Katarzyna L. P. Warburton

The Greenland and Antarctic ice sheets exhibit high variability in flow speed, over multiple orders of magnitude. This flow integrates forcings from complex, multi-scale and spatially heterogeneous pressure gradient and friction fields into smooth and continuous flow fields, over a finite scale known as the longitudinal coupling length (LCL). The strongly nonlinear, shear-thinning rheology of ice complicates the stress transmission, but previous work has relied on either linear (Newtonian) models or linearized, small-perturbation models, to determine the coupling length. Here, we derive new exact solutions to the nonlinear shallow shelf/shelfy-stream approximation (SSA), which explain how nonlinear feedbacks between the stress state and the nonlinear rheology of ice determine the coupling length. For complex and multi-scale flow fields, these exact solutions provide a foundation for Green's function approximations that can reconstruct the effects of a non-local stress balance, given input data for the driving stress and friction fields. This allows us to rapidly reconstruct the ice velocity field, asses changes in basal drag and interpret the effect of rheology on shear margins.

Subglacial water flow is critical to basal sliding and ice dynamics. Modelling the coupled evolution of subglacial drainage and ice flow remains challenging, however. This study investigates the evolution of the basal ice–water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid laminar–turbulent melt scheme captures heat generation and melting from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. Whilst the flow of ice tends to increase the eccentricity of the channel, we find that elliptical channels tend towards a circular shape when laminar melting dominates due to differential melting between the roof and walls of the channel. Our hybrid melt model predicts the existence of stable, non-circular cross-sections. Unlike circular channels, these channels obey pressure-flux relationships that, beyond a critical volume flux threshold, suggest a preference for flux sharing, a behaviour characteristic of distributed drainage networks. This contrasts with circular channels, which undergo channelisation towards fewer, larger conduits. These idealised channels suggest potential simplifications to modelling subglacial drainage networks and the dynamics of evolving subglacial hydrological networks.

Subglacial water flow is critical to basal sliding and ice dynamics. Modelling the coupled evolution of subglacial drainage and ice flow remains challenging, however. This study investigates the evolution of the basal ice-water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid laminar–turbulent melt scheme captures heat generation and melting from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. Whilst the flow of ice tends to increase the eccentricity of the channel, we find that elliptical channels tend toward a circular shape when laminar melting dominates due to differential melting between the roof and walls of the channel. Our hybrid melt model predicts the existence of stable, non-circular cross-sections. Unlike circular channels, these channels obey pressure-flux relationships that, beyond a critical volume flux threshold, suggest a preference for flux sharing, a behaviour characteristic of distributed drainage networks. This contrasts with circular channels, which undergo channelisation towards fewer, larger conduits. These idealised channels suggest potential simplifications to modelling subglacial drainage networks and the dynamics of evolving subglacial hydrological networks.

Subglacial water modulates glacier velocity across a wide range of space and time scales by influencing friction at the glacier bed. Observations show ice acceleration due to supraglacial lake drainage and water draining through moulins, where both configurations involve water inputs to the bed. Here we consider the reverse: water extraction from the subglacial hydrologic system, which is a proposed intervention method intended to slow the flow of glaciers and reduce the associated sea-level rise. Removing subglacial water results in different dynamics than injecting water, and we hypothesize that understanding these processes will allow for improved characterization of the physics of subglacial hydrology. We set up these model experiments in the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model coupled with the Ice-sheet and Sea-level System Model (ISSM). By analyzing the problem of an isolated borehole in a background pressure field to determine the region of extraction influence, we find an approximate analytical solution which shows that the water pressure returns to the background value approximately as a logarithm with distance. The benefit of the analytical solution is that the dependence of uncertain parameters is clear and may be used alongside data to constrain subglacial hydrology models. We find good agreement between this analytical result and numerical SHAKTI simulations. Using the coupled SHAKTI-ISSM model, we perform transient model experiments on Helheim Glacier, Greenland and Thwaites Glacier, Antarctica, to determine the effects of water extraction on glacier velocity. With continuous pumping, we simulate a velocity decrease on the order of 1 %, which depends on the site location. The response time to pumping initiation and the recovery time, following cessation, scale according to effective pressure, with typical times on the order of hours to days. These results demonstrate that water extraction is a method of probing the subglacial hydrologic system to better constrain the uncertain physics, and that further research is required to assess its effectiveness as an intervention method.

