Volume 46, Issue 14 p. 8184-8193
Research Letter
Free Access

Thermal Weakening, Convergent Flow, and Vertical Heat Transport in the Northeast Greenland Ice Stream Shear Margins

N. Holschuh

Corresponding Author

N. Holschuh

Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA

Correspondence to: N. Holschuh,

[email protected]

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D. A. Lilien

D. A. Lilien

Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA

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K. Christianson

K. Christianson

Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA

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First published: 28 June 2019
Citations: 19

Abstract

Ice streams are bounded by abrupt transitions in speed called shear margins. Some shear margins are fixed by subglacial topography, but others are thought to be self-organizing, evolving by thermal feedback to ice viscosity and basal drag which govern the stress balance of ice sheets. Resistive stresses (and properties governing shear-margin formation) manifest nonuniquely at the surface, motivating the use of subsurface observations to constrain ice sheet models. In this study, we use ice-penetrating radar data to evaluate three 3-D thermomechanical models of the Northeast Greenland Ice Stream, focusing on model reproductions of ice temperature (a primary control on viscosity) and subsurface velocity. Data/model agreement indicates elevated temperatures in the Northeast Greenland Ice Stream margins, with depth-averaged temperatures between 2 °C and 6 °C warmer in the southeast margin compared to ice in streaming flow, driven by vertical heat transport rather than shear heating. This work highlights complexity in ice divergence across stagnant/streaming transitions.

Key Points

  • Thermal softening of ice is present in the Northeast Greenland Ice Stream (NEGIS) shear margins, despite low strain rates
  • Vertical advection of heat dominates the shear-margin temperature structure here, validated by radar reflectivity and isochron geometry
  • Radar data can be used to constrain ice temperature and subsurface velocity to evaluate ice sheet model spin-up and inversions

Plain Language Summary

Ice sheet models used to project future sea level rise are calibrated using modern observations of ice flow at the ice sheet surface. However, the subsurface ice and rock properties that ultimately control the patterns of ice flow cannot be uniquely determined using observations of the surface alone. In this study, we use the structural and electromagnetic characteristics of the Greenland Ice Sheet (determined from ice-penetrating radar data) to evaluate the subsurface performance of three different ice-flow models of the Northeast Greenland Ice Stream. We show that fast flow in Northeast Greenland is, in part, controlled by softer, warmer ice, and that correctly modeling heat transport at the boundaries of ice streams is critical for realistic projections of their future behavior. Ultimately, we provide insight into a sensitive region of Greenland together with a new approach to geophysical data use in model evaluation, with the goal of reducing the range of plausible models projecting the future of the Greenland and Antarctic Ice Sheets.

1 Introduction

Ice-dynamic models require a large number of subsurface properties as inputs, many of which are difficult to observe directly. The material properties that control the large-scale behavior of glacier systems, ice viscosity and basal friction, are typically inferred from observations of ice thickness and ice velocity made at the surface (Joughin et al., 2004; MacAyeal, 1992; Morlighem et al., 2010). Using surface observations alone, the inverse problem for subsurface properties is underconstrained (Arthern & Gudmundsson, 2010). A range of reasonable property values can reproduce the modern ice sheet surface behavior, but these drive different behaviors in the subsurface, and can provide divergent projections for the ice sheet response to climate forcing (Goelzer et al., 2018).

In this study, we pursue radar constraints on ice temperature and subsurface velocity, allowing the joint evaluation of surface and subsurface behavior when characterizing ice sheet model performance. Developing these methods is especially important for areas where englacial stresses, ice temperature, and ice velocity vary over short spatial scales. Thus, we focus here on the shear margins of the Northeast Greenland Ice Stream (NEGIS), where reproducing anomalous shear localization likely requires capturing complex subsurface dynamics.

