TCThe CryosphereTCThe Cryosphere1994-0424Copernicus GmbHGöttingen, Germany10.5194/tc-9-1039-2015Ice-dynamic projections of the Greenland ice sheet in response to atmospheric and oceanic warmingFürstJ. J.johannes.fuerst@vub.ac.beGoelzerH.https://orcid.org/0000-0002-5878-9599HuybrechtsP.https://orcid.org/0000-0003-1406-0525Earth System Science & Departement Geografie, Vrije Universiteit Brussel, Brussels, Belgium
Invited contribution by J. J. Fürst, recipient of the EGU Outstanding Student Poster Award 2011.
J. J. Fürst (johannes.fuerst@vub.ac.be)20May2015931039106210June201416July20145March201516April2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.the-cryosphere.net/9/1039/2015/tc-9-1039-2015.htmlThe full text article is available as a PDF file from https://www.the-cryosphere.net/9/1039/2015/tc-9-1039-2015.pdf
Continuing global warming will have a strong impact on the Greenland
ice sheet in the coming centuries. During the last decade (2000–2010), both
increased melt-water runoff and enhanced ice discharge from calving
glaciers have contributed 0.6±0.1 mm yr-1 to
global sea-level rise, with a relative contribution of 60 and 40 % respectively.
Here we use a higher-order ice flow model, spun up to present day, to simulate future ice volume changes driven by
both atmospheric and oceanic temperature changes. For these
projections, the flow model accounts for runoff-induced basal
lubrication and ocean warming-induced discharge increase at the
marine margins. For a suite of 10 atmosphere and ocean general
circulation models and four representative concentration pathway
scenarios, the projected sea-level rise between 2000 and 2100 lies in the range of +1.4 to
+16.6 cm. For two low emission scenarios,
the projections are conducted up to 2300. Ice loss rates are found
to abate for the most favourable scenario where the warming peaks in this century, allowing
the ice sheet to maintain a geometry close to the
present-day state. For the other moderate scenario, loss rates remain at a constant level over 300 years. In any scenario, volume loss is
predominantly caused by increased surface melting as the
contribution from enhanced ice discharge decreases over time and is
self-limited by thinning and retreat of the marine margin, reducing
the ice–ocean contact area. As confirmed by other studies, we find that the effect of enhanced basal
lubrication on the volume evolution is negligible on
centennial timescales. Our projections show that the
observed rates of volume change over the last decades cannot simply
be extrapolated over the 21st century on account of
a different balance of processes causing ice loss over time. Our
results also indicate that the largest source of uncertainty arises
from the surface mass balance and the underlying climate change
projections, not from ice dynamics.
Introduction
Volume changes of the Greenland
ice sheet result from a balance between ice accumulation on its
surface and ice loss around its margin by both meltwater runoff and
ice discharge into the surrounding ocean. In the 30-year period
prior to 1990, the ice sheet has been in a virtual balance
with the prevailing climate but has since been losing mass at an
increasing rate
.
Almost
half of this recent mass loss is attributed to increased ice discharge
at the marine margins
, with a tendency towards
relatively more surface melting since 2005 . During
the period 1972 to 1995, glacier terminus positions and ice flow were
rather stable around Greenland
. Over the last
decade, however, ice-sheet-wide surface velocity observations reveal
complex spatial and temporal changes with accelerated glacier flow in
the northwest, more variability in the southeast and relatively steady
flow elsewhere .
A prominent example of recent dynamic changes of outlet glaciers in
west Greenland is Jakobshavn Isbræ. Starting in 1998, its frontal
zone sped up from about 6 to
12 km yr-1 within 5 years
. One hypothesis links the acceleration
to a successive loss of buttressing on the grounded ice as the
floating ice tongue destabilised and collapsed. Another
hypothesis points to a speed-up initiated by a weakening of the ice at
the lateral glacier margins . In any
case, the initiation of the glacier acceleration and retreat coincides
with an intrusion of warm Atlantic Water into Disco Bay that likely
entered the local fjord systems .
In southeast Greenland, speed-up and retreat peaked in 2005 for Helheim
and Kangerlussuaq glaciers, which are both located at the end of ∼80 km long fjords. Before 2005, the speed and retreat pattern
of both glaciers were not synchronous
. While Helheim
showed a continuous acceleration starting in 2002 with a cumulative
retreat of the ice front of 8 km by 2005, Kangerlussuaq exhibited an
abrupt retreat and acceleration between 2004 and 2005. Yet for both
glaciers, the acceleration events were temporary and glacier speeds
dropped again to the pre-speed-up level
. There is evidence that relatively warm waters
temporarily reached the Greenland coast in this region in 2003 and 2004 . Similar temperature anomalies were not observed thereafter, coinciding with the dynamic re-stabilisation of outlet glaciers.
At the northern margin of the Greenland ice sheet, Petermann
Glacier recently lost a major part of its 80 km long floating
tongue. On 4 August 2010, about one-fifth of the ice tongue broke off
and drifted out of the fjord into Nares Strait
. In line with the above speed-up
examples, this breakup event was also preceded by ocean warming in the
100 m above the 300 m deep sill at the southern end of Nares
Strait .
Warm and saline waters of tropical origin are in fact found at
intermediate depth beyond the continental shelf break all around
Greenland. There is evidence that these waters can flow over the sills
of individual fjord systems around Greenland
. Warming of deep fjord water can
intensify submarine melt below an existing ice shelf or mélange
cover , or directly at the calving front
. The ice mélange is thought to play a role in
the mechanical backstress it applies on the calving face. Thinning in the frontal zone, in
turn, reduces the buttressing on the upstream glacier trunk and alters
the local stress regime in favour of glacier acceleration
. This provides a physical explanation
of the simultaneous occurrence of recent glacier accelerations with warm waters
reaching the respective shorelines.
Apart from the oceanic influence, the ice flow towards the margin is
also affected by seasonal meltwater production at the surface that
finds its way to the ice-sheet base
e.g.. Observations on both ice velocity and local
runoff at various positions along the western flank of the Greenland
ice sheet show distinct speed-up events during the melt season
. Though observations and simulations indicate that the effect might be small on annual timescales , basal lubrication is
hypothesised to enhance ice flow towards the marine margin and thereby
influence ice discharge.
While ice discharge changes explain about 40 % of the recent ice loss
on Greenland, the remainder is attributed to
a decreasing surface mass balance
. Most direct observations of the surface mass balance (SMB)
components have local and at most regional character and are limited to the last
decade . Therefore, they are too short and
not representative to directly infer ice-sheet-wide trends. Yet SMB
modelling has improved with the availability of validation
data. Regional climate models are now capable of producing
a physically based, ice-sheet-wide SMB estimate
. SMB model results show that the
5 years with highest annual meltwater runoff since 1870 fall into the
period after 1998 . This concentrated
occurrence of years with peak runoff exemplifies the general increase in
runoff or decrease in SMB since the late 1990s . In addition,
the melt area has continuously increased, and melt extents
since 2000 are on average twice as large as in the early 1980s
.
