scholarly journals A simple equation for the surface-elevation feedback of ice sheets

2016 ◽  
Author(s):  
A. Levermann ◽  
R. Winkelmann
Keyword(s):  
Numerical Models ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
The Self ◽  
Simple Equation ◽  
Surface Elevation ◽  
Coastal Protection ◽  
Temperature Threshold ◽  
Surface Mass ◽  
Logarithmic Equation

Abstract. In recent decades, the Greenland Ice Sheet is been losing mass and thereby contributed to global sea-level rise. The ice loss is likely to increase under future warming. Beyond a critical temperature threshold, a meltdown of the Greenland Ice Sheet is induced by the self-enforcing feedback between its lowering surface elevation and its increasing surface mass loss: The more ice is lost, the lower the ice surface reaches into the atmosphere and the warmer the surrounding air becomes which fosters melting and further ice loss. The rate of ice loss is highly relevant for coastal protection worldwide. The computation of this rate so far relies on complex numerical models as it should be. In order to contribute a little to the conceptual understanding, we derive here a simple equation for the self-enforcing feedback and use it to estimate the melt time for different levels of warming using three observable characteristics of the ice sheet itself and its surroundings. When the volume loss is dominated by the feedback, the resulting logarithmic equation unifies existing numerical simulations and shows that the melt time depends critically on the level of warming with a critical slowing-down near the threshold: The median time to lose 10 % of the present-day ice volume varies between about 3500 years for a temperature level of 0.5 °C above the threshold and 500 years for 5 °C. Unless future observations show a significantly higher melting sensitivity than currently observed, a complete melt down is unlikely within the next 2000 years without significant ice-dynamical contributions.

scholarly journals A simple equation for the melt elevation feedback of ice sheets

2016 ◽  
Vol 10 (4) ◽  
pp. 1799-1807 ◽  
Author(s):  
Anders Levermann ◽  
Ricarda Winkelmann
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Numerical Models ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
The Self ◽  
Simple Equation ◽  
Coastal Protection ◽  
Temperature Threshold ◽  
Ice Dynamics

Abstract. In recent decades, the Greenland Ice Sheet has been losing mass and has thereby contributed to global sea-level rise. The rate of ice loss is highly relevant for coastal protection worldwide. The ice loss is likely to increase under future warming. Beyond a critical temperature threshold, a meltdown of the Greenland Ice Sheet is induced by the self-enforcing feedback between its lowering surface elevation and its increasing surface mass loss: the more ice that is lost, the lower the ice surface and the warmer the surface air temperature, which fosters further melting and ice loss. The computation of this rate so far relies on complex numerical models which are the appropriate tools for capturing the complexity of the problem. By contrast we aim here at gaining a conceptual understanding by deriving a purposefully simple equation for the self-enforcing feedback which is then used to estimate the melt time for different levels of warming using three observable characteristics of the ice sheet itself and its surroundings. The analysis is purely conceptual in nature. It is missing important processes like ice dynamics for it to be useful for applications to sea-level rise on centennial timescales, but if the volume loss is dominated by the feedback, the resulting logarithmic equation unifies existing numerical simulations and shows that the melt time depends strongly on the level of warming with a critical slowdown near the threshold: the median time to lose 10 % of the present-day ice volume varies between about 3500 years for a temperature level of 0.5 °C above the threshold and 500 years for 5 °C. Unless future observations show a significantly higher melting sensitivity than currently observed, a complete meltdown is unlikely within the next 2000 years without significant ice-dynamical contributions.

scholarly journals Surface mass balance of the Greenland ice sheet from climate-analysis data and accumulation/runoff models

2002 ◽  
Vol 35 ◽  
pp. 67-72 ◽  
Author(s):  
Edward Hanna ◽  
Philippe Huybrechts ◽  
Thomas L. Mote
Keyword(s):  
Mass Balance ◽  
Satellite Data ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Snow Accumulation ◽  
Surface Elevation ◽  
Great Promise ◽  
Surface Mass Balance ◽  
Ice Dynamics ◽  
Surface Mass