1.1 Inferring Temperature and Velocity From Radar

Qualitative interpretation of radar imagery across shear margins is common in the literature. Reflectivity analysis has been focused on the bed, interpreting contrasts in reflection strength as wet to dry transitions across shear margins in Antarctica (Bentley et al., 1998; MacGregor et al., 2013; Raymond et al., 2006) and Greenland (Christianson et al., 2014; Vallelonga et al., 2014). Disruptions in internal layering have been used to characterize shear-margin evolution, primarily as evidence of past margin position (Catania et al., 2006; Keisling et al., 2014). But, as new methods emerge in radioglaciology, radar data have the potential to provide more quantitative insight into shear-margin temperature and heat transport.

The electrical conductivity of ice varies with ice temperature, resulting in power lost to conduction as radio waves propagate through warm or impure ice (MacGregor et al., 2007). This relationship has been leveraged in two ways. For those interested in validating thermomechanical models, substantial work has been done to develop methods capable of empirically estimating wave attenuation (and thereby, temperature) from radar data alone (Matsuoka, Pattyn, et al., 2012; Schroeder et al., 2016). However, because radio waves measured at the surface are a product of reflection in the subsurface, variations in power driven by attenuation and variations in power driven by the reflection process (typically attributed to interface properties such as dielectric permittivity and roughness) are challenging to disentangle over short spatial scales, leaving large uncertainties in direct estimates of temperature. Alternatively, radioglaciologists interested in reflector properties have used ice sheet models to directly estimate attenuation effects (Matsuoka, MacGregor, & Pattyn, 2012) and remove attenuation signals from radar data for more robust reflector interpretation (Chu et al., 2018). This assumes high confidence in the temperature and subsurface velocity fields generated by their chosen thermomechanical ice sheet model.

In this study, we take a different approach. Recognizing uncertainties in both the physical controls on observed radar signals and the subsurface performance of ice sheet models, we seek out local correlation between reflection strength and modeled temperature across a range of model realizations of NEGIS. When patterns in the models and data agree, we can (a) build confidence in the physical interpretation of our radar data and (b) select better performing ice-dynamic models, which can then be used to understand processes governing ice temperature.

In addition to their radiometric information, radar data have been identified as a tool for characterizing the subsurface velocity structure of ice sheets (using englacial layer shapes; e.g., Hindmarsh et al., 2006; Holschuh et al., 2017; Leysinger Vieli et al., 2007). The temperature distribution in shear margins, controlled by viscous heat production and transport, is ultimately a product of the subsurface velocity field. Our goal is to use the radiometric and englacial structural information in radar data together, to fully characterize the performance of NEGIS models, and isolate both the formation mechanism and magnitude of thermal anomalies in the NEGIS margins.

1.2 Shear-Margin Mechanics in Ice-Flow Models

Much of our understanding of thermally controlled ice stream shear margins comes from a mix of 1-D analysis (Meyer & Minchew, 2018; Perol & Rice, 2015) and 2-D, flow-orthogonal thermomechanical modeling. Diagnostic modeling efforts first highlighted the role of frictional heat production in margin weakening (Jacobson & Raymond, 1998), predicting enhanced shear localization relative to isothermal ice when ice softening is included in model physics. Model sophistication has increased dramatically since then, with modern models capable of simulating margin evolution, including the dynamic effects of melt-water production and subglacial hydrology (Elsworth & Suckale, 2016; Meyer et al., 2018; Perol et al., 2015; Suckale et al., 2014). However, to maintain numerical efficiency at very high resolution, 2-D models use simplified ice dynamics, assuming that the along-stream velocity evolves according to a reduced form of the momentum equations (excluding longitudinal stresses). Boundary-layer treatments of shear margins address this by solving the 3-D Stokes equations, reproducing the heat production and advective cooling underpinning margin migration (Haseloff et al., 2015; Schoof, 2012); however, these models omit the temperature dependence of ice viscosity, and rely on an idealized geometry (assuming no vertical velocities in basal ice resting on a flat bed) to simplify the calculation.