For ice loss on Greenland over the next few centuries, a major
contribution is expected from a decreasing SMB, or more precisely an
increase in surface meltwater runoff . By now,
the modelling community has managed to improve regional
climate models (RCMs) to the point that they reproduce past and present
changes in various components of the SMB rather well
. Owing to a shortage in the observational
coverage, the largest source of model uncertainty remains in the
treatment and quantification of meltwater percolation and refreezing
within the snowpack. Computational constraints typically limit RCM
applications on ice-sheet-wide scales to coarse-grid resolution
(often beyond 10 km). Yet it is within a narrow band of
several tens of kilometres around the ice-sheet margin that the largest SMB
changes are expected under atmospheric warming. Assuming small perturbations, RCM simulations
often use a fixed ice-sheet geometry, thus neglecting feedbacks between surface elevation and SMB as well as between surface albedo and ice margin retreat. Under strong future warming, thinning and the resulting elevation changes at margins may become large enough that these simplifying assumptions no longer hold. For small perturbations, a downsampling procedure for RCM SMB fields could be used to correct the RCM SMB a posteriori for a changing geometry . In large-scale ice-flow models however, the SMB component often relies on temperature-index approaches
for surface melting . Though
such approaches rely on parameterisations of individual SMB
components, ice volume projections can then account for the feedback between
changes in ice sheet geometry and extent and consequent changes in SMB.
Here we include additional ice-dynamical processes
in a thermomechanically coupled, three-dimensional ice flow model
with the aim of better assessing the
impact of ice dynamics on ice volume projections. These projections
are driven by the four representative concentration pathways
(RCPs), specified by and used for the IPCC's Fifth
Assessment Report AR5; . The ice dynamic model
component includes parameterisations for ocean warming-induced
discharge increase and runoff-induced basal lubrication
(Sect. ). To sample the range of climate sensitivities,
a selection of 10 atmosphere and ocean
general circulation models (AOGCMs) from the CMIP5 data set
is used. From this climatic input, both atmospheric and oceanic forcing is
applied as anomalies to drive the ice-sheet model
(Sect. ). We first evaluate the model against observations from the recent past (Sect. ) and then explore the influence of changes in ice discharge and in SMB on the contribution of the Greenland ice sheet to future sea-level rise (Sect. ).
Model description and spin-upThe ice-sheet model
The three-dimensional, thermomechanically coupled ice-sheet model
comprises three main components that respectively describe the mass
balance at the upper and lower ice-sheet boundaries, the ice sheet dynamics and thermodynamics, and the isostatic adjustment of the Earth lithosphere
.
Ice-sheet dynamics
The simulated ice flow arises as a viscous response of the material to
gravitational forcing. Using a higher-order approximation to the Stokes momentum balance, the model accounts for effects from both vertical shear stresses and horizontal gradients in
membrane stresses . More specifically, the model adopts a multilayer
longitudinal stresses approximation of the force balance, abbreviated as LMLa in . This ice-dynamical core
allows for a more realistic inland transmission of perturbations at
the ice-sheet margin . The model is run on a 5 km uniform-resolution grid in the horizontal
plane and uses 30 non-equidistant layers in the vertical. The vertical
grid spacing is refined towards the bottom where vertical shearing is
concentrated. The flow component
of the ice-sheet model also accounts for the direct effect of ocean
warming on ice discharge and for runoff-induced lubrication. Both
effects are parameterised and presented in the following sections.
Surface mass balance
The SMB model comprises snow
accumulation, meltwater runoff and meltwater retention in the
snowpack. The background field for surface accumulation is based on the
accumulation map
for the period 1950–2000. For the ablation component,
the melt and runoff model relies on the widely used positive
degree-day runoff/retention approach
. This
approach first determines the positive degree-day sum from monthly air
temperature input, assuming a statistical variability of daily
near-surface temperatures around the monthly mean (with a standard
deviation of 4.2 ∘C). Melt rates are then determined
with different degree-day factors for snow and ice. Their values are determined by
tuning during the model spin-up (Sect. and Table 1). Surface melt is first stored as capillary
water until the snowpack becomes saturated and runoff occurs. In the
snowpack model, formation of superimposed ice occurs when water-saturated snow survives
above the impermeable
ice layer until the end of the season, and subsequently refreezes. The
SMB model relies on a parameterisation of the surface temperature
calibrated for the period 1960–1990 . The model is forced by monthly
surface air temperature and annual precipitation anomalies relative to
the 1960–1990 mean. For the period 1958–2010, the positive
degree-day runoff/retention approach has been compared to RACMO2.1/GR,
a physical snow model coupled to a high-resolution model for
atmosphere dynamics . Both approaches
for SMB agree well in terms of interannual variability (R2 coefficients of determination
of 0.79 for SMB, 0.84 for precipitation, and 0.75 for runoff).
Input data
Geometric input has been updated from the
data set with slight adjustments for our
specific model requirements . A geoid correction is applied to
reference the data set to mean sea level, which is subsequently
re-projected and interpolated from the original 1 km grid to
the ice-sheet model grid. The geothermal heat flux is inferred from
seismic data . The values were adjusted with
Gaussian functions at the deep ice core sites (NEEM, GRIP, NGRIP, Dye3
and Camp Century), assuming a radius of 100 km
to gradually blend in the difference with the background field, such that the model reproduces observed basal temperatures .
Effect of surface runoff on basal lubrication
Observations of ice velocities show seasonal speed-up in the summer
melt period
. Surface
runoff generally finds a way into the ice body through moulins and the
water is assumed to reach the bed near the ice-sheet margin. The rate
of basal meltwater discharge determines the two-fold character of the
subglacial drainage system, which in turn controls lubrication and its
effect on the sliding velocity e.g.. Observational studies often report on
successive distinct speed-up events during the melt
season .
For our model application, however, the interest is on their integrated effect over 1 year.
find that mean summer speed-up is positively correlated with daily runoff, as long as runoff
rates do not exceed a certain threshold. Above this threshold, average speed-up is somewhat
reduced as exemplified in the two-fold character of basal drainage. The annual runoff will
strongly depend on the number of days for which this threshold is exceeded. Therefore,
we assume a relation between the
annual surface runoff and the annual increase in sliding relative to the winter reference.
In this way, the speed-up parameterisation will not distinguish between years of comparable annual runoff,
caused primarily by moderate but constant melting during the entire summer season or by individual high melt peaks.
In the ice flow model, the Weertman sliding relation is therefore extended
with a multiplier SBL that depends on the annual rate of basal
meltwater discharge.
vb=SBLASHτb3
Here sliding velocities are denoted with vb, basal drag with
τb (the sum of all resistive forces), the sliding factor with AS and the ice
thickness with H. In this parameterisation, the basal meltwater discharge
rate is assumed equal to the local surface runoff R, whilst neglecting
contributions from basal melting or meltwater routing beneath the ice sheet.
The chosen 5 km spacing supports the concept that surface meltwater reaches the bed within the distance of one grid cell.
Theoretical work on subglacial drainage systems indicates a speed-up peak for
a specific rate of basal water discharge . Above this
discharge rate, a channelised basal drainage system develops, which is
associated with lower relative speed-up values. In the absence of local
runoff, no lubrication effect is simulated (SBL=1). Informed by
the best-fit parameterisation in , we apply a Poisson-like
functional dependence (Fig. ) between relative speed-up and
runoff.
SBL= 1+cRa⋅exp-bR
In this notation, the unknown parameters a, b and c are assumed
positive. Within a comprehensive uncertainty study on the chosen functional dependence (covering a large range for our three parameters),
find that the lubrication effect is of secondary importance in terms of
the centennial ice volume evolution. Therefore, only one set of parameters is used for the projections here.
