Subglacial Hydrology Model Research Articles

Characterizing Subglacial Hydrology Within the Amery Ice Shelf Catchment Using Numerical Modeling and Satellite Altimetry

AbstractMeltwater forms at the base of the Antarctic Ice Sheet due to geothermal heat flux (GHF) and basal frictional dissipation. Despite the relatively small volume, this water has a profound effect on ice‐sheet dynamics. However, subglacial melting and hydrology in Antarctica remain highly uncertain, limiting our ability to assess their impact on ice‐sheet dynamics. Here we examine subglacial hydrology within the Amery Ice Shelf catchment, East Antarctica, using the subglacial hydrology model GlaDS. We calculate subglacial melt rates using a higher‐order ice‐flow model and two GHF estimates. We find a catchment‐wide melt rate of 7.03 Gt year−1 (standard deviation = 1.94 Gt year−1), which is ≥50% greater than previous estimates. The contribution from basal dissipation is approximately 40% of that from GHF. However, beneath fast‐flowing ice streams, basal dissipation is an order of magnitude larger than GHF, leading to a significant increase in channelized subglacial flux upstream of the grounding line. We validate GlaDS using high‐resolution interferometric‐swath radar altimetry, with which we detect active subglacial lakes and fine‐scale ice‐shelf basal melting. We find a network of subglacial channels that connects areas of deep subglacial water coincident with active subglacial lakes, and channelized discharge at the grounding line coinciding with enhanced ice‐shelf basal melting. The concentrated discharge of meltwater provides 36% of the freshwater released into the ice‐shelf cavity, in addition to ice‐shelf basal melting. This suggests that ice‐shelf basal melting is strongly influenced by subglacial hydrology and could be affected by future changes in subglacial discharge, such as lake drainage or channel rerouting.

Accelerating Subglacial Hydrology for Ice Sheet Models With Deep Learning Methods

AbstractSubglacial drainage networks regulate the response of ice sheet flow to surface meltwater input to the subglacial environment. Simulating subglacial hydrology evolution is critical to projecting ice sheet sensitivity to climate, and contribution to sea‐level change. However, current numerical subglacial hydrology models are computationally expensive, and, consequently, evolving subglacial hydrology is neglected in large‐scale ice sheet simulations. We present a deep learning emulator of a state‐of‐the‐art subglacial hydrology model, trained at multiple Greenland glaciers. Our emulator performs strongly in both temporal (R2 > 0.99) and spatial (R2 > 0.95) generalization, offers high computational savings, and can be used to force numerical ice sheet models. This will enable century‐ and large‐scale ice sheet model simulations, including interactions between ice flow and increased meltwater input to the subglacial environment. Generally, our work demonstrates that machine learning can further improve ice sheet models, reduce computational bottlenecks, and exploit information from high‐fidelity models and novel observational platforms.

Basal conditions of Denman Glacier from glacier hydrology and ice dynamics modeling

Abstract. Basal sliding in Antarctic glaciers is often modeled using a friction law that relates basal shear stresses to the effective pressure. As few ice sheet models are dynamically coupled to subglacial hydrology models, variability in subglacial hydrology associated with the effective pressure is often implicitly captured in the basal friction coefficient – an unknown parameter in the basal friction law. We investigate the impact of using effective pressures calculated from the Glacier Drainage System (GlaDS) model on basal friction coefficients calculated using inverse methods in the Ice-sheet and Sea-level System Model (ISSM) at Denman Glacier, East Antarctica, for the Schoof and Budd friction laws. For the Schoof friction law, a positive correlation emerges between the GlaDS effective pressure and basal friction coefficient in regions of fast ice flow. Using GlaDS effective pressures generally leads to smoother basal friction coefficients and basal shear stresses, and larger differences between the simulated and observed ice surface velocities compared with using an effective pressure equal to the ice overburden pressure plus the gravitational potential energy of the water. Compared with the Budd friction law, the Schoof friction law offers improved capabilities in capturing the spatial variations associated with known physics of the subglacial hydrology. Our results indicate that ice sheet model representation of basal sliding is more realistic when using direct outputs from a subglacial hydrology model, demonstrating the importance of coupling between ice sheet and subglacial hydrological systems. However, using our outputs we have also developed an empirical parameterization of effective pressure that improves the application of the Schoof friction law without requiring explicit hydrological modeling.

