Drainage through Subglacial Water Sheets

Subglacial drainage plays an important role in controlling coupling between glacial ice and underlying bed. Here, we study the flow of water in thin, macroporous sheets between ice and bed. Previous work shows that small perturbations in depth of a nearly parallel-sided water film grow unstably because these areas have enhanced viscous dissipation that leads to enhanced melting of an ice roof. We argue that in the presence of bed protrusions bridging a water sheet, downward motion of the ice roof can stabilize this sheet. Stability results when the rate of roof closure increases faster with water depth than the rate of viscous dissipation. We therefore modify existing theory to include protrusions that partially support the overlying glacier. Differences in the pressure on protrusions relative to water pressure drive roof closure. The mechanisms of both regelation and creep normal to the bed close the overlying ice roof and decrease the icebed gap. In order to account for multiple protrusion sizes along the bed (for instance, resulting from an assortment of various-sized sediment grains), we incorporate a method of partitioning overburden pressure among different protrusion size classes and the water sheet. Partitioning is dependent on the amount of ice protrusion contact and, therefore, water depth. This method allows prediction of roof closure rates. We then investigate stable, steady sheet configurations for reasonable parameter choices and find that these steady states can occur for modest water depths at very low effective pressures, as is appropriate for ice streams. Moreover, we find that multiple steady sheet thicknesses exist, raising the possibility of switches between low and high hydraulic conductivity regimes for the subglacial water system

A Numerical Model of Glaciohydraulic Supercooling: Thermodynamics and Sediment Entrainment

Beneath many glaciers and ice sheets, hydrology influences or controls a variety of basal processes. Glaciohydraulic supercooling is a process whereby water freezes englacially or subglacially because its internal temperature is below the bulk freezing temperature. Water supercools when it is at its freezing point and flows from an area of higher pressure (lower ambient temperature) to an area of lower pressure (higher ambient temperature) without equilibrating its internal energy. The process is dependent on the configuration of the water flow path relative to the pressure gradient driving flow. I formulate the governing equations of mass, linear momentum, and internal energy for time-dependent clear water flow based on previous work (Clarke, 2003; Spring & Hutter, 1981, 1982). Because field evidence and steady-state theory point to water distributing laterally across the bed, I modify this theory to account for an aperture that is much wider than deep, which I refer to as a sheet. Ice accretion terms are formulated with porosity because accreting ice has residual porosity. Ice intrusion into such a water sheet is not described in the literature, and I formulate intrusion based on previous work as well as ideas gained from subglacial cavity formation. In addition, I modify the clear water equations to include erosion and deposition of sediment along the glacier bed and incorporation of sediment into the accreted ice. Furthermore, water may leave the ice-bed interface and flow through the glacier pore space because subglacial water pressure is relatively high when supercooling occurs. To this end, I develop an englacial waterflow model that incorporates changes in ice porosity based on creep closure and ice melt or accretion. Simulations reveal behavior that cannot be inferred from simplified models. For example, while total ice accretion is comparable to field estimates, locations of simulated ice accretion along the ice-bed interface conflict with steady state models, which tend to overpredict accretion amounts. Simulations also indicate that much sediment deposition occurs prior to water being supercooled. Sediment deposition tends to smooth subglacial topography rather than enhance it. Additional results and implications of numerical simulations are discussed

Hydraulics of Subglacial Supercooling: Theory and Simulations for Clear Water Flows

Glaciohydraulic supercooling is a mechanism for accreting ice and sediment to the base of glaciers. We extend existing models by reworking the Spring‐Hutter model for subglacial water flow in tubular conduits to allow for distributed water sheets. Our goal is to determine diagnostic features of supercooling relative to controlling variables. Results focus on along‐path water flow under time‐varying conditions, with attention to ice accretion in and along subglacial overdeepenings. We contrast simulations with constant recharge to diurnally‐varying recharge and expose behavior that cannot be inferred from simple models. For example, locations of simulated ice accretion differ from those found for steady state models, even though total ice accretion remains comparable to field estimates. Downstream accretion influences upstream effective pressures that then modify the hydraulic gradient that drives water flow. This modified gradient tends to inhibit additional accretion by increasing velocity and heat production via viscous dissipation. During diurnal cycles, accretion varies considerably: in daytime, viscous dissipation dominates the heat balance and ice melts. In morning and evening, when flow is rising or falling, viscous dissipation is lower and accretion can proceed. Over nighttime, the largest temperature depressions occur in the subglacial system, but water flux is lowest and accretion rates are negligible. We conclude by inferring that overdeepened glaciers with only clear water flows evolve toward stronger supercooling regimes rather than toward a dynamic equilibrium. Stabilizing feedbacks are unlikely to occur through glacier hydrology alone, and other processes, such as erosion, sedimentation, and sliding, must play an important role

Evolution of Subglacial Overdeepenings in Response to Sediment Redistribution and Glaciohydraulic Supercooling

Glaciers erode bedrock rapidly, but evacuation of sediments requires efficient subglacial drainage networks. If glaciers erode more rapidly than evacuation proceeds, a protective subglacial till layer can form to armor the bed. Where glaciers cross overdeepenings, local closed depressions, the bed slope opposes the ice surface and lowers the hydraulic potential gradient that drives water flow. Here, we present results of a dynamic, distributed model of coupled basal water flow and sediment transport to show how overdeepenings evolve over the course of a melt season. We use steady-state calculations as well as numerical simulations to understand how alluvial bed erosion alters overdeepenings. Numerical results from a modified form of the Spring-Hutter equations show behaviors that cannot be inferred from either local or steady-state calculations. In general, opposition of surface and bed slopes lessens sediment transport regardless of ice accretion from glaciohydraulic supercooling. Drainage efficiency strongly affects erosion and deposition rates. Results show characteristic behaviors of flow through overdeepenings such as overpressured water systems and accretion rates compatible with field measurements. Simulations that start with overdeepened glacier configurations progress out of a freezing regime where glaciohydraulic supercooling occurs. This progression indicates that glacier hydrology is more strongly affected by erosion and deposition than by freezing from glaciohydraulic supercooling. We discuss how this outcome affects glacier erosion and sediment transport under modern and past ice sheets

Similarity of organized patterns in driving and basal stresses of Antarctic and Greenland ice sheets beneath extensive areas of basal sliding

The rate of ice transport from the interior of ice sheets to their margins, and hence the rate with which it contributes to sea level, is determined by the balance of driving stress, basal resistance, and ice internal deformation. Using recent high-resolution observations of the Antarctic and Greenland ice sheets, we compute driving stress and ice deformation velocities, inferring basal traction by inverse techniques. The results reveal broad-scale organization in 5–20 km band-like patterns in both the driving and basal shear stresses located in zones with substantial basal sliding. Both ice sheets experience basal sliding over areas substantially larger than previously recognized. The likely cause of the spatial patterns is the development of a band-like structure in the basal shear stress distribution that is the results of pattern-forming instabilities related to subglacial water. The similarity of patterns on the Greenland and Antarctic ice sheets suggests that the flow of ice sheets is controlled by the same fundamental processes operating at their base, which control ice sheet sliding and are highly variable on relatively short spatial and temporal scales, with poor predictability. This has far-reaching implications for understanding of the current and projection of the future ice sheets' evolution

Projected changes in the physical climate of the Gulf Coast and Caribbean

As the global climate warms due to increasing greenhouse gases, the regional climate of the Gulf of Mexico and Caribbean region will also change. This study presents the latest estimates of the expected changes in temperature, precipitation, tropical cyclone activity, and sea level. Changes in temperature and precipitation are derived from climate model simulations produced for the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR4), by comparing projections for the mid- and late-21st century to the late 20th century and assuming a “middle-of-the-road” scenario for future greenhouse gas emissions. Regional simulations from the North America Regional Climate Change Program (NARCCAP) are used to corroborate the IPCC AR4 rainfall projections over the US portion of the domain. Changes in tropical cyclones and sea level are more uncertain, and our understanding of these variables has changed more since IPCC AR4 than in the case of temperature and precipitation. For these quantities, the current state of knowledge is described based on the recent peer-reviewed literature