AbstractWe used surface climate fields from high-resolution (~0.5660.56˚) European Centre for Medium-RangeWeather Forecasts (ECMWF) operational analyses (1992–98), together with meteorological and glaciological models of snow accumulation and surface meltwater runoff/retention, to produce novel maps of Greenland ice sheet (GIS) net accumulation, net runoff and surface mass balance (SMB). We compared our runoff maps with similar-scaled runoff (melt minus refreezing) maps based on passive-microwave satellite data. Our gross spatial/temporal patterns of runoff compared well with those from the satellite data, although amounts of modelled runoff are likely too low. Mean accumulation was 0.287 (0.307)ma–1, and mean runoff was 0.128 (0.151)ma–1, averaged across the W. Abdalati (T. L. Mote) GIS mask. Corresponding mean SMB was 0.159 (0.156)ma–1, with considerable interannual variability (standard deviation ~0.11ma–1) primarily due to variations in runoff. Considering best estimates of current iceberg calving, overall the GIS is probably currently losing mass. Our study shows great promise for meaningfully modelling SMB based on forthcoming ``second-generation’’ ECMWF re-analysis (ERA-40) data, and comparing the results with ongoing laser/radarmeasurements of surface elevation. This should help elucidate to what extent surface elevation changes are caused by short-term SMB variations or other factors (e.g. ice dynamics).

scholarly journals Elevation change of the Greenland Ice Sheet due to surface mass balance and firn processes, 1960–2014

2015 ◽  
Vol 9 (6) ◽  
pp. 2009-2025 ◽  
Author(s):  
P. Kuipers Munneke ◽  
S. R. M. Ligtenberg ◽  
B. P. Y. Noël ◽  
I. M. Howat ◽  
J. E. Box ◽  
...  
Keyword(s):  
Mass Balance ◽  
Volume Change ◽  
Climate Model ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Elevation ◽  
Surface Mass Balance ◽  
Elevation Change ◽  
Ice Dynamics ◽  
Surface Mass

Abstract. Observed changes in the surface elevation of the Greenland Ice Sheet are caused by ice dynamics, basal elevation change, basal melt, surface mass balance (SMB) variability, and by compaction of the overlying firn. The last two contributions are quantified here using a firn model that includes compaction, meltwater percolation, and refreezing. The model is forced with surface mass fluxes and temperature from a regional climate model for the period 1960–2014. The model results agree with observations of surface density, density profiles from 62 firn cores, and altimetric observations from regions where ice-dynamical surface height changes are likely small. In areas with strong surface melt, the firn model overestimates density. We find that the firn layer in the high interior is generally thickening slowly (1–5 cm yr−1). In the percolation and ablation areas, firn and SMB processes account for a surface elevation lowering of up to 20–50 cm yr−1. Most of this firn-induced marginal thinning is caused by an increase in melt since the mid-1990s and partly compensated by an increase in the accumulation of fresh snow around most of the ice sheet. The total firn and ice volume change between 1980 and 2014 is estimated at −3295 ± 1030 km3 due to firn and SMB changes, corresponding to an ice-sheet average thinning of 1.96 ± 0.61 m. Most of this volume decrease occurred after 1995. The computed changes in surface elevation can be used to partition altimetrically observed volume change into surface mass balance and ice-dynamically related mass changes.

scholarly journals SeaRISE experiments revisited: potential sources of spread in multi-model projections of the Greenland ice sheet

2016 ◽  
Vol 10 (1) ◽  
pp. 43-63 ◽  
Author(s):  
F. Saito ◽  
A. Abe-Ouchi ◽  
K. Takahashi ◽  
H. Blatter
Keyword(s):  
Numerical Models ◽  
Ice Sheet ◽  
Flow Characteristics ◽  
Greenland Ice Sheet ◽  
Temperature History ◽  
Model Parameters ◽  
Surface Mass ◽  
Surface Climate ◽  
Model Flow ◽  
Potential Sources

Abstract. The present paper revisits the future surface-climate experiments on the Greenland ice sheet proposed by the Sea-level Response to Ice Sheet Evolution (SeaRISE; Bindschadler et al., 2013) study. The projections of the different SeaRISE participants show dispersion, which has not been examined in detail to date. A series of sensitivity experiments are conducted and analyzed using the ice-sheet model for integrated Earth-system studies (IcIES) by replacing one or more formulations of the model parameters with those adopted in other model(s). The results show that large potential sources of the dispersion among the projections of the different SeaRISE participants are differences in the initialization methods and in the surface mass balance methods, and both aspects have almost equal impact on the results. The treatment of ice-sheet margins in the simulation has a secondary impact on the dispersion. We conclude that spinning up the model using fixed topography through the spin-up period while the temperature is allowed to evolve according to the surface temperature history is the preferred representation, at least for the experiment configuration examined in the present paper. A benchmark model experimental setup that most of the numerical models can perform is proposed for future intercomparison projects, in order to evaluate the uncertainties relating to pure ice-sheet model flow characteristics.

