Jason M. Amundson

A unifying framework for iceberg-calving models

We propose a general framework for iceberg-calving models that can be applied to any calving margin. The framework is based on mass continuity, the assumption that calving rate and terminus velocity are not independent and the simple idea that terminus thickness following a calving event is larger than terminus thickness at the event onset. The theoretical, near steady-state analysis used to support and analyze the framework indicates that calving rate is governed, to first order, by ice thickness, thickness gradient, strain rate, mass-balance rate and backwards melting of the terminus; the analysis furthermore provides a physical explanation for a previously derived empirical relationship for ice-shelf calving (Alley and others, 2008). In the calving framework the pre- and post-calving terminus thicknesses are given by two unknown but related functions. The functions can vary independently of changes in glacier flow and geometry, and can therefore account for variations in calving behavior due to external forcings and/or self-sustaining calving processes (positive feedbacks). Although the calving framework does not constitute a complete calving model, any thickness-based calving criterion can easily be incorporated into the framework. The framework should be viewed as a guide for future attempts to parameterize calving.

Time-dependent basal stress conditions beneath Black Rapids Glacier, Alaska, USA, inferred from measurements of ice deformation and surface motion

Observations of surface motion and ice deformation from 2002-03 were used to infer mean stress fields in a cross-section of Black Rapids Glacier, Alaska, USA, over seasonal timescales. Basal shear stresses in a well-defined zone north of the center line (orographic left) were approximately 7% and 16% lower in spring and summer, respectively, than in winter. Correspondingly higher stresses were found near the margins. These changes in the basal shear stress distribution were sufficiently large to cause mean surface velocities to be 1.2 and 1.5 times larger in spring and summer than in winter. These results were inferred with a simple inverse finite-element flow model that can successfully reproduce bulk surface velocities and tiltmeter data. Stress redistribution between the well-defined zone and the margins may also occur over much shorter time periods as a result of rapidly changing basal conditions (ice-bed decoupling or enhanced till deformation), thereby causing large variations in surface velocity and strongly influencing the glaciers net motion during summer.

A computational investigation of iceberg capsize as a driver of explosive ice-shelf disintegration

Abstract Potential energy released from the capsize of ice-shelf fragments (icebergs) is the immediate driver of the brief explosive phase of ice-shelf disintegration along the Antarctic Peninsula (e.g. the Larsen A, Larsen B and Wilkins ice shelves). The majority of this energy powers the rapidly expanding plume of ice-shelf fragments that expands outward into the open ocean; a smaller fraction of this energy goes into surface gravity waves and other dynamic interactions between ice and water that can sustain the continued fragmentation and break-up of the original ice shelf. As an initial approach to the investigation of ice-shelf fragment capsize in ice-shelf collapse, we develop a simple conceptual model involving ideal rectangular icebergs, initially in unstable or metastable orientations, which are assembled into a tightly packed mass that subsequently disassembles via massed capsize. Computations based on this conceptual model display phenomenological similarity to aspects of real ice-shelf collapse. A promising result of the conceptual model presented here is a description of how iceberg aspect ratio and its statistical variance, the two parameters related to ice-shelf fracture patterns, influence the enabling conditions to be satisfied by slow-acting processes (e.g. environmentally driven melting) that facilitate ice-shelf disintegration.

Dynamic jamming of iceberg-choked fjords

We investigate the dynamics of ice melange by analyzing rapid motion recorded by a time-lapse camera and terrestrial radar during several calving events that occurred at Jakobshavn Isbrae, Greenland. During calving events (1) the kinetic energy of the ice melange is 2 orders of magnitude smaller than the total energy released during the events, (2) a jamming front propagates through the ice melange at a rate that is an order of magnitude faster than the motion of individual icebergs, (3) the ice melange undergoes initial compaction followed by slow relaxation and extension, and (4) motion of the ice melange gradually decays before coming to an abrupt halt. These observations indicate that the ice melange experiences widespread jamming during calving events and is always close to being in a jammed state during periods of terminus quiescence. We therefore suspect that local jamming influences longer timescale ice melange dynamics and stress transmission.

Subglacial discharge at tidewater glaciers revealed by seismic tremor

Abstract Subglacial discharge influences glacier basal motion and erodes and redeposits sediment. At tidewater glacier termini, discharge drives submarine terminus melting, affects fjord circulation, and is a central component of proglacial marine ecosystems. However, our present inability to track subglacial discharge and its variability significantly hinders our understanding of these processes. Here we report observations of hourly to seasonal variations in 1.5–10 Hz seismic tremor that strongly correlate with subglacial discharge but not with basal motion, weather, or discrete icequakes. Our data demonstrate that vigorous discharge occurs from tidewater glaciers during summer, in spite of fast basal motion that could limit the formation of subglacial conduits, and then abates during winter. Furthermore, tremor observations and a melt model demonstrate that drainage efficiency of tidewater glaciers evolves seasonally. Glaciohydraulic tremor provides a means by which to quantify subglacial discharge variations and offers a promising window into otherwise obscured glacierized environments.