Functional dependence of relative annual speed-up on local
runoff. Dark grey symbols indicate either direct field observations
or observed speed-up combined
with output from a SMB model
. Observational data originate from
Russell Glacier, east of Kangerlussuaq. The parameterisation considers a functional
dependence (black line) that is a compromise
among all observations. Grey thin lines indicate a best fit to the
respective data sets.
The three unknown parameters are determined using observational data on
annual velocity increase and runoff at two locations along the western flank
of the Greenland ice sheet (Fig. ). The first location is east
of Kangerlussuaq and upstream of Russell Glacier, often referred to as the
K-transect
.
Here a consistent picture emerges with annual mean velocities of up to
20 % above the winter background for runoff rates below 3.5 m ice
equivalent yr-1. For the Russell Glacier transect,
find the highest velocities for observed
runoff rates above 3 m yr-1. In the larger vicinity of the K-transect,
link the speed-up of several glaciers to runoff
extracted from a monthly degree-day surface meltwater runoff/retention
model. Their findings indicate a velocity peak for an annual runoff below
1 m. This difference between observed and modelled critical runoff rates is
considered in our functional dependence. For our simulated ice-sheet
geometry, our mass balance model gives annual runoff rates of up to
4 m yr-1 near the K-transect. Due to a faster inland decrease in
modelled runoff, as compared to observations, upstream speed-up would be
underestimated. Taking this into account, the following parameter values are
chosen: a=1.8, b=0.9 yr m-1 and c=0.43. For these parameters,
the maximum annual velocity lies 25 % above the winter reference for an
annual runoff rate of 2 m yr-1 (Fig. ). In this way, the presented parameterisation might be affected by the observational bias towards the western flank of the Greenland ice sheet.
However, the magnitude of
the runoff rate causing maximum speed-up agrees with theoretical estimates
using an idealised ice-sheet geometry .
Observations near Swiss Camp upstream of Jakobshavn Isbræ serve as independent
validation for the chosen functional dependence
.
Near Swiss Camp, observed annual flow increases by 2 % for an annual
runoff of not more than 1 m yr-1. Further down the glacier and
considering other outlet glaciers in the vicinity of Jakobshavn Isbræ
, a different picture
emerges with 10 % annual velocity increase for runoff rates of about
1 m yr-1. At these locations however, the velocity variations are also
influenced by seasonal changes at the marine termini.
Ice discharge response to a linear increase in ocean
temperature. The atmospheric forcing is unchanged and based on the
SMB of one climate model (i.e. 2005 MPI-ESM-LR). Ocean temperature
increase is linear for 100 years and is then kept at the same
level.
Sensitivity of future sea-level change to main model
parameters. Values from a previous tuning are indicated together with the reference values for this study. Mean and rms values are given for the ensemble
projections forced with CanESM2/RCP4.5. Positive degree day factors are given in ice equivalent
(i.e.).
21002300Degree-Degree-Enhan-SlidingSeaSeadaydaycementcoef-levellevelfactorfactorfactorficientcontri-contri-for snowfor icebutionbution[10-10][mi.e.d-1[mi.e.d-1[m2yr-1∘C-1]∘C-1][–]Pa-3][cm s.l.e.][cm s.l.e.]Previous tuning0.003000.008003.501.000Reference values0.002970.007913.280.839.332.7parameter set 10.003030.008003.220.9369.332.0parameter set 20.002940.008003.280.8289.030.5parameter set 30.002670.007763.470.9728.728.6parameter set 40.002760.007493.400.9368.428.2parameter set 50.002850.007493.401.0808.929.8parameter set 60.003030.007493.281.0809.030.4parameter set 70.003220.007493.400.7929.130.6Mean0.002930.007703.340.9329.030.1rms deviation±0.00016±0.00022±0.08±0.10±0.2±1.1Effect of ocean warming on ice discharge
With the aim to parameterise ocean-induced changes in ice discharge, outlet
glacier accelerations are linked to oceanic warming assuming a uniform
functional dependence. This choice ignores the local and regional details of the many processes
that may affect the dynamics of calving glaciers and thus the ice discharge.
Their representation is limited by the large-scale character of the envisaged
simulation, not resolving geometric details. We therefore assume that ocean
temperature changes have a first-order control on the discharge response,
being aware that the individual response depends strongly on the local fjord
and glacier geometries e.g.. Despite this
non-uniform behaviour from glacier to glacier, the pattern of recent glacier
accelerations is, to a certain degree, consistent with the variability in
offshore ocean temperatures around Greenland
. The
functional dependence is derived by relating velocity observations
to temperature
variability diagnosed from five ocean basins in available AOGCMs for the
decade 2000–2010. Observations during this decade show an average speed-up of
outlet glaciers in the southeast of 34 % and in the northwest of
28 %, while other regions show no significant trend
. Scaling these accelerations to the entire ice
sheet and weighting them with the regional discharge distribution
results in an average ice discharge
increase of about 10 to 15 %. This increase shows an almost linear trend
over the last decade . Using the residual
between observed volume changes and SMB estimates from RCMs as an indicator for
ice discharge changes , the decadal discharge
increase explains between 25 and 40 % of the total mass loss
. Considering the oceanic temperature forcing
at hand together with the fast marginal adjustment properties of the
ice-sheet model , a linear increase in discharge
is best simulated by a non-linear relation between ocean temperatures and
sliding velocities. In addition, results from a generalisation of the
flow-line response of individual outlet glaciers to a large-scale Greenland
ice-sheet application
support the choice for an exponential dependence. The selected relationship is
calibrated such that the ice-sheet model reproduces the relative contribution
of the discharge increase to the total ice loss over the last decade in
response to the considered climate models.
ASoutlet=AS⋅αΔTocean/1∘C
Here, AS is the sliding factor in Eq. (). For the tuning goal described above, we find α=5.2. The sensitivity of the projections to changes in parameter α is described in Sect. . The amplification of the sliding factor ASoutlet
applies exclusively to marine-terminated glaciers using the
temperature anomaly ΔTocean in the adjacent ocean
basins. In this way, we circumvent directly quantifying how efficiently offshore waters
enter the fjords to facilitate melt at the glacier fronts. Consequently, the parameterisation
is assumed to be valid for long-term gradual ocean warming and is not applicable for short-term warming events.
In addition, any delays in the ocean system are intrinsically neglected.
The forcing is applied up to 20 km inland from the
calving front for ice grounded below sea level to account for
a far-reaching loss in backstress on a length scale appropriate to longitudinal stress coupling
.
For a set of idealised experiments prescribing a linear increase in ocean temperatures
under constant atmospheric forcing, the ice-sheet model shows an
increase in ice discharge (Fig. ). For a 1 ∘C ocean warming over 100 years,
the sliding coefficient is increased by a factor 5.2 after 100 years. Yet, ice discharge does
not even double. One reason is that the resultant thinning at the marine margins limits
the attainable ice export . Another reason is that basal velocities do not necessarily scale linearly
with changes of AS in a higher-order flow model. After 100 years, ocean
temperatures are kept constant and ice discharge remains at an
elevated level. Yet the ongoing geometric adjustment causes a general
decrease of the ice discharge in this latter period.