scholarly journals Ice dynamics will remain a primary driver of Greenland ice sheet mass loss over the next century

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Youngmin Choi ◽  
Mathieu Morlighem ◽  
Eric Rignot ◽  
Michael Wood
Keyword(s):  
Mass Loss ◽  
Mass Balance ◽  
Numerical Models ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Ice Dynamics ◽  
Surface Mass ◽  
Flow Acceleration ◽  
Total Mass Loss

AbstractThe mass loss of the Greenland Ice Sheet is nearly equally partitioned between a decrease in surface mass balance from enhanced surface melt and an increase in ice dynamics from the acceleration and retreat of its marine-terminating glaciers. Much uncertainty remains in the future mass loss of the Greenland Ice Sheet due to the challenges of capturing the ice dynamic response to climate change in numerical models. Here, we estimate the sea level contribution of the Greenland Ice Sheet over the 21st century using an ice-sheet wide, high-resolution, ice-ocean numerical model that includes surface mass balance forcing, thermal forcing from the ocean, and iceberg calving dynamics. The model is calibrated with ice front observations from the past eleven years to capture the recent evolution of marine-terminating glaciers. Under a business as usual scenario, we find that northwest and central west Greenland glaciers will contribute more mass loss than other regions due to ice front retreat and ice flow acceleration. By the end of century, ice discharge from marine-terminating glaciers will contribute 50 ± 20% of the total mass loss, or twice as much as previously estimated although the contribution from the surface mass balance increases towards the end of the century.

scholarly journals Effect of uncertainty in surface mass balance–elevation feedback on projections of the future sea level contribution of the Greenland ice sheet – Part 1: Parameterisation

2013 ◽  
Vol 7 (1) ◽  
pp. 635-674 ◽  
Author(s):  
T. L. Edwards ◽  
X. Fettweis ◽  
O. Gagliardini ◽  
F. Gillet-Chaulet ◽  
H. Goelzer ◽  
...  
Keyword(s):  
Mass Balance ◽  
Sea Level ◽  
Global Climate ◽  
Probability Distributions ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Elevation ◽  
Surface Mass Balance ◽  
Surface Mass ◽  
The North

Abstract. We present a new parameterisation that relates surface mass balance (SMB: the sum of surface accumulation and surface ablation) to changes in surface elevation of the Greenland ice sheet (GrIS) for the MAR regional climate model. The motivation is to dynamically adjust SMB as the GrIS evolves, allowing us to force ice sheet models with SMB simulated by MAR while incorporating the SMB–elevation feedback, without the substantial technical challenges of coupling the two models. This also allows us to assess the effect of elevation feedback uncertainty on the GrIS contribution to sea level, using multiple global climate and ice sheet models, without the need for additional, expensive MAR simulations. We estimate this relationship separately below and above the equilibrium line altitude (ELA, separating negative and positive SMB) and for regions north and south of 77° N, from a set of MAR simulations in which we alter the ice sheet surface elevation. These give four "SMB lapse rates", gradients that relate SMB changes to elevation changes. We assess uncertainties within a Bayesian framework, estimating probability distributions for each gradient from which we present best estimates and credibility intervals (CIs) that bound 95% of the probability. Below the ELA our gradient estimates are mostly positive, because SMB usually increases with elevation: 0.54 (95% CI: −0.22 to 1.34) kg m−3 a−1 for the north, and 1.89 (1.03 to 2.61) kg m−3 a−1 for the south. Above the ELA the gradients are much smaller: 0.09 (−0.03 to 0.22) kg m−3 a−1 in the north, and 0.06 (−0.07 to 0.56) kg m−3 a−1 in the south, because SMB can either increase or decrease in response to increased elevation. Our statistically based approach allows us to make probabilistic assessments for the effect of elevation feedback uncertainty on sea level projections. In a companion paper we use the best estimates and upper and lower CI bounds in five ice sheet models, and the full probability distributions in another, to adjust simulated SMB from MAR forced by two global climate models for the SRES A1B scenario (Edwards et al., 2013).

scholarly journals Elevation change of the Greenland ice sheet due to surface mass balance and firn processes, 1960–2013

