scholarly journals A Discontinuous ODE Model of the Glacial Cycles with Diffusive Heat Transport

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 316
Author(s):  
James Walsh ◽  
Esther Widiasih
Keyword(s):  
Heat Transport ◽  
Ice Sheet ◽  
Ode Model ◽  
Glacial Cycles ◽  
Transport Efficiency ◽  
Orbital Parameters ◽  
Perturbation Problem ◽  
Transport Component ◽  
Ice Sheet Mass Balance ◽  
Unique Limit

We present a new discontinuous ordinary differential equation (ODE) model of the glacial cycles. Model trajectories flip from a glacial to an interglacial state, and vice versa, via a switching mechanism motivated by ice sheet mass balance principles. Filippov’s theory of differential inclusions is used to analyze the system, which can be viewed as a nonsmooth geometric singular perturbation problem. We prove the existence of a unique limit cycle, corresponding to the Earth’s glacial cycles. The diffusive heat transport component of the model is ideally suited for investigating the competing temperature gradient and transport efficiency feedbacks, each associated with ice-albedo feedback. It is the interplay of these feedbacks that determines the maximal extent of the ice sheet. In the nonautonomous setting, model glacial cycles persist when subjected to external forcing brought on by changes in Earth’s orbital parameters over geologic time. The system also exhibits various bifurcation scenarios as key parameters vary.

Greenland ice sheet mass balance: a review

2015 ◽  
Vol 78 (4) ◽  
pp. 046801 ◽  
Author(s):  
Shfaqat A Khan ◽  
Andy Aschwanden ◽  
Anders A Bjørk ◽  
John Wahr ◽  
Kristian K Kjeldsen ◽  
...  
Keyword(s):  
Mass Balance ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Sheet Mass Balance

scholarly journals Monitoring southwest Greenland’s ice sheet melt with ambient seismic noise

2016 ◽  
Vol 2 (5) ◽  
pp. e1501538 ◽  
Author(s):  
Aurélien Mordret ◽  
T. Dylan Mikesell ◽  
Christopher Harig ◽  
Bradley P. Lipovsky ◽  
Germán A. Prieto
Keyword(s):  
Mass Loss ◽  
Mass Balance ◽  
Sea Level ◽  
Seismic Noise ◽  
Seismic Velocity ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Sea Level Changes ◽  
Ice Sheet Mass Balance ◽  
Velocity Changes

The Greenland ice sheet presently accounts for ~70% of global ice sheet mass loss. Because this mass loss is associated with sea-level rise at a rate of 0.7 mm/year, the development of improved monitoring techniques to observe ongoing changes in ice sheet mass balance is of paramount concern. Spaceborne mass balance techniques are commonly used; however, they are inadequate for many purposes because of their low spatial and/or temporal resolution. We demonstrate that small variations in seismic wave speed in Earth’s crust, as measured with the correlation of seismic noise, may be used to infer seasonal ice sheet mass balance. Seasonal loading and unloading of glacial mass induces strain in the crust, and these strains then result in seismic velocity changes due to poroelastic processes. Our method provides a new and independent way of monitoring (in near real time) ice sheet mass balance, yielding new constraints on ice sheet evolution and its contribution to global sea-level changes. An increased number of seismic stations in the vicinity of ice sheets will enhance our ability to create detailed space-time records of ice mass variations.

scholarly journals Constraining GRACE-derived cryosphere-attributed signal to irregularly shaped ice-covered areas

2013 ◽  
Vol 7 (6) ◽  
pp. 1901-1914 ◽  
Author(s):  
W. Colgan ◽  
S. Luthcke ◽  
W. Abdalati ◽  
M. Citterio
Keyword(s):  
Monte Carlo ◽  
Mass Loss ◽  
Mass Balance ◽  
Spherical Harmonic ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Caps ◽  
Ice Coverage ◽  
Ice Sheet Mass Balance ◽  
Harmonic Representation

Abstract. We use a Monte Carlo approach to invert a spherical harmonic representation of cryosphere-attributed mass change in order to infer the most likely underlying mass changes within irregularly shaped ice-covered areas at nominal 26 km resolution. By inverting a spherical harmonic representation through the incorporation of additional fractional ice coverage information, this approach seeks to eliminate signal leakage between non-ice-covered and ice-covered areas. The spherical harmonic representation suggests a Greenland mass loss of 251 ± 25 Gt a−1 over the December 2003 to December 2010 period. The inversion suggests 218 ± 20 Gt a−1 was due to the ice sheet proper, and 34 ± 5 Gt a−1 (or ~14%) was due to Greenland peripheral glaciers and ice caps (GrPGICs). This mass loss from GrPGICs exceeds that inferred from all ice masses on both Ellesmere and Devon islands combined. This partition therefore highlights that GRACE-derived "Greenland" mass loss cannot be taken as synonymous with "Greenland ice sheet" mass loss when making comparisons with estimates of ice sheet mass balance derived from techniques that sample only the ice sheet proper.

scholarly journals The sensitivity of the Greenland Ice Sheet to glacial–interglacial oceanic forcing

2018 ◽  
Vol 14 (4) ◽  
pp. 455-472 ◽  
Author(s):  
Ilaria Tabone ◽  
Javier Blasco ◽  
Alexander Robinson ◽  
Jorge Alvarez-Solas ◽  
Marisa Montoya
Keyword(s):  
Sea Level ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
High Sensitivity ◽  
Glacial Cycles ◽  
The Past ◽  
Primary Driver ◽  
Oceanic Forcing ◽  
Atmospheric Variations

