusion.
The application of the model to the steady-state Laika Glacier, using present-day conditions, results in a wholly cold glacier with a cold sole, in sharp contrast to observations. The present polythermal state of this glacier is suspected to be a remnant of the varying climatic conditions and glacier geometry during the past few centuries. Steady-state solutions representing a polythermal structure can indeed be found within a range of prescribed conditions which are judged to be realistic for Laika Glacier at the last maximum extent of the glacier.
A simple method is described for detecting annual stratification of ice cores, and layers of high acidity due to violent volcanic eruptions in the past. The method is based on a relationship between the H3O+ concentration (pH) of melted samples and the electrical current between two brass electrodes moved along the cleaned ice-core surface. The “conductivity” is explained in terms of the initial current in the build-up of space charges. Acidity and current profiles are shown through layers deposited soon after historically well-known volcanic eruptions, such as Katmai, a.d. 1912, Tambora, a.d. 1815, Laki, a.d. 1783, Hekla, a.d. 1104, and Thera (Santorin) c. 1400 b.c. High-acidity layers seem to be the cause for the internal radio-echo layers in polar ice sheets.
A water table appearing every summer where the ice begins, at a gerpth of approximately 30 m, accelerates the transformation of firn into ice during the summer (80% of the ice formed every year appears in less than 2 months). The ice formed in this way contains from 0 to 0.6% water. The average water content increases gradually with the gerpth because of the heat of gerformation. But, near bedrock, between 180 and 187 m, the permeability of the blue ice is such that the water content drops (0.3% as compared to 1.3% between 160 and 180 m).
From a gerpth of 33 m, a foliation of sedimentary origin gradually gervelops in the ice. Its dip increases regularly to a gerpth of 145 m. At 145 m it jumps sudgernly freom 20° to 40°, then at 170 m freom 40° to 65°, which can be explained by old modifications in the bergschrund. This foliation disappears near bedrock (180-187 m), where there are no bubbles in the ice.
The average size of an ice crystal increases slowly in the firn, shows seasonal fluctuations between 30 and 50 m, then jumps freom a diameter of 1 or 2 mm to 10 or 20 mm between 50 and 80 m. Between 180 and 187 m, the ice is mager of large crystals (3-10 cm diameter; the figure, however, is probably inexact due to a recrystallization of the samples).
The very strong sub-vertical orientation of the optic axes of the firn crystals disappears quickly, and freom 66 m on, in ice with large crystals, a fabric of multiple maxima appears (generally, 3 or 4 directions, forming a triangle or a rhombus). On the other hand, in the small crystals that form bands parallel to the plane of foliation, only one direction of preferential orientation can be seen, or two close to one another. Crystals of intermediate size (10 to 50 mm) generally have two directions of preferred orientation at an angle of approximately 50° to one another. No matter how big the crystals are, the angle between the most common c-axis orientation and the vertical does not change freom 60 to 170 m gerpth.
The closure of water-filled glacier bore holes is considered and it is concluded that freezing due to conduction to the surrounding ice is usually the dominant process. On this basis englacial temperatures are obtained from a bore hole near the equilibrium line of Blue Glacier, U.S.A., where the ice thickness is about 125 m. Temperatures range from −0.03° C near the surface to −0.13° C at a depth of 105 m, with an estimated uncertainty of 0.02 or 0.03 deg. On the average the temperature is about 0.05 deg colder than the equilibrium temperature of ice and pure water. It is shown that at this temperature small amounts of water-soluble impurities play an important role in the thermal behavior of the ice. This leads to a new definition of temperate ice in terms of its effective heat capacity. The effective heat capacity of the Blue Glacier ice is apparently much larger than that of pure ice at the same temperature.
In this paper we develop a theoretical model describing water motion in a coupled borehole-subglacial flow system. The theory applies to basal drainage systems having multiple and extensive interconnected flow paths. Within this domain it encompasses a broad range of flow regimes, from laminar Darcian flow in a thick permeable unit to turbulent sheet flow in a very thin layer. Important terms in the model are highlighted by recasting the problem in dimensionless form. The non-dimensional formulation indicates that there are four free parameters in the coupled system. These parameters characterize skin friction in the borehole, and diffusion, transmissivity and turbulent transport in the subglacial flow layer. Dimensionless results show that, under most circumstances, the effects of skin friction in the borehole are negligible. Diffusion, transmissivity and especially turbulent transport in the basal layer are found to influence subglacial water flow strongly. We use our model to predict fluctuations of borehole-water levels that result from different types of disturbances. We show how this framework can be used to estimate subglacial hydraulic properties by comparing model results with data collected during field experiments on Trapridge Glacier, Yukon Territory, Canada in 1989 and 1990.