Examining the effect of ice dynamic changes on subglacial hydrology through modelling of a synthetic Antarctic glacier

Abstract Hydrologic pathways beneath ice sheets and glaciers play an important role in regulating ice flow. Antarctica has experienced, and will continue to experience, changes in ice dynamics and geometry, but the associated changes in subglacial hydrology have received less attention. Here, we use the GlaDS subglacial hydrology model to examine drainage evolution beneath an idealised Antarctic glacier in response to steepening ice surface slopes, accelerating ice velocities and subglacial lake drainages. Ice surface slope changes exerted a dominant influence, redirecting basal water to different outlet locations and substantially increasing channelised discharge crossing the grounding line. Faster ice velocities had comparatively negligible effects. Subglacial lake drainage results indicated that lake refilling times play a key role in drainage system evolution, with lake flux more readily accommodated following shorter refilling times. Our findings are significant for vulnerable Antarctic regions currently experiencing dynamic thinning since subglacial water re-routing could destabilise ice shelves through enhanced sub-shelf melting, potentially hastening irreversible retreat. These changes could also affect subglacial lake activity. We, therefore, emphasise that including a nuanced and complex representation of subglacial hydrology in ice-sheet models could provide critical information on the timing and magnitude of sea-level change contributions from Antarctica.

SUHMO: an adaptive mesh refinement SUbglacial Hydrology MOdel v1.0

Abstract. Water flowing under ice sheets and glaciers can have a strong influence on ice dynamics, particularly through pressure changes, suggesting that a comprehensive ice sheet model should include the effect of basal hydrology. Modeling subglacial hydrology remains a challenge, however, mainly due to the range of spatial and temporal scales involved – from subglacial channels to vast subglacial lakes. Additionally, networks of subglacial drainage channels dynamically evolve over time. To address some of these challenges, we have developed an adaptive mesh refinement (AMR) model based on the Chombo software framework. We extend the model proposed by Sommers et al. (2018) with a small but significant change to accommodate the transition from unresolved to resolved flow features. We handle the strong nonlinearities present in the equations by resorting to an efficient nonlinear full approximation scheme multigrid (FAS-MG) algorithm. We outline the details of the algorithm and present convergence analysis results demonstrating its good performance. Additionally, we present results validating our approach, using test cases from the Subglacial Hydrology Model Intercomparison Project (SHMIP) (de Fleurian et al., 2018). We finish by presenting a more complex, 100 km-by-100 km synthetic test case with peaks and valleys that we use to investigate the effective pressure distribution as the number of AMR levels increases. These preliminary results suggest that a minimum spatial resolution is needed to properly capture channel features, but additional work is required to precisely quantify this and its impact on accurately modeling the coupled ice sheet–hydrology system. The efficiency of our approach, relying on localized refinement, is also demonstrated. Future work will include coupling the SUbglacial Hydrology MOdel (SUHMO) with the BISICLES AMR ice sheet model (Cornford et al., 2013), both built on the same numerical framework.

Seasonal Acceleration of Petermann Glacier, Greenland, From Changes in Subglacial Hydrology

AbstractPetermann Glacier is a major outlet glacier of northern Greenland that drains a marine‐based basin vulnerable to destabilization from enhanced oceanic and atmospheric forcings. Using satellite radar interferometry data from the Sentinel‐1a/b missions, we observe a seasonal glacier acceleration of 15% in the summer, from 1,250 to 1,500 m/yr near the grounding line, but the physical drivers of this seasonality have not been elucidated. Here, we use a subglacial hydrology model coupled one‐way to an ice sheet model to evaluate the role of subglacial hydrology as a physical mechanism explaining the seasonal acceleration. We find excellent agreement between the observed and predicted velocity in terms of timing and magnitude with the addition of an applied lower limit on effective pressure of 6% of ice overburden pressure. We conclude that seasonal changes in subglacial hydrology are sufficient to explain the observed seasonal speed up of Petermann Glacier.