2015 ◽  
Vol 9 (3) ◽  
pp. 3541-3580 ◽  
Author(s):  
P. Kuipers Munneke ◽  
S. R. M. Ligtenberg ◽  
B. P. Y. Noël ◽  
I. M. Howat ◽  
J. E. Box ◽  
...  
Keyword(s):  
Mass Balance ◽  
Volume Change ◽  
Climate Model ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Elevation ◽  
Surface Mass Balance ◽  
Elevation Change ◽  
Ice Dynamics ◽  
Surface Mass

Abstract. Observed changes in the surface elevation of the Greenland ice sheet are caused by ice dynamics, basal elevation change, surface mass balance (SMB) variability, and by compaction of the overlying firn. The latter two contributions are quantified here using a firn model that includes compaction, meltwater percolation, and refreezing. The model is forced with surface mass fluxes and temperature from a regional climate model for the period 1960–2013. The model results agree with observations of surface density, density profiles from 62 firn cores, and altimetric observations from regions where ice-dynamical surface height changes are likely small. We find that the firn layer in the high interior is generally thickening slowly (1–5 cm yr−1). In the percolation and ablation areas, firn and SMB processes account for a surface elevation lowering of up to 20–50 cm yr−1. Most of this firn-induced marginal thinning is caused by an increase in melt since the mid-1990s, and partly compensated by an increase in the accumulation of fresh snow around most of the ice sheet. The total firn and ice volume change between 1980 and 2013 is estimated at −3900 ± 1030 km3 due to firn and SMB, corresponding to an ice-sheet average thinning of 2.32 ± 0.61 m. Most of this volume decrease occurred after 1995. The computed changes in surface elevation can be used to partition altimetrically observed volume change into surface mass balance and ice-dynamically related mass changes.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

Contemporary (1960–2012) Evolution of the Climate and Surface Mass Balance of the Greenland Ice Sheet

2013 ◽  
Vol 35 (5) ◽  
pp. 1155-1174 ◽  
Author(s):  
J. H. van Angelen ◽  
M. R. van den Broeke ◽  
B. Wouters ◽  
J. T. M. Lenaerts
Keyword(s):  
Mass Balance ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Surface Mass

scholarly journals Simulation of the future sea level contribution of Greenland with a new glacial system model

2018 ◽  
Vol 12 (10) ◽  
pp. 3097-3121 ◽  
Author(s):  
Reinhard Calov ◽  
Sebastian Beyer ◽  
Ralf Greve ◽  
Johanna Beckmann ◽  
Matteo Willeit ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Surface Temperature ◽  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
System Model ◽  
Surface Mass Balance ◽  
Surface Mass

Abstract. We introduce the coupled model of the Greenland glacial system IGLOO 1.0, including the polythermal ice sheet model SICOPOLIS (version 3.3) with hybrid dynamics, the model of basal hydrology HYDRO and a parameterization of submarine melt for marine-terminated outlet glaciers. The aim of this glacial system model is to gain a better understanding of the processes important for the future contribution of the Greenland ice sheet to sea level rise under future climate change scenarios. The ice sheet is initialized via a relaxation towards observed surface elevation, imposing the palaeo-surface temperature over the last glacial cycle. As a present-day reference, we use the 1961–1990 standard climatology derived from simulations of the regional atmosphere model MAR with ERA reanalysis boundary conditions. For the palaeo-part of the spin-up, we add the temperature anomaly derived from the GRIP ice core to the years 1961–1990 average surface temperature field. For our projections, we apply surface temperature and surface mass balance anomalies derived from RCP 4.5 and RCP 8.5 scenarios created by MAR with boundary conditions from simulations with three CMIP5 models. The hybrid ice sheet model is fully coupled with the model of basal hydrology. With this model and the MAR scenarios, we perform simulations to estimate the contribution of the Greenland ice sheet to future sea level rise until the end of the 21st and 23rd centuries. Further on, the impact of elevation–surface mass balance feedback, introduced via the MAR data, on future sea level rise is inspected. In our projections, we found the Greenland ice sheet to contribute between 1.9 and 13.0 cm to global sea level rise until the year 2100 and between 3.5 and 76.4 cm until the year 2300, including our simulated additional sea level rise due to elevation–surface mass balance feedback. Translated into additional sea level rise, the strength of this feedback in the year 2100 varies from 0.4 to 1.7 cm, and in the year 2300 it ranges from 1.7 to 21.8 cm. Additionally, taking the Helheim and Store glaciers as examples, we investigate the role of ocean warming and surface runoff change for the melting of outlet glaciers. It shows that ocean temperature and subglacial discharge are about equally important for the melting of the examined outlet glaciers.

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