Daniel Goldberg

Effect of near‐terminus subglacial hydrology on tidewater glacier submarine melt rates

Submarine melting of Greenlandic tidewater glacier termini is proposed as a possible mechanism driving their recent thinning and retreat. We use a general circulation model, MITgcm, to simulate water circulation driven by subglacial discharge at the terminus of an idealized tidewater glacier. We vary the spatial distribution of subglacial discharge emerging at the grounding line of the glacier and examine the effect on submarine melt volume and distribution. We find that subglacial hydrology exerts an important control on submarine melting; under certain conditions a distributed system can induce a factor 5 more melt than a channelized system, with plumes from a single channel inducing melt over only a localized area. Subglacial hydrology also controls the spatial distribution of melt, which has the potential to control terminus morphology and calving style. Our results highlight the need to constrain near-terminus subglacial hydrology at tidewater glaciers if we are to represent ocean forcing accurately.

Modeling the impact of glacial runoff on fjord circulation and submarine melt rate using a new subgrid‐scale parameterization for glacial plumes

The injection at depth of ice sheet runoff into fjords may be an important control on the frontal melt rate of tidewater glaciers. Here we develop a new parameterization for ice marginal plumes within the Massachusetts Institute of Technology General Circulation Model (MITgcm), allowing three-dimensional simulation of large (500 km2) glacial fjords on annual (or longer) time scales. We find that for an idealized fjord (without shelf-driven circulation), subglacial runoff produces a thin, strong, and warm down-fjord current in the upper part of the water column, balanced by a thick and slow up-fjord current at greater depth. Although submarine melt rates increase with runoff due to higher melt rates where the plume is in contact with the ice front, we find that annual submarine melt rate across the ice front is relatively insensitive to variability in annual runoff. Better knowledge of the spatial distribution of runoff, controls on melt rate in those areas not directly in contact with plumes, and feedback mechanisms linking submarine melting and iceberg calving are necessary to more fully understand the sensitivity of glacier mass balance to runoff-driven fjord circulation.

A variationally derived, depth-integrated approximation to a higher-order glaciological flow model

An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.

Scalings for Submarine Melting at Tidewater Glaciers from Buoyant Plume Theory

AbstractRapid dynamic changes at the margins of the Greenland Ice Sheet, synchronous with ocean warming, have raised concern that tidewater glaciers can respond sensitively to ocean forcing. Understanding of the processes encompassing ocean forcing nevertheless remains embryonic. The authors use buoyant plume theory to study the dynamics of proglacial discharge plumes arising from the emergence of subglacial discharge into a fjord at the grounding line of a tidewater glacier, deriving scalings for the induced submarine melting. Focusing on the parameter space relevant for high discharge tidewater glaciers, the authors suggest that in an unstratified fjord the often-quoted relationship between total submarine melt volume and subglacial discharge raised to the ⅓ power is appropriate regardless of plume geometry, provided discharge lies below a critical value. In these cases it is then possible to formulate a simple equation estimating total submarine melt volume as a function of discharge, fjord temperature...

Stick-slip motion of an Antarctic Ice Stream: The effects of viscoelasticity

Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream (Siple Coast, Antarctica). Distinct from stick slip on Northern Hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be controlled by basal processes and by tidally induced stress. However, the connection between stick-slip behavior and flow of the ice stream on long time scales, if any, is not clear. To address this question we develop a new ice flow model capable of reproducing stick-slip cycles similar to ones observed on the Whillans Ice Plain. The model treats ice as a viscoelastic material and emulates the weakening and healing that are suggested to take place at the ice-till interface. The model results suggest the long-term ice stream flow that controls ice discharge to surrounding oceans is somewhat insensitive to certain aspects of stick-slip behavior, such as velocity magnitude during the slip phase and factors that regulate it (e.g., elastic modulus). Furthermore, it is found that factors controlling purely viscous flow, such as temperature, influence stick-slip contribution to long-term flow in much the same way. Additionally, we show that viscous ice deformation, traditionally disregarded in analysis of stick-slip behavior, has a strong effect on the timing of slip events and therefore should not be ignored in efforts to deduce bed properties from stick-slip observations.