Seismic-reflection methods were used to determine the ice thickness and basal topography of Jakobshavns Isbræ, a large, fast-moving ice stream/outlet glacier in West Greenland. A method of data analysis was developed which involves the pointwise migration of data from a linear seismic array and a single explosive source; the method yields the depth, horizontal position and slope of the basal reflector. A deep U-shaped subglacial trough was found beneath the entire length of the well-defined ice stream. The trough is incised up to 1500 m into bedrock, and its base lies 1200–1500 m below sea level for at least 70 km inland. Center-line ice thickness along most of the channel is about 2500 m, or about 2.5 times that of the surrounding ice sheet. This prominent bedrock trough was not apparent in existing radio-echo-sounding data. Reflection coefficients indicate that much of the basal interface is probably underlain by compacted, non-deforming sediment. The large ice thickness, coupled with relatively steep surface slopes, leads to high basal shear stresses (200–300 k Pa) along the ice stream. The large shear stresses and lack of a deformable bed imply that internal deformation plays a dominant role in the dynamics of Jakobshavns Isbræ.
Ice at depth in ice sheets can be softer in bed-parallel shear than Glen’s flow law predicts. For example, at Dye 3, Greenland, enhancement factors of 3 4 are needed in order to explain the rate of borehole tilting Previous authors have identified crystal fabric as the dominant contributor, but the role of impurities and crystal size is still incompletely resolved. Here we use two formulations of anisotropic flow laws for ice (Azuma’s and Sachs’ models) to account for the effects of anisotropy, and show that the measured anisotropy of the ice at Dye 3 cannot explain all the detailed variations in the measured strain rates, the jump in enhancement across the Holocene–Wisconsin boundary is larger than expected from the measured fabrics alone. Dust and soluble-ion concentration divided by crystal size correlates well with the residual enhancement, indicating that most of the “excess deformation” may be due to impurities or crystal size. While the major features of the deformation at Dye 3 are explained by anisotropy and temperature, results also suggest that further research into the role of impurities and crystal size is warranted.
We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments are described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model's prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.
There are many kinds of metamorphic ice, each of which follows a different creep law. Putting aside transient creep, for which intrinsic state variables measuring work-hardening must be introduced, these behaviors may be modelled by a power law viscosity. This law is precisely defined for a macroscopically anisotropic material; when the power is 1 or 3 and there is rotational symmetry, it is deduced from the dissipation potentials of individual grains. Values of the parameters for isotropic secondary creep and for tertiary creep with a multic-maxima fabric are given. Data from the inclinometer survey of Byrd borehole are analyzed. -from Authors
Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character.
As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored.
The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law.
When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail.
Seismic-refl ection methods were used to determine the ice thickness and basal topography of Jakobshavns lsbra:: , a large, fast-moving ice stream/outlet glacier in \Vest Greenland. A method of data analysis was developed which iil\'olves the pointwise migration of data fr om a linear seism ic array and a si ngle explosive so urce; the method yields the depth, horizontal position and slo pe of the basal reflector. A deep U-shaped subglacial trough was fo und beneath the entire length of the well-defined ice stream . The trough is incised up to 1500 m into bed rock, and its base lies 1200-1 50 0 111 below sea level fo r at least 70 km inland. Center-line ice thickness along most of the channel is about 2500 m, or about 2.5 times that of the su rrounding ice sheet. This prominent bedrock trough was not apparent in existing radio-echo-sounding data. Reflection coefficients indi cate that much of the basal interface is probably underlain by com pacted, non-deforming sediment. The large ice thickness, co upled with relati\'cly steep surface slopes, leads to high basal shear stresses (200-300 k Pa) along th e ice stream. The large shear stresses and lack of a deformable bed imply that in ternal deformation plays a dominant role in the dynamics of Jakobshavns Isbra:: .
