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The Cryosphere, 11, 805–825, 2017
www.the-cryosphere.net/11/805/2017/
doi:10.5194/tc-11-805-2017
© Author(s) 2017. CC Attribution 3.0 License.
Sensitivity, stability and future evolution of the world’s
northernmost ice cap, Hans Tausen Iskappe (Greenland)
Harry Zekollari1,2, Philippe Huybrechts1, Brice Noël3, Willem Jan van de Berg3, and Michiel R. van den Broeke3
1Earth System Science & Departement Geografie, Vrije Universiteit Brussel, Brussels, Belgium
2Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zürich, Zurich, Switzerland
3Institute for Marine and Atmospheric Research, Universiteit Utrecht, Utrecht, the Netherlands
Correspondence to: Harry Zekollari (harry.zekollari@vub.be)
Received: 24 November 2016 – Discussion started: 16 December 2016
Revised: 28 February 2017 – Accepted: 1 March 2017 – Published: 24 March 2017
Abstract. In this study the dynamics and sensitivity of Hans
Tausen Iskappe (western Peary Land, Greenland) to climatic
forcing is investigated with a coupled ice flow–mass bal-
ance model. The surface mass balance (SMB) is calculated
from a precipitation field obtained from the Regional Atmo-
spheric Climate Model (RACMO2.3), while runoff is calcu-
lated from a positive-degree-day runoff–retention model. For
the ice flow a 3-D higher-order thermomechanical model is
used, which is run at a 250 m resolution. A higher-order solu-
tion is needed to accurately represent the ice flow in the outlet
glaciers. Under 1961–1990 climatic conditions a steady-state
ice cap is obtained that is overall similar in geometry to the
present-day ice cap. Ice thickness, temperature and flow ve-
locity in the interior agree well with observations. For the
outlet glaciers a reasonable agreement with temperature and
ice thickness measurements can be obtained with an addi-
tional heat source related to infiltrating meltwater. The simu-
lations indicate that the SMB–elevation feedback has a major
effect on the ice cap response time and stability. This causes
the southern part of the ice cap to be extremely sensitive to
a change in climatic conditions and leads to thresholds in the
ice cap evolution. Under constant 2005–2014 climatic con-
ditions the entire southern part of the ice cap cannot be sus-
tained, and the ice cap loses about 80 % of its present-day
volume. The projected loss of surrounding permanent sea ice
and resultant precipitation increase may attenuate the future
mass loss but will be insufficient to preserve the present-day
ice cap for most scenarios. In a warmer and wetter climate
the ice margin will retreat, while the interior is projected to
thicken, leading to a steeper ice cap, in line with the present-
day observed trends. For intermediate- (+4◦C) and high-
warming scenarios (+8◦C) the ice cap is projected to disap-
pear around AD 2400 and 2200 respectively, almost indepen-
dent of the projected precipitation regime and the simulated
present-day geometry.
1 Introduction
Glaciers and ice caps (GICs) made an important contribu-
tion to sea level rise in the 20th century. In the 21st century
they are also projected to be major contributors (Gardner et
al., 2011; Jacob et al., 2012; Church et al., 2013; Gregory
et al., 2013). The Greenland GICs are no exception as they
have contributed significantly in the recent past (Bolch et
al., 2013) and will continue to do so in the coming decades
(Machguth et al., 2013; Huss and Hock, 2015). To estimate
the magnitude of this regional and global contribution, sim-
plified models have been applied at the regional and global
scale (e.g. Marzeion et al., 2012; Slangen et al., 2012; Giesen
and Oerlemans, 2013; Radi´
c et al., 2014; Clarke et al., 2015;
Huss and Hock, 2015). In order to improve the many parame-
terizations on which these models rely and for a better under-
standing of the dynamics of GICs in a changing climate, in-
depth modelling studies are needed in which detailed models
are used at a high spatial resolution. A variety of recent stud-
ies exist for individual glaciers (e.g. Le Meur and Vincent,
2003; Jouvet et al., 2009, 2011; Aðalgeirsdóttir et al., 2011;
Duan et al., 2012; Zekollari et al., 2013, 2014; Hannesdóttir
et al., 2015; Réveillet et al., 2015), but for ice caps such de-
tailed studies are limited (Aðalgeirsdóttir et al., 2005, 2006;
Flowers et al., 2005, 2007, 2008; Giesen and Oerlemans,
Published by Copernicus Publications on behalf of the European Geosciences Union.
806 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
2010). Because of their fundamentally different behaviour,
parameterizations developed for mountain glaciers are not
valid for ice caps. Whereas a glacier can retreat up the moun-
tain and re-adjust to the new climatic conditions, an ice cap is
unable to do so. Glaciers derive their highest elevation from
the surrounding topography, while an ice cap is (largely) self-
sustained due to its own height. A decrease in height leads to
a decrease in surface mass balance (SMB), a process that can
reinforce itself due to a positive feedback and lead to fast
collapse. To exactly understand these mechanisms and to ex-
plore the stability of ice caps and possible thresholds in the
system related to the SMB–elevation feedback, it is neces-
sary to couple the SMB with the ice flow.
Pioneering work on the 3-D modelling of ice caps was un-
dertaken by Mahaffy (1976), who modelled the dynamics of
the Barnes ice cap and compared observed and modelled ice
cap geometries. In this study an equilibrium ice cap with a
similar size as observed could not be obtained, and the ice
cap grew far beyond the present-day state or evolved to a
very small ice cap. Since then several modelling studies have
been performed on individual ice caps in Iceland (Aðalgeirs-
dóttir et al., 2005, 2006; Flowers et al., 2005, 2007, 2008) and
on Hardangerjøkulen (southern Norway) (Giesen and Oerle-
mans, 2010; Åkesson et al., 2017) with models based on the
shallow-ice approximation (SIA). Schäfer et al. (2015) used
a full-Stokes ice flow model with an englacial temperature
parameterization for a study on the Vestfonna ice cap (Sval-
bard) with a particular focus on the SMB–elevation feed-
back. In a recent study Ziemen et al. (2016) modelled the
temporal evolution of the Juneau ice field (Alaska), which
exhibits some similarities to ice caps. To date, however, no
detailed time-dependent thermomechanical modelling stud-
ies exist on individual high Arctic ice caps, although these
ice caps are projected to be important contributors to sea
level rise in the coming decades to century (e.g. Giesen and
Oerlemans, 2013; Radi´
c et al., 2014). This contribution is
largely driven by an above-average rise in high Arctic tem-
peratures due to the polar amplification (Masson-Delmotte et
al., 2006; Bekryaev et al., 2010; Khan et al., 2014; Lee, 2014;
Pithan and Mauritsen, 2014; Seneviratne et al., 2016), which
could eventually be attenuated by an increased precipitation
(Machguth et al., 2013).