Mean annual surface air temperature anomaly over the present
ice sheet extent with respect to the reference period
1960–1990. For illustration, the monthly temperature forcing is
smoothed with a 5-year running mean. Panels cover different time
periods up to 2100 (a) and 2300 (b). Thin lines
represent individual projections and the lighter background shading
covers the area between the minimum and maximum realisation for each
RCP except when they overlap with other scenarios. Prior to the year
2005, the temperature forcing comes from the ECMWF ERA-40 and
ERA-Interim meteorological reanalyses (black line).
Glacial cycle spin-up
In order to initialise to the present day, the model is spun up over a full
glacial cycle as described in . The ice sheet geometry
evolves freely in response to past changes in regional surface temperatures,
precipitation and sea level. Although the general approach is unchanged from
earlier applications of this model , the underlying
reconstruction for past temperature changes is updated with recent proxy
information from several ice cores (for details see Appendix A). A new
compilation of accumulation observations over the Greenland ice sheet
is used as basis for scaling past precipitation
changes with the mean annual temperature change (by
5 % ∘C-1). Finally, a new parameterisation to improve the
retreat history from the Last Glacial Maximum is applied
, which is constrained by proxies for relative
sea level. Switching at 3 kyr BP from a shallow ice approximation to the
higher-order formulation appeared to be sufficiently early to resolve the
main effects of including horizontal stress gradients by the present day.
Observed ice sheet geometry. Surface elevation for ice sheet
and bed topography are given in different grey shading. Over the ice
sheet, contour lines for surface elevation are indicated with
1000 m spacing. The five ocean basins are labelled (bold, dark
blue). They are separated by the three shown latitudes and Greenland.
Oceanographic names are given in black and the Irminger Current is
delineated.
Using an unconstrained model evolution during the spin-up phase guarantees
a self-consistent model state in the present day but the geometry
deviates from the observed state. Therefore, key model parameters are tuned to
minimise geometric and dynamic differences after the spin-up. For a
statistically sufficient and efficient coverage of the parameter space,
a Latin hypercube sampling (LHS) was chosen ,
relying on 100 combinations. This sampling technique has previously been used
for assessing the parameter sensitivity when spinning up ice-sheet models
. We vary
the positive degree-day factors for both ice
(DDFice) and snow (DDFsnow)
together with an enhancement factor (m) to the rate factor and the sliding
coefficient (AS). These four parameters control both the SMB and
the dynamic state of the modelled ice sheet. Parameters are selected in
ranges of 75–125 % for the degree-day factors, 36–450 % for the
enhancement factor m and 50–200 % for AS with respect to
a previous calibration. Parameter ranges were estimated from the respective
sensitivity of the model, known from previous tuning. For the parameter tuning, a shallow ice-approximation variant of the model was used during the entire spin-up.
Eight criteria were chosen to quantify differences between the modelled ice
sheet and the observed present-day state. The minimisation reduces the
mismatch of the following quantities: total ice volume; ice-covered area; ice
area above 3000 m and below 1500 m surface elevation; southwest
position of the land-terminated ice margin; global ice thickness and surface
elevation. Instead of exclusively focussing on geometric tuning diagnostics,
as in , a final criterion evaluates the dynamic state
of the ice sheet. Ice discharge in the decades prior to 1990 is assumed to
have compensated for ∼60 % of the average accumulation
. This additional criterion considerably reduces
the parameter space. One best-fit, reference parameter set and seven additional
combinations were selected on the basis of a qualitative assessment of
respectively all or individual criteria (Table 1). Very
similar positive degree-day factors were found as compared to a previous
tuning while parameters controlling the ice flow magnitude are slightly
reduced. This reduction is necessary because of higher velocities in the
ablation zone when using the parameterisation for runoff-induced speed-up.
Mean annual ocean temperature anomaly around Greenland with
respect to the reference period 1960–1990. Panels cover different
time periods up to 2100 (a) and 2300 (b). Thin
lines represent individual projections and the lighter background
shading covers the area between the minimum and maximum realisation
for each RCP except when they overlap with other
scenarios. Temperature anomalies are averaged over the five ocean
basins. Prior to 2005, ocean forcing is taken from each individual
climate model (grey shading and black lines).
Climatic forcingReference period
For the
period 1958 to 2005, the SMB model is forced with monthly temperature
anomalies and annual precipitation ratios from a combination of ECMWF
ERA-meteorological reanalysis and ECMWF operational analysis data as
described in . Anomalies and ratios are
calculated with respect to the period 1960–1990.
This assumes that
the ice sheet was in quasi-equilibrium with the prevailing climate of
that time, as in previous studies
e.g.. The reference precipitation
is from . In the same way, the
oceanic temperature anomalies are calculated from the atmosphere and
ocean general circulation models (AOGCMs). Discontinuities in these anomalies,
when switching the forcing in 1958 and 2005, are comparable to the internal climate variability of individual AOGCMs.
Future scenarios
For
future ice-sheet simulations, climate projection data from 10 AOGCMs were
selected from the WCRP's CMIP5 multi-model data set prepared for the IPCC AR5
. The selection of climate models was based on the
scenario coverage, the covered projection period and whether surface air
temperatures, averaged for 1960–1990, generally agreed with the ECMWF
product. Outliers in terms of average warming by 2100 and 2300 were
identified from the AOGCM ensemble and hence rejected.
(Table B1 gives a complete overview of the considered AOGCMs).
For these projections, the AOGCMs were forced with four CMIP5 RCP scenarios . The same
anomaly approach as for the reference period is used to avoid any potential
bias associated with the mean states. Monthly surface air temperature
anomalies, annual precipitation ratios and annual ocean temperature anomalies
are therefore considered with respect to the same 1960–1990 reference
period.
Comparison of present-day modelled (a) and observed
(b) surface velocities. Observations are averaged over
the years 2000 and 2005–2008 (Joughin et al., 2010).
Atmospheric forcing
Monthly surface air
temperature anomalies and annual precipitation ratios are derived for
each individual AOGCM over the ice-sheet model domain. These future
atmospheric anomalies drive the SMB model starting from the year
2005. In most cases, the data cover the period up to 2100 or 2300. Missing data in the last year of two AOGCMs were filled by
repeating the previous year.
The annual air temperature anomaly averaged over the present ice-sheet extent
(Fig. ) is instructive as a general trend but conceals the 2-D
pattern of the warming (not shown). In general, the spatial pattern of the
temperature forcing shows an expressed north–south gradient of up to
10 ∘C by 2100, with stronger warming in the north. This
latitudinal gradient depends on the climate sensitivity and the polar
amplification of each AOGCM. For a given latitude, the difference in warming
between the east and west of the ice sheet depends strongly on the individual
AOGCM. The patterns of future precipitation changes are also AOGCM dependent
and cannot be generalised. Yet the average precipitation increases and scales
with the scenario intensity. By 2100, the ensemble averages per RCP show 13,
19, 23 and 37 % additional precipitation for RCP2.6, RCP4.5, RCP6.0 and
RCP8.5, respectively. For RCP2.6 and RCP4.5, these values increase to
respectively 19 and 31 % by 2300.