A water table appearing every summer where the ice begins, at a gerpth of approximately 30 m, accelerates the transformation of firn into ice during the summer (80% of the ice formed every year appears in less than 2 months). The ice formed in this way contains from 0 to 0.6% water. The average water content increases gradually with the gerpth because of the heat of gerformation. But, near bedrock, between 180 and 187 m, the permeability of the blue ice is such that the water content drops (0.3% as compared to 1.3% between 160 and 180 m).
From a gerpth of 33 m, a foliation of sedimentary origin gradually gervelops in the ice. Its dip increases regularly to a gerpth of 145 m. At 145 m it jumps sudgernly freom 20° to 40°, then at 170 m freom 40° to 65°, which can be explained by old modifications in the bergschrund. This foliation disappears near bedrock (180-187 m), where there are no bubbles in the ice.
The average size of an ice crystal increases slowly in the firn, shows seasonal fluctuations between 30 and 50 m, then jumps freom a diameter of 1 or 2 mm to 10 or 20 mm between 50 and 80 m. Between 180 and 187 m, the ice is mager of large crystals (3-10 cm diameter; the figure, however, is probably inexact due to a recrystallization of the samples).
The very strong sub-vertical orientation of the optic axes of the firn crystals disappears quickly, and freom 66 m on, in ice with large crystals, a fabric of multiple maxima appears (generally, 3 or 4 directions, forming a triangle or a rhombus). On the other hand, in the small crystals that form bands parallel to the plane of foliation, only one direction of preferential orientation can be seen, or two close to one another. Crystals of intermediate size (10 to 50 mm) generally have two directions of preferred orientation at an angle of approximately 50° to one another. No matter how big the crystals are, the angle between the most common c -axis orientation and the vertical does not change freom 60 to 170 m gerpth.
ABSTRACT Inclinometer surveys of deep boreholes provide valuable infor mation on the flow properties of modern ice (Holocene ice) and ice from the last glaciation (Wisconsin ice). The Dye 3 borehole on the south Greenland ice sheet has been surveyed seven times in the period 1981-1986. A least squares method has been used to derive the shear deformation rates directly from all the surveys. In the analysis, Glen's flow law has been used to calcu late a flow law parameter from the shear deformation rates. Local stress fields due to the rough bedrock are used in these calculations; this has a large effect on the interpretation of the data. The results show that the Wisconsin ice flows a factor of three more,readily than the Holocene ice. The enhanced flow is believed to be due primarily to the high concentration of dust and other impuri ties highly correlated with it and/or to the small crystal size. Une loi rhéologique pour la glace déduite de l'inclinometrie a Dye 3, Groen
Intercept analysis of approximately bi-yearly vertical thin sections from the upper part of the GISP2 ice core, central Greenland, shows that grain-size ranges increase with increasing age. This demonstrates that something in the ice affects grain-growth rates, and that grain-size cannot be used directly in paleothermometry as has been proposed. Correlation of grain-growth rates to chemical and isotopic data indicates slower growth in ice with higher impurity concentrations, and especially slow growth in "forest-fire" layers containing abundant ammonium; however, the impurity/grain-growth relations are quite noisy. Little correlation is found between growth rate and isotopic composition of ice.
Several holes were drilled to depths of 1500–1630 m along a profile across Jakobshavns Isbræ, 50 km upstream from the calving front. Drilling was by hot water and required approximately 20 h. The holes were rapidly closed by refreezing, but it was possible to instrument them with thermistors and tilt sensors before this occurred.
Near the margins of the ice stream the holes reached the bed and connected with the subglacial drainage system. Water-level changes recorded in these holes are discussed in terms of the basal hydraulic system. The temperature measurements show that the glacier is temperate-based. Moreover, extrapolation of a measured temperature profile and its curvature suggests that a temperate layer of substantial thickness may exist at the bed near the center of the ice stream. There is a striking difference in the shapes of temperature profiles measured at different locations: beneath the center line the temperature minimum is at a considerably smaller relative depth than near the margins, but it is nearly the same in magnitude (−22.1°C). This may indicate a disproportionately large vertical stretching of the basal ice in the center of the ice stream. Since the basal ice is warmer and much less viscous than the ice above, a thickening of that layer would cause a corresponding increase of surface velocity. We presume that this mechanism contributes to the fast flow of Jakobshavns Isbræ.