Here we present a 3-D modelling study on Hans Tausen
Iskappe (Peary Land, Greenland), the world’s northernmost
ice cap, located between 82.2 and 83.0◦N (Fig. 1). Despite
its remoteness, a considerable body of field data exist that
can be used for model calibration and validation, such as ob-
servations on surface mass balance, ice thickness, elevation
changes, ice temperature and surface velocity. There are indi-
cations that Hans Tausen Iskappe is very sensitive to changes
in climatic conditions. Several palaeorecords suggest that af-
ter being connected to the Greenland Ice Sheet (GrIS) during
the Last Glacial Maximum (LGM) (Bennike, 1987; Larsen
et al., 2010) the ice cap (largely) disappeared during the
Holocene Thermal Maximum (HTM), after which it started
Figure 1. Hans Tausen Iskappe in the mid-1990s. Figure created
with the TopoZeko toolbox (Zekollari, 2016). Map in lower right
corner shows the location (red dot) of the ice cap in Greenland.
to rebuild around 3500–4500 cal BP (Hammer et al., 2001;
Madsen and Thorsteinsson, 2001). In this study we investi-
gate the sensitivity and dynamics of the ice cap and analyse
the feedback mechanisms that can lead to fast changes and
thresholds in the ice cap evolution. For this purpose we use a
coupled SMB–ice flow model at a high horizontal resolution
(250 m). In order to resolve the ice flow in the many out-
let glaciers accurately, a higher-order (HO) approximation
to the full force balance is used. This differs from other de-
tailed ice cap and ice field modelling studies (Aðalgeirsdóttir
et al., 2005, 2006; Flowers et al., 2005, 2007, 2008; Giesen
and Oerlemans, 2010; Hannesdóttir et al., 2015; Ziemen et
al., 2016; Åkesson et al., 2017) that are based on the SIA
or similar approaches. We investigate the influence of the
model complexity (SIA/HO) and resolution on the modelled
geometries and run the ice cap into a steady state that is com-
pared to field observations. At first the thermomechanical
ice flow model (Sect. 3) and SMB model (Sect. 4) are de-
scribed, after which the model is extensively tuned and val-
idated (Sect. 5). Subsequently thresholds are analysed that
could inhibit ice cap growth or decay, followed by the sen-
sitivity of the ice cap to changes in climatic conditions and
their implications for the future ice cap evolution (Sect. 6).
2 Site description and field data
Hans Tausen Iskappe is an ice cap located in western Peary
Land and is separated from the GrIS by the Wandel Dal,
which is 10–20 km wide (Weidick, 2001) (see Fig. 1). With
an area of around 4000 km2(ca. 75 km from north to south
and 50 km from west to east) (Starzer and Reeh, 2001) it is
the second-largest ice cap in northern Greenland after Flade
Isblink (ca. 8500 km2) (Kelly and Lowell, 2009; Rinne et
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 807
Figure 2. (a) Bedrock elevation (Starzer and Reeh, 2001). Areas below sea level (fjords with semi-permanent sea ice) are depicted in white;
the thick black line corresponds to the outline of the observed glaciated area. (b) Ice thickness in the mid-1990s based on the DEM from
Starzer and Reeh (2001).
al., 2011). It corresponds to around 4–5 % of the total area for
all GICs in Greenland (ca. 90 000 km2; Rastner et al., 2012)
and around 0.5 % of the worldwide GICs area. The ice cap
has a typical elevation of 1000–1200ma.s.l., except for local
domes that reach up to 1200–1300 ma.s.l. The outlet glaciers
are mostly land-terminating, and many of them terminate
up to several hundred metres above sea level. Some calv-
ing glaciers exist, but overall their activity is limited, and all
fjords have a semi-permanent ice cover which melts only at
rare intervals (>30 years) (Higgins, 1990; Weidick, 2001;
Möller et al., 2010). Hans Tausen Iskappe largely covers
the underlying topography and therefore qualifies as an ice
cap, while other ice masses in Peary Land are smaller and
more controlled by the surrounding topography and there-
fore rather qualify as valley glaciers or ice fields (e.g. Bure
Iskappe, Heimdal Iskappe, Heinrich Wild Iskappe and other
ice masses to the north) (Weidick, 2001).
The first documented observations on and around Hans
Tausen Iskappe date from the first half of the 20th cen-
tury (Koch, 1928, 1940) and the mid-20th century (Davies
and Krinsley, 1962), but the first detailed field campaign
only occurred in 1975–1976, when several shallow ice and
firn cores were drilled. In 1978 an aerial photography cam-
paign was conducted (Starzer and Reeh, 2001), while in the
1990s an elaborate field campaign was set up during the
three summers of 1993, 1994 and 1995 (Hammer, 2001).
In 1993 different reconnaissance flights were made. Exten-
sive airborne ice thickness measurements were performed
from Twin Otter aircrafts (Thomsen et al., 1996; Starzer and
Reeh, 2001). Additional ground-based ice thickness mea-
surements were performed in 1994 and 1995 at a variety
of locations (Gundestrup et al., 2001). From these measure-
ments it is known that the ice cap rests on a 800–1100m a.s.l.
elevated plateau in the northern part, while in the southern
part the bedrock elevation is lower and varies between 600
and 900 m a.s.l. (Fig. 2a). Consequently in the southern part
the ice is substantially thicker and locally reaches more than
500 m along a north–south-oriented deep canyon (Gunde-
strup et al., 2001) (Fig. 2b). Based on an interpolation of
these measurements the ice cap had an estimated volume of
around 760 km3in the mid-1990s (Starzer and Reeh, 2001).
Whereas the interior of the ice cap has a dense network of
ice thickness measurements (up to several points per square
kilometre), measurements on the outlet glaciers are scarcer,
and here a parameterization relating the surface slope to the
ice thickness is used (Starzer and Reeh, 2001). Note that the
direct ice thickness measurements on Hans Tausen Iskappe
from the 1990s are not included in the Bamber et al. (2013)
data set, and therefore local differences exist with the recon-
structed bedrock from Starzer and Reeh (2001). The surface
elevation in both data sets is largely similar, and only small
discrepancies exist that may partly be linked to the different
time of acquisition.
From 1994 to 1995 a strain network was set up around
the central dome, which is sometimes referred to as “the
southeastern dome” (Reeh, 1995; Gundestrup et al., 2001;
Hvidberg et al., 2001; Jonsson, 2001). A mass balance mea-
surement programme was established between the north
dome (1320 m a.s.l.) and Hare glacier, a small outlet glacier
with its front at 220 m a.s.l. (see Fig. 1) (Reeh et al., 2001;
Machguth et al., 2016). Here different components of the
energy balance were measured, and a detailed stake farm
was set up (Braithwaite et al., 1995). In 1995 a 345 m ice
core was drilled at the central dome (1271 m a.s.l.) (Ham-
mer et al., 2001; Johnsen et al., 2007), which combined
with glacial geological investigations (Landvik et al., 2001)
provide constraints on the palaeo-ice-cap evolution. Addi-
tionally englacial temperatures (Reeh, 1995; Thomsen et
al., 1996) and surface velocities (Reeh, 1995; Hvidberg et
al., 2001) were measured and were used for model tuning
and validation in this study.
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808 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Surface velocities are known from interferometric syn-
thetic aperture radar (InSAR) measurements for the win-
ters of 2000/01, 2005/06, 2006/07, 2007/08, 2008/09 and
2009/10 (Joughin et al., 2010, 2015). These are around a
few metres per year for the interior, around 30–60ma−1
for medium-sized outlet glaciers (e.g. Hare glacier) and up
to 200 m a−1for the largest outlet glaciers (Fig. 8a). These
values are in agreement with the surface velocities derived
from the mass balance stakes on Hare glacier (Thomsen et
al., 1996) and a strain network setup around the central dome
(Hvidberg et al., 2001). The InSAR velocities are consistent
with the 1947–1978 average surface velocities deduced from
aerial photography (Higgins, 1990), although direct compar-
isons are not always straightforward as the exact location
of the aerial measurement is often not clearly stated (see
Joughin et al., 2010, for an elaborate discussion).