A model for tidewater glacier undercutting by submarine melting

Dynamic change at the marine-terminating margins of the Greenland Ice Sheet may be initiated by the ocean, particularly where subglacial runoff drives vigorous ice-marginal plumes and rapid submarine melting. Here we model submarine melt-driven undercutting of tidewater glacier termini, simulating a process which is key to understanding ice-ocean coupling. Where runoff emerges from broad subglacial channels we find that undercutting has only a weak impact on local submarine melt rate but increases total ablation by submarine melting due to the larger submerged ice surface area. Thus, the impact of melting is determined not only by the melt rate magnitude but also by the slope of the ice-ocean interface. We suggest that the most severe undercutting occurs at the maximum height in the fjord reached by the plume, likely promoting calving of ice above. It remains unclear, however, whether undercutting proceeds sufficiently rapidly to influence calving at Greenlands fastest-flowing glaciers.

Channelized Melting Drives Thinning Under a Rapidly Melting Antarctic Ice Shelf

Ice shelves play a vital role in regulating loss of grounded ice and in supplying freshwater to coastal seas. However, melt variability within ice shelves is poorly constrained and may be instrumental in driving ice shelf imbalance and collapse. High-resolution altimetry measurements from 2010 to 2016 show that Dotson Ice Shelf (DIS), West Antarctica, thins in response to basal melting focused along a single 5 km-wide and 60 km-long channel extending from the ice shelfs grounding zone to its calving front. If focused thinning continues at present rates, the channel will melt through, and the ice shelf collapse, within 40–50 years, almost two centuries before collapse is projected from the average thinning rate. Our findings provide evidence of basal melt-driven sub-ice shelf channel formation and its potential for accelerating the weakening of ice shelves.

Ocean-Forced Ice-Shelf Thinning in a Synchronously Coupled Ice-Ocean Model

The first fully synchronous, coupled ice shelf-ocean model with a fixed grounding line and imposed upstream ice velocity has been developed using the MITgcm (Massachusetts Institute of Technology general circulation model). Unlike previous, asynchronous, approaches to coupled modeling our approach is fully conservative of heat, salt, and mass. Synchronous coupling is achieved by continuously updating the ice-shelf thickness on the ocean time step. By simulating an idealized, warm-water ice shelf we show how raising the pycnocline leads to a reduction in both ice-shelf mass and back stress, and hence buttressing. Coupled runs show the formation of a western boundary channel in the ice-shelf base due to increased melting on the western boundary due to Coriolis enhanced flow. Eastern boundary ice thickening is also observed. This is not the case when using a simple depth-dependent parameterized melt, as the ice shelf has relatively thinner sides and a thicker central “bulge” for a given ice-shelf mass. Ice-shelf geometry arising from the parameterized melt rate tends to underestimate backstress (and therefore buttressing) for a given ice-shelf mass due to a thinner ice shelf at the boundaries when compared to coupled model simulations.

The Response of Ice Sheets to Climate Variability

West Antarctic Ice Sheet loss is a significant contributor to sea level rise. While the ice loss is thought to be triggered by fluctuations in oceanic heat at the ice shelf bases, ice sheet response to ocean variability remains poorly understood. Using a synchronously coupled ice-ocean model permitting grounding line migration, this study evaluates the response of an ice sheet to periodic variations in ocean forcing. Resulting oscillations in grounded ice volume amplitude is shown to grow as a nonlinear function of ocean forcing period. This implies that slower oscillations in climatic forcing are disproportionately important to ice sheets. The ice shelf residence time offers a critical time scale, above which the ice response amplitude is a linear function of ocean forcing period and below which it is quadratic. These results highlight the sensitivity of West Antarctic ice streams to perturbations in heat fluxes occurring at decadal time scales.