Age stratigraphy in the East Antarctic Ice Sheet inferred from radio-echo sounding horizons

The East Antarctic Ice Sheet contains a wealth of information that can be extracted from its internal architecture such as distribution of age, past flow features, and surface and basal properties. Airborne radar surveys can sample this stratigraphic archive across broad areas. Here, we identify and trace key horizons across several radar surveys to obtain the stratigraphic information. We transfer the age–depth scales from ice cores to intersecting radar data. We then propagate these age scales across the ice sheet using the high fidelity continuity of the radar horizons. In Dronning Maud Land, including Dome Fuji, we mapped isochrones with ages of 38 and 74 ka. In the central region of East Antarctica around Dome Concordia, Vostok and Dome Argus, we use isochrone ages of 38, 48, 90 and 161 ka. Taking together both regions, we provide isochrone depths traced along a combined profile length of more than 40 000 km and discuss uncertainties of the obtained stratigraphy, as well as factors important to consider for further expansion. This data set is the most extensive distribution of internal horizons in East Antarctica to date. The isochrone depths presented in this study are available on PANGAEA (https://doi.org/10.1594/PANGAEA.895528; Winter et al., 2018)

Overturned folds in ice sheets: Insights from a kinematic model of traveling sticky patches and comparisons with observations

Overturned folds are observed in regions of the Greenland ice sheet where driving stress is highly variable. Three mechanisms have been proposed to explain these folds: freezing subglacial water, traveling basal slippery patches, and englacial rheological contrasts. Here we explore how traveling basal sticky patches can produce overturned folds. Transitions from low to high stress cause a tradeoff in ice flow between basal slip and internal deformation that deflects ice stratigraphy vertically. If these transitions move, the slip-deformation tradeoff can produce large folds. Those folds record the integrated effects of time-varying basal slip. To understand how dynamic changes in basal slip influence ice sheet stratigraphy, we develop a kinematic model of ice flow in a moving reference frame that follows a single traveling sticky patch. The ice flow field forms a vortex when viewed in the moving reference frame, and this vortex traps ice above the traveling patch and produces overturned folds. Sticky patches that travel downstream faster produce larger overturned folds. We use the model as an interpretive tool to infer properties of basal slip from three example folds. Our model suggests that the sticky patches underneath these folds propagated downstream at rates between one half and the full ice velocity. The regional flow regime for the smaller two folds requires substantial internal deformation whereas the regime for the largest fold requires substantially more basal slip. The distribution and character of stratigraphic folds reflect the evolution and propagation of individual sticky patches and their effects on ice sheet flow

Modeling oscillations in connected glacial lakes

Mountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies

Accumulation rates from 38 ka and 160 ka radio-echo sounding horizons in East Antarctica

The internal layering architecture of ice sheets, as detected with radio-echo sounding (RES), contains clues to past ice-flow dynamics and mass balance and supplies flow models with starting and boundary conditions. In comparison to the Greenland Ice Sheet, the coverage of the East Antarctic Ice Sheet with information on internal ice structure is still sparse. This hampers the constraining or initialization of ice-flow models with geometry and surface mass balance data inadequate resolution.We traced two RES horizons, 38 ka and 160 ka, over great parts and in the most remote areas of the East Antarctic Ice Sheet.We dated the horizons at the EPICA Dome C Ice Core and followed them along RES lines of the Alfred Wegener Institute to Vostok and Dome A. There, they could be connected to the RES grid, covering the Gamburtsev mountains, that was collected as part ofthe AGAP (Antarctica’s Gamburtsev Province) project, and continued to South Pole. From this widespread age-depth distribution we reconstruct mean accumulation rates and analyze spatial variations in surface mass balance, as well as differences between the two time periods