GlaDS subglacial hydrology model outputs and radar reflectivity data for Institute Ice Stream (IIS), Mӧller Ice Stream (MIS), Support Force Glacier (SFG), and Foundation Ice Stream/Academy Glacier (FIS-AG), Antarctica

GlaDS subglacial hydrology model outputs and radar reflectivity data for Institute Ice Stream (IIS), Mӧller Ice Stream (MIS), Support Force Glacier (SFG), and Foundation Ice Stream/Academy Glacier (FIS-AG), Antarctica

Impact of runoff temporal distribution on ice dynamics

Abstract. Record highs of meltwater production at the surface of the Greenland ice sheet have been recorded with a high recurrence over the last decades. Those melt seasons with longer durations, larger intensities, or with both increased length and melt intensity have a direct impact on the surface mass balance of the ice sheet and on its contribution to sea level rise. Moreover, the surface melt also affects the ice dynamics through the meltwater lubrication feedback. It is still not clear how the meltwater lubrication feedback impacts the long-term ice velocities on the Greenland ice sheet. Here we take a modeling approach with simplified ice sheet geometry and climate forcings to investigate in more detail the impacts of the changing characteristics of the melt season on ice dynamics. We model the ice dynamics through the coupling of the Double Continuum (DoCo) subglacial hydrology model with a shallow shelf approximation for the ice dynamics in the Ice-sheet and Sea-level System Model (ISSM). The climate forcing is generated from the ERA5 dataset to allow the length and intensity of the melt season to be varied in a comparable range of values. Our simulations present different behaviors between the lower and higher part of the glacier, but overall, a longer melt season will yield a faster glacier for a given runoff value. However, an increase in the intensity of the melt season, even under increasing runoff, tends to reduce glacier velocities. Those results emphasize the complexity of the meltwater lubrication feedback and urge us to use subglacial drainage models with both inefficient and efficient drainage components to give an accurate assessment of its impact on the overall dynamics of the Greenland ice sheet.

Sensitivity of subglacial drainage to water supply distribution at the Kongsfjord basin, Svalbard

Abstract. By regulating the amount, the timing, and the location of meltwater supply to the glacier bed, supraglacial hydrology potentially exerts a major control on the evolution of the subglacial drainage system, which in turn modulates ice velocity. Yet the configuration of the supraglacial hydrological system has received only little attention in numerical models of subglacial hydrology so far. Here we apply the two-dimensional subglacial hydrology model GlaDS (Glacier Drainage System model) to a Svalbard glacier basin with the aim of investigating how the spatial distribution of meltwater recharge affects the characteristics of the basal drainage system. We design four experiments with various degrees of complexity in the way that meltwater is delivered to the subglacial drainage model. Our results show significant differences between experiments in the early summer transition from distributed to channelized drainage, with discrete recharge at moulins favouring channelization at higher elevations and driving overall lower water pressures. Otherwise, we find that water input configuration only poorly influences subglacial hydrology, which instead is controlled primarily by subglacial topography. All experiments fail to develop channels of sufficient efficiency to substantially reduce summertime water pressures, which we attribute to small surface gradients and short melt seasons. The findings of our study are potentially applicable to most Svalbard tidewater glaciers with similar topography and low meltwater recharge. The absence of efficient channelization implies that the dynamics of tidewater glaciers in the Svalbard archipelago may be sensitive to future long-term trends in meltwater supply.

Drygalski Ice Tongue stability influenced by rift formation and ice morphology

AbstractThe Drygalski Ice Tongue in East Antarctica stretches 90 km into the Ross Sea and influences the local ocean circulation, and persistence of the Terra Nova Bay Polynya. We examine the controls on the size of this floating ice body by comparing the propagation of six large fractures on the ice tongue's northern side using 21 years of Landsat imagery with hydrostatic ice thickness maps and strain rate calculations. We also apply a subglacial hydrology model to estimate the location and discharge from subglacial channels over the grounding line and compare these with basal channels identified along the ice tongue using remote sensing and airborne radar data. Our results suggest that large fractures are inhibited from full-width propagation by thicker ice between basal channels. We hypothesize that only once the ice tongue thins towards the terminus, can fractures propagate and cause large calving events. This suggests an important relationship between the melting of floating ice from subglacial and ocean sources and the expansion of fractures that lead to ice tongue calving.