3 Thermomechanical ice flow model
3.1 Ice flow model and experimental setup
Nye’s generalization of Glen’s flow law is used as a consti-
tutive equation for ice deformation (Glen, 1955; Nye, 1957),
where the deviatoric stresses (τij ) are defined as
τij =2η˙εij ,(1)
η=1
2A(t)−1/n (˙εe+ ˙ε0)1
n−1.(2)
Here ηis the viscosity, nis the power-law exponent (set to
3); A(t)is the rate factor, which is temperature-dependent
following an Arrhenius type function; and ˙ε0is a small offset
(10−30) that ensures finite viscosity (Fürst et al., 2011). The
effective stress ˙εeis determined from the second invariant of
the strain-rate tensor:
˙ε2
e=1
2˙εij ˙εij ,(3)
where the strain tensor ˙εij is defined as
˙εij =1
2∂iuj+∂jui.(4)
A widely used approximation for ice sheet and ice cap mod-
elling is the SIA in which only the local shear stresses are
accounted for and the longitudinal components are neglected
(Hutter, 1983). Under the SIA Eqs. (1)–(4) are simplified and
the shear stress results from vertical plane shearing:
∂zτiz =ρg∂is. (5)
Here ρis the ice density, gis the gravitational accelera-
tion and sis the surface elevation. The SIA approximation
is based on a large width /depth ratio and is valid for the
interior of the ice cap, but not for its many narrow outlet
glaciers. To more accurately represent the ice flow in the
outlet glaciers, a HO approximation to the Stokes momen-
tum balance is therefore used in which longitudinal stress
components are accounted for (Blatter, 1995; Pattyn, 2003;
Fürst et al., 2011). More specifically a multilayer longitudi-
nal stresses approximation of the force balance, abbreviated
as LMLa in Hindmarsh (2004), is used, where a cryostatic
equilibrium in the vertical is assumed by neglecting bridging
effects (i.e. neglecting vertical resistive stresses):
∂i2τii +τjj +∂jτij +∂zτiz =ρg∂is (for i6= j ), (6)
˙εiz =1
2∂zui.(7)
This HO approximation and its numerical implementation
(Fürst et al., 2011) have been successfully applied at differ-
ent scales, ranging from small mountain glaciers (Zekollari
et al., 2013, 2014; Zekollari and Huybrechts, 2015) to entire
ice sheets (Fürst et al., 2013, 2015).
All ice-free patches located within the present-day ice cap,
which mainly coincide with mountain peaks and steep ridges,
are explicitly kept ice-free in the simulations, as the pro-
cesses that prevent accumulation here (mostly snowdrift by
wind and related to the steep topography) are not captured in
our models. To prevent confluence of ice flow from nearby
small ice masses (mainly from Bure Iskappe and Heimdal
Iskappe in the east) and from the GrIS, which only partly be-
long to the domain and can therefore not be modelled explic-
itly, ice is only allowed to grow from areas that are covered
by Hans Tausen Iskappe at present. The ice can subsequently
expand freely, without any constraints (e.g. it can connect
to the GrIS), and both negative and positive surface mass
balance can thus be obtained for areas outside the present-
day ice cap. The ice cap cannot expand for areas where the
bedrock elevation is lower than −50m, where the ice is re-
moved to crudely represent calving. Field and aerial obser-
vations (Weidick, 2001) suggest that calving is very limited
(up to 2–3 % of total mass loss) in occurrence and magnitude,
and this is also the case in our numerical simulations.
3.2 Thermodynamics and role of meltwater
A full 3-D calculation of the ice temperature is performed
simultaneously with the velocity calculations as the ice tem-
perature relates to the ice stiffness (rate factor in Glen’s flow
law) and determines whether or not basal sliding occurs (see
e.g. Huybrechts, 1996, for a more detailed account). Sur-
face temperature is calculated from the mean annual temper-
ature (TMA) and a warming component related to the super-
imposed ice formation. Observed refreezing of slush fields
(Reeh, 1995), (sub-)surface temperature and surface isotopes
measurements (Thomsen et al., 1996; Reeh et al., 2001) sug-
gest that refreezing occurs. Based on field measurements
(Reeh et al., 2001) a surface warming of 22 K (m w.e.)−1of
refreezing is used. At the base of the ice cap heat is produced
by the geothermal heat flux, and friction is generated by basal
sliding.
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 809
In the percolation zone of the ice cap, temperature mea-
surements suggest an additional heat source from infiltrating
supraglacial meltwater that can reach the bed. We incorpo-
rate this additional heat source by imposing a basal-water
heat flux (similar to geothermal heating), following the ap-
proach of Wohlleben et al. (2009). This mechanism differs
from cryo-hydrologic warming (Phillips et al., 2010), where
meltwater heating also plays a crucial role (through flowing,
ponding and refreezing) but where the heat source is spread
and leads to a warming of the whole ice column. A heating
through meltwater is supported by high values from englacial
temperature measurements in the percolation zone of the ice
cap (Thomsen et al., 1996) and is also observed on the GrIS
(Thomsen et al., 1991; Phillips et al., 2010, 2013; Lüthi et
al., 2015). There are also observations on other Arctic ice
caps, such as the Laika ice cap (Canada), where repeatedly
measured high englacial temperatures cannot be explained
without an additional heat source (Blatter and Kappenberger,
1988; Blatter and Hutter, 1991), and a 200m thick ice col-
umn in the ablation zone of the Barnes ice cap, where the
10 m depth temperature is −10 ◦C, while temperatures at 130
m depth are close to the pressure melting point (Classen,
1977). In a recent study on the Qaanaaq ice cap (NW Green-
land), Sugiyama et al. (2014) indicate that the observed ve-
locities cannot be reproduced without accounting for a heat
transfer from meltwater when solving for thermodynamics,
and Schäfer et al. (2014) also stress the possible effect of
meltwater on thermodynamics and ice flow for the Vestfonna
ice cap (Svalbard).
4 Surface mass balance
The SMB model used in this study calculates melt and runoff
from the widely used positive-degree-day (PDD) runoff–
retention approach (Reeh, 1989; Janssens and Huybrechts,
2000; Gregory and Huybrechts, 2006). This approach allows
for the SMB to be calculated at any time for any geome-
try. In this study the SMB model is coupled to the thermo-
mechanical ice flow model once a year, avoiding potential
problems related to a long coupling interval (see Schäfer et
al., 2015). The SMB is also available from the Regional At-
mospheric Climate Model (RACMO2.3) (Noël et al., 2015)
for a fixed geometry, but it is not directly used as the PDD is
more flexible for generating the SMB under an evolving ge-
ometry without the need to modify RCM output for a differ-
ent surface elevation (Franco et al., 2012; Helsen et al., 2012;
Edwards et al., 2014). The implications of using such correc-
tion methods to account for the interaction between surface
elevation and SMB were investigated in detail by Schäfer et
al. (2015) for the Vestfonna ice cap (Svalbard), suggesting
that such approaches should not be used for simulations of
more than several decades and under extreme climate change
scenarios.
4.1 Model setup
4.1.1 Positive-degree-day approach
The PDD runoff–retention model determines the PDD sum
from monthly air temperatures assuming a variability of daily
near-surface (2m) temperatures around the monthly mean.
Melt rates are proportional to this melt potential. In snow-
covered regions the meltwater from surface melting is ini-
tially stored as capillary water within the snowpack, until the
snowpack becomes saturated, typically when melt reaches
around 60 % of the annual precipitation (Janssens and Huy-
brechts, 2000) and runoff occurs. The formation of superim-
posed ice occurs when water-saturated snow survives above
the impermeable ice layer until the end of the season and
subsequently refreezes (Janssens and Huybrechts, 2000).