Comparing results of simplified models to realistic ice stream systems requires evaluating the impact of their simplifying assumptions. This is especially important for margins with ice that flows across the stagnant/streaming boundary, as previous studies show that reproducing the depth-velocity structure across abrupt boundary-condition transitions requires the inclusion of longitudinal stresses (Hindmarsh et al., 2006). In this study, we use 3-D, full-Stokes diagnostic modeling (Gagliardini et al., 2013) to simulate the complex heat generation and transport across the NEGIS ice stream margins.

We focus on the incipient shear margins of NEGIS (Figure 1), where shear localization manifests amid diffuse flow acceleration. As with other shear margins, the position of the incipient margin may be imposed by the underlying geology (Anandakrishnan et al., 1998; MacGregor et al., 2013). But it is also possible that these margins are self-organizing, forming by a thermal perturbation reinforced by temperature feedback within the ice (Jacobson & Raymond, 1998; Suckale et al., 2014), fabric development (Minchew et al., 2018), and/or subglacial hydrologic organization (Elsworth & Suckale, 2016; Kyrke-Smith et al., 2015; Perol et al., 2015; Perol & Rice, 2015). By diagnosing the thermal structure in the incipient margin, we can evaluate whether geologic controls are required to explain the velocity pattern, or if the margin is collocated with a thermal anomaly that will influence its future evolution.

Details are in the caption following the image
Regional context for the Northeast Greenland Ice Stream (a), including (b and c) the ice surface velocity, (d) continental gridded bed topography (Bamber et al., 2013), and (e) bed topography from inverse distance-weighted interpolation of radar derived ice thicknesses presented in this study. The full catchment and high-resolution model domain are provided as dotted lines in (a) and (b) and (d), respectively, with radar profile locations plotted as black lines in (b). Ice-flow streamlines are provided in (c), highlighting cross-marginal flow in the SE margin of NEGIS (Map projection—EPSG:3413).

2 Methods

2.1 Modeling the Northeast Greenland Ice Stream

We use a 3-D, full-Stokes, thermomechanical model, implemented in Elmer/Ice (Gagliardini et al., 2013; Zwinger et al., 2007) to reproduce the dynamics of the NEGIS margins. This is done in two stages. The first stage, a full-catchment model (nine vertical layers, 500–5,000-m mesh refined around the area of interest), was used to generate temperature and velocity boundary conditions for the second stage, a higher-resolution (~100-m mesh) model, designed to span the 2012 radar survey across the incipient NEGIS margins. The model experiment setup, boundary conditions, and implementation are described in the supporting information.

In modeling this system, we found that the observed surface velocity, accumulation rate, and ice thickness are difficult to rectify with one another assuming steady state mass balance. This mismatch likely arises from a combination of data limitations (e.g., spatially incomplete ice thickness measurements or poorly known accumulation rates) and missing physics in the model (e.g., ice fabric evolution), and is a common challenge in ice sheet modeling. Models typically address this mismatch using one of three approaches: (1) the ice surface is allowed to relax in accordance with ice velocities (as in Larour et al., 2014; Brondex et al., 2019), resulting in a model with matching surface velocities but erroneous ice thickness; (2) the horizontal velocities are calculated from the observed ice geometry and accumulation rate to bring the system into mass balance, resulting in a disagreement between observed and modeled horizontal flow speeds (Dansgaard & Johnsen, 1969); or (3) the ice thickness and horizontal velocities are imposed, and the vertical velocities are assumed to provide balance, allowing disagreement with accumulation rates at the surface (as in Pattyn, 2010).

Without an a priori justification for one approach over the others, we produced three realizations of our model domain following these published procedures. This resulted in two NEGIS reproductions in mass balance equilibrium with observed accumulation rates (following 1 and 2 above, which we refer to as “equilibrium models”) and one model with surface velocities out of balance with observed accumulation rates but matching in ice thickness and horizontal speed (following 3, which we refer to as a “disequilibrium model”). We differentiate these models in text and figures according to their agreement with ice thickness (H), horizontal velocities at the surface (u,v, for polar-stereographic coordinate axes x and y), and vertical velocities at the surface (w, with positive values upward). Ultimately, our goal is to use radar data to evaluate the performance of these three models and use observations together with the best fit model to better understand the dynamics of the NEGIS shear margins.