Ocean forcing
Oceanic forcing is decomposed into time series for five different
oceanic basins. Their delineation is based on the circulation
pattern of Atlantic Water (AW) around Greenland
and references therein (cf. Fig. ). The
North Atlantic Current brings warm and saline water from the Atlantic
Ocean and splits into the Irminger Current and the Norwegian Atlantic
Current. The latter enters the Nordic seas where sinking occurs but AW
partly submerges under fresh polar waters and continues northwards to
Fram Strait. There, one portion enters the Arctic Ocean ultimately
reaching the north Greenland continental shelf break (northern
region). The other portion turns back at Fram Strait along the eastern
flank of Greenland at intermediate depth (northeastern region). South
of Denmark Strait, it joins warmer AW provided by the Irminger Current
and continues southwards along the shelf break (southeastern
region). At the southern tip of Greenland, it feeds into the Labrador
Sea where further sinking occurs (southwestern region). A fraction of
these waters remain at intermediate depth flowing northward and
potentially overcome the sill into Baffin Bay (northwestern
region). Warm AW with subtropical origin is therefore found at
intermediate depth all around Greenland. For our projections, ocean
temperature changes in these basins are related to ice discharge
changes at the marine-terminating margin of the Greenland ice sheet.
Ocean circulation in the deeper ocean around Greenland, off the continental
shelf, is resolved in most AOGCMs. Ocean basins are latitudinally delineated
by the 60, 70, 80∘ N parallels and the North
Pole at 90∘ N, and confined by the Greenland coastline
(Fig. ). In each individual basin, AOGCM grid box centres that
lie within a 300 km radius from the Greenland coastline are considered. This
belt covers the continental shelf and a part of the deep ocean beyond the
shelf break. The resulting basin temperature anomalies are not very sensitive
to a radius increase to 500 km. In the vertical, temperatures are averaged
over a depth of 200 to 600 m. The upper limit is inspired by the average
freshwater layer thickness in Greenlandic fjords
together with intermediate depth locations of offshore AW
. The latter argument combined with the fact
that Greenlandic fjords have typical sill depths of several hundred metres
gives rise to the lower bound. Averaging area and depth of all AOGCM grid
points in each basin provides five temperature time series for each AOGCM and
each RCP.
Ocean temperature anomalies for each basin are considered with respect to the
1960–1990 average (Fig. ). For each basin, the annual
temperature anomaly records are filtered with a 5-year moving average. This is
necessary to prevent high-frequency oscillations when forcing the ice-dynamic
model. Though there is a tendency for stronger warming in the northern ocean
basins in many of the AOGCMs, differences in trends within the five basins are
highly dependent on the individual climate model.
Ice sheet evolution in the recent past
After the glacial-cycle spin-up, the present-day ice-sheet geometry is
in a self-consistent state concerning ice geometry, dynamics,
temperature and SMB. The geometry and temperature naturally carry the
long-term memory of the ice-sheet evolution. The main shortcoming from
such a spin-up is that for the present day the modelled geometry does
not exactly match observations. Like in other studies with a similar
spin-up technique, ice thicknesses near the margin tend to be overestimated and therefore the ice extent is somewhat larger
e.g.. Though
the geometric mismatch biases the SMB near the margin, the ice-sheet-wide SMB compares well with other approaches (see
below). Thicker margins also affect the modelled ice flow as margin surface slopes are somewhat reduced. A flatter ice surface leads to an underestimation of margin velocity magnitudes
(Fig. ). A side-by-side comparison shows that
the locations and the magnitudes of channelised ice flow towards
the marine margin are well reproduced on the 5 km
grid. In this spin-up technique, regions of fast flow naturally arise
from the interplay among deformation, sliding and thermodynamics.
More
meaningful than matching velocities at the margin is that the model
is capable of reproducing ice discharge rates and their regional distribution
around Greenland (Table 2). The simulated present-day state
shows a total ice discharge that slightly exceeds otherwise inferred values
. The 5 % overestimation mostly arises
from simulated ice–ocean contact in regions where no ice-sheet cover is
observed, i.e. in the north and the east. A 20 km model spin-up is only
capable of reproducing the large-scale regional distribution and the total
ice discharge. Compared to this coarser model version, ice flow towards the
margin is more channelised for the presented 5 km grid and the agreement between modelled and inferred discharge improves, on a regional
level and down to the level of major outlet glaciers. The match on a drainage
basin level arises naturally without specific model tuning. In this regard,
the glacial-cycle spin-up method is preferable to another initialisation
technique that aims at inverting for observed ice velocities using the
observed geometry . Though it reproduces
observed velocities, this latter initialisation technique is confronted with
a strong initial model drift. Such a drift can be reduced by improving the inversion approach e.g.. We believe that the free-geometry
spin-up, using a model with increased dynamic complexity on high resolution,
provides a useful initial state for projecting the future dynamic response of
the Greenland ice sheet on centennial timescales.
Ice discharge prior to 2000 as inferred by
and as simulated with the ice
sheet model using two resolutions. Observationally inferred values
are representative of 1996 (or 2000) while simulated values are
averaged over the period 1960–1990. These values therefore
represent ice discharge prior to any major acceleration in the
outlet glaciers. All values are given in km3 yr-1 (bold font indicates regional values).
Observations20 km model5 km modelNorth50.076.776.4Humboldt3.714.26.1Petermann11.85.112.2Storstrømmen0.15.00.8Nioghalvfjerdsbræ andZachariae Isbræ23.428.020.2West165.8132.9129.0Jakobshavn23.615.821.9Rink Glacier11.82.24.1East141.0141.1165.9Helheim26.39.926.2Kangerlussuaq27.816.922.0Total356.8350.7371.3
Averaged over the 1960–1990 period, the positive-degree-day runoff/retention
approach gives a total SMB of 373 Gt yr-1, when forced with ECMWF
ERA-reanalyses data. Other physically based models show a spread between 341
and 479 Gt yr-1 in the same period .
Somewhat at the lower end, the difference in our model might arise from the
underlying reference precipitation map
. Moreover, recent changes
in the total SMB agree fairly well between inferred values and the used
positive-degree-day approach (Table ). SMB changes estimated
from observations and given by various other model approaches
can be compared on the
basis of six main drainage basins . On this drainage
basin level, differences among various methods become more expressed. For
one drainage basin (in southeast Greenland; C in Table ),
discharge-corrected observations from GRACE cannot be reconciled with any
model estimate. This indicates some large remaining uncertainties in both
modelled SMB changes and otherwise inferred estimates. However, in most cases
our SMB model reproduces the trends of other models within stated uncertainty
bounds.
Recent SMB changes in six main drainage basins. Values for four SMB
model estimates are averaged from . The GRACE
observational mass change record is corrected for ice discharge D based on
Fig. 2 in . SMB changes are given in
Gt yr-1.
Ice-sheet-wide mean atmospheric warming, basin-mean oceanic warming, and ensemble-average contribution of the Greenland ice sheet to global
sea-level change by 2100 and 2300. Sea-level changes are calculated with respect to the year 2000. Ensemble averages for each scenario use equal weights for
individual AOGCMs. The root mean square deviation from the mean ensemble realisation is added to estimate the
variability.
When forced with ECMWF atmospheric reanalysis data and using ocean
temperatures from one climate model with expressed warming over that period
(i.e. HadGEM2-ES in Table B1), the simulated ice sheet loses
mass at a rate of 0.62 mm yr-1 for the period 2005–2010. This is in
good agreement with the inferred average trend of 0.7±0.1 mm yr-1. For this same forcing scenario, the model simulates ∼ 41 % (or
0.25 mm yr-1) of the mass loss as arising from increased discharge.