Temperate glacier ice is neither dry nor impermeable, as the standard theory of glacier sliding assumes. This fact leads to the already published concept of locally stress-controlled temperatures. Why the temperature is determined by the highest principal pressure, why the microscopic stress equals more or less the macroscopic one, and why water may flow in the capillary network even when water lenses at grain boundaries are freezing is explained. The new concept is applied to ice sliding on a hard bed having a sine profile, without cavitation. -from Author
Uniaxial compression tests under constant crosshead speed were carried out on 22 new specimens from the 268, 1890, 1944 and 2006 m depths of the Dye 3, Greenland, ice core. The measurements were made in a laboratory cold-room, using an Instron model 1131 apparatus. Test temperatures were held constant between −17° and −13° C, the approximate sample in-situ temperature. Specimens were prepared with various test orientations in relation to the long vertical core axis. The specimens were analyzed in terms of the content of dust, Cl ⁻ , NO 3⁻ and SO 4²⁻ concentrations and various other physical parameters, such as ultrasonic wave velocities, c -axis orientation patterns and grain-size. The results of the previous uniaxial compression tests show that most of the flow occurs in the Wisconsin-age ice between 1786 m and the bottom of the ice sheet. This entire depth interval is strongly anisotropic, with a vertical c -axis fabric pattern. The enhancement factor, E, which was calculated from these tests ranges from 0.03 to 17. The Wisconsin-age ice is about ten times softer (E s = 10) than artificially made laboratory ice (E = 1). The combined results of the multi-parameter correlation analyses show that E is controlled primarily by the orientation strength of c -axes and that the impurity concentration-level variations contribute to a lesser degree.
The Greenland Ice Sheet Project 2 (GISP2) electrical conductivity measurement (ECM) record is an indication of the concentration of H+ in the core. The ECM detected seasonal variations in the nitrate concentration of the core which were used to assist in dating the core by annual layer counting. Volcanic eruptions that produce acidic aerosols are recorded in the ECM record. Evidence of biomass burning is detected by the ECM because fire-related ammonium emissions neutralize the acids in the core. Rapid climate transitions associated with the Younger Dryas and Dansgaard/Oeschger interstadial events alter the concentration of alkaline dust and are detected by the ECM. The ECM has been used to develop stratigraphic ties between the GISP2 and the Greenland Ice Core Project cores. Users of the data should be aware of some instrument-related artifacts in the ECM recod.
The Greenland Ice Sheet Project 2 glaciochemical series (sodium, potassium, ammonium, calcium, magnesium, sulfate, nitrate, and chloride) provides a unique view of the chemistry of the atmosphere and the history of atmospheric circulation over both the high latitudes and mid-low latitudes of the northern hemisphere. Interpretation of this record reveals a diverse array of environmental signatures that include the documentation of anthropogenically derived pollutants, volcanic and biomass burning events, storminess over marine surfaces, continental aridity and biogenic source strength plus information related to the controls on both high- and low-frequency climate events of the last 110,000 years. Climate forcings investigated include changes in insolation of the order of the major orbital cycles that control the long-term behavior of atmospheric circulation patterns through changes in ice volume (sea level), events such as the Heinrich events (massive discharges of icebergs first identified in the marine record) that are found to operate on a 6100-year cycle due largely to the lagged response of ice sheets to changes in insolation and consequent glacier dynamics, and rapid climate change events (massive reorganizations of atmospheric circulation) that are demonstrated to operate on 1450-year cycles. Changes in insolation and associated positive feedbacks related to ice sheets may assist in explaining favorable time periods and controls on the amplitude of massive rapid climate change events. Explanation for the exact timing and global synchroneity of these events is, however, more complicated. Preliminary evidence points to possible solar variability-climate associations for these events and perhaps others that are embedded in our ice-core-derived atmospheric circulation records.