Abstract. Observations suggest that during the last decades the Greenland Ice Sheet (GrIS) has experienced a gradually accelerating mass loss, in part due to the observed speed-up of several of Greenland's marine-terminating glaciers. Recent studies directly attribute this to warming North Atlantic temperatures, which have triggered melting of the outlet glaciers of the GrIS, grounding-line retreat and enhanced ice discharge into the ocean, contributing to an acceleration of sea-level rise. Reconstructions suggest that the influence of the ocean has been of primary importance in the past as well. This was the case not only in interglacial periods, when warmer climates led to a rapid retreat of the GrIS to land above sea level, but also in glacial periods, when the GrIS expanded as far as the continental shelf break and was thus more directly exposed to oceanic changes. However, the GrIS response to palaeo-oceanic variations has yet to be investigated in detail from a mechanistic modelling perspective. In this work, the evolution of the GrIS over the past two glacial cycles is studied using a three-dimensional hybrid ice-sheet–shelf model. We assess the effect of the variation of oceanic temperatures on the GrIS evolution on glacial–interglacial timescales through changes in submarine melting. The results show a very high sensitivity of the GrIS to changing oceanic conditions. Oceanic forcing is found to be a primary driver of GrIS expansion in glacial times and of retreat in interglacial periods. If switched off, palaeo-atmospheric variations alone are not able to yield a reliable glacial configuration of the GrIS. This work therefore suggests that considering the ocean as an active forcing should become standard practice in palaeo-ice-sheet modelling.

scholarly journals Widespread distribution of supraglacial lakes around the margin of the East Antarctic Ice Sheet

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Chris R. Stokes ◽  
Jack E. Sanderson ◽  
Bertie W. J. Miles ◽  
Stewart S. R. Jamieson ◽  
Amber A. Leeson
Keyword(s):  
Ice Sheet ◽  
Ice Shelf ◽  
Typically Develop ◽  
Ice Shelves ◽  
Supraglacial Lakes ◽  
Marginal Areas ◽  
Surface Slopes ◽  
Highly Sensitive ◽  
Ice Sheet Mass Balance ◽  
High Resolution Satellite Imagery

Abstract Supraglacial lakes are important to ice sheet mass balance because their development and drainage has been linked to changes in ice flow velocity and ice shelf disintegration. However, little is known about their distribution on the world’s largest ice sheet in East Antarctica. Here, we use ~5 million km2 of high-resolution satellite imagery to identify >65,000 lakes (>1,300 km2) that formed around the peak of the melt season in January 2017. Lakes occur in most marginal areas where they typically develop at low elevations (<100 m) and on low surface slopes (<1°), but they can exist 500 km inland and at elevations >1500 m. We find that lakes often cluster a few kilometres down-ice from grounding lines and ~60% (>80% by area) develop on ice shelves, including some potentially vulnerable to collapse driven by lake-induced hydro-fracturing. This suggests that parts of the ice sheet may be highly sensitive to climate warming.

scholarly journals Basal temperature conditions of the Greenland ice sheet during the glacial cycles

1996 ◽  
Vol 23 ◽  
pp. 226-236 ◽  
Author(s):  
Philippe Huybrechts
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Cores ◽  
Ice Thickness ◽  
Glacial Cycle ◽  
Glacial Cycles ◽  
Temperature Conditions ◽  
Strongly Damped

A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.

scholarly journals Using the temporal variability of satellite radar altimetric observations to map surface properties of the Antarctic ice sheet

1998 ◽  
Vol 44 (147) ◽  
pp. 197-206 ◽  
Author(s):  
Benoît Legrésy ◽  
Frédérique Rémy
Keyword(s):  
Ice Sheet ◽  
Temporal Variations ◽  
Radar Altimeter ◽  
Height Measurement ◽  
Radar Echoes ◽  
Measuring Surface ◽  
Antarctic Continent ◽  
Ice Sheet Mass Balance ◽  
Satellite Radar ◽  
The Antarctic

AbstractThe problem of measuring surface height and snowpack characteristics from satellite radar altimeter echoes is investigated. In this paper, we perform an analysis of the ERS1 altimeter dataset acquired during a 3 day repeat orbit. The analysis reveals that there are temporal variations in shapes of the radar altimeter echo and that these variations are linked to meteorological phenomena. The time- and space-scales over which these variations apply are a few to tens of days and a few hundred kilometres, respectively. This phenomenon, if not accounted for, can create error in the height measurement. A numerical echo model is used to recover snowpack characteristics by taking advantage of the temporal variations of the radar echoes. A map of penetration depth of the radar waves in the Ku band over the Antarctic continent is obtained and suggests that grain-size produces the dominant effect on radar extinction in the snowpack at this frequency. Finally, a procedure is proposed to correct the height measurement within the context of ice-sheet mass-balance survey.

scholarly journals Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume

Nature ◽  
2013 ◽  
Vol 500 (7461) ◽  
pp. 190-193 ◽  
Author(s):  
Ayako Abe-Ouchi ◽  
Fuyuki Saito ◽  
Kenji Kawamura ◽  
Maureen E. Raymo ◽  
Jun’ichi Okuno ◽  
...  
Keyword(s):  
Ice Sheet ◽  
Glacial Cycles
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