For the full ensemble of climate models, the average mass loss rate for the
period 2005–2010 is lower at 0.32 mm yr-1. This reflects that AOGCMs
are not expected to correctly reproduce the real trend over such a short time
period. The climate system shows an inherent variability which is also seen in climate models. Yet the timing of this variability is not expected to match. Therefore climate models have difficulties to reproduce short-term trends. For the ensemble member with the highest initial oceanic and
atmospheric warming, the sea-level contribution reaches a maximum rate of
0.71 mm yr-1 for the period 2005–2010. This might suggest that the
Greenland ice sheet is for now responding to the upper end of temperature
changes provided by the CMIP5 climate model ensemble.
Over all climate models and scenarios, this approach gives an average
increase in ice discharge of about 0.14 mm yr-1 with a maximum of
0.23 mm yr-1 for the period 2005 to 2010 with respect to the average
value in the 1990s. The average increase in discharge caused by the climate
model ensemble produces the inferred ∼40 % share of the total mass
loss. However, the mean is at the lower end of observations during this
period and results from a weak oceanic warming around Greenland over the last
decade in the used climate models (Fig. ).
Greenland ice sheet contribution to future global sea-level
change. Given are ensemble averages for each scenario during the
21st century (a) and the next 3 centuries
(b). The modelled rate of mass loss during the
observational period (2000–2010) is on average
0.32 mm yr-1. Colours indicate the respective RCP
scenario and the lighter background colour represents 1 standard
deviation from each mean trajectory. Vertical bars indicate the
spread of sea-level contributions arising from individual AOGCMs at
the end of each scenario. The jump across the year 2100 in the right
panel arises from the use of a different number of climate models in simulations out to 2100 vs. out to 2300.
Future projections
Figure and Table summarise the volume
projections of the Greenland ice sheet for all models and all scenarios under
investigation. A breakdown by individual climate models is presented in
Appendix B. By 2100, the full model and scenario range of Greenland
sea-level contributions is between 1.4 and 16.6 cm (Fig. and
Table B1). This range is slightly higher than the 1–12 cm
found for the IPCC AR4 , which included the
additional uncertainty arising from the SMB model. The higher maximum in
sea-level projections is somewhat unexpected because the RCP scenarios have
a reduced upper bound for radiative forcing by 2100, when compared to the
previously used scenarios. Yet the larger range is attributed to directly
accounting for future changes in ice discharge. In terms of the SMB
contribution to future ice loss, the IPCC AR5 gives
a range of 1–11 cm, confirming the results of the previous AR4. Yet the AR5
is the first to attempt to quantify the contribution from future changes in
ice discharge. It states an additional contribution from dynamic changes of
1–9 cm for all RCP scenarios. The new AR5 is however not able to quantify
the importance of the interaction between ice dynamics and surface mass
balance, as it suffers from the fact that the considered studies are not
directly comparable either in terms of forcing or setup.
Until 2050, there is hardly any difference in the mean sea-level
contribution among the four scenarios. This is in agreement with similar
behaviour for the underlying atmospheric and oceanic forcings
(Sect. ). The ensemble spread in
sea-level evolution for each scenario arises from the different climate
trajectories followed by the individual AOGCMs. This spread is largely
overlapping during the first century for three scenarios. The exception is
RCP8.5, a high-impact scenario assuming a high-emission, fossil-fuel-orientated world. This scenario causes a mean centennial sea-level
contribution of 10.2 cm, which is about twice as large as for other RCPs.
The reason is an average warming of ∼7∘C over Greenland that
is also more than twice as high as for other RCPs. In addition, RCP8.5 is the
only scenario for which mass loss rates significantly increase throughout the
next century.
As AOGCM input was not available for RCP6.0 beyond 2100 and as the divergent
temperature response of the few AOGCMs under RCP8.5 is not considered compatible with our
ensemble approach, projections were continued until 2300 only for the two lowest emission scenarios. Both assume a stringent climate policy with a focus either on
terrestrial carbon for mitigation (RCP4.5) or on negative emissions (RCP2.6).
Both scenarios aim for a climate stabilisation but only RCP2.6 has a peak
greenhouse gas concentration before 2100 and declines afterwards
. For both scenarios, the Greenland contribution
to global sea-level rise increases continuously, but for RCP2.6 the rate of
increase gradually levels off. In this case, the SMB remains positive in the
last decade of the projection. Therefore, it appears that a new ice-sheet
equilibrium with limited ice loss (<20 cm of sea-level rise) is
attainable. For RCP4.5, the rate of mass loss is almost constant over 300 years with a total volume loss equivalent to 20.1 cm sea-level
increase. Average SMB values during the last decade are negative for most
ensemble members. A typical thinning pattern for RCP4.5 shows extensive
marginal thinning and inland retreat of calving fronts after 300
years (Fig. ). Mass loss near the margin is partially balanced
by increased snow accumulation and thickening in the interior.
Total ice thickness change by 2300. The initial ice extent
is indicated with a black contour line while thickness changes are
exclusively shown within the ice extent at the end of the
experiment. This particular result for
RCP4.5 was obtained with CanESM2, which shows most expressed warming over Greenland for all climate models in the
ensemble (Table B1). The thinning patterns for other ensemble members are
qualitatively similar.
Partitioning of mass changes by 2010 (a), 2100
(b) and 2300 (c). Values are given relative to the total ice loss of the
individual AOGCM projection and grouped by climate scenario. Each
vertical column represents one AOGCM projection. The dark blue
columns denote the contribution to the total mass change arising
from oceanic forcing, diagnosed from a control run with SMB
forcing only. The diagnostics comprise the directly induced ice
discharge changes as well as the indirect feedback with the SMB via
the ice geometry. The mass change of the projections is
subsequently partitioned into contributions from changes in both
basal melt and SMB (orange columns) or in ice discharge (light
blue and red columns). The presented partitioning of the mass
change is cumulative. Changes with respect to the average 1990–2000 values of all
contributors in the mass budget are integrated over time. The scenario averages are then given in per cent. At a certain point in the future, ice discharge
falls below present-day values and therefore becomes a source term in the mass partitioning. Consequently, the cumulative sea-level contribution from ice discharge changes can become negative (red).
Ice thickness changes from ocean warming-induced
discharge increase (a) and runoff-induced lubrication
(b). In this particular experiment, obtained with CanESM2
for RCP4.5, additional oceanic forcing accounts for 7.4 cm
of the total sea-level contribution of 32.0 cm. The effect
of basal lubrication increases mass loss by 0.1 cm. This
small extra contribution results from a general ice displacement
expressed by relative thinning of the upper ablation area and
resulting thickening of the marine margin as shown in .
In all climate scenarios, oceanic warming causes additional mass loss from
the ice sheet by 2100 (upper dark blue columns in Fig. ).
This comprises both the directly induced changes in ice discharge and
their effect on the SMB via ice-sheet thinning. For individual AOGCM
projections, the inclusion of oceanic forcing can explain more than 50 %
of the total contribution to sea-level rise by a given time period with an
average increase of the total mass loss by ∼40 %. In absolute
terms, the ocean-induced contribution to sea-level change ranges from 1.8 to
2.6 cm (scenario averages) and 1.1 to 3.2 (full spread) after 1 century,
and from 3.8 to 5.4 cm after 3 centuries (full spread is 2.3 to
7.4 cm). The oceanic influence on the total ice loss becomes relatively less
important for more intense atmospheric warming; while it explains about half of the mass loss for RCP2.6, it only explains 27 % of the mass loss for RCP8.5. This
indicates that decreasing SMB and increasing discharge are mutually
competitive processes for ice removal at the marine margin. In addition, ice
further upstream is efficiently removed by ablation before it actually
reaches the marine margin for calving. The oceanic forcing typically induces
a diffusive thinning wave at the marine margin which is gradually transmitted
inland (Fig. a). In areas with a marine margin, this
additional thinning wave explains a large share of the total thinning
(Figs. and
a).