2.2 Radar Processing and Interpretation

The radar data used in this study were collected in summer 2012 and were first published as part of Christianson et al. (2014), who detail the initial processing (including geolocation, band-pass filtering, correction for antenna spacing, travel time correction for firn density, interpolation to standard trace spacing, along-track migration, and geometric spreading correction to return amplitude). For this study, the effects of geometric spreading and refractive focusing through a spatially variable firn column (Riverman et al., 2019). were removed following the methods of Holschuh et al. (2016). Remaining variations in the bed reflection power are attributed to spatial variability in ice conductivity or substrate permittivity. Physical interpretation of measured reflection power requires disambiguating the effects of these two properties.

2.3 Conductivity Modeling

Converting modeled ice temperature to radar-wave attenuation requires conductivity modeling. Using average impurity concentrations during the Holocene and Glacial period as observed in the GRIP ice core (which has the most complete, local, soluble impurity record; De Angelis et al., 1997), and the reflector known to separate these two periods in the radar data (Karlsson et al., 2013), we define a depth-impurity profile for each radar trace. This assumes constant impurity concentration within a given layer package, requiring that layer thickness differences primarily reflect differential divergence and not a spatially variable snow accumulation rate upstream (which could drive impurity dilution). Using the modeled temperature profiles, we calculate the associated conductivity and depth-averaged attenuation rates using parameters found in the literature (Gudmandsen, 1971; MacGregor et al., 2007; MacGregor et al., 2015; Wolff et al., 1997), and present a modeled-temperature/data intercomparison for the best fit conductivity model (see Figures S2 and S3 in the supporting information for the conductivity model selection process).

2.4 Model/Data Correlation

To evaluate consistency between model temperature and radar reflectivity, we compute local fits between modeled attenuation (AT) and observed reflection strength (Robs) using linear regressions assuming two free fit parameters (C0,C1):
urn:x-wiley:00948276:media:grl59240:grl59240-math-0001(1)

Without an absolute calibration for reflection strength, Robs is a relative measure, indicating return power (in dB) relative to the maximum observed within the radar survey. Estimates of C1 characterize the agreement in magnitude between modeled temperature gradients and observed power gradients. Regression R2 values indicate agreement in the spatial pattern of modeled temperature and observed reflection power, regardless of the agreement in magnitude. If all the variance in return power is explained by the modeled temperature field and the magnitude of observed signal attenuation is equal to the modeled value, both the C1 and the R2 values of local regressions would equal 1. We compute regressions over 3-km windows, which capture the half-width of the shear margins (the expected scale for spatial variability in temperature) while minimizing errors due to longer-wavelength variability in bed reflection power.

Overall model performance for each realization of NEGIS is presented as an additional R2 statistic, computed using the aggregated residual sum of squares from the local fits.

3 Results

3.1 Depth-Averaged Temperature Fields

The depth-averaged temperature fields for our three model realizations are presented in Figure 2. Figure 2a presents the results for a model of NEGIS with a relaxed surface, in which ice thickness is 30 m thicker than observed in the shear margins. Figure 2b presents a model with horizontal flow speeds reduced to bring the system into mass balance, with streaming flow speeds 10–15 m/a slower than observed. Figure 2c presents the model that matches the observed geometry and horizontal flow speeds, but has a mean error of ~2 m/a for vertical velocities at the surface (see Figure S4 in the supporting information).

Details are in the caption following the image
Depth-averaged temperature anomalies (relative to −14 °C) for models using three different boundary forcings: (a) equilibirum, relaxed surface conditions; (b) equilibrium, forced geometry but reduced velocity conditions; and (c) surface elevation and horizontal velocity matching, but surface-flux imbalance conditions. Modeled surface velocity contours (5 m/a) are presented to highlight the position of the ice stream shear margins.