A two-dimensional, higher-order, enthalpy-based thermomechanical ice flow model for mountain glaciers and its benchmark experiments

Understanding the dynamics of glaciers is essential for the knowledge of global sea-level rise, local freshwater resources in high mountain and arid regions, and the potential glacial hazards. In this paper, we present a two-dimensional thermomechanically coupled ice flow model named PoLIM (Polythermal Land Ice Model). The velocity solver of PoLIM is developed based on the Blatter–Pattyn approximation of Stokes flow. It uses an enthalpy formulation of the energy balance, an approach that is suitable for modeling the polythermal glaciers. PoLIM also includes a scheme for gravity-driven drainage of water in temperate ice, a subglacial hydrology model coupled with ice dynamics, and multiple basal sliding laws. The model has been verified by standard benchmark problems, including the ISMIP-HOM experiments, the enthalpy benchmark experiments, and the SHMIP experiments. PoLIM shows good performances and agrees well with these benchmark results, indicating its robust capability of simulating the thermomechanical behaviors of glaciers.

Exceptionally high heat flux needed to sustain the Northeast Greenland Ice Stream

Abstract. The Northeast Greenland Ice Stream (NEGIS) currently drains more than 10 % of the Greenland Ice Sheet area and has recently undergone significant dynamic changes. It is therefore critical to accurately represent this feature when assessing the future contribution of Greenland to sea level rise. At present, NEGIS is reproduced in ice sheet models by inferring basal conditions using observed surface velocities. This approach helps estimate conditions at the base of the ice sheet but cannot be used to estimate the evolution of basal drag in time, so it is not a good representation of the evolution of the ice sheet in future climate warming scenarios. NEGIS is suggested to be initiated by a geothermal heat flux anomaly close to the ice divide, left behind by the movement of Greenland over the Icelandic plume. However, the heat flux underneath the ice sheet is largely unknown, except for a few direct measurements from deep ice core drill sites. Using the Ice Sheet System Model (ISSM), with ice dynamics coupled to a subglacial hydrology model, we investigate the possibility of initiating NEGIS by inserting heat flux anomalies with various locations and intensities. In our model experiment, a minimum heat flux value of 970 mW m−2 located close to the East Greenland Ice-core Project (EGRIP) is required locally to reproduce the observed NEGIS velocities, giving basal melt rates consistent with previous estimates. The value cannot be attributed to geothermal heat flux alone and we suggest hydrothermal circulation as a potential explanation for the high local heat flux. By including high heat flux and the effect of water on sliding, we successfully reproduce the main characteristics of NEGIS in an ice sheet model without using data assimilation.

Sensitivity of the Northeast Greenland Ice Stream to Geothermal Heat

Recent observations of ice flow surface velocities have helped improve our understanding of basal processes on Greenland and Antarctica, though these processes still constitute some of the largest uncertainties driving ice flow change today. The Northeast Greenland Ice Stream is driven largely by basal sliding, believed to be related to subglacial hydrology and the availability of heat. Characterization of the uncertainties associated with Northeast Greenland Ice Stream is crucial for constraining Greenland's potential contribution to sea level rise in the upcoming centuries. Here, we expand upon past work using the Ice Sheet System Model to quantify the uncertainties in models of the ice flow in the Northeast Greenland Ice Stream by perturbing the geothermal heat flux. Utilizing a subglacial hydrology model simulating sliding beneath the Greenland Ice Sheet, we investigate the sensitivity of the Northeast Greenland Ice Stream ice flow to various estimates of geothermal heat flux, and implications of basal heat flux uncertainties on modeling the hydrological processes beneath Greenland's major ice stream. We find that the uncertainty due to sliding at the bed is 10 times greater than the uncertainty associated with internal ice viscosity. Geothermal heat flux dictates the size of the area of the subglacial drainage system and its efficiency. The uncertainty of ice discharge from the Northeast Greenland Ice Stream to the ocean due to uncertainties in the geothermal heat flux is estimated at 2.10 Gt/yr. This highlights the urgency in obtaining better constraints on the highly uncertain subglacial hydrology parameters.