In Fig. , we also attribute simulated mass changes to either
changes in ice discharge, arising from oceanic forcing and inland ice
dynamics, or from changes of the mass balance at the ice sheet surface or
base (although in all cases, basal melting contributes less than 3 % of
the total land ice loss). While increased discharge explains about 40 %
of the average mass loss between 2000 and 2010 (light blue columns), its
relative contribution generally decreases afterwards and changes in SMB
become the dominant factor in mass loss. This is because total ice export
across calving fronts eventually falls below year 2000 levels, despite warmer
ocean temperatures. Limitations on the ice discharge increase are a direct
result of gradual thinning at the marine margins with a fast adjustment of
the ice inflow from upstream but are also
a consequence of a retreat of the ice-sheet margin back on land. For the
CanESM2 model under RCP4.5, the ice sheet loses more than half of its contact
area with the ocean by 2300 (Fig. ). In general, ice discharge
increase is more relevant for the total mass loss in emission scenarios with higher
mitigation efforts (RCP2.6, RCP4.5). The reason is that an ice discharge
increase causes dynamic thinning further upstream, draws down the ice surface to lower and warmer elevation, and thereby intensifies surface
melting. Surface melting in turn competes with the discharge increase by
removing ice before it reaches the marine margin. Margin thinning and retreat
limit the ice discharge and increase the relative importance of surface
melting in the future volume evolution. The total 2100 ice loss, from SMB
changes only, increases by more than 70 % when including ice–ocean
interaction. This share is about 42 % of the combined total ice loss in
2100 (Fig. b), but only 10 % of it is directly caused by
ice discharge increase at the marine margin. By 2300, the cumulative
effect from ice discharge changes becomes even negative as ice discharge rates
have, on average, fallen below the pre-2000 level.
Detailed flow-line projections of the ice discharge evolution of four
major outlet glaciers on Greenland show a general increase by 2100 and
2200 . Such a widespread increase of ice
discharge is not confirmed by our projections. The glaciers in the
Nick et al. (2013) study are however driven with only one specific
climate model and only represent the response of four individual,
well-studied outlet glaciers. In our large-scale model approach, ice
discharge of main outlet glaciers can also show a significant increase
while the ice-sheet-wide discharge increase is more moderate. This is because many of the smaller glaciers become
land-based. Therefore, scaling up the discharge response of only those
glaciers with the most prolific ice export is not necessarily
representative of the future ice-dynamic evolution of an entire ice
sheet. A generalisation of the discharge evolution of the four outlet
glaciers modelled in to the entire ice sheet
is in line with our finding that the relative importance of ice
discharge changes to the future ice loss is self-limited by thinning
and retreat of ice in contact with the ocean
. Though not linking ice discharge changes
directly to climatic variables, other projections of the Greenland ice sheet under future
warming also found evidence for this self-limiting effect
.
Sensitivity of future sea-level contribution from the Greenland ice
sheet to the parameterisation of ocean warming-induced discharge increase.
Values are ensemble averages with respect to the year 2000, given in cm s.l.e.
In all experiments, the additional effect of basal lubrication on total mass
loss is very small, corresponding to an additional sea-level contribution of
less than 1 % (Fig. b). This is in agreement with recent
observational evidence and results from
a parametric approach to link runoff to basal lubrication
. As also shown by , lubrication-induced speed-up displaces inland
ice mass from the interior towards the coast, but in general does not remove it. In the upper ablation area, the
ice thins as it accelerates, while for melt rates exceeding 2 m yr-1
near the margin, the relative speed-up decreases under warming, causing
a relative thickening (Fig. b, also see Eq. and
Fig. ). The reason is that when meltwater export rates exceed
a threshold, a channellisation of the basal drainage system is assumed with
concurrent reduction of basal lubrication. Ice flow is mainly enhanced close
to the equilibrium line where runoff rates cause maximal speed-up. This may even
lead to a negative feedback as the relative thickening of the ablation zone
reduces runoff rates through the height–mass-balance feedback (Huybrechts
et al., 2002).
For both projection periods to 2100 and 2300, the mass loss projections do
not depend much on the parameters tuned during the model spin-up
(Sect. ). For seven additional and acceptable parameter
sets (Table 1), the future sea-level contribution lies within
4 % of the reference model (i.e. ±2 or ±12 mm by 2100 or 2300,
respectively). The sensitivity of the projections to the parameterisation for
warming-induced discharge increase (Eq. ) is assessed from
additional results for the full ensemble obtained with α= 1.8 and
2.6. For the period 2000–2010, we find that the relative contribution from
ice discharge to total mass loss is ∼20, ∼27 or
∼40 % for α equal to 1.8, 2.6 or 5.2, respectively. The
effect on the projections is however somewhat reduced, as ice discharge
increase is even more limited. For the sea-level projections
(Table ), variations reach ∼25 % compared to the
reference run (α= 5.2). Relative to increasing values for α,
a saturation of the ice loss increase can be stated. The root-mean-square (rms) deviation around
these ensemble values is not much affected by the choice of α, and
differences mostly fall below 10 %. If one excludes the value 1.8, as the
2000–2010 contribution from ice discharge in this case is rather low,
differences between ensemble-mean mass loss lie within 15 % of the
standard results. In this case, the sensitivity to changes in α of the
mass loss in 2300 is about 10 %, even lower than in 2100. For
α values of 2.6 and 5.2, ocean forcing explains about 30 or
40 % of the total mass loss in 2100, respectively. By increasing α
beyond 5.2, the present-day ice discharge can certainly be increased further.
If the value is chosen such that the present
discharge contribution stays in a realistic range, we would however not expect the projection results to qualitatively change.
In summary, the projections are sensitive to the choice of α but the sensitivity decreases with the
length of the projection period and the warming magnitude. Despite this sensitivity, the spread in future ice loss, introduced by the climate
model ensemble, is several times larger
(Table ). This is in line with other studies recognising the importance of the climate trajectory
as the main source for the large spread in sea-level
projections of the Greenland ice sheet e.g..
Summary and conclusion
In this study, we included additional dynamic processes in
a thermomechanically coupled, three-dimensional ice flow model, with the aim
of better assessing the impact of ice dynamics on the future evolution of the
Greenland ice sheet. We suggested parameterisations that link ice discharge
increase to ocean warming and allow for runoff-induced lubrication. To assess
the likely range of the future contribution from the Greenland ice sheet to
sea-level change, climate anomalies were taken from a suite of 10
atmosphere–ocean general circulation models (Table B1). They
were selected from the WCRP's CMIP5 multi-model data set prepared for the IPCC
AR5 and forced by four RCP climate scenarios. When considering climate forcing
from ECMWF reanalysis data and ocean temperatures from an AOGCM that shows an
expressed warming over the period 2005–2010, we find an ice loss rate of
0.62 mm yr-1 over the same period that is explained by ∼40 %
from increased ice discharge, in agreement with the observational range.
Changes in ice discharge are attributed to oceanic warming in the surrounding
ocean basins. The mean ice volume loss for the CMIP5 ensemble is however
biased low with 0.32 mm yr-1. This bias arises from the spread in
climate models that are not expected to correctly simulate the observed trend
over such a short period of time. The ensemble maximum of the ice loss during
this recent period is 0.71 mm yr-1 and equally covers values inferred
from observations. For the climate model ensemble, increased ice discharge
also explains ∼40 % of the total mass loss during the last decade.
Accounting for the four RCP scenarios, we find a Greenland ice-sheet
contribution to global sea-level rise of between 1.4 and 16.6 cm by 2100.
For the two low-impact scenarios, ice loss attains respectively 11.1 and
32.0 cm by 2300. Despite an average increase in mass loss of ∼40 % in 2100, when accounting for ice–ocean interaction, mass loss is
predominantly caused by changes in SMB. The reason is that ice discharge is
limited by margin thinning and retreat as well as by a competition with surface
melting that removes ice before it reaches the calving fronts. These
geometric limits on ice discharge explain that most of the mass loss by 2100
is caused by changes in SMB. Beyond 2100, modelled ice discharge rates fall
below the pre-2000 level and this decrease is compensated by the dominant
changes in SMB. The results therefore suggest that the largest source of
uncertainty in future mass loss arises from the SMB and the underlying
climate change projections, and not from ice dynamics.
Our results have implications for attempts to estimate the role of ice
discharge on the future mass loss of the Greenland ice sheet. Observed rates
of change over the last decade cannot simply be extrapolated over the 21st
century on account of a different balance of processes causing mass loss over
time. Extrapolating recently inferred mass trends or even changes therein to a century timescale or linking observed Greenland
sea-level trends to temperature change implies
continued glacier acceleration and a multifold increase of the ice discharge
that is not found attainable in numerical
ice-sheet models. Ice discharge at calving fronts is self-limited by ice
dynamics, supporting the view that centennial mass changes are dominantly
driven by SMB changes, and thus by changes in surface climate
conditions.
Climate conditions over the last glacial cycleTemperature history
The model spin-up over several glacial cycles requires information on the
past climate, which is reconstructed from ice core data. The glacial
temperature forcing is obtained from synthesised isotope records
representative of central Greenland conditions. For the period prior to
122.6 kyr BP, the forcing reconstruction is based on a synthesised
Greenland δ18O record derived from Antarctica Dome C using
a bipolar seesaw model . Subsequently, the NGRIP
δ18O record is used before switching to
GRIP information at 103.8 kyr BP . For the
last 4 kyr, a direct reconstruction of snow temperatures is available based
on a δ15N/δ40Ar record from GISP2
.
Assembled temperature forcing during the last 5 kyr
based on the δ18O GRIP ice core record and a direct
temperature reconstruction. The splicing point of these two records
is indicated by a change in the background shading at
4 kyr BP. Note that the original GRIP record shows
sub-decadal resolution during the Holocene period while the
temperature forcing, used here, is linearly interpolated for a decadal sampling
rate.
The synthesised δ18O record from
matches well with the GRIP record. Therefore, the fabricated isotope values
are transformed into temperature changes according to one single transfer
function as given by . For the NGRIP record the same
transfer function gives lower temperatures during the Last Glacial Maximum compared to the
GRIP reconstruction. For the purpose of splicing NGRIP to GRIP, an overlap
period for rescaling the transfer function is defined between 102.4 and
90.9 kyr BP. Since present-day δ18O values match between
GRIP and NGRIP, only the scaling factor is adjusted from 2.40 to
2.13 mm yr-1. By replacing information from GRIP with NGRIP during the
period 122.6–103.8 kyr BP, the spliced record does not contain the
disturbed lower part of the GRIP ice core. The
snow temperature reconstruction for the last
4 kyr is offset by its average of -19.6 ∘C during the reference
period 1960–1990. Thereafter, the temperature reconstruction shows
a mismatch of 0.4 ∘C with the GRIP reconstruction at 4 kyr BP.
Before splicing these two records, the
temperatures are lowered over time with a linear function that removes the
past mismatch but keeps the present-day values (Fig. ). In
a final step, the temperature reconstruction is linearly interpolated on time
intervals of 10 years.
Assembling the forcing record in this way prolongs any records exclusively
based on Greenland ice cores by several hundred millennia. In addition, the
intermediate switch to the NGRIP record gives more reliable information
during the late Eemian period than GRIP. This is because of known
disturbances in the lower parts of the GRIP ice core prior to 105 kyr BP.
The last splice with surface snow temperature reconstructions at GISP2 seems
favourable because this reconstruction method was validated against
observations and model reconstructions starting in 1850. One remarkable
feature of our assembled temperature forcing record is the Little Ice Age
cooling on the Greenland ice sheet (Fig. ). This cold
period 200–500 years ago influences our spin-up into the present day and
causes ice-sheet growth up to the beginning of the 20th century.
Breakdown of projections by climate model
For most of the climate model ensemble members (Table B1), air temperature anomalies
correlate better with the centennial contribution of the Greenland ice
sheet to sea-level change than ocean temperature anomalies. Linear
correlation coefficients for air temperature in general exceed 0.7
while this threshold is not surpassed for ocean temperatures except in
RCP8.5. By 2300, the correlation with ocean forcing dominates for
RCP2.6. The spread in centennial sea-level contributions and atmospheric warming
(Fig. ) reflects both uncertainties in the realised future
scenario and differences in the respective AOGCM. Up to 2100, this spread
is explained by differences in individual AOGCM projections rather than
scenario differences. In particular the three low-impact scenarios show
a large overlap in AOGCM realisations. By 2300, the spread introduced by the
different scenarios is largest. For the two lowest scenarios, the 2300
temperature spread remains similar to the centennial spread while deviations
in sea-level contribution become more than twice as large.
Greenland ice sheet contribution to global sea level change
as a function of regional atmospheric warming by 2100 (a)
and 2300 (b). Temperature changes are taken as
differences between 10 yr averages at either end of the
projection period. Small dots represent each individual realisation
with colours indicating the RCP scenario. The respectively coloured
lines are a linear fit to each RCP response. Larger dots indicate
the model averages for each RCP. Ellipses indicate rms deviations in
both temperature change and sea-level change.
Atmospheric and oceanic temperature forcing as provided by the AOGCMs given together with the resulting Greenland ice sheet contribution to sea-level change by 2100 and 2300. Sea-level contribution is determined with respect to 2000. Ocean temperatures are basin averages. Also provided are model means and root mean square deviations (RMSDs) from the mean for each RCP scenario. En dashes indicate no data for the selected model and period.
Ensemble averages are given in bold.
We thank the two anonymous reviewers for their constructive comments that
helped to
improve the clarity of this paper.
This research received funding from the ice2sea programme from the
European Union's 7th Framework Programme grant number
226375. Additional funding came from the Belgian Federal Science
Policy Office within its Research Programme on Science for
a Sustainable Development under contract SD/CS/06A (iCLIPS). We
thank R. Bales for providing the precipitation data set and E. Hanna
for the ECMWF data on our model grid. We also acknowledge the World
Climate Research Programme's Working Group on Coupled Modelling,
responsible for CMIP, and thank the climate modelling groups for
producing and making available their model output. This publication
is ice2sea contribution no. 132.
Edited by: H. Gudmundsson
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