The daily variability in temperatures is expressed as a stan-
dard deviation (σ) around the monthly mean. A value of 3◦C
is used, lower than the widely used value of 4.2◦C for the
whole of Greenland (e.g. Fürst et al., 2015) but consistent
with 1994–1995 observations of temperatures, SMB and re-
freezing for six locations on Hare glacier (Reeh et al., 2001).
The melt rates are determined with separate degree-day fac-
tors for snow and ice, which are respectively equal to 0.0027
and 0.0065 m ice equivalent/degree day based on detailed
stake observations on the ice cap (Braithwaite et al., 1995;
Reeh, 1995).
4.1.2 Temperature parameterization
The PDD sum is calculated from a parameterization of the
TMA and the mean July temperature (TMJ), assuming a si-
nusoidal annual march. A temperature parameterization is
preferred over lapse-rate-corrected RCM temperatures to re-
move the bias from the present-day imprint of the ice cap
on its own temperature field in a different geometric set-
ting. Furthermore the temperature parameterization is flex-
ible and allows for a direct application at different resolu-
tions, without the need for complex downscaling methods
(needed for RCM data). The TMJ has the largest influence
on the SMB as this field largely determines the amount of
summer melt, while the TMA sets the amplitude of the an-
nual sinusoidal signal and thereby determines the tempera-
tures of the other seasons when little to no melt occurs. The
rain–snow temperature threshold is set at 1◦C. TMA and
TMJ are parameterized for the mass balance year 1994/95
based on detailed field measurements (Reeh, 1995; Reeh
et al., 2001), and this parameterization is subsequently ex-
tended to the period 1961–1990 by comparing both peri-
ods in the regional climate model RACMO2.3 (with ERA-
40 and ERA-Interim boundary conditions): the 1994–1995
TMA was 0.53 ◦C higher than the 1961–1990 average, while
the 1995 TMJ was about 0.27 ◦C lower than the 1961–1990
average. The temperatures are parameterized as a function of
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810 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Table 1. Comparison of measured accumulation and modelled precipitation (RACMO2.3) for the period 1975–1995. Site location is shown
in Fig. 1.
Location 1975–1995 average annual accumulation 1975–1995 average annual precipitation
(and elevation in ma.s.l.) (from shallow ice core) (mw.e.a−1) from RACMO2.3 (mw.e.a−1)
North dome (1318 m) 0.27 0.24
Central dome (1275 m) 0.09 0.11
BH75 (1150 m) 0.11 0.13
BH76 (1125 m) 0.10 0.15
latitude and elevation, and they can therefore be determined
at any model resolution.
The measured temperature lapse rate in July is
−0.0056 ◦Cm−1(Reeh et al., 2001), and as a latitudi-
nal gradient we adopt the value of −0.1681 ◦C◦N−1from
Fausto et al. (2009). Altogether this results in the following
parameterization for the 1961–1990 mean July temperature
(in ◦C) (see Fig. 3a):
TMJ =19.47 −0.1681 ×LAT −0.0056 ×ELEV,(8)
where LAT is the latitude (◦) and ELEV the elevation (m).
Notice that given the limited latitudinal range of the ice cap
(0.8◦) the influence of the latitudinal gradient is limited. The
parameterized 1961–1990 TMJ agrees well with output from
RACMO2.3 for the period 1961–1990 (Fig. 3b), with mean
July temperatures around 5.5–6 ◦C at sea level and around
−1 to −1.5 ◦C at the domes (1200–1300 m a.s.l.).
The mean annual temperature has not been measured on
the ice cap directly. The latitudinal and elevation gradients
are therefore also taken from Fausto et al. (2009). A pa-
rameterization is derived to fit with measurements from the
nearby meteorological station Kap Harald Moltke (Reeh et
al., 2001). For areas lower than 300m, no elevation gradient
is applied in order to represent the temperature inversion that
occurs here following Reeh et al. (2001). For 1961–1990 the
TMA (in ◦C) is parameterized as follows (see Fig. 3c):
for ELEV <300 m :TMA =45.07 −0.734 ×LAT;
for ELEV >300 m :TMA =46.97 −0.734 ×LAT
−0.00638 ×ELEV.(9)
With this parameterization the 1961–1990 TMA at sea level
is around −15 ◦C, while at north dome this is −22.2 ◦C and
at the central dome −21.7 ◦C. The TMA at the domes agree
well with the local measurements of 10 m depth temperature,
which are respectively −21.0 and −20.8 ◦C (Reeh, 1995;
Reeh et al., 2001). The slight difference between parame-
terized and observed values may be linked to firn warming
due to refreezing, although this process is generally limited at
those high elevations. Furthermore the parameterized TMA
is in fairly good agreement with RACMO2.3 output for this
period (see Fig. 3d).
4.1.3 Precipitation parameterization
The accumulation has been derived from field measurements
and four shallow cores that cover most of the 20th century
(Reeh et al., 2001). The accumulation is the highest in the
north(-west), which is related to the proximity to the ocean,
acting as a moisture source (see Fig. 3e). Due to a topo-
graphic shielding the precipitation is much lower in the cen-
tral part. In the south(east) the precipitation is also very low,
but generally a bit higher than in the centre. Based on ac-
cumulation measurements from the shallow cores Reeh et
al. (2001) tried to derive a parameterization to describe this
pattern as a function of latitude and elevation, but this re-
sulted in an unrealistic field with very low (in some cases
even negative) precipitation at low elevation. We therefore
opt to use the precipitation field from the regional climate
model simulation RACMO2.3, which is run at 11km and
was bilinearly downscaled to a 1km resolution (see Fig. 3e
for 1961–1990 average field) (Noël et al., 2016). For all
simulations this precipitation field is further interpolated to
the model resolution. This regional climate model is able
to reproduce the observed precipitation patterns closely as
is shown by a comparison with accumulation from four
sites for the period 1975–1995 (Table 1). Field observations
and model output (both from our SMB model and from
RACMO2.3) indicate that for the four high-elevation sites
the solid precipitation is nearly equal to the accumulation
(annual rain fraction varies between 0 and 5 %).
4.2 SMB model evaluation
The SMB model is applied to the observed geometry (Starzer
and Reeh, 2001) for the mass balance year 1994/95 and com-
pared to the measured SMB. For Hare outlet glacier (see
Fig. 1), where an extensive mass balance network was in-
stalled (Braithwaite et al., 1995; Reeh et al., 2001), the mod-
elled SMB agrees with the observations. For this relatively
wet year (Reeh et al., 2001) for Hare glacier the SMB at the
glacier terminus is below −1 m w.e.a−1, the equilibrium line
altitude (ELA) is around 700–750 m and the highest SMB
is around 0.3 m i.e.a−1at 1300m (Thomsen et al., 1996;
Machguth et al., 2016) (Fig. 4a). SMB measurements in the
ablation area were performed between 25 July 1994 and
17 August 1995 and mainly reflect the 1994/95 SMB and
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 811
Figure 3. (a) 1961–1990 parameterized mean July temperature, (b) 1961–1990 RACMO2.3 mean July temperature (11km resolution),
(c) 1961–1990 parameterized mean annual temperature, (d) 1961–1990 RACMO2.3 mean annual temperature (11km resolution) and
(e) 1961–1990 RACMO2.3 mean annual precipitation. In all figures the thick black line corresponds to the outline of the observed glaciated
area (Starzer and Reeh, 2001).
some late summer melt from the 1993/94 balance year. They
should therefore be considered as an underestimation (lower
bound) for the 1994/95 SMB (Fig. 4a). The SMB measure-
ments in the accumulation area span the period between
4 August 1994, after which the local melt is very limited, and
23 June 1995, before which melt is limited, and are therefore
close to the 1994/95 SMB (Fig. 4a).