Totten Glacier subglacial hydrology determined from geophysics and modeling

Aurora Subglacial Basin (ASB), which feeds Totten Glacier, is a marine basin lying below sea level and contains up to 3.5m of global sea level equivalent. Rates of future sea level rise from this area are primarily dependent on the stability of Totten Ice Shelf and the controls on ice flow dynamics upstream of the grounding line, both of which may be influenced by subglacial hydrology. We apply the GlaDS subglacial hydrology model to ASB to examine whether the spatial patterns of distributed and efficient drainage systems impact the dynamics of Totten Glacier. We determine the most appropriate model configuration from our series of sensitivity tests by comparing the modeled basal water pressure and water depth results with specularity content data. Those data are derived from ICECAP radar surveys over the same region and represent regions of basal water accumulation. The best match between simulated basal hydrology properties and specularity content shows a strong correspondence in regions of distributed water in the ASB troughs for both water depth and water pressure, but weak correspondence between water depth and specularity content near the grounding line. This may be due to the presence of several large channels draining over the grounding line into the head of Totten Ice Shelf, which are likely not as well represented in the specularity content data as distributed systems. These channels may have a significant impact on melt, and therefore the stability, of Totten Ice Shelf. Within ASB, regions of high water pressure and greater water accumulation correspond well with regions of faster ice flow, suggesting some control of basal hydrology on ice dynamics in this region.

A Numerical Model for Fluvial Transport of Subglacial Sediment

Sediment discharge from glaciers impacts downstream aquatic habitats, hydropower operations, and river infrastructure. Since discharge of subglacial sediment will evolve in response to glacier retreat, estimating future subglacial sediment dynamics is of great relevance. To develop tools and methods to better constrain the responsible processes, we present a till dynamics model that accounts for limited sediment access coupled to a subglacial hydrology model to describe the evolution of a subglacial till layer over a glacier's longitudinal profile in one dimension. Synthetic simulations examining the effects of changing hydrology highlight the importance of properly constraining both the erosion of underlying bedrock and the subglacial sediment connectivity. This is because changes in hydrology alter the timing of peak sediment discharge but only marginally affect total sediment discharge once the subglacial sediment reservoir is exhausted. Model simulations for real‐world glaciers yield insights into the distribution of sediment along the glacier bed, including locations where sediments are deposited or exhausted. Comparison between model results and field data shows that total and peak sediment discharge, as well as interannual variability, can be captured with acceptable skill for periods ranging from hours to decades. The results from this model show that modeling subglacial sediment transport on decadal to subdaily scales is possible but requires processes such as bedrock erosion and sediment connectivity to be considered.

SHMIP The subglacial hydrology model intercomparison Project

ABSTRACTSubglacial hydrology plays a key role in many glaciological processes, including ice dynamics via the modulation of basal sliding. Owing to the lack of an overarching theory, however, a variety of model approximations exist to represent the subglacial drainage system. The Subglacial Hydrology Model Intercomparison Project (SHMIP) provides a set of synthetic experiments to compare existing and future models. We present the results from 13 participating models with a focus on effective pressure and discharge. For many applications (e.g. steady states and annual variations, low input scenarios) a simple model, such as an inefficient-system-only model, a flowline or lumped model, or a porous-layer model provides results comparable to those of more complex models. However, when studying short term (e.g. diurnal) variations of the water pressure, the use of a two-dimensional model incorporating physical representations of both efficient and inefficient drainage systems yields results that are significantly different from those of simpler models and should be preferentially applied. The results also emphasise the role of water storage in the response of water pressure to transient recharge. Finally, we find that the localisation of moulins has a limited impact except in regions of sparse moulin density.

MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids

Abstract. We introduce MPAS-Albany Land Ice (MALI) v6.0, a new variable-resolution land ice model that uses unstructured Voronoi grids on a plane or sphere. MALI is built using the Model for Prediction Across Scales (MPAS) framework for developing variable-resolution Earth system model components and the Albany multi-physics code base for the solution of coupled systems of partial differential equations, which itself makes use of Trilinos solver libraries. MALI includes a three-dimensional first-order momentum balance solver (Blatter–Pattyn) by linking to the Albany-LI ice sheet velocity solver and an explicit shallow ice velocity solver. The evolution of ice geometry and tracers is handled through an explicit first-order horizontal advection scheme with vertical remapping. The evolution of ice temperature is treated using operator splitting of vertical diffusion and horizontal advection and can be configured to use either a temperature or enthalpy formulation. MALI includes a mass-conserving subglacial hydrology model that supports distributed and/or channelized drainage and can optionally be coupled to ice dynamics. Options for calving include “eigencalving”, which assumes that the calving rate is proportional to extensional strain rates. MALI is evaluated against commonly used exact solutions and community benchmark experiments and shows the expected accuracy. Results for the MISMIP3d benchmark experiments with MALI's Blatter–Pattyn solver fall between published results from Stokes and L1L2 models as expected. We use the model to simulate a semi-realistic Antarctic ice sheet problem following the initMIP protocol and using 2 km resolution in marine ice sheet regions. MALI is the glacier component of the Energy Exascale Earth System Model (E3SM) version 1, and we describe current and planned coupling to other E3SM components.