Pressure and tracer measurements in boreholes drilled to the bottom of Ice Stream B, West Antarctica, are used to obtain information about the basal water conduit system in which high water pressures are developed. These high pressures presumably make possible the rapid movement of the ice stream. Pressure in the system is indicated by the borehole water level once connection to the conduit system is made. On initial connection, here also called 'breakthrough' to the basal water system, the water level drops in a few minutes to an initial depth in the range 96-117 m below the surface. These water levels are near but mostly somewhat deeper than the flotation level of about 100 m depth (water level at which basal water pressure and ice overburden pressure are equal), which is calculated from depth-density profiles and is measured in one borehole. The conduit system can be modelled as a continuous or somewhat discontinuous gap between ice and bed; the thickness of the gap δ has to be about 2mm to account for the water-level drop on breakthrough, and about 4 mm to fit the results of a salt-tracer experiment indicating downstream transport at a speed of 7.5 mm s-1. The above gap-conduit model is, however, ruled out by the way a pressure pulse injected into the basal water system at breakthrough propagates outward from the injection hole, and also by the large hole-to-hole variation in measured basal pressure, which if present in a gap-conduit system with δ = 2 or 4 mm would result in unacceptably large local water fluxes. An alternative model that avoids these objections, called the 'gap opening' model, involves opening a gap as injection proceeds: starting with a thin film, the injection of water under pressure lifts the ice mass around the borehole, creating a gap 3 or 4 mm wide at the ice/bed interface. Evaluated quantitatively, the gap-opening model accounts for the volume of water that the basal water system accepts on breakthrough, which obviates the gap-conduit model. In order to transport basal meltwater from upstream it is then necessary for the complete hydraulic model to contain also a network of relatively large conduits, of which the most promising type is the 'canal' conduit proposed theoretically by Walder and Fowler (1994): flat, low conduits incised into the till, ~0.1 m deep and perhaps ~1 m wide, with a flat ice roof. The basal water-pressure data suggest that the canals are spaced ~50-300 m apart, much closer than R-tunnels would be. The deepest observed water level, 117 m, is the most likely to reflect the actual water pressure in the canals, corresponding to a basal effective pressure of 1.6 bar. In this interpretation, the shallower water levels are affected by loss of hydraulic head in the narrow passageway(s) that connect along the bed from borehole to canal(s). Once a borehole has frozen up and any passageways connecting with canals have become closed, a pressure sensor in contact with the unfrozen till that underlies the ice will measure the pore pressure in the till, given enough time for pressure equilibration. This pressure varies considerably with time, over the equivalent water-level range from 100 to 113 m. Basal pressure sensors 500 m apart report uncorrelated variations, whereas sensors in boreholes 25 m apart report mostly (but not entirely) well-correlated variations, of unkonwn origin. In part of the record, remarkable anticorrelated variations are interspersed with positively correlated ones, and there are rare, abrupt excurisons to extreme water levels as deep as 125 m and as shallow as 74 m. A diurnal presure fluctuation, intermittently observed, may possibly be caused by the ocean tide in the Ross Sea. The lack of any observed variation in ice-stream motion, when large percentagewise variations in basal effective pressure were occurring according to our data, suggests that the observed pressure variations are sufficiently local, and so ramdonly variable from place to place, that they are averaged out in the process by which the basal motion of the ice stream is determined by an integration over a large area of the bed.
The University of Kansas developed a coherent radar depth sounder during the 1980s. This system was originally developed for glacial ice-thickness measurements in the -Antarctic. During the field tests in the Antarctic and Greenland, we found the system performance to be less than optimum. The field tests in Greenland were performed in 1993, as a part of the NASA Program for Arctic Climate Assessment (PARCA). We redesigned and rebuilt this system to improve the performance.
The radar uses pulse compression and coherent signal processing to obtain high sensitivity and fine along-track resolution. It operates at a center frequency of 150 MHz with a radio frequency bandwidth of about 17 MHz., which gives a range resolution of about 5m in ice. We have been operating it from a NASA P-3 aircraft for collecting ice-thickness data in conjunction with laser surface-elevation measurements over the Greenland ice sheet during the last 4years. We have demonstrated that this radar can measure the thickness of more than 3 km of cold ice and can obtain ice-thickness information over outlet glaciers and ice margins.
In this paper we provide a brief survey of radar sounding of glacial ice, followed by a description of the system and subsystem design and performance. We also show sample results from the held experiments over the Greenland ice sheet and its outlet glaciers.