Observing calving-generated ocean waves with coastal broadband seismometers, Jakobshavn Isbræ, Greenland

Abstract We use time-lapse photography, MODIS satellite imagery, ocean wave measurements and regional broadband seismic data to demonstrate that icebergs that calve from Jakobshavn Isbræ, Greenland, can generate ocean waves that are detectable over 150 km from their source. The waves, which are recorded seismically, have distinct spectral peaks, are not dispersive and persist for several hours. On the basis of these observations, we suggest that calving events at Jakobshavn Isbræ can stimulate seiches, or basin eigenmodes, in both Ilulissat Icefjord and Disko Bay. Our observations furthermore indicate that coastal, land-based seismometers located near calving termini (e.g. as part of the new Greenland Ice Sheet Monitoring Network (GLISN)) can aid investigations into the largely unexplored, oceanographic consequences of iceberg calving.

Subseasonal changes observed in subglacial channel pressure, size, and sediment transport

Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited. Here we demonstrate that detailed analysis of seismic ground motion caused by subglacial water flow at Mendenhall Glacier (Alaska) allows for continuous measurement of daily to subseasonal changes in basal water pressure gradient, channel size, and sediment transport. We observe intermittent subglacial water pressure gradient changes during the melt season, at odds with common assumptions of slowly varying, low-pressure channels. These observations indicate that changes in channel size do not keep pace with changes in discharge. This behavior strongly affects glacier dynamics and subglacial channel erosion at Mendenhall Glacier, where episodic periods of high water pressure gradients enhance glacier surface velocity and channel sediment transport by up to 30% and 50%, respectively. We expect the application of this framework to future seismic observations acquired at glaciers worldwide to improve our understanding of subglacial processes.

The influence of ice melange on fjord seiches

Abstract We compute the eigenmodes (seiches) of the barotropic and baroclinic hydrodynamic equations for an idealized fjord having length and depth scales similar to those of Ilulissat Icefjord, Greenland, into which Jakobshavn Isbræ (also known as Sermeq Kujalleq) discharges. The purpose of the computation is to determine the fjord’s seiche behavior when forced by iceberg calving, capsize and melange movement. Poorly constrained bathymetry and stratification details are an acknowledged obstacle. We are, nevertheless, able to make general statements about the spectra of external and internal seiches using numerical simulations of ideal one-dimensional channel geometry. Of particular significance in our computation is the role of weakly coupled ice melange, which we idealize as a simple array of 20 icebergs of uniform dimensions equally spaced within the fjord. We find that the presence of these icebergs acts to (1) slow down the propagation of both external and internal seiches and (2) introduce band gaps where energy propagation (group velocity) vanishes. If energy is introduced into the fjord within the period range covered by a band gap, it will remain trapped as an evanescent oscillatory mode near its source, thus contributing to localized energy dissipation and ice/melange fragmentation.

Impact of hydrodynamics on seismic signals generated by iceberg collisions

Abstract Full-glacier-thickness icebergs are frequently observed to capsize as they calve into the ocean. As they capsize they may collide with the glaciers’ termini; previous studies have hypothesized that such collisions are the source of teleseismic ‘glacial earthquakes’. We use laboratory-scale experiments, force-balance modeling and theoretical arguments to show that (1) the contact forces during these collisions are strongly influenced by hydrodynamic forces and (2) the associated glacial earthquake magnitudes (expressed as twice-integrated force histories) are related to the energy released by the capsizing icebergs plus a hydrodynamic term that is composed of drag forces and hydrodynamic pressure. Our experiments and first-order modeling efforts suggest that, due to hydrodynamic forces, both contact force and glacial earthquake magnitudes may not be directly proportional to the energy released by the capsizing icebergs (as might be expected). Most importantly, however, our results highlight the need to better understand the hydrodynamics of iceberg capsize prior to being able to accurately interpret seismic signals generated by iceberg collisions.

Blocking a wave: frequency band gaps in ice shelves with periodic crevasses

Abstract We assess how the propagation of high-frequency elastic-flexural waves through an ice shelf is modified by the presence of spatially periodic crevasses. Analysis of the normal modes supported by the ice shelf with and without crevasses reveals that a periodic crevasse distribution qualitatively changes the mechanical response. The normal modes of an ice shelf free of crevasses are evenly distributed as a function of frequency. In contrast, the normal modes of a crevasse-ridden ice shelf are distributed unevenly. There are ‘band gaps’, frequency ranges over which no eigenmodes exist. A model ice shelf that is 50 km in lateral extent and 300 m thick with crevasses spaced 500 m apart has a band gap from 0.2 to 0.38 Hz. This is a frequency range relevant for ocean-wave/ice-shelf interactions. When the outermost edge of the crevassed ice shelf is oscillated at a frequency within the band gap, the ice shelf responds very differently from a crevasse-free ice shelf. The flexural motion of the crevassed ice shelf is confined to a small region near the outermost edge of the ice shelf and effectively ‘blocked’ from reaching the interior.