Each of our three model realizations produced a different depth-averaged temperature field, with the most dramatic differences between our equilibrium and disequilibrium cases (Figures 2a and 2b versus 2c). The model with a relaxed surface resulted in the highest average temperature over the full domain (Figure 2a). This model showed slightly elevated temperatures in the SE margin (~2–3 °C relative to streaming flow), with no clear temperature anomaly in the NW margin. The equilibrium model with lower streaming flow speeds (Figure 2b) has a clear thermal signature in both margins (~2 °C), but generally colder ice within the ice stream. In contrast, the disequilibrium model has much stronger thermal anomalies in the margins (SE, ~5–6 °C and NW, ~4–5 °C, relative to ice in streaming flow). While the equilibrium models predict stronger thermal anomalies on the upstream end of the domain, the disequilibrium model has no along-flow trend.

3.2 Radar Isochrons, Subsurface Velocity, and Heat Advection

Temperature differences between models can arise in two ways: variability in heat production by lateral strain and variability in heat transport. Because the difference in lateral shear strain rates between models is small (~0.001 a-1), the temperature differences observed in Figure 2 must come from differential heat transport within the domain. Radar imaged isochrons provide an observational constraint on subsurface heat advection, as their relative heights in the ice column reflect differential subsurface velocities experienced by the ice. Thus, we use the isochron shapes as an independent constraint on model performance, a tool capable of validating the 3-D velocity field that controls the modeled temperatures.

There is always ambiguity when interpreting layer shapes within an ice column. Assuming steady state, structures form in place and reflect the local velocity structure along-flow (Holschuh et al., 2017); but, with boundary condition changes through time, it is possible to form a fold elsewhere and advect to its observed location in the modern ice sheet. Because the observed folds are collocated with the modern shear margins along the full length of NEGIS, we assume they formed locally.

There are several characteristics of the imaged isochrons (when combined with the surface velocity field) that can inform our understanding of the system:
  1. Distinct fold structures were imaged in the shear margins in all flow-orthogonal lines (Figure 3a).
  2. Isochrons are at their shallowest (highest) point in the ice column within the shear margins.
  3. Layer slopes are steepest in the deepest imaged layers, with flatter layers nearer to the surface.
  4. Ice passes through the SE margin (from where isochrons are deep, to where they are shallow, back to deep) within our model domain. Ice flow is subparallel to the NW margin fold (see Figures 1c and S5 in the supporting information).
Details are in the caption following the image
(a) Characteristic radargram collected at the downstream end of the model domain, with the (b) associated bed reflection power. (c) Layers imaged in the shear margins show increasing fold amplitudes with depth (with depth range measured for blue and red plotted isochrons in (a)), down to where they can no longer be imaged (dashed lines). Two end-member layer patterns for basal ice are represented schematically by (c, i and ii). Near the bed, layers must either be bed conformal, with increasing fold amplitudes up column due to layer thickening by flow convergence (i), or nonconformal, forming a fold in the basal ice with thickness equal to the amount of basal freeze-on (ii). (d–f) For the same transect, synthetic isochrons and modeled temperature are presented.

These conditions constrain the fold generation mechanism in several ways. Ice passing through the SE shear margin must be driven upward within our model domain by substantial vertical velocities at depth. These velocities could be imparted by direct forcing at the bed in the form of basal freeze-on (represented by the fold amplitude pattern in Figure 3c (ii)) or could be the result of convergence and layer thickening in the deepest parts of the ice, increasing velocities and fold amplitudes up column to the point where layers are imaged (represented by the fold amplitude pattern in Figure 3c (i)). Decreasing fold amplitudes higher in the ice column indicate divergence and layer thinning of shallow ice as it flows into the margin, reducing the magnitude of vertical velocities imposed by the deep ice. As ice passes out of the SE shear margin into streaming flow the layers drop; deep layers must thin by divergence (as observed in Riverman et al., 2019), or there must be compensating basal melt at depth within streaming flow, driving negative vertical velocities.