Various published data from constant-stress creep tests on ice, relating minimum strain-rate to applied stress at different temperatures, are presented and compared. A temperature dependent rate factor is constructed from the Mellor and Testa (1969a) uni-axial compression data at uni-axial stress 1.18 × 106 N m−2 over the temperature range 212.15 K–273.15 K. This factor is used to normalise the different sets of data at different temperatures to a common temperature for comparison, but normalised strain-rates at a fixed stress still vary by a factor of 3. Furthermore, it is shown that no alternative single rate factor will adequately correlate the data at two different temperatures.A least-squares method is used to express the strain-rate as an odd polynomial in the stress; distinct polynomials are found for different sets of data. Good matches are generally obtained over a uni-axial stress range 0–106 N m−2 by three terms: first, third and fifth powers of stress; but less satisfactory non-monotonic polynomials involving negative coefficients are obtained in most cases if the seventh power is also included. Expressing the stress as an odd polynomial in the strain-rate, however, is not satisfactory, which is a reflection of the shape of the response at higher strain-rates. Inverse sinh function expansions failed in general, but inverse tan function expansions give good agreement to some data.
Englacial temperature measurements in Arctic valley glaciers suggest in the ablation zone the existence of a basal layer of temperate ice lying below the bulk of cold ice. For such a polythermal glacier, a mathematical model is presented that calculates the temperature in the cold part and the position of the cold-temperate transition surface (CTS). The model is based on the continuum hypothesis for ice and the ice-water mixture, and on the conservation laws for moisture and energy. Temperate ice is treated as a binary mixture of ice and water at the melting point of pure ice. Boundary and transition conditions are formulated for the free surface, the base and the intraglacial cold-temperate transition surface. The model is reduced to two dimensions (plane flow) and the shallow-ice approximation is invoked. The limit of very small moisture diffusivity is analysed by using a stationary model with further reduction to one dimension (parallel-sided slab), thus providing the means of a consistent formulation of the transition conditions for moisture and heat flux through the CTS at the limit of negligibly small moisture diffusion.
The application of the model to the steady-state Laika Glacier, using present-day conditions, results in a wholly cold glacier with a cold sole, in sharp contrast to observations. The present polythermal state of this glacier is suspected to be a remnant of the varying climatic conditions and glacier geometry during the past few centuries. Steady-state solutions representing a polythermal structure can indeed be found within a range of prescribed conditions which are judged to be realistic for Laika Glacier at the last maximum extent of the glacier.
During September 1991, April 1992 and June/July 1993, a NASA P–3 aircraft, equipped with a scanning laser altimeter, flew numerous transects of the Greenland ice sheet. The aeroplane location was measured precisely using dilTerential Global Positioning System (GPS) surveying techniques, allowing all altimetry data to be converted into measurements of ice-surface elevation relative to the Earth ellipsoid. Results from flight data indicate that icc-surface elevations can be reliably measured to an accuracy of 20cm (and possibly to s lOcm) over baselines of more than seven hundred kilometres.
The closure of water-filled glacier bore holes is considered and it is concluded that freezing due to conduction to the surrounding ice is usually the dominant process. On this basis englacial temperatures are obtained from a bore hole near the equilibrium line of Blue Glacier, U.S.A., where the ice thickness is about 125 m. Temperatures range from −0.03° C near the surface to −0.13° C at a depth of 105 m, with an estimated uncertainty of 0.02 or 0.03 deg. On the average the temperature is about 0.05 deg colder than the equilibrium temperature of ice and pure water. It is shown that at this temperature small amounts of water-soluble impurities play an important role in the thermal behavior of the ice. This leads to a new definition of temperate ice in terms of its effective heat capacity. The effective heat capacity of the Blue Glacier ice is apparently much larger than that of pure ice at the same temperature.
Steady-state and transient climate-change computations are performed with the author's three-dimensional polythermal ice sheet model Simulation Code for Polythermal Ice Sheets for the Greenland Ice Sheet. The distinctive feature of this model is the detailed consideration of the basal temperate ice layer, in which the water content and its impact on the ice viscosity are computed; its transition surface to the cold ice region is accounted for by continuum-mechanical jump conditions on this interface. The simulations presented include steady states subject to a range of physical parameters and two different climates (present and glacial conditions), as well as three types of transient scenarios, namely (i) sinusoidal Milankovi-period forcing, (ii) paleoclimatic forcing from the Greenland Ice Core Project core reconstruction, and (iii) future greenhouse warming forcing.