Subglacial water flow plays a critical role in basal sliding and, consequently, in glacier and ice-sheet dynamics. However, modelling the coupled evolution of subglacial drainage and ice flow remains challenging. This study investigates the evolution of the basal ice–water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid turbulent–laminar melt scheme captures heat generation from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. The flow and temperature profiles in elliptical channels are solved for with differential melting between the roof and walls of the channel. We find that elliptical channels tend towards a circular shape when laminar melting dominates, whilst the flow of ice tends to increase the eccentricity of the channel. Our hybrid laminar-turbulent melt model permits variations in the distribution of melting along the ice-water boundary and the existence of stable, non-circular cross-sections. These stable channels obey pressure-flux relationships that we use to explore the evolution and dynamics of hydrologically interacting channels in a wider subglacial drainage network, working towards a simplified and scalable subglacial hydrology model.

Numerous mechanisms have been proposed for the formation of step‐pools in steep streams. Which of these mechanisms is responsible for constructing step‐pools may depend on flow conditions, with existing theory best developed for near‐critical flow conditions. Under subcritical flow conditions, however, channel roughness has been observed to exert control on step formation. To improve representation of step‐pool development under sub‐critical flow conditions, we develop a quantitative model exploring step‐pool construction in response to roughness variation. We incorporate variable roughness into a quasi‐2D Saint‐Venant Exner model in which steps emerge around roughness patches, consistent with the roughness‐based mechanism observed in previous experimental work. We compare model results to a field site that developed step‐pools in areas of high roughness in an initially plane‐bedded reach. Model results provide a mechanistic link between roughness variation and step spacing. For disturbed rivers similar to our field site, the location of rough patches may help inform expectations for early step‐pool evolution following river disturbance.

Ice-stream grounding zones are critical parts of the Antarctic Ice Sheet and we must be able to model how they retreat with confidence. This is because for most of Antarctica, the grounding-zone location determines the flux of ice to the ocean. As such, future grounding-zone locations (as the ice-sheet edge retreats inland) dictate the pattern and rate of ice loss and the associated sea-level rise. Ice flow across the grounding zone is opposed by a combination of ice-shelf buttressing if lateral drag or pinning points are present, and by friction between the ice and its bed - basal drag. While the loss of buttressing and ocean-forced melting of ice shelves are popular research foci, far less attention is paid to resistance at the bed. Here, we revisit the treatment of grounding zones in models and argue for a new approach to basal drag: evolving bed conditions result in highly variable drag that is not captured by existing sliding laws. We begin by reviewing the complex basal processes operating in grounding zones over different timescales, such as tides, evolving subglacial hydrology, and sedimentation. Then, to illustrate the significance of the basal drag term, we run retreat scenarios in the UFEMISM model using an accepted basal sliding law that only varies in its treatment of subglacial hydrology (via effective pressure). Appreciable differences in retreat patterns motivate us to consider how modelling grounding zones may be improved. To reduce uncertainty in ice-loss projections, in tandem with refining ice-shelf melt parameterisations, careful observations from grounding zones and physically-based basal drag parameterisations are required.