Because folds in the NW margin are morphologically similar to folds in the SE, we believe that they form by similar processes; but, because the flow vectors in the NW are nearly parallel to the fold axis, we lack direct evidence that folds in the NW margin form within our model domain. They could form in place by cross-flow convergence, or form upstream and propagate into our domain where they are observed.

Using the 3-D velocity field for each of our three models, we synthesize layers assuming that they enter the domain at constant depth. The resulting synthetic isochrons highlight perturbations to layer depth that occur within the model domain, where local structures such as the SE shear-margin folds must have formed. We produce these for all three model realizations, extract the layer geometries at the radar observation sites, and plot the results against the modeled depth-temperature profiles (Figures 3d–3f).

Vertical advection of ice dominates the modeled thermal structure in all three cases, with high temperatures shallower in the ice column where upwarping layers are predicted. The equilibrium models resulted in flat or slightly downwarped layers in the margins, different from both the disequilibrium model and the observations, which have fold amplitudes of ~500 m in the central portion of the ice column. These form in the model by deep along- and across-flow convergence without requiring basal freeze-on. Together with the relatively flat bed across the margins of NEGIS (when bed-elevation gradients are required for the formation of basal freeze-on plumes; Dow et al., 2018; Leysinger Vieli et al., 2018), the fact that basal folds arise naturally in the model by convergence leads us to favor the mechanism described in Figure 3c (i).

There is unresolved disagreement between the modeled and observed isochrons in the upper portion of the ice column, where fold amplitudes are damped in the data. This could be explained by compensating divergence in the upper half of the ice column not captured in our model (but seen in models of flow over bed friction anomalies in Holschuh et al. (2017) and Whillans and Johnsen (1983)).

3.3 Radar Reflection Strength and Modeled Temperature

Within the shear margins, weaker bed returns are collocated with upwarped englacial layers (Figures 3b and 4a). In general, reflection power/temperature agreement is better for the SE margin across all models, and better for the disequilibrium model than the equilibrium models. Local fits between expected and observed power losses (Figure 4b) show the equilibrium models systematically underestimating power losses in the margins (C1 > 1), and in many cases showing increases in temperature where there are increases in observed reflection power (C1 < 0), with little ability to explain trends in reflection power (R2 < 0.5). The disequilibrium model typically overestimates the magnitude of the temperature anomaly (fit coefficients between 0 and 1), but has substantial ability to explain the spatial pattern of power losses. This is highlighted in the overall model fits (Figure 4c) with better performance by the disequilibrium model across all highlighted regions. Surprisingly, the western edge of the NW margin shows a negative correlation between expected and observed power loss for all models (Figure 4b (i)), indicating that either (a) all temperature models have warm ice where it should be cold, or (b, more likely) that the modeled spatial pattern of warm ice, which matches the spatial pattern of bright reflection, is an indicator of basal water outside the NW margin.

Details are in the caption following the image
(a) Plot of the bed reflection power. The correlation between modeled and observed bed power (colored by model boundary forcing) is computed for each radar line as they cross in-to (i, iv) and out-of (ii, iii) the shear margins. (b) The coefficient relating modeled and observed power loss for each local fit is presented (with opacity representing the R2 significance of each local regression). (c) The overall R2 for subdomains i–iv, indicative of the total agreement between model and observation, is presented, highlighting the superior performance of our disequilibrium model across all four regions of interest.

4 Discussion

4.1 Evidence for Elevated Temperature at NEGIS

NEGIS is defined by its 400-km-long shear margins, with no indication of topographic control in the upstream reaches (Figures 1d and 1e). Shear localization (as opposed to diffuse acceleration as seen in most ice stream catchments) implies that there is an abrupt change in strength across the stagnant-streaming transition, but it is otherwise unknown if this is a change in rock properties, effective stress at the bed, ice viscosity, or a combination of all three. The spatial pattern of bed reflection power matches the disequilibrium modeled temperature field well in the SE margin, suggesting that significant vertical advection (and warm ice) is present at NEGIS and weakens the margins.