Relationship Between Greenland Ice Sheet Surface Speed and Modeled Effective Pressure

AbstractWe use a numerical subglacial hydrology model and remotely sensed observations of Greenland Ice Sheet surface motion to test whether the inverse relationship between effective pressure and regional melt season surface speeds observed at individual sites holds on a regional scale. The model is forced with daily surface runoff estimates for 2009 and 2010 across an ~8,000‐km2 region on the western margin. The overall subglacial drainage system morphology develops similarly in both years, with subglacial channel networks growing inland from the ice sheet margin and robust subglacial pathways forming over bedrock ridges. Modeled effective pressures are compared to contemporaneous regional surface speeds derived from TerraSAR‐X imagery to investigate spatial relationships. Our results show an inverse spatial relationship between effective pressure and ice speed in the mid‐melt season, when surface speeds are elevated, indicating that effective pressure is the dominant control on surface velocities in the mid‐melt season. By contrast, in the early and late melt seasons, when surface speeds are slower, effective pressure and surface speed have a positive relationship. Our results suggest that outside of the mid‐melt season, the influence of effective pressures on sliding speeds may be secondary to the influence of driving stress and spatially variable bed roughness.

BrAHMs V1.0: a fast, physically based subglacial hydrology model for continental-scale application

Abstract. We present BrAHMs (BAsal Hydrology Model): a physically based basal hydrology model which represents water flow using Darcian flow in the distributed drainage regime and a fast down-gradient solver in the channelized regime. Switching from distributed to channelized drainage occurs when appropriate flow conditions are met. The model is designed for long-term integrations of continental ice sheets. The Darcian flow is simulated with a robust combination of the Heun and leapfrog–trapezoidal predictor–corrector schemes. These numerical schemes are applied to a set of flux-conserving equations cast over a staggered grid with water thickness at the centres and fluxes defined at the interface. Basal conditions (e.g., till thickness, hydraulic conductivity) are parameterized so the model is adaptable to a variety of ice sheets. Given the intended scales, basal water pressure is limited to ice overburden pressure, and dynamic time stepping is used to ensure that the Courant–Friedrichs–Lewy (CFL) condition is met for numerical stability. The model is validated with a synthetic ice sheet geometry and different bed topographies to test basic water flow properties and mass conservation. Synthetic ice sheet tests show that the model behaves as expected with water flowing down gradient, forming lakes in a potential well or reaching a terminus and exiting the ice sheet. Channel formation occurs periodically over different sections of the ice sheet and, when extensive, displays the arborescent configuration expected of Röthlisberger channels. The model is also shown to be stable under high-frequency oscillatory meltwater inputs.

SHAKTI: Subglacial Hydrology and Kinetic, Transient Interactions v1.0

Abstract. Subglacial hydrology has a strong influence on glacier and ice sheet dynamics, particularly through the dependence of sliding velocity on subglacial water pressure. Significant challenges are involved in modeling subglacial hydrology, as the drainage geometry and flow mechanics are constantly changing, with complex feedbacks that play out between water and ice. A clear tradition has been established in the subglacial hydrology modeling literature of distinguishing between channelized (efficient) and sheetlike (inefficient or distributed) drainage systems or components and using slightly different forms of the governing equations in each subsystem to represent the dominant physics. Specifically, many previous subglacial hydrology models disregard opening by melt in the sheetlike system or redistribute it to adjacent channel elements in order to avoid runaway growth that occurs when it is included in the sheetlike system. We present a new subglacial hydrology model, SHAKTI (Subglacial Hydrology and Kinetic, Transient Interactions), in which a single set of governing equations is used everywhere, including opening by melt in the entire domain. SHAKTI employs a generalized relationship between the subglacial water flux and the hydraulic gradient that allows for the representation of laminar, turbulent, and transitional regimes depending on the local Reynolds number. This formulation allows for the coexistence of these flow regimes in different regions, and the configuration and geometry of the subglacial system evolves naturally to represent sheetlike drainage as well as systematic channelized drainage under appropriate conditions. We present steady and transient example simulations to illustrate the features and capabilities of the model and to examine sensitivity to mesh size and time step size. The model is implemented as part of the Ice Sheet System Model (ISSM).