A comprehensive study of textures and fabrics has been carried out on the Greenland Ice Core Project (GRIP) ice core. Crystal sizes and c axis orientations have been measured on thin sections with conventional techniques, yielding new information on the growth, rotation and recrystallization of ice crystals in the Greenland Ice Sheet. Normal grain growth is found to persist to a depth of 700 m in the core, where the onset of polygonization due to increasing strain prevents a further increase in grain size in the Holocene ice. Smaller crystals are observed in the Wisconsin ice, larger crystals are found in the Eemian ice, and the crystal size is found to vary with climatic parameters in these periods. This dependence, which probably results from variable impurity content in the ice, persists to a depth of 2930 m. Coarse-grained ice, probably resulting from rapid growth of crystals at comparatively high temperatures, is found in the lowest 100 m of the core. The data on c axis orientations reveal a steady evolution of the fabric from random near the surface to a strong single maximum in the lower part of the ice sheet. A significant strengthening is not observed at the Holocene-Wisconsin transition. The fabric development indicates that vertical compression at the ice divide is the main mode of deformation down to a depth of 2850 m. The evolution toward a single maximum fabric hardens the ice against vertical compression but softens it against simple shear. Evidence of simple shear deformation is clearly observed between 2850 m and 2950 m depth. Stretched fabrics in coarse-grained ice in the lowest 100 m could be due to tensional stresses; this ice is unlikely to be undergoing any significant horizontal deformation at the present time.
A simple method is described for detecting annual stratification of ice cores, and layers of high acidity due to violent volcanic eruptions in the past. The method is based on a relationship between the H 3O + concentration (pH) of melted samples and the electrical current between two brass electrodes moved along the cleaned ice-core surface. Acidity and current profiles are shown through layers deposited soon after historically well-known volcanic eruptions, such as Katmai, AD 1912, Tambora, AD l8l5, Laki, AD 1973, Hekla, AD 1104, and Thera (Santorin) c.l400 B.C. High-acidity layers seem to be the cause for the internal radio- echo layers in polar ice sheets.-from Author
The lower 80 km of the fast-moving Jakobshavns Isbræ, West Greenland, is subject to significant melting during the summer season. The melt water drains into large supraglacial rivers which pour into moulins or feed into beautiful supraglacial lakes, some of which are observed to drain periodically. Except for a few streams that drain directly off the margins of the ice sheet within the drainage basin of this glacier, the fate of this melt water is unknown. However, a localized upwelling of highly turbid water is often observed during the melt season in the fjord adjacent Io the terminal cliff of the glacier, indicating that water from some source does move along the glacier bed.
As part of an investigation on the mechanisms of rapid flow on Jakobshavns Isbræ, measurements of surface velocity at several (∼25) locations along the ice stream at and below the equilibrium line were made in order to investigate the effects of this seasonally varying input of melt water on the speed of the glacier.
No significant seasonal variation in speed was found at any location. This indicates that, unlike many other sub-polar and temperate glaciers, surface melt-water production does not affect the motion of this glacier on a seasonal basis, and, thus, does not cause a significant temporal variation in basal sliding. This finding has important ramifications on the mechanisms of flow for this ice stream.
Computations over 50 000 years into steady state with Greve’s polythermal ice-sheet model and its numerical code are performed for the Greenland ice sheet with today’s climatological input (surface temperature and accumulation function) and three values of the geothermal heat flux: (42, 54.6, 29.4) mW m ⁻² . It is shown that through the thermomechanical coupling the geometry as well as the thermal regime, in particular that close to the bed, respond surprisingly strongly to the basal thermal heat input. The most sensitive variable is the basal temperature field, but the maximum height of the summit also varies by more than ±100m. Furthermore, some intercomparison of the model outputs with the real ice sheet is carried out, showing that the model provides reasonable results for the ice-sheet geometry as well as for the englacial temperatures.
Accumulation studies along the lowermost 100 km of Jakobshavns Isbrae show that the local net balance above the equilibrium line (1210 m elevation in 1986) is significantly less than that measure along the EGIG line about 100 km further north. This indicates the presence of a precipitation low in this region which will affect any global mass-balance assessment for the Jakobshavns Isbrae drainage basin. Comparison of the estimated calving and ablation fluxes shows that calving removes about twice as much mass from this drainage basin as does melting. Basal melting over the entire basin accounts for about 20% of the total ice loss by ablation. -from Authors