4.2 The Role of Advection in the Thermal Balance of Shear Margins

Heat retention in shear margins is ultimately an advection-diffusion problem, illustrated conceptually by the heat equation:
urn:x-wiley:00948276:media:grl59240:grl59240-math-0002(2)

Comparing the product of modeled temperature gradients urn:x-wiley:00948276:media:grl59240:grl59240-math-0003 and their corresponding velocities (u,v,w, respectively) with the total rate of strain heating (defined as the product of the Cauchy stress tensor σij and strain rate tensor ϵij), it is possible to determine the dominant processes acting to modify temperature within our model domain. We do this using published values for the presented physical constants (density ρ: 917 kg/m3, specific heat capacity cp: 2,050 J kg−1 K−1, and thermal conductivity K: 2.1 W m−1 K−1). Given maximum lateral shear strain rates in our domain of 0.005 a-1, and modeled vertical and horizontal temperature gradients of ~0.01 and ~0.001 K/m, respectively, the advective terms of the thermal balance have comparable influence to shear heating when the vertical velocity is ~0.02 m/a or cross-marginal velocities exceed ~0.2 m/a.

Cross-marginal velocities rise well above this threshold at NEGIS, with values of ~4 m/a for the western margin and ~10 m/a in the eastern margin (see Figure S6 in the supporting information). Thus, we would expect advective cooling to dominate over shear heating. In addition, simple treatments of vertical velocity (assuming that it is negative and less than or equal to the accumulation rate of ~0.1 m/a at our site) imply that accumulation-driven cooling would overcome any strain warming.

However, subglacial topography and flow convergence drive vertical velocities deep in the ice column across all three models, resulting in values of w well above the significance threshold. Maximum vertical velocities in our equilibrium model runs fall between 0.25 and 0.5 m/a, and exceed 1 m/a in our disequilibrium run, which is consistent with the steep layer slopes in the NEGIS margins (Holschuh et al., 2017). With high vertical temperature gradients, even small differences in vertical velocity become important. Ultimately, velocities deep in the ice column dominate the thermal structure and attenuation signal at NEGIS (as variations in the thickness of high-temperature ice have a disproportionate effect on depth-averaged conductivity). Isochron geometries (which follow isotherms in our model results; Figures 3d–3f) may provide a direct observational method for estimating relative temperature across slow flowing regions, as relative layer depths reflect differences in net-vertical advection.

5 Conclusions

We show that surface observations at NEGIS can be equally well reproduced with models that differ significantly in their englacial velocity structure, temperature field, and ice viscosity. Structural and intensity information from radar data act as independent checks on subsurface model performance, and through their application here, have highlighted a previously undescribed role for vertical advection in shear margins that dominates over heat production and shear-margin cooling by cross-marginal flow. This mechanism may drive thermal margin development at other incipient shear margins around Antarctica and Greenland, as vertical advection creates the initial thermal weakness that is reinforced by subsequent shear localization.

We present here the first radar-validated, 3-D thermomechanical model of an ice stream shear margin and show that fast flow at NEGIS is facilitated in part by thermally softened ice. Models that fail to capture the deep vertical velocity structure will underestimate thermal softening in the ice, compensate by underestimating the strength of the ice bed, and ultimately fail to reproduce the system dynamics.

Acknowledgments

N. Holschuh developed the study and performed the radar analysis and radar-model intercomparison. D. Lilien implemented the model. K. Christianson collected and processed the radar data and contributed to the interpretation. All authors participated in writing. We would also like to thank K. Riverman, A. Muto, and L. Peters for collecting the data at NEGIS. Radar data and model output are accessible through the University of Washington's Research Works Archive (http://hdl.handle.net/1773/43810). NASA grant NNX16AM01G and NSF grant 1643353 supported N. Holschuh and K. Christianson. NASA grant NNX15AN53H supported D. Lilien.