For the period 1961–1990 the average SMB from our
PDD runoff–retention model is compared to the 1km down-
scaled SMB version v1.0 from the regional climate model
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812 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Figure 4. (a) 1994–1995 SMB for Hare glacier based on the PDD melt–runoff model and SMB measurements (lower-bound estimate in the
ablation area; see text). (b) SMB vs. elevation for the period 1961–1990 for the PDD melt–runoff model and RACMO 2.3. Average SMB for
the period 1961–1990 from (c) PDD melt–runoff model and (d) RACMO2.3 RCM model. The masking and the calculations for panels (b,
c, d) are based on the 1 km GIMP DEM ice mask and topography (Howat et al., 2014).
RACMO2.3, which is reconstructed by adding up daily-
downscaled runoff, sublimation, snowdrift erosion and total
precipitation (rain and snow) (Noël et al., 2016) (Fig. 4). For
this comparison the SMB is modelled using the same 1 km
Greenland Mapping Project (GIMP) digital elevation model
(DEM) ice mask and topography (Howat et al., 2014) for
both models. The output from both models is in relatively
good agreement (see Fig. 4b), which is in part related to the
fact that the precipitation forcing is the same in both models.
For both approaches the integrated 1961–1990 SMB over the
ice cap is close to 0: −0.02 m w.e.a−1in RACMO2.3 and
+0.02 m w.e.a−1in the PDD approach. The slightly lower
SMB in RACMO2.3 results from a stronger melt/sublimation
component, due to which the ELA, especially for the south-
ern part of the ice cap, is lower than with the PDD approach
(see Fig. 4c, d). As a result the RACMO2.3 SMB field has
a more pronounced imprint of the elevation field, while the
PDD SMB field has a stronger imprint of the precipitation
field. In another widely used RCM for Greenland, Mod-
èle Atmosphérique Régional (MAR3.5.2; 20 km run, down-
scaled to the 5 km DEM; Bamber et al., 2013) (Fettweis et
al., 2013), an integrated SMB of +0.03 m w.e.a−1is ob-
tained. Given the different topographic input, a direct com-
parison between with RACMO2.3 and the PDD approach
is difficult, but also here the RCM output suggests a near-
zero SMB for this period. Reconstructions for other peri-
ods, which are addressed below, show that the PDD/RCM
approaches are also in generally good agreement for other
periods of time, which is in line with an earlier study by
Hanna et al. (2011). They compared the PDD approach and
RACMO2.1 output for Greenland for the period 1958–2010
in terms of interannual variability and found a reasonable
agreement.
5 Ice cap under 1961–1990 climatic conditions
5.1 1961–1990 modelled steady state (250 m, HO) vs.
observations
The 1961–1990 SMB conditions are imposed, and the
ice cap is run into a steady state using the coupled HO
thermomechanical–PDD model, which is run at a 250 m hor-
izontal resolution.
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 813
Figure 5. (a) 1961–1990 steady-state ice thickness from the HO 250 m resolution run. The thick black lines represent the outlines from the
glaciated areas from the DEM (Starzer and Reeh, 2001). The dotted white line is the transect at UTM x=602.5 km that is illustrated in
Fig. 11. (b) Ice thickness difference between the 1961–1990 modelled steady-state geometry and the observed geometry.
5.1.1 Ice cap extent and SMB
The steady-state ice cap obtained from the 250 m HO run
(Fig. 5) is close in extent to the observed ice cap in 1995
(Fig. 2). A few discrepancies exist in the south-western part,
where the steady-state ice cap is somewhat smaller in ex-
tent, and for a few outlet glaciers in the central northern
part, which are a bit shorter than in the observations. No-
tice that the latter outlet glaciers are very thin (Starzer and
Reeh, 2001), and satellite-derived surface velocities indicate
that these areas are almost stagnant (Joughin et al., 2010,
2015). In the south-eastern and north-western part the mod-
elled steady-state ice cap extends slightly further than the ob-
servations, and some of the present-day ice-free ridges be-
tween the outlet glaciers are ice-covered. Except for this, the
agreement is overall relatively good, especially given that
there is no imposed constraint on the ice cap extent.
The modelled limited areal changes under the 1961–1990
average conditions are supported by the RCM output that in-
dicates a near-zero average integrated SMB over this period
(see Sect. 4.2). Furthermore the limited geometrical changes
under the 1961–1990 climatic conditions are also in line with
field evidence. While a maximum extent was reached around
1900, which is known from Little Ice Age (LIA) moraines
(Koch, 1928, 1940), and a slight retreat occurred in the first
part of the 20th century (Davies and Krinsley, 1962), aerial
photography from the 1970s and 1990s (Weidick, 2001) sug-
gests that the second part of the 20th century is character-
ized by a slower recession (limited to tens of metres), stand-
still or even slight readvances. A recent study by Kjeldsen
et al. (2015), where aerial photography and SMB modelling
are combined, also suggests limited mass changes in north-
ern Greenland for the period 1900–1983 and an ice sheet near
balance during the 1970s and 1980s.
5.1.2 Englacial ice temperatures
The measured temperature profiles at central dome and at
Hare glacier (Reeh, 1995; Thomsen et al., 1996) are used
to tune the geothermal heat flux component and the heat-
ing component related to infiltrating meltwater in the abla-
tion area (Fig. 6). To reproduce the observed englacial tem-
peratures at the central dome (Reeh, 1995) (see Fig. 6c),
a geothermal heat flux of 45 mWm−2is applied. Here the
modelled steady-state ice thickness (318 m) is close to the
observed one (345 m). The measured almost-linear decrease
in temperature, from −21 ◦C at 10 m depth (−21.7 ◦C in
our model, corresponding to the TMA at the surface) to
−16 ◦C, is closely reproduced. A geothermal heat flux of
45 mW m−2is lower than the 60mW m−2interpolated from
Shapiro and Ritzwoller (2002) to the location of Hans Tausen
Iskappe. However with 60mW m−2the modelled basal tem-
perature is equal to −13.8 ◦C, and the local ice thickness is
295 m. For the ablation area an additional basal-water heat
flux of 150 mWm−2is adopted to reproduce the englacial
temperatures measured in the ablation area of Hare glacier
(Reeh, 1995). With this additional basal heating the ob-
served temperatures, ranging from −18.5 ◦C (at 10 m depth)
to about −1.5 ◦C at the bottom (see Fig. 6), are well re-
produced. Despite the fact that the modelled ice thickness
(269 m) is close to the measured one (289 m), a direct com-
parison is difficult to make as the imposed surface tempera-
ture (−15.3 ◦C, corresponding to the local TMA) is slightly
higher than the observed one. The modelled basal tempera-
tures for Hare glacier are close to the pressure melting point
(see Fig. 6b), but nowhere does basal sliding occurs. The
pressure melting point is only reached for a few larger outlet
glaciers and only very locally (see Fig. 6a), and the mod-
elled contribution of basal sliding is therefore very limited.
Our value of 150 mW m−2differs significantly from the the
350 mW m−2found by Wohlleben et al. (2009), which is ex-
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814 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Figure 6. (a) Modelled basal temperatures for the 1961–1990 steady-state ice cap. The shaded grey box represents Hare glacier, the area
shown in (b); the black dot represents the drill site at the central dome. (b) Englacial temperatures at Hare glacier; the colour scale is the
same as in (a). The black dot represents the location of the drill site where englacial temperatures were measured. (c) Modelled and measured
(observed) temperature profiles for the central dome and at Hare glacier.
pected given the very different setting (location, SMB, melt-
water production and infiltration mechanisms) and the dif-
ferent methodological approach. Here we tune based on an
evolving/modelled geometry, while Wohlleben et al. (2009)
model the thermodynamics for a fixed geometry. With a
value of 350mW m−2almost the entire ablation area of the
ice cap would be at the pressure melting point, and basal slid-
ing would have an important role, which is not supported by
the field evidence. Notice that on the other hand, without any
additional basal heating component for the ablation area, the
basal temperatures would be severely underestimated (e.g.
