Response of Marine‐Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics

Recent observations indicate that many marine‐terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long‐term trends in climate forcing. In this study, we describe a simple two‐stage model that accurately emulates the response to external forcing of marine‐terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine‐terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine‐terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state

The role of ice stream dynamics in deglaciation

Since the mid-Pleistocene transition, deglaciation has occurred only after ice sheets have grown large while experiencing several precession and obliquity cycles, indicating that large ice sheets are more sensitive to Milankovitch forcing than small ice sheets are. Observations and model simulations suggest that the development of ice streams in the Laurentide Ice Sheet played an as yet unknown role in deglaciations. In this study, we propose a mechanism by which ice streams may enhance deglaciation and render large ice sheets more sensitive to Milankovitch forcing. We use an idealized configuration of the Parallel Ice Sheet Model that permits the formation of ice streams. When the ice sheet is large and ice streams are sufficiently developed, an upward shift in equilibrium line altitude, commensurate with Milankovitch forcing, results in rapid deglaciation, while the same shift applied to an ice sheet without fully formed ice streams results in continued ice sheet growth or slower deglaciation. Rapid deglaciation in ice sheets with significant streaming behavior is caused by ice stream acceleration and the attendant enhancement of calving and surface melting at low elevations. Ice stream acceleration is ultimately the result of steepening of the ice surface and increased driving stresses in ice stream onset zones, which come about due to the dependence of surface mass balance on elevation. These ice sheet simulations match the broad features of geomorphological observations and add ice stream dynamics that are missing from previous model studies of deglaciation

A Simple Model for Deglacial Meltwater Pulses

Evidence from radiocarbon dating and complex ice sheet modeling suggests that the fastest rate of sea level rise in Earth's recent history coincided with collapse of the ice saddle between the Laurentide and Cordilleran ice sheets during the last deglaciation. In this study, we derive a simple, two‐equation model of two ice sheets intersecting in an ice saddle. We show that two conditions are necessary for producing the acceleration in ice sheet melt associated with meltwater pulses: the positive height‐mass balance feedback and an ice saddle geometry. The amplitude and timing of meltwater pulses is sensitively dependent on the rate of climate warming during deglaciation and the relative size of ice sheets undergoing deglaciation. We discuss how simulations of meltwater pulses can be improved and the prospect for meltwater pulses under continued climate warming

Tidal modulation of ice shelf buttressing stresses

Ocean tides influence the flow of marine-terminating glaciers. Observations indicate that the large fortnightly variations in ice flow at Rutford Ice Stream in West Antarctica originate in the floating ice shelf. We show that nonlinear variations in ice shelf buttressing driven by tides can produce such fortnightly variations in ice flow. These nonlinearities in the tidal modulation of buttressing stresses can be caused by asymmetries in the contact stress from migration of the grounding line and bathymetric pinning points beneath the ice shelf. Using a simple viscoelastic model, we demonstrate that a combination of buttressing and hydrostatic stress variations can explain a diverse range of tidal variations in ice shelf flow, including the period, phase and amplitude of flow variations observed at Rutford and Bindschadler Ice Streams

A Simple Model for Deglacial Meltwater Pulses

Evidence from radiocarbon dating and complex ice sheet modeling suggests that the fastest rate of sea level rise in Earth's recent history coincided with collapse of the ice saddle between the Laurentide and Cordilleran ice sheets during the last deglaciation. In this study, we derive a simple, two‐equation model of two ice sheets intersecting in an ice saddle. We show that two conditions are necessary for producing the acceleration in ice sheet melt associated with meltwater pulses: the positive height‐mass balance feedback and an ice saddle geometry. The amplitude and timing of meltwater pulses is sensitively dependent on the rate of climate warming during deglaciation and the relative size of ice sheets undergoing deglaciation. We discuss how simulations of meltwater pulses can be improved and the prospect for meltwater pulses under continued climate warming

Persistence and variability of ice-stream grounding lines on retrograde bed slopes

In many ice streams, basal resistance varies in space and time due to the dynamically evolving properties of subglacial till. These variations can cause internally generated oscillations in ice-stream flow. However, the potential for such variations in basal properties is not considered by conventional theories of grounding-line stability on retrograde bed slopes, which assume that bed properties are static in time. Using a flow-line model, we show how internally generated, transient variations in ice-stream state interact with retrograde bed slopes. In contrast to predictions from the theory of the marine ice-sheet instability, our simulated grounding line is able to persist and reverse direction of migration on a retrograde bed when undergoing oscillations in the grounding-line position. In turn, the presence of a retrograde bed may also suppress or reduce the amplitude of internal oscillations in ice-stream state. We explore the physical mechanisms responsible for these behaviors and discuss the implications for observed grounding-line migration in West Antarctica

Experimental Constraints on Ocean Wave Erosion of Icebergs and Glaciers

Loss of ice from glaciers and ice sheets has been steadily increasing over recent decades due to rising oceanic and atmospheric temperatures. White (1980) developed a theoretical estimate for the erosion rate of icy surface by wave activity, which has since been used as the sole basis for calculating wave melting effects in ocean and ice sheet models. In this study, we conduct the first new experiments since White (1980) to test the established parameterization and extend it to a wider range of wave and water properties. A custom-built 1.2 meter long wave tank is used to simulate the behavior of ocean waves on ice shelves in a laboratory-scaled manner. White’s theory is tested for a wide range of conditions to within a reasonable margin of error (given the limitations of the tank and required assumptions). We further discuss how the results from this experiment can help to improve models of the high-latitude oceans for the benefit of predicting future climate, and assessing iceberg hazards to shipping

Response of Marine‐Terminating Glaciers to Forcing: Time Scales, Sensitivities, Instabilities, and Stochastic Dynamics

Recent observations indicate that many marine‐terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long‐term trends in climate forcing. In this study, we describe a simple two‐stage model that accurately emulates the response to external forcing of marine‐terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine‐terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine‐terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state

Processes controlling the downstream evolution of ice rheology in glacier shear margins: case study on Rutford Ice Stream, West Antarctica

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics