The Greenland ice sheet contributes increasingly to global sea level
rise. Its history during past warm intervals is a valuable reference
for future sea level projections. We present ice sheet simulations for
the Eemian interglacial period (∼130000 to 115 000 years ago), a period with warmer-than-present summer climate over Greenland. The evolution of the Eemian Greenland ice sheet is simulated with a 3-D higher-order ice sheet model, forced with a surface mass balance derived from regional climate simulations. Sensitivity experiments with various surface mass balances, basal friction, and ice flow approximations are discussed. The surface mass balance forcing is identified as the
controlling factor setting the minimum in Eemian ice volume, emphasizing the importance of a reliable surface mass balance model. Furthermore, the results indicate that the surface mass balance forcing is more important than the representation of ice flow for simulating the large-scale ice sheet evolution. This implies that modeling of the future contribution of the Greenland ice sheet to sea level rise highly depends on an accurate surface mass balance.
Introduction
The simulation of the Greenland ice sheet (GrIS) under past warmer
climates is a valuable way to test methods used for sea level rise
projections. This study investigates ice sheet simulations for the
Eemian interglacial period. The Eemian (∼130 000 to
115 000 years ago; hereafter 130 to 115 ka) is the most recent
warmer-than-present period in Earth's history and thereby provides an
analogue for future warmer climates
e.g.,. The
Eemian summer temperature is estimated to have been
4–5 ∘C above present over most Arctic land areas
e.g., and an ice core record from NEEM
the North Greenland Eemian Ice Drilling project in northwest Greenland; indicates a local warming of
8.5±2.5∘C compared to
pre-industrial levels. In spite of this strong warming, total gas
content measurements from the Greenland ice cores at the Greenland Ice Sheet Project 2 (GISP2), Greenland Ice Core Project (GRIP),
North Greenland Ice Core Project (NGRIP), and NEEM indicate an Eemian surface elevation no more than a
few hundred meters lower than present (at these locations). NEEM data
indicate that the ice thickness in northwest Greenland decreased by
400±250 m between 128 and 122 ka with a surface elevation of
130±300 m lower than the present at 122 ka, resulting in a
modest sea level rise estimate of 2 m
. Nevertheless, coral-reef-derived
global mean sea level estimates show values of at least 4 m above the
present level . While this could
indicate a reduced Antarctic ice sheet, the contribution from the GrIS
to the Eemian sea level highstand remains unclear. Previous modeling
studies focusing on Greenland
e.g.,
used very different setups and forcing, and show highly variable
results.
Ice sheets lose mass either due to a reduced surface mass balance
(SMB) or accelerated ice dynamical processes. Ice dynamical processes
may have contributed to the Eemian ice loss, for example, through
changes in basal conditions, similar to what is seen today and what is
discussed for the future of the ice sheet.
associate surface melt with an acceleration of GrIS flow and argue
that surface-melt-induced enhanced basal sliding provides a mechanism
for rapid, large-scale, dynamic responses of ice sheets to climate
warming. Several other studies have attributed the recent and future
projected sea level rise from Greenland partly to dynamical
responses. , for example, use a
3-D higher-order model to simulate sea level rise caused by the
dynamical response of the GrIS, and they find an upper bound of 45 mm
by 2100 (without assuming any changes to basal sliding in the
future). This dynamical contribution is of similar magnitude to
previously published SMB-induced sea level rise estimates by 2100
40–50 mm;.
provide a sea level rise estimate of 165 mm from the GrIS by 2100
based on a kinematic scenario with doubling ice transport through
topographically constrained outlet glaciers. Furthermore,
present synthetic ice sheet simulations and
argue that the early part of the deglaciation of large ice sheets is
strongly influenced by an acceleration of ice streams as a response to
changes in climate forcing.
In this study, we apply a computationally efficient 3-D higher-order
ice flow approximation also known as Blatter–Pattyn; BP; implemented in the
Ice Sheet System Model ISSM;. Including higher-order stress
gradients provides a comprehensive ice flow representation to test the
importance of ice dynamics for modeling the Eemian GrIS. Furthermore,
we avoid shortcomings in regions where simpler ice flow
approximations, often used in paleo applications, are inappropriate,
especially regions with fast-flowing ice in the case of the shallow ice
approximation SIA; and
regions dominated by ice creep in the case of the shallow shelf
approximation SSA;. The higher-order approximation is equally well
suited to simulate slow- as well as fast-flowing ice.
show that the derivation of the
Eemian SMB strongly depends on the SMB model choice. Here, we test SMB
forcing derived from dynamically downscaled Eemian climate simulations
and two SMB models (a full surface energy balance model and an
intermediate complexity SMB model) as described in
. Furthermore, we perform sensitivity
experiments varying basal friction for the entire GrIS, and localized
changes below the outlet glaciers.
The aim of this study is to compare the impact of SMB and basal
sliding on the evolution of the Eemian GrIS. Furthermore, employing a
3-D higher-order ice flow model, instead of simpler ice dynamical
approximations often used in millennial-scale ice sheet simulations,
is a novelty of this study. It allows us to evaluate the importance of
the ice flow approximation used for Eemian studies.
Models and experimental setupSMB methods
The SMB forcing is based on Eemian time slice simulations with a fast
version of the Norwegian Earth System Model
NorESM1-F; representing the climate of
130, 125, 120, and 115 ka using respective greenhouse gas
concentrations and orbital parameters details in. In the climate model simulations,
the present-day GrIS topography is used. These global simulations are
dynamically downscaled over Greenland with the regional climate model
Modèle Atmosphérique Régional
MAR;. Subsequently, the
SMB is calculated with (1) a full surface energy balance (SEB) model
as implemented within MAR (MAR-SEB) and (2) an intermediate complexity
SMB model MAR-BESSI; BErgen Snow SImulator; BESSI;. Both models are physically based SMB
models including a snowpack explicitly solving for the impact of solar
shortwave radiation this is essential for the Eemian period which has a significantly different solar insolation compared to today, e.g.,. MAR-SEB is bidirectionally coupled to the
atmosphere of MAR (i.e., evolving SEB impacts atmospheric processes;
for example, albedo changes impact surface temperature, cloud cover,
and humidity), while MAR-BESSI is uncoupled. These two models are
selected as the most plausible Eemian SMBs from a wider range of
simulations discussed in ; they show
a negative total SMB during the Eemian peak warming. While MAR-SEB is
chosen as the control because it has been extensively validated
against observations in previous studies
, MAR-BESSI is used to test the
sensitivity of the ice sheet simulations to the SMB forcing. MAR-SEB
and MAR-BESSI employ a different temporal model time step; while
MAR-SEB uses steps of 180 s, MAR-BESSI calculates in daily time
steps. The longer time steps used by MAR-BESSI imply that extreme
temperatures (e.g., lowest temperatures at night can lead to more
refreezing) are damped and this is likely the cause for a lower amount
of refreezing in MAR-BESSI compared to MAR-SEB. Furthermore, MAR-BESSI
uses a simpler albedo representation than MAR-SEB. Lower refreezing
and simpler steps in albedo changing from fresh snow to glacier ice
are identified as the main reasons for more negative SMB, as calculated
by MAR-BESSI. For a detailed discussion of the differences between the
models, the reader is referred to
. The two different SMB models are
employed to test the sensitivity of the ice sheet simulations to the
prescribed SMB forcing.
All SMB time slice simulations are calculated offline using the modern
ice surface elevation, given the lack of data constraining the
configuration of the Eemian GrIS surface elevation. The evolution of
the SMB with the changing ice surface elevation is simulated with
local SMB–altitude gradients following . The SMB gradient method is used to calculate
SMB–altitude gradients at each grid point from the surrounding grid
points within a default radius of 150 km (linear regression of SMB
vs. altitude). Since the SMB–altitude gradients in the accumulation
and the ablation zones are very different, they are calculated
separately. If the algorithm is unable to find more than 100 grid
points (of either accumulation or ablation), the radius is extended
until a threshold of 100 data points for the regression is
reached. For simplicity, the local gradients are calculated from the
respective pre-industrial SMB simulations. Further details on the SMB
gradient method are discussed in .
Between the SMBs calculated for 130, 125, 120, and 115 ka, a linear
interpolation is applied, giving a transient SMB forcing over 15 000 years. A more complicated interpolation approach is unnecessary given
the smooth climate forcing and the uncertainties related to the Eemian
climate and SMB simulations. give a
detailed discussion of the simulated climate evolution and show, for
example, an Eemian peak warming of 4–5 ∘C over Greenland,
which is in agreement with proxy reconstructions
. The SMBs in the present
study (after being corrected for topography) are shown and discussed
in Sect. .
The Ice Sheet System Model (ISSM)
The ISSM is a finite-element, thermo-mechanical ice flow model based
on the conservation laws of momentum, mass, and energy
– here, model version 4.13 is used
. ISSM employs an anisotropic mesh,
which is typically refined by using observed surface ice velocities,
allowing fast-flowing ice (i.e., outlet glaciers) to be modeled at
higher resolution than slow-flowing ice (i.e., interior of an ice
sheet). Furthermore, ISSM offers inversion methods to ensure that an
initialized model matches the observed (modern) ice sheet
configuration i.e., observed ice surface velocities are inverted for basal friction or ice rheology;.
While ISSM offers a large range of ice flow representations, in this
study, the computationally efficient 3-D higher-order configuration
is used. This configuration uses
an interpolation based on higher-order polynomials between the
vertical layers instead of the default linear interpolation which
requires a much higher number of vertical layers to capture the sharp
temperature gradient at the base of an ice sheet. By using a quadratic
interpolation, five vertical layers are sufficient to capture the thermal
structure accurately, while a linear vertical interpolation requires
25 layers to achieve a similar result. This lower number of vertical
layers reduces the computational demand for the thermal model and the
stress balance calculations, and makes it possible to run
3-D higher-order simulations for thousands of years. The simulations
over 12 000 years in this study take between 3 and 4 weeks on a single
node with 16 cores.
Experimental setup
All simulations (forced with MAR-SEB and MAR-BESSI) run from 127 to
115 ka following the Paleoclimate Modeling Intercomparison Project
PMIP4; experimental design and
initiating the Eemian simulations at 127 ka with a modern GrIS. The
thermal structure is derived using a thermal steady-state simulation
with prescribed pre-industrial temperature at the ice surface (from
the regional climate model simulations) and an enthalpy formulation
at the base to determine the basal
conditions (cold or temperate ice). At the base of the ice sheet, a
prescribed geothermal heat flux as
provided by the SeaRISE dataset is
imposed. The basal friction coefficients are kept constant over time
and are derived from an inversion of spatially varying, observed
surface velocities. In this case, an algorithm chooses the basal
friction coefficients in a way that the modeled velocities match the
observed velocities. In a first inversion, an initial ice viscosity is
prescribed. After the thermal steady-state simulation, the ice
viscosity is updated as a function of the new thermal profile
. In a second inversion, the basal
friction coefficients are iterated to minimize three cost functions
(Table ). A map of the basal friction coefficients is
provided as the Supplement to this paper. The inversion depends on
the chosen ice flow approximation due to the different representations
of the stress balance. Hence, simulations with the 2-D SSA and the
3-D higher-order approximation, respectively, use different inversions.
ISSM model parameters.
ISSM model parameters Minimum mesh resolution (adaptive)40 kmMaximum mesh resolution (adaptive)0.5 kmNumber of horizontal mesh vertices7383Number of vertical layers5Ice flow approximation3-D higher order Degree of finite elements (stress balance)P1 × P1Degree of finite elements (thermal)P1 × P2Minimum time step (adaptive)0.05 yearsMaximum time step (adaptive)0.2 yearsBasal friction lawp. 151; Eqs. () and ()Basal friction coefficient inversion cost functions101, 103, 501Ice rheologyp. 75
Degree of finite elements: P1 – linear finite elements, P2 –
quadratic finite elements, horizontal × vertical; inversion cost functions:
101 – absolute misfit of surface velocities, 103 – logarithmic misfit of surface
velocities, 501 – absolute gradient of the basal drag coefficients.
We use the ISSM default friction law based on the empirically derived
friction law by p. 151:
τb=-α2Neffvb,
where τb is the basal shear stress (vector),
α the basal friction coefficient (derived by inversion from
surface velocities), Neff the effective pressure of the
water at the glacier base (i.e., the difference between the overburden
ice stress and the water pressure), and vb the
horizontal basal velocity (vector). The effective pressure is
simulated with a first-order approximation :
Neff=gρiceH+ρwaterzb,
where ρice and ρwater are the densities
of ice and water, respectively, H is the ice thickness, and
zb is the bedrock elevation. From these equations, it
follows that the initial (modern) basal friction coefficients stay
constant, while the basal shear stress evolves over time with the ice
thickness and the effective pressure.
Basal sensitivity experiments with changed basal friction are
performed to investigate the importance of uncertainties related to
basal friction. In order to minimize the number of 3-D higher-order
experiments, a number of test experiments are performed with the
simpler 2-D SSA configuration of ISSM to identify the range of basal
friction coefficients which yield plausible results. For example, if
the basal friction coefficients for the entire ice sheet are reduced
by factors of 0.8 and 0.5 (in the 2-D SSA test experiments; not
shown), the ice surface elevation at the NEEM location shows a
late Eemian lowering of 300 and 800 m, respectively. Proxy data
indicate a surface lowering of no more than 300 m
at this point in time. In order to
stay clearly within the proxy reconstructions, the friction for the
entire ice sheet is reduced by a factor of 0.9 in the 3-D higher-order
ice flow experiments. Two 2-D SSA experiments (forced with MAR-SEB and
MAR-BESSI) are discussed in detail here to illustrate the difference
of the two ice flow approximations
(Table ). A full list of 2-D SSA
experiments is given as the Supplement to this paper.
Overview of the experiments.
Type of experimentSMB methodBasal frictionIce flow approx.controlMAR-SEBmodern3-D higher orderSMBMAR-BESSImodern3-D higher orderbasal (reduced)MAR-SEB0.9× modern (entire ice sheet)3-D higher orderbasal (reduced)MAR-BESSI0.9× modern (entire ice sheet)3-D higher orderbasal (enhanced)MAR-SEB1.1× modern (entire ice sheet)3-D higher orderbasal (enhanced)MAR-BESSI1.1× modern (entire ice sheet)3-D higher orderoutlets (reduced)MAR-SEB0.5× modern (outlet glaciers)3-D higher orderoutlets (reduced)MAR-BESSI0.5× modern (outlet glaciers)3-D higher orderoutlets (reduced)MAR-SEB0.9× modern (outlet glaciers)3-D higher orderoutlets (reduced)MAR-BESSI0.9× modern (outlet glaciers)3-D higher orderoutlets (enhanced)MAR-SEB1.1× modern (outlet glaciers)3-D higher orderoutlets (enhanced)MAR-BESSI1.1× modern (outlet glaciers)3-D higher orderoutlets (enhanced)MAR-SEB2.0× modern (outlet glaciers)3-D higher orderoutlets (enhanced)MAR-BESSI2.0× modern (outlet glaciers)3-D higher orderaltitudeMAR-SEBmodern3-D higher orderaltitudeMAR-BESSImodern3-D higher orderrelaxedMAR-SEBmodern3-D higher orderice flowMAR-SEBmodern2-D SSAice flowMAR-BESSImodern2-D SSA
Due to the high computational demand of the 3-D higher-order model,
compromises are necessary. The simulations are initiated with the
modern GrIS topography and the bedrock remains fixed at modern values
(glacial isostatic adjustment – GIA – is not yet implemented for
transient simulations with ISSM). The ice sheet is initialized with
observed ice surface velocities from
v4Aug2014;. The anisotropic ice sheet mesh
is refined with these velocities with a minimum resolution of 40 km
in the slow interior and a maximum resolution of 0.5 km at the fast
outlet glaciers. Since the mesh is based on observed velocities, the
resolution of the mesh remains unchanged over time, and the ice sheet
domain is fixed to the present-day ice sheet extent. The ice sheet can
freely evolve within this domain but is unable to grow outside the
present-day limits.
The air temperature prescribed at the ice surface remains fixed at
pre-industrial levels. Ice formed during the 12 000-year simulations
will only reach several hundred meters deep (not reaching the bottom
layers which experience most deformation) and surface air temperature
is not influencing the SMB as it would in a degree-day model; because SMB is computed by
either MAR-SEB or MAR-BESSI, models that account for temperature
changes over the Eemian (as simulated by NorESM).
The simplified transient ISSM model configuration does not explicitly
resolve processes related to basal hydrology, ocean forcing, and
calving. The ice rheology is calculated as a function of temperature
following p. 75. Initial (modern) ice
sheet surface, ice thickness, and bed topography are derived from
BedMachine v3 v2017-09-20;. The
most important parameters of the ice sheet model are summarized in
Table . Finally, the shortcomings of this simplified
configuration are discussed in Sect. .
Control and sensitivity experiments
The experiments performed are described below and summarized in
Table . As discussed in
Sect. –, the experiments test
the sensitivity to two different SMB models as well as different
representations of the basal friction: the control experiment
applies SMB from MAR-SEB and unchanged (modern) basal friction; the
SMB experiment tests the simplified but efficient SMB model,
MAR-BESSI; the basal experiments test spatially uniform
changes to the basal friction for the entire ice sheet; the
outlets experiments test the sensitivity to changes of basal
friction locally at the outlet glaciers (slowdown/speed-up of outlet
glaciers, defined as high velocity regions with >500 m yr-1). For the
basal and outlets experiments, the basal friction
coefficient is multiplied by factors of 0.9 and 1.1. Furthermore, the
outlets experiments are repeated with more extreme factors of
0.5 and 2.0.
In additional experiments, with the more efficient SSA version of the
model, a larger range of basal friction for the entire ice sheet is
explored doubling/halving of basal friction similar to. However, applying factors of 0.5 and 2.0
for the entire ice sheet results in unrealistic surface height changes
at the central Greenland ice core locations (not shown). Therefore,
these extreme changes of basal friction are only applied to the outlet
glaciers in our 3-D higher-order experiments.
The altitude experiments test the impact of the SMB–altitude
feedback by ignoring this feedback; which means that the transient SMB
forcing is prescribed without correcting for altitude
changes. Finally, we perform a relaxed experiment testing the
sensitivity to a larger, relaxed initial ice sheet (with the same SMB
and ice dynamics as the control experiment). This
relaxed experiment starts with a larger ice sheet which is
spun up for 10 000 years under constant pre-industrial SMB from
MAR-SEB. The differences arising from the different ice flow
approximations are illustrated in the ice flow experiments.
Results
The importance of the SMB forcing is illustrated in
Fig. , showing the evolution of the Greenland ice
volume in the control experiment (MAR-SEB; bold orange line)
and the SMB sensitivity experiment (MAR-BESSI; bold purple
line). The corresponding subsets of experiments testing the basal
friction (basal, outlets) are indicated in lighter
colors. There is a distinct difference between the model experiments
forced with the two SMBs: forcing the ice sheet with MAR-SEB SMB (bold
orange line) gives a minimum ice volume of 2.73×1015 m3
at 124.7 ka, corresponding to a sea level rise of 0.5 m – the basal
sensitivity experiments give a range of 0.3 to 0.7 m (thin orange
lines). On the other hand, the experiments forced with MAR-BESSI (bold
purple line) give a minimum of 1.77×1015 m3 at 123.8 ka
(2.9 m sea level rise) with a range from 2.7 to 3.1 m (thin purple
lines). The minimum ice volume and the corresponding sea level rise
from all experiments are summarized in Table .
Evolution of the ice volume for the control
(MAR-SEB, orange, bold) and the SMB (MAR-BESSI, purple,
bold) experiments in comparison with the basal/outlets
sensitivity experiments. The basal (friction ×0.9/×1.1
for the entire ice sheet) and outlets sensitivity
experiments (friction ×0.5/×2.0 at the outlet glaciers) are
indicated with thin solid and thin dashed lines,
respectively. Note that the lower friction experiments give lower
volumes. The minimum of the respective experiments is indicated
with circles. See Table for the exact
values.
Summary of the simulated ice sheet minima for all experiments.
For the outlets sensitivity experiments, the basal friction in regions with
>500 m yr-1 is changed. Sea level rise (SLR) values are relative to the initial ice sheet at
127 ka, i.e., the modern ice sheet for all experiments except the relaxed initial ice sheet experiment.
The lost ice volume is equally spread over the modern ocean area. ΔSLR refers to anomalies
relative to the respective SMB forcing experiments with unchanged friction.
Negative ΔSLR values are indicated in bold.
The basal experiments (thin solid lines;
Fig. ; friction ×0.9/×1.1 for the entire ice
sheet) show a stronger influence on the ice volume than the
outlets experiments: changing the basal friction locally at
the outlet glaciers (outlets) by factors of 0.9 and 1.1 has
very little effect on the integrated ice volume (not shown). However,
a halving/doubling of the friction at the outlet glaciers does show a
notable effect on the ice volume (0.05 to 0.15 m at the ice minimum;
thin dashed lines; Fig. ).
The importance of the SMB–altitude feedback is illustrated in
Fig. which shows the evolution of the ice
volume with the two SMB forcings (control, bold orange;
SMB, bold purple) and without applying the SMB gradient
method (altitude, thin orange/purple). Neglecting the
correction of the SMB for a changing ice surface elevation, that is,
using the offline calculated SMBs directly, results in significantly
less melt. This is particularly pronounced in experiments forced with
MAR-BESSI, because the ablation area in these simulations is larger,
and therefore larger regions are affected by melt-induced surface
lowering. The differences between the 3-D higher-order and the 2-D SSA are
surprisingly small, particularly at the beginning of the simulations
while the ice volume is decreasing (ice flow, black and
gray). The differences between the ice flow approximations become
larger as the ice sheet enters a colder state, at the end of the
simulations. Finally, in the relaxed experiment (dark green),
the volume decrease is more pronounced because the relaxed initial ice
sheet is larger and the SMB forcing is negative enough to melt the
additional ice at the margins. However, at the end of the simulations,
the control and the relaxed experiments become
indistinguishable.
Evolution of the ice volume for the control (MAR-SEB,
orange, bold) and the SMB experiments (MAR-BESSI, purple, bold)
in comparison with the altitude, relaxed, and ice flow
sensitivity experiments. The corresponding altitude (no
SMB–altitude feedback) and ice flow (2-D SSA) sensitivity
experiments are shown in lighter colors and black/gray,
respectively. The relaxed sensitivity experiment (relaxed larger
initial ice sheet but otherwise control forcing) is
shown in dark green.
Comparing the SMB forcing for the control experiment
(MAR-SEB; Fig. a–d) and the SMB
experiment (MAR-BESSI; Fig. e–h) emphasizes the
importance of the SMB–altitude feedback. While the offline calculated
SMBs (using a modern ice surface) are similar, the surface lowering in
combination with the SMB gradient method cause the resulting SMB to
become very negative in the southwest (for both MAR-SEB and MAR-BESSI)
and in the northeast (particularly for MAR-BESSI). Regions with
extremely low SMB at 125 ka are ice free at the time of the
simulation (ice margins are indicated with a black solid line).
SMB forcing corrected for surface elevation changes at 127,
125, 120, and 115 ka for the control (a–d, MAR-SEB) and the
SMB (e–h, MAR-BESSI) experiments. The ice margin is
indicated with a solid black line (10 m ice thickness
remaining). A nonvisible ice margin is identical to the domain
margin. For a consistent comparison, the SMB is shown at 125 ka
instead of the individual minimum (control at 124.7 ka
and SMB at 123.8 ka).
The simulated ice sheet thickness in the control experiment
(Fig. a–d; MAR-SEB) shows only moderate
changes. However, there is a significant retreat of the ice margin in
the southwest at 125 ka (Fig. b). The
SMB sensitivity experiment (Fig. e–h;
MAR-BESSI) on the other hand gives a very different evolution of the
ice thickness: at 125 ka, the SMB experiment
(Fig. f) shows an enhanced retreat in the
southwest and additionally a particularly strong retreat in the
northeast. Furthermore, the ice sheet takes longer to recover in the
SMB experiment, giving a smaller ice sheet at 120 ka
(Fig. g), mainly due to the large ice loss in
the northeast.
Ice thickness at 127, 125, 120, and 115 ka for the
control (a–d, MAR-SEB) and the SMB (e–h,
MAR-BESSI) experiments. The ice margin is indicated with a solid
yellow line (10 m ice thickness remaining). A nonvisible ice
margin is identical to the domain margin. For a consistent
comparison, the ice thickness is shown at 125 ka instead of the
individual minimum (control at 124.7 ka and SMB
at 123.8 ka).
The MAR-SEB forced experiments give only small changes
(±200 m) in ice surface elevation at the ice core locations of
Camp Century, NEEM, NGRIP, GRIP, Dye-3, and East Greenland Ice-Core Project (EGRIP)
(Fig. ). At most locations, the surface elevation
increases due to a positive SMB, which is not in equilibrium with the
initial ice sheet. The relaxed experiment (dark green), which
is in equilibrium with the initial climate, shows damped elevation
changes. Notably, Dye-3 (Fig. c) shows the strongest
initial lowering due to its southern location affected by the early
Eemian warming. The MAR-BESSI-forced experiments show the largest
changes in surface elevation, particularly at Dye-3
(Fig. c) and NGRIP (Fig. b) with a
maximum lowering of around 600 m, and at EGRIP
(Fig. f), where the largest lowering is around
1500 m. In contrast to the ice volume evolution, where differences
between the control and the ice flow experiments are
small (Fig. ), there is a larger difference in
ice surface elevation changes between the ice flow approximations. The
2-D SSA experiments (Fig. , black and gray) show ice
surface changes up to 200 m different from the 3-D higher-order
experiments (Fig. , bold orange and purple).
Ice surface evolution at Greenland ice core locations for
the control, SMB, basal,
outlets, ice flow, and relaxed
experiments – Camp Century, NEEM, NGRIP, GRIP, and Dye-3 are
shown on the same scale; EGRIP is shown on a different scale. Same
color coding as in Figs. and . Surface
elevation reconstructions from total gas content at NEEM are
indicated with gray shading. Note that the 2-D experiments are
plotted in the background and therefore hardly visible in some
cases, particularly at NEEM.
The impact of all sensitivity experiments on the ice volume minimum is
summarized in Fig. . The choice of SMB model
(SMB, black) shows the strongest influence with a difference
in sea level rise of ∼2.5 m between the
control experiment (with MAR-SEB) and the SMB
experiment (with MAR-BESSI). Furthermore, the SMB–altitude feedback is
particularly important for the MAR-BESSI-forced altitude
experiment, due to the large regions affected by melt-induced surface
lowering. The basal and outlets sensitivity
experiments show a limited effect on the simulated ice volume
minimum. Finally, using a larger, relaxed initial ice sheet
(relaxed) results in a ∼0.3 m larger sea
level rise. A complete summary of the respective ice volume minima is
given in Table .
Differences between the minimum Eemian ice sheet simulated
by the respective sensitivity experiments: SMB (black):
difference between the control and the SMB
experiment (MAR-SEB and MAR-BESSI, respectively); basal:
experiments with changed friction for the entire ice
sheet; outlets: experiments with changed friction at the
outlet glaciers; altitude: experiments without the
SMB–altitude feedback; relaxed: experiment with a larger,
relaxed initial ice sheet; ice flow: experiments with
2-D SSA instead of the default 3-D higher-order ice flow
approximation. The different SMB forcing is shown in orange
(MAR-SEB) and purple (MAR-BESSI). The basal/outlets
experiments show positive and negative values because they are
performed with enhanced and reduced friction. The exact values are
given in Table .
There are small differences between the simulated ice thickness
minimum of the control experiment
(Fig. a; MAR-SEB and 3-D higher-order) and the
corresponding ice flow experiment
(Fig. b; MAR-SEB and 2-D SSA). Only minor
differences are visible on the east coast, where the 2-D SSA experiment
shows a stronger thickening than the 3-D higher-order experiment.
Ice thickness anomalies simulated with the control
(a; 3-D higher-order) and the ice flow (b; 2-D SSA)
experiments at the respective ice minimum. Anomalies are relative
to the initial modern ice sheet. The respective minimum time is
indicated at the top of each panel. The ice margin is indicated
with a solid black line (10 m ice thickness remaining). A nonvisible ice margin is identical to the domain margin.
Reducing the friction at the base of the entire ice sheet by a factor
of 0.9 (basal×0.9; Fig. b)
results in a thinning on the order of 100 m in large parts of the ice
sheet relative to the ice sheet minimum in the control
experiment (Fig. a). The faster-flowing
ice sheet leads to a buildup of ice at the margins and the
topographically constrained outlet glaciers, particularly visible in
the northeast. In contrast, reducing the basal friction only at the
outlet glaciers by a factor of 0.5 (outlets×0.5;
Fig. c) leads to a regional thinning of
several hundred meters focused around the outlet glaciers. Note that
the thinning also affects ice thickness upstream from the outlet
region.
Ice thickness of the control experiment (a), the
basal×0.9 (b; reduced friction of the entire ice sheet),
and the outlets×0.5 (c; reduced friction at outlet
glaciers) experiments at their respective ice sheet minimum (time
indicated at the top of the panels). Anomalies are relative to the
control experiment. The ice margin is indicated with a
solid yellow/black line (10 m ice thickness remaining). A nonvisible ice margin is identical to the domain margin. The outlet regions are indicated with bright green
contours (c).
The ice velocities in the basal×0.9 experiments indicate that a
Greenland-wide reduction of basal friction by a factor of 0.9 leads to
a speed-up of the outlet glaciers by up to several 100 m yr-1
(Fig. b) relative to the
control experiment. Furthermore, reducing the friction at the
outlet glaciers by a factor of 0.5 (outlets×0.5) results in a
regional speed-up of several 100 m yr-1
(Fig. c). Although the outlets×0.5
experiment also shows a speed-up further upstream (on the order of
several meters per year), in combination with the local ice thinning
(Fig. c), the effects of halving the
friction at the outlet glaciers show a minimal effect on the total
ice volume (see also Fig. ).
Ice velocity of the ice sheet in the control
experiment (a) and the basal×0.9 (b; reduced friction of
the entire ice sheet), and the outlets×0.5 (c; reduced
friction at outlet glaciers) experiments at their respective ice
sheet minimum (time indicated at the top of the panels). Anomalies are
relative to the control experiment. The ice margin is
indicated with a solid yellow/black line (10 m ice thickness
remaining). A nonvisible ice margin is identical to the domain margin. The outlet regions are indicated with bright
green contours (c).
Discussion
Changing the SMB forcing – between a full surface energy balance
model (MAR-SEB) and an intermediate complexity SMB model (MAR-BESSI)
– gives the largest difference in our simplified simulations of the
Eemian ice sheet evolution (Fig. ). Compromises
such as the lack of ocean forcing and GIA, and limited changes of
basal friction are necessary to keep 3-D higher-order millennial-scale
simulations feasible and are discussed in this section.
MAR-SEB and MAR-BESSI are two estimates of Eemian SMBs selected from a
wider range of simulations analyzed in
. The same Eemian global climate
simulations from NorESM, downscaled over Greenland with the regional
climate model MAR, are used as forcing for the SMB models. Since only
one global climate model is used in this study, uncertainties related
to the Eemian climate cannot be evaluated here. Instead, the reader is
referred to the discussion in .
Our control experiment with the 3-D higher-order ice flow
model with modern, unchanged basal friction coefficients, and forced
with MAR-SEB SMB shows minor melting (equivalent to 0.5 m sea level
rise), while the SMB sensitivity experiment with MAR-BESSI
SMB causes a much larger ice sheet retreat (2.9 m sea level rise;
Fig. ). The basal sensitivity experiments
(basal/outlets) give an uncertainty of ±0.2 m sea
level rise on top of the SMB simulations (Fig. );
with the Greenland-wide basal friction change (basal) showing
the largest influence on the minimum ice volume. Reducing/enhancing
the friction at the outlet glaciers (outlets) by a factor of
0.9/1.1 shows mainly local thinning/thickening at the outlets
(Fig. c) with limited effect on the total
ice volume (Fig. ,
Table ). However, doubling the friction at the
outlet glaciers reduces the sea level rise contribution by 0.15 and
0.10 m for MAR-SEB and MAR-BESSI SMB forcing, respectively (relative
to the control experiment; Table ).
The basal friction sensitivity experiments (basal/outlets)
are non-exhaustive and further experiments could be envisioned,
including a lower velocity threshold to define the outlet glaciers,
continuous identification of outlet regions, and combining
basal×0.9 and outlets×0.5 experiments. In such
experiments, the impact on the ice sheet evolution might be larger than
in the experiments discussed. Regardless of the specific formulation
of the anomalous basal friction, the sensitivity experiments shown
here represent a substantial change in basal properties and they
illustrate the magnitude of the uncertainties related to the basal
conditions, implying that caution is required when deriving the basal
friction. Finding appropriate basal conditions of past ice sheets is
challenging. We show that after applying a large range of frictions it
is unlikely that friction at the base has a stronger influence than
changing the SMB forcing. This might be different if subglacial
hydrology fed by SMB is dynamically included.
The importance of coupling climate (SMB) and ice sheet has been
demonstrated in previous studies, e.g., recently for regional climate
models in a projected future climate assessment by
. However, running a high-resolution
regional climate model over several thousand years is presently
unfeasible due to the exceedingly high computational cost. This is
even more true when the goal is to run an ensemble of long sensitivity
simulations as presented here. Although the presented simulations are
lacking the ice–climate coupling, the SMB–altitude feedback is
accounted for by applying the SMB gradient method. The SMB is
significantly lowered as the ice surface is lowered: neglecting the
SMB–altitude feedback gives less than half the volume reduction
(MAR-SEB: 0.2 vs. 0.5 m; MAR-BESSI: 1.2 vs. 2.9 m;
Figs. and ).
Towards the end of the simulations, all model experiments develop a
new ice sheet state which is larger than the initial state
(Figs. and ). This
development towards a larger ice sheet is likely related to a
relaxation of the initial pre-industrial ice sheet (initial ice sheet
is not in equilibrium with the initial SMB forcing) and the
colder-than-present 115 ka climate. A simulation over 10 000 years
with constant pre-industrial SMB gives a ∼10 %
larger relaxed modern ice sheet. The relaxed sensitivity
experiments with this relaxed initial ice sheet
(∼0.5 m global sea level equivalent larger initial
state) result in a ∼0.3 m larger sea level rise (at
the minimum) compared to the control experiment. Although the
127 ka GrIS is not expected to be in equilibrium with pre-industrial
forcing, the relaxed experiment demonstrates the impact of a
larger initial ice sheet on our estimates of the contribution of
Greenland to the Eemian sea level highstand. Furthermore, the
relaxed experiment illustrates the strong, but slow, impact
of the SMB forcing. Even when starting with a different initial ice
sheet configuration, the final size is similar to the control
experiment, because late Eemian SMB results in a steady state of the
ice sheet.
Furthermore, the simplified initialization implies that the thermal
structure of the simulated ice sheet is lacking the history of a full
glacial–interglacial cycle; i.e., the ice rheology of our ice sheet is
different from an ice sheet which is spun up through a glacial
cycle. demonstrate the importance of
the ice rheology for the pre-Eemian ice sheet size. They find
differences of up to 20 % in initial ice volume after a spin-up
forced with different glacial temperatures (in simulations with basal
conditions not based on assimilation of surface velocities as is
the case here). In our approach, a biased thermal structure is partly
compensated by basal friction optimized so that the simulated surface
velocities represent the observed modern velocities. A viable way to
test the influence of the thermal structure on the ice rheology would
be to perform additional sensitivity experiments using a
3-D higher-order model (the 2-D SSA setup neglects vertical shear).
Starting the simulations with a smaller ice sheet would influence the
simulated maximum sea level contribution. A smaller ice sheet, in
combination with the SMB–altitude feedback, would result in a more
negative SMB at the lower surface regions. This could potentially lead
to smaller differences between the MAR-SEB and MAR-BESSI results
because large regions in the MAR-BESSI simulations melted away
completely, and a more negative SMB would show limited effect in such
regions. However, the MAR-SEB simulations are more likely to be
affected by the lower initial ice elevation. Note that neglecting GIA
could counteract the effect of a lower initial ice sheet as well as a
negative SMB, as the isostatic rebound of the regions affected by melt
would partly compensate for the height loss.
The ice flow experiments (2-D SSA) show very similar results
to the corresponding 3-D higher-order experiments (control and SMB experiments;
Fig. ). The minor differences in the east, a
stronger thickening in the 2-D SSA experiments, might be explained by
the complex topography in this region. The differences in ice volume
between 3-D higher-order and 2-D SSA experiments
(Fig. ) become larger towards the end of the
simulations under colder climate conditions (less negative
SMB). Furthermore, the ice surface evolution at the ice core locations
shows a similar behavior with both ice flow approximations, differences
are less than ∼150 m (at most locations). The strong
similarities between the 3-D higher-order and the
2-D SSA, also noted by
using ISSM for centennial simulations
are likely related to the inversion of the friction coefficients from
observed velocities. The dynamical deficiencies of the 2-D SSA ice flow
are partly compensated by the inversion algorithm. This algorithm
chooses basal conditions such that the model simulates surface
velocities as close to the observations as possible. The relatively
small difference between the 3-D higher-order and 2-D SSA experiments
emphasizes the controlling role of the SMB forcing and the SMB–altitude
feedback in our simulations. However, ice-flow-induced thinning (for
example, due to increased basal sliding) could initiate or enhance the
SMB–altitude feedback.
Basal hydrology is neglected in the simulations because it is not well
understood and therefore difficult to implement in a robust
way. However, it is recognized that basal hydrology might have been
important for the recent observed acceleration of Greenland outlet
glaciers e.g.,. Therefore, the
impact of changing basal conditions is tested by varying the friction
at the bed of the outlet glaciers. Although basal hydrology is not
explicitly simulated, its possible consequences in form of a slowdown or speed-up of the outlet glaciers is assessed
(Figs. and ).
The focus of this study is on the minimum Eemian ice sheet, which has
likely been land based. Our Greenland-wide simulations neglect ocean
forcing and processes such as grounding line migration. Although ocean
interaction is deemed an important process for marine-termination
glaciers in observations , a recent study
presenting ocean forcing sensitivity experiments for the Eemian GrIS
indicates that the Eemian minimum is governed by the atmospheric
forcing, due to a lack of ice–ocean contact
. In contrast, the size of the glacial
pre-Eemian ice sheet in their simulations is strongly influenced by
the ocean heat flux and submarine melting parameter choice, implying a
large impact of ocean forcing on the magnitude of ice loss over the
transition into the Eemian. Our simulations, however, are initiated at
127 ka with the observed modern GrIS geometry, not with a large
glacial ice sheet following the PMIP4 protocol;. Similar to
, we therefore do not expect our
smaller-than-present Eemian minimum ice sheet to be strongly sensitive
to ocean forcing and conclude that the disregard of ocean forcing and
processes such as grounding line migration only represents a
negligible error in the magnitude of ice loss and our sea level rise
estimates.
The choice of starting the simulations with the observed modern GrIS
geometry is based on the fact that the present-day ice sheet is
relatively well known, whereas the configuration of the pre-Eemian ice
sheet is highly uncertain. Since global sea level went from a glacial
lowstand to an interglacial highstand, during the course of the
Eemian interglacial period, it is a fair assumption that the Eemian
GrIS, at some point during this transition, resembled the present-day
ice sheet. In this study, this point is chosen to be at 127 ka. One
advantage of this initialization procedure is that it allows for a
basal friction configuration based on inverted observed modern surface
velocities. A spin-up over a glacial cycle without adapting basal
friction would be unrealistic. Furthermore, a spin-up would require
ice sheet boundary migration, i.e., implementation of calving,
grounding line migration, and a larger ice domain. This would be
challenging, as the mesh resolution is based on observed surface
velocities and the domain therefore limited to the present-day ice
extent. Additionally, a time-adaptive mesh, to allow for the migration
of the high-resolution mesh with the evolving ice streams, would be
necessary. Unfortunately, a realistic spin-up with all these additions
is presently unfeasible due to the high computational cost of the
model. Moreover, the lack of a robust estimate of the pre-Eemian GrIS
size and the climate uncertainties over the last glacial cycle would
introduce many more uncertainties to the initial ice sheet
configuration.
The Eemian GrIS sea level contribution of ∼0.5 m in
the control experiment is low compared to previous Eemian
model studies (Fig. ). Proxy studies based
on marine sediment cores and ice cores
provide a sea level rise estimate of 2 m
from the Greenland ice sheet during the Eemian, while assuming no
contribution from the northern part of the ice sheet where no proxy
constraints are available. However, scenarios with larger
contributions from the north could be possible as in the MAR-BESSI-forced experiments. Although the SMB sensitivity experiment
forced with SMB from MAR-BESSI shows a larger global sea level
contribution of ∼3.0 m, which is closer to previous
model estimates, this does not necessarily mean that the MAR-BESSI SMB
is more realistic. The low sea level contribution of the
control experiment could indicate systematic biases in the
experimental setup, causing a general underestimation of the Eemian
sea level contribution in all simulations.
Simulated sea level rise contributions from this study and
previous Eemian studies. For this study, the results of the control
(MAR-SEB; lower bound) and the SMB experiments (MAR-BESSI; upper bound)
are shown (the ranges show the results of the respective basal/outlets fraction sensitivity experiments). Previous studies are color coded according to the type of climate forcing used. More likely estimates are indicated with darker colors if provided in the respective studies. A common sea level rise conversion (distributing the meltwater volume equally on Earth's ocean area) is applied to , , , , , and . Tendencies of a GIA inclusion are indicated by blue arrows. The simulations of were repeated with an updated ice sheet model version in 2016 (Ralf Greve, personal communication, 2016).
No GIA processes are currently included in the transient mode of
ISSM. However, including rebound of the solid Earth would have the
tendency to counteract the surface melting. Especially, the MAR-BESSI
experiments are affected by considerable melt-induced surface
lowering. The solid Earth responds in timescales of several thousand
years and therefore can oppose part of the extreme surface lowering
during the warmest part of the Eemian, resulting in a reduced GrIS
contribution to global sea level rise. The MAR-SEB experiments show
less extensive melting and less surface lowering and as a result the
potential for GIA to influence the MAR-SEB SMBs is smaller. The
tendencies of how the sea level rise estimates could be influenced by
an inclusion of GIA are indicated by blue arrows in
Fig. .
Both SMB models are forced with a regionally downscaled climate based
on simulations with the global climate model NorESM. NorESM, as other
climate models, has biases, which end up in the SMBs through
downscaling procedures. This present study can be seen as a
sensitivity study to SMB forcing for millennial-scale ice sheet
simulations. While the simplified setup has its limits, the study
emphasizes the importance of the accurate SMB forcing in general,
independent of how well the presented SMBs describe the Eemian
SMB. Furthermore, it is important to keep in mind that an accurate SMB
forcing not only depends on the choice of SMB model but also the
climate simulations used as input.
Conclusions
This study emphasizes the importance of an accurate surface mass
balance (SMB) forcing over a more complex ice flow approximation for
the simulation of the Greenland ice sheet during the
Eemian. Experiments with two SMBs – a full surface energy balance
model and an intermediate complexity SMB model – result in different
Eemian sea level contributions (∼0.5 to 3.0 m) when
forced with the same detailed regional climate over Greenland. In
contrast, the comparison of experiments with 3-D higher-order and
2-D SSA ice flow gives only small differences in ice volume
(<0.2 m). Furthermore, the importance of the SMB–altitude feedback is
shown; neglecting this feedback reduces the simulated sea level
contribution by more than 50 %. A non-exhaustive set of basal
friction sensitivity experiments, affecting the entire ice sheet and
only the outlet glacier regions, indicates their limited influence on
the total ice volume (maximum difference of ∼0.2 m
compared to experiments with default friction). While basal friction
sensitivity experiments with larger impacts on the ice configuration
could be envisioned, it is unlikely that such experiments would exceed
the magnitude of uncertainty related to SMB. While it is challenging
and arguably unfeasible at present to perform an exhaustive set of
sensitivity experiments with 3-D higher-order ice flow models,
cost-efficient hybrid models (SIA + SSA) could be an option to further
investigate the ice dynamical processes (such as ocean forcing or
basal hydrology) neglected here.
In conclusion, simulations of the long-term response of the Greenland
ice sheet to warmer climates, such as the Eemian interglacial period,
should focus on an accurate SMB estimate. Moreover, it is important to
note that uncertainties in SMB are not only a result of the choice of
SMB model but also the climate simulations used as input. Climate
model uncertainties and biases are neglected in this study. However,
they should be included in future Eemian ice sheet model studies in an
effort to provide reliable estimates of the Eemian sea level
contribution from the Greenland ice sheet.
Code availability
The ISSM code can be freely downloaded from http://issm.jpl.nasa.gov
(last accessed: 18 October 2018). The NorESM model
code can be obtained upon request. Instructions on how to obtain a
copy are given at https://wiki.met.no/noresm/gitbestpractice (last
accessed: 18 October 2018). The source code for BESSI is available as a supplement to . The MAR code is available at
http://mar.cnrs.fr (last accessed: 18 October 2018). ISSM and BESSI model setup scripts can be
obtained upon request from the corresponding author.
Data availability
The ISSM simulations and the MAR-SEB and MAR-BESSI SMBs are available
upon request from the corresponding author. The SeaRISE dataset used
is freely available at
http://websrv.cs.umt.edu/isis/images/e/e9/Greenland_5km_dev1.2.nc (last
accessed: 18 October 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-13-2133-2019-supplement.
Author contributions
AP and KHN designed the study with contributions
from PML and AB. SLC performed the MAR simulations. AP performed the
ISSM simulations, made the figures and wrote the text with input
from KHN, PML, AB, and SLC.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The research leading to these results has received funding from the
European Research Council under the European Community's Seventh
Framework Programme (FP7/2007-2013)/ERC grant agreement 610055 as
part of the ice2ice project. The simulations were performed on
resources provided by UNINETT Sigma2, the National Infrastructure for
High Performance Computing and Data Storage in Norway (NN4659k;
NS4659k). The publication of this paper was supported by the open-access funding of the University of Bergen. Petra M. Langebroek was supported by the RISES project of the Centre for Climate Dynamics at the Bjerknes
Centre for Climate Research. Sébastien Le clec'h acknowledges the financial support
from the French–Swedish GIWA project, the ANR AC-AHC2, as
well as the iceMOD project funded by the Research Foundation
– Flanders (FWO-Vlaanderen). We thank Joshua K. Cuzzone for
assisting in setting up the higher-order ISSM runs, Michiel M. Helsen for
helping with the SMB gradient method, and Basile de Fleurian for helping
to resolve technical issues with ISSM. Furthermore, we very much thank
Bas de Boer, an anonymous referee, and the editor Arjen Stroeven for
their comments which significantly improved the manuscript.
Financial support
This research has been supported by the European Commission (ICE2ICE (grant no. 610055)).
Review statement
This paper was edited by Arjen Stroeven and reviewed by Bas de Boer and one anonymous referee.
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