−10.2 ◦C at the base of the Hare glacier drill site), which
would also strongly affect the ice cap geometry.
5.1.3 Ice cap geometry
The 1961–1990 modelled steady-state geometry is gener-
ally in good agreement with the observed geometry. The
observed ice thickness (Fig. 2b) is well reproduced in the
model (Fig. 5), and so is the surface elevation (as the ob-
served bedrock elevation is used in the model). The root
mean square error (RMSE) between the observed and mod-
elled ice thickness (and surface elevation) is 55.6m. For the
interior of the ice cap the regions with high ice thickness are
generally well reproduced, despite some differences in the
north, where the ice cap is generally thicker in the model.
The steady-state outlet glaciers agree reasonably well with
observations (RMSE of 67.1 m), but some modelled out-
let glaciers, especially in the north, have a tendency to be
slightly thicker. This difference is partly linked to the com-
plexity of ice flow in the outlet glaciers, which may not
be fully captured by the model. The ice flow in the outlet
glaciers is strongly influenced by thermodynamics as the ice
temperature determines the stiffness, through the rate factor,
and potentially also through basal sliding. Without the ad-
ditional heat source in the ablation area, which was needed
to reproduce the observed temperatures, the modelled out-
let glaciers are thicker, and the discrepancy between obser-
vations and model substantially increases (RMSE of 74.7 m
for the ablation area). Notice that, given the limited amount
of direct ice thickness measurements in the outlet glaciers
(Starzer and Reeh, 2001), part of the model–observation dis-
crepancy may be related to local errors in the bedrock DEM.
5.1.4 Surface velocities
The surface velocity patterns derived from InSAR data
(Joughin et al., 2010, 2015) are well reproduced in the mod-
elled steady-state ice cap (Fig. 7). The low velocities in the
interior and the ice flow direction are very similar, which in-
dicates that the modelled position of the ice divides corre-
sponds well with the observations. For the outlet glaciers,
many of the observed velocity patterns are closely repro-
duced. This is for instance illustrated for the main outlet
glaciers at the eastern side of the ice cap (Fig. 7c, d), for
which the modelled geometry is in relatively good agreement
with the observations (see Figs. 2b and 5).
The main differences between the modelled and observed
ice velocities occur along the south-western edge of the ice
cap, where the geometrical differences are the largest, and for
two high-velocity floating tongues, which we do not model
explicitly as this is of limited importance to the larger-scale
dynamics of the ice cap. For a few outlet glaciers in the north
the modelled surface velocities are slightly higher than the
observed ones, which can partly be linked to the differences
in geometry. Notice that, as the surface velocities and the
modelled geometry are related, the surface velocity discrep-
ancy may be a consequence of the geometry discrepancy. The
inverse may however also be true: i.e. the surface velocity
discrepancy is the cause for the geometry discrepancy.
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 815
Figure 7. (a) InSAR-derived surface velocities (Joughin et al., 2010, 2015) and (b) 1961–1990 steady-state surface velocities (250 m HO
run). Black lines represent the observed ice cap outline from the Starzer and Reeh (2001) DEM; the shaded box delineates the area shown in
(c, d, e, f).(c) InSAR-derived surface velocities, (d) 250m HO surface velocities, (e) 500 m HO surface velocities and (f) 250 m SIA surface
velocities. For the InSAR velocities (c) the geometry corresponds to the observed one (Starzer and Reeh, 2001), while for the model runs (d,
e, f) the geometry corresponds to the steady-state geometry. Notice that for the model runs the SMB is fixed in time (1961–1990 climatology
applied on the present-day geometry) in order to avoid effects related to the SMB–elevation feedback.
5.1.5 Steady state and implications
Given its long response time, the ice cap in 1995 is not
expected to be in steady state with the 1961–1990 condi-
tions. Our model simulations however suggest that the ice
cap changes only little under these conditions, and this is sup-
ported by field and SMB modelling evidence, but in reality
the ice cap cannot have been in a full dynamic equilibrium
with these climatic conditions. In order to calibrate (for ther-
modynamics) and validate (geometry, surface velocities) our
model we however need to rely on a steady-state geometry.
A part of the described differences between observations and
modelling is therefore not only linked to the model errors
and uncertainties in the input data but may also be attributed
to the fact that the observed ice cap was not in steady state
in 1995. This is particularly the case for the outlet glaciers,
which are the most dynamic parts of the ice cap and where
the model–observation discrepancies in geometry and sur-
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816 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Figure 8. (a) Difference in ice thickness between 250 and 500m resolution HO steady states and (b) difference in ice thickness between
HO and SIA steady states (at 250 m resolution). Notice that the SMB is fixed in time (1961–1990 climatology applied on the present-day
geometry) in order to avoid effects related to the SMB–elevation feedback.
face velocities are the largest. In order to fully investigate the
transient behaviour of the ice cap, which would be needed
to reproduce the recently observed changes and to make ac-
curate projections for the near future (coming decades), sim-
ulations encompassing the long-term ice cap evolution are
needed. This is however not the focus of this study as we are
aiming to understand the large-scale dynamics, response time
and climatic sensitivity of this ice cap, and their implications
for its long-term evolution.
5.2 Impact of horizontal resolution and model
complexity
In order to analyse the impact of the horizontal resolution,
the model is also run at a 500 m resolution. The main dif-
ferences occur for the narrow outlet glaciers (Fig. 8a), which
are typically only a few kilometres wide and which are there-
fore difficult to accurately represent at a 500m resolution as
they only encompass a few grid cells at this resolution. At a
250 m resolution the modelled surface velocities are gener-
ally higher than for the 500 m run (see Fig. 7d, e), which
leads to a slightly lower local ice thickness in the outlet
glaciers (see Fig. 8a). This results in a 3 % higher volume for
the 500 m run, which translates into a 1 % larger area due to
the SMB–elevation feedback as the integrated mass balance
of the ice cap needs to be 0 for it to be in steady state. Notice
that treatment of the ice mask in the downscaling approach
has an important effect on the modelled geometry at a 250m
resolution. It is important that the area of the ice cap and
ice-free regions be the same at both resolutions in order to
ensure that the large-scale dynamics, which are determined
by the overall mass balance, are similar.
The effect of a change in model complexity (SIA vs. HO)
is also mostly visible in the outlet glaciers (Fig. 8b). Whereas
the SIA is a local solution, which depends on the local ice
thickness and surface slope, the HO solution accounts for
the longitudinal stress gradients, which result in smooth-
ing of the velocity field (i.e. non-local solution) (cf. Fürst
et al., 2013). As a result the highest velocities, i.e. situated
around the ELA, are lower in the HO simulations than in
the SIA simulations (Fig. 7d, f), and the SIA surface veloci-
ties are overestimated compared to the observations (Fig. 7c).
This leads to thicker outlet glaciers in the HO solution than
in the SIA solution. The ice cap steady-state volume is 7 %
higher, and as a result the area increases by 2.5%.