Subglacial water modulates glacier velocity across a wide range of space and time scales by influencing friction at the glacier bed. Observations show ice acceleration due to supraglacial lake drainage and water draining through moulins, where both configurations involve water inputs to the bed. Here we consider the reverse: water extraction from the subglacial system. Removing subglacial water results in different dynamics than injecting water, and we hypothesize that understanding these processes will allow for improved characterization of the physics of subglacial hydrology. Water extraction is a proposed intervention method for slowing glaciers that requires significant further investigation before it should be tested or implemented in the field. Here we set up model experiments in the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model coupled with the Ice-sheet and Sea-level System Model (ISSM). By analyzing the problem of an isolated borehole in a background pressure field to determine the region of extraction influence, we find an analytical solution which shows that the water pressure returns to the background value approximately as a logarithm with distance. The benefit of the analytical solution is that the dependence of uncertain parameters is clear and may be used to constrain subglacial hydrology models. We find good agreement between this analytical result and full SHAKTI simulations. Using the coupled SHAKTI-ISSM model, we perform transient model experiments on an idealized tidewater glacier geometry and on Helheim Glacier in Greenland to determine the effects of water extraction on glacier velocity. With continuous pumping, we simulate a modest impact on velocity, which is sensitive to the extraction rate and site location. The response time to pumping initiation and the recovery time following cessation scale according to effective pressure, with typical times on the order of hours to days. These results are encouraging that water extraction is a method of probing the subglacial hydrologic system to better constrain the uncertain physics, with further research required to determine if it is an effective intervention method.

Subglacial water modulates glacier velocity across a wide range of space and time scales by influencing friction at the glacier bed. Observations show ice acceleration due to supraglacial lake drainage and water draining through moulins, where both configurations involve water inputs to the bed. Here we consider the reverse: water extraction from the subglacial system. Removing subglacial water results in different dynamics than injecting water, and we hypothesize that understanding these processes will allow for improved characterization of the physics of subglacial hydrology. Water extraction is a proposed intervention method for slowing glaciers that requires significant further investigation before it should be tested or implemented in the field. Here we set up model experiments in the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model coupled with the Ice-sheet and Sea-level System Model (ISSM). By analyzing the problem of an isolated borehole in a background pressure field to determine the region of extraction influence, we find an analytical solution which shows that the water pressure returns to the background value approximately as a logarithm with distance. The benefit of the analytical solution is that the dependence of uncertain parameters is clear and may be used to constrain subglacial hydrology models. We find good agreement between this analytical result and full SHAKTI simulations. Using the coupled SHAKTI-ISSM model, we perform transient model experiments on an idealized tidewater glacier geometry and on Helheim Glacier in Greenland to determine the effects of water extraction on glacier velocity. With continuous pumping, we simulate a modest impact on velocity, which is sensitive to the extraction rate and site location. The response time to pumping initiation and the recovery time following cessation scale according to effective pressure, with typical times on the order of hours to days. These results are encouraging that water extraction is a method of probing the subglacial hydrologic system to better constrain the uncertain physics, with further research required to determine if it is an effective intervention method.

Subglacial water modulates glacier velocity across a wide range of space and time scales by influencing friction at the glacier bed. Observations show ice acceleration due to supraglacial lake drainage and water draining through moulins, where both configurations involve water inputs to the bed. Here we consider the reverse: water extraction from the subglacial system. Removing subglacial water results in different dynamics than injecting water, and we hypothesize that understanding these processes will allow for improved characterization of the physics of subglacial hydrology. Water extraction is a proposed intervention method for slowing glaciers that requires significant further investigation before it should be tested or implemented in the field. Here we set up model experiments in the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model coupled with the Ice-sheet and Sea-level System Model (ISSM). By analyzing the problem of an isolated borehole in a background pressure field to determine the region of extraction influence, we find an analytical solution which shows that the water pressure returns to the background value approximately as a logarithm with distance. The benefit of the analytical solution is that the dependence of uncertain parameters is clear and may be used to constrain subglacial hydrology models. We find good agreement between this analytical result and full SHAKTI simulations. Using the coupled SHAKTI-ISSM model, we perform transient model experiments on an idealized tidewater glacier geometry and on Helheim Glacier in Greenland to determine the effects of water extraction on glacier velocity. With continuous pumping, we simulate a modest impact on velocity, which is sensitive to the extraction rate and site location. The response time to pumping initiation and the recovery time following cessation scale according to effective pressure, with typical times on the order of hours to days. These results are encouraging that water extraction is a method of probing the subglacial hydrologic system to better constrain the uncertain physics, with further research required to determine if it is an effective intervention method.