6 Ice cap stability and sensitivity to climatic forcing
6.1 Importance of initial conditions
The evolution of the ice cap shows evidence of hysteresis as
for certain climatic conditions the final steady-state geometry
is a function of the initial condition. Four different cases arise
depending on the imposed climatic conditions.
In case 1, under conditions colder than −0.2 ◦C or colder
than the 1961–1990 average climatic conditions, the ini-
tial geometry does not influence the final steady state: i.e.
whether starting from an ice-free surface or from the 1961–
1990 steady state (or from the present-day geometry), the
ice cap evolves to the same steady-state geometry (see
Figs. 9a, b, 10). Under these climatic conditions the SMB al-
lows for an ice-cap-wide build-up, even when starting from
ice-free conditions.
Case 2 occurs for slightly warmer conditions, for a forcing
of −0.2 to +0.35 ◦C compared to 1961–1990, where the ice
cap also evolves to the same steady state but where the ice
supply from the northern to the southern plateau plays a cru-
cial role. When the 1961–1990 average climatic conditions
are imposed on an ice-free surface, the ice initially builds up
on the northern plateau and at a few isolated locations on the
lower-lying southern plateau. On the northern plateau the ice
cap quickly builds up, and a mass flux to the southern plateau
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Figure 9. (a) Volume build-up of Hans Tausen Iskappe for different initial states (ice-free surface and 1961–1990 steady-state geometry) and
under different climatic conditions. The four coloured regions (cases) represent clusters of simulations with a similar build-up and thresholds
in the system and are defined and discussed in the text. (b, c, d, e) Modelled steady-state geometry for different climatic forcings.
initiates around 2.5–3 ka. This ice flux from the northern to
the southern part leads to a colonization of the deep southern
canyons, and a fast build-up of the southern ice cap occurs
as a result of the SMB–elevation feedback. This evolution is
clear from the volume evolution rate (Fig. 9a), which, after
starting to decrease between 1.5 and 3 ka, remains at a steady
level between 3 and 8ka and finally gradually decreases un-
til a new steady state is reached. As a consequence of this
particular ice supply, here the growth is substantially slower
than in case 1 (Fig. 9, 1961–1990 −0.5 ◦C).
Case 3 corresponds to further warming for a tempera-
ture forcing between +0.35 and +0.65 ◦C (relative to 1961–
1990). Here, the initial geometry will influence the final
steady state; i.e. a hysteresis occurs (Fig. 10). This is the case
for the evolution under the 1981–2010 conditions, which ac-
cording to the RACMO2.3 simulations are 0.6◦C warmer
than the 1961–1990 average conditions. The 1981–2010 cli-
matic conditions are simulated by applying a +0.6 ◦C offset
compared to the 1961–1990 temperature field (see Eqs. 9 and
10), while precipitation is directly derived from RACMO2.3
for this period. Under these conditions and starting from an
ice-free surface the ice flow from the northern plateau to the
southern lower-lying areas is insufficient, and as a conse-
quence the southern part of the present-day ice cap cannot
start to grow due to the SMB–elevation feedback (Fig. 9d).
Compared to 1961–1990 conditions, less time is needed for
the ice cap to build up under 1981–2010 conditions, as there
is no interaction between the northern and southern part of
the ice cap. The volume response time, defined as the time
needed to reach 1 −e−1of the final volume, is in this case
1053 years. Under the same climatic conditions and consid-
ering the 1961–1990 steady-state ice cap geometry as a start-
ing point, the southern part of the ice cap does not disap-
pear as the SMB is more positive due to the higher eleva-
Figure 10. Final steady-state volumes under different climatic con-
ditions and for different starting geometries. The four cases are the
same as in Fig. 9 and are described in the text. Bold circle outlines
mean that the final steady state is independent from the initial con-
ditions.
tion (Fig. 9c). The existence of this threshold in the system is
therefore strongly related to the particular bedrock geometri-
cal setting, with the high plateau in the north and the ice flow
feeding mechanism to the lower-lying southern plateau.
In case 4, for even warmer conditions, a warming of more
than +0.65 ◦C compared to 1961–1990, the SMB of the
southern part of the present-day ice cap crosses a lower
bound, “the collapse threshold”, at which this part fully dis-
appears because of the SMB–elevation feedback (Fig. 9e).
Here the ice cap also evolves to a similar steady state
(Fig. 10) with no ice on the southern plateau, independent
of the initial condition.
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818 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
Figure 11. (a) Volume evolution of Hans Tausen Iskappe under different climatic conditions. The solid lines represent simulations where
the precipitation is unaltered (i.e. P+0 %), while the dotted lines represent simulation with a modified precipitation. The starting point
of all simulations is the 1961–1990 steady-state geometry. (b) Evolution of the Hans Tausen Iskappe along UTMx=602.5 km transect
under the 2005–2014 forcing, starting from the 1961–1990 steady state, for 200-year time intervals. The black area represents the bedrock,
and the white area represent the final steady-state geometry. The location of the transect is shown in Fig. 5. (c) Temperature forcing and
corresponding precipitation forcing (scale factor) needed for 1961–1990 steady-state volume to be preserved. The polynomial fit is based on
five simulations (1961–1990 +0/1/2/3/4 ◦C), which are represented by the black dots. The blue area broadly corresponds to the range where
an attenuation of the mass loss is possible, while the red area represents the range under which the ice cap is to (largely) disappear. (d) Ice
cap profiles along the UTM x=602.5 km transect. The shaded grey area is the 1961–1990 steady-state ice cap geometry. The three other
geometries correspond to the 1981–2010 (P+25 %), 2005–2014 (P+75 %) and 1961–1990 +4◦C (P+340 %) steady states and follow
the same colour scheme as in (a). The location of the transect is shown in Fig. 5.
6.2 Ice cap sensitivity to climatic forcing and future
evolution
6.2.1 Sensitivity to temperature changes
As the previous experiments point out, the ice cap is very
sensitive to a change in climatic conditions. For a cooling of
only 0.5 ◦C compared to the 1961–1990 conditions the ice
cap strongly expands (21 % area increase) (see Fig. 9b) and
the volume increases by 26 %. These are the coldest condi-
tions for which the ice cap can be modelled explicitly, as for
lower temperatures the ice cap starts to connect to the GrIS
and other nearby ice masses and expands beyond the domain
boundaries.
Under the 1981–2010 average climatic conditions (ca.
+0.6 ◦C vs. 1961–1990, 4 % higher precipitation than the
1961–1990 mean) the SMB of the southern part of the
present-day ice cap is still above the collapse threshold (cf.
case 3; see Fig. 9a). While the northern part of the ice cap
and the local domes change little, an overall slight decrease
in surface elevation occurs at lower elevations, and a frontal
retreat of the southern part of the ice cap occurs, but then
the ice cap quickly stabilizes. This agrees with observations
from airborne surveys that indicate that between 1994 and
2004 limited changes in surface elevation occurred around
the central dome (Dalå et al., 2005). About one-fifth of the
ice mass is lost under these conditions (Fig. 11a). Also the
output from the RCMs, MAR3.5.2 (−0.15 m w.e.a−1) and
RACMO2.3 (−0.11 mw.e.a−1), and from our PDD melt–
retention approach (−0.08 m w.e.a−1based on the GIMP to-
pography) suggests a limited negative SMB over the ice cap
for this period.
For slightly warmer conditions the collapse threshold of
the southern part of the ice cap is crossed (cf. case 4, Fig. 9a),
and eventually, after thousands of years, the entire southern
part of the ice cap is lost. This is for instance the case under
the 2005–2014 climatic conditions, which are around 1.6 ◦C
warmer than the 1961–1990 average conditions over Hans
Tausen Iskappe (6 % higher precipitation than 1961–1990
mean) and for which the specific SMB of the present-day ice
cap is very negative (−0.39, −0.32 and −0.32 mw.e.a−1in
MAR3.5.2, RACMO2.3 and PDD melt–retention approach
respectively). At first the elevation changes at the southern
domes are limited (local SMB is almost at the 1961–1990
level), but as a large mass loss occurs at low elevations the
geometry adapts, and the rate of ice loss subsequently in-
creases as a result of the SMB–elevation feedback (Fig. 11b)
until after 1500 years all ice has disappeared. Due to this
feedback the volume response time of the ice cap is very
short and only amounts to 616 years. The northern part of
the ice cap also changes (see Fig. 9e), but the domes remain
stable (Fig. 11b), and most of the remaining ice mass, cor-
responding to 19 % of the initial mass, is stored here. This
is in line with elevation changes derived from ICESat for
the period 2003–2008 (Bolch et al., 2013), which indicate
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H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 819
that the domes are stable during this time period and even
tend to slightly gain mass (typically elevation change up to
0.2 m a−1), while the lowest regions are losing mass at a high
rate (typically more than 0.5 ma−1). A more in-depth com-
parison between these observations and our model results is
difficult given our initial steady-state assumption and the role
of the ice cap response time, but the large-scale features are
in reasonable agreement.
For a high-emission scenario (IPCC RCP8.5) the 2100
global average surface temperature is projected to rise by 3–
5◦C compared to the 1961–1990 average. Over high Arc-
tic regions such as Peary Land the temperature could po-
tentially increase by up to 7–11 ◦C due to the polar ampli-
fication (Collins et al., 2013). This warming is most pro-
nounced in winter, and summer temperatures (June–July–
August) are projected to rise up to 8 ◦C over northern Green-
land by 2100 (vs. 1961–1990) (van Oldenborgh et al., 2013).
To simulate the evolution of the ice cap in a warming climate,
we consider a +4◦C warming, which broadly represents an
intermediate-emission scenario (in the line of RCP4.5), and
a+8◦C warming, representing a high-emission scenario (cf.
RCP8.5) (both vs. 1961–1990). For the +4◦C scenario and
by maintaining the precipitation at the 1961–1990 level, the
ice cap entirely disappears within 350–400 years (i.e. before
2400) (Fig. 11a), disregarding whether the forcing is imme-
diately applied at present or incrementally until 2100. Under
the high-emission scenario (+8◦C) it takes about 140 years
for all ice to be gone or 180 years when the forcing is ap-
plied linearly; i.e. the last ice disappears in the second half
of the 22nd century (Fig. 11a). Different model simulations
indicate that under such warm conditions the large-scale ice
cap evolution is not much affected by its initial state, whether
starting from the observed geometry, the 1961–1990 steady-
state geometry or a somewhat similar geometry. Modelling
the transient evolution of the ice cap over the last centuries
to millennia is therefore of relatively limited interest when it
comes to simulating the future mid- to long-term ice cap evo-
lution in a (much) warmer climate as the evolution is almost
fully driven by the SMB rather than by the ice dynamics.
6.2.2 Sensitivity to precipitation changes
Precipitation changes influence the SMB and have the po-
tential to (partly) attenuate the ice loss in the case of warm-
ing. In order to prevent the modelled 20% total mass loss
under 1981–2010 conditions, the precipitation has to in-
crease by about 25 %: i.e. under these conditions the in-
tegrated SMB of the present-day ice cap is again close to
0 m w.e.a−1(see Fig. 11a). For 2005–2014 conditions a
considerably higher precipitation increase, around 75 %, is
needed for the present-day 1961–1990 steady-state ice cap
volume to be maintained, while for the intermediate future
warming (+4◦C vs. 1961–1990) the precipitation needs a
dramatic increase, by about around 340 % (Fig. 11a). Based
on five simulations (1961–1990 +0/+1/+2/+3/+4◦C) this
non-linear relationship is approximated as a 2nd-order poly-
nomial (Fig. 11c):
P=0.1321T 2+0.3161T +1,(10)
where 1T is the temperature forcing and Pthe correspond-
ing precipitation forcing (scaling factor) (both vs. 1961–
1990) needed to prevent a mass loss (vs. 1961–1990 steady
state).
6.2.3 Implications for future ice cap evolution and
geometry
A future increase in precipitation over the ice cap is pro-
jected as the surrounding ocean is to become ice-free in a
warmer climate and to act as an important moisture source
(e.g. Braithwaite, 2005). The 20th-century conditions are
at the borderline between ice-free fjords and fjords with
semi-permanent ice cover (Weidick, 2001) and from palaeo-
records it is known that in the warmer mid-Holocene period,
when the Arctic ocean was seasonally ice-free, the precip-
itation was up to twice as high as at present (Madsen and
Thorsteinsson, 2001). Based on this the future precipitation
increase could be well above the one that would follow from
a Clausius–Clapeyron relationship.
It is therefore expected that for a moderately warmer cli-
mate, up to 2–2.5 ◦C warmer than the 1961–1990 condi-
tions, the ice loss as a result of a temperature increase may
be partly attenuated (cf. Machguth et al., 2013). Under cli-
matic conditions needed to preserve the steady-state vol-
ume (e.g. 1981–2010 (P+25 %) and 2005–2014 (P+75 %))
the ice cap total SMB would change only little compared
to 1961–1990, but the SMB spatial distribution is more af-
fected. Whereas the temperature increase mainly decreases
the SMB in the present-day lower areas, the temperature in-
crease in the higher areas leads to higher precipitation and a
higher SMB. As a result the steady-state ice cap margin re-
treats (smaller steady-state area), while the interior thickens,
resulting in a steeper ice cap (Fig. 11d). This is in agreement
with recent ICESat observations on Arctic ice caps, which
indicate a marginal ice loss and local thickening (for the in-
terior). This is the case for Hans Tausen Iskappe (Bolch et
al., 2013), and for instance also for the Austfonna ice cap
(Svalbard) (Moholdt et al., 2010) and the Flade Isblink ice
cap (Greenland) (Rinne et al., 2011; Bolch et al., 2013). An
in-depth comparison between our modelling study and these
observations is again not possible given the differences in
timing and the model setup, but our simulations show the po-
tential to reproduce the observed trends and the implications
this can have on the future ice cap evolution.
For even warmer conditions (>3◦C) the required precipi-
tation increase of more than 200 % needed to counteract the
mass loss is much higher than expected from climate mod-
elling and palaeoclimatic records, and as a consequence the
ice cap will in all cases (largely) disappear. This is for in-
stance clear from the 1961–1990 (+4◦C, P+100 %) sim-
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820 H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe
ulation, where only very little ice survives, corresponding to
around 2.5–3 % of the present-day volume (see Fig. 11a). For
the high-emission scenario (+8◦C vs. 1961–1990), all ice
disappears, and even under an extreme precipitation increase
of for instance 200 % it would only take 10–15 years longer
for all ice to be gone compared to a constant-precipitation
scenario.
7 Conclusions and recommendations
In this study a SMB–thermomechanical ice flow model was
developed for Hans Tausen Iskappe, the world’s northern-
most ice cap, and tested for various parameter settings and
model complexities. Despite the remoteness of the ice cap, a
large data set is available encompassing ice thickness (at high
spatial resolution, not included in the Greenland data sets),
surface mass balance measurements (and related temperature
and precipitation measurements), ice temperature measure-
ments and surface velocities (both from the field and remote-
sensing techniques). The numerical simulations were tuned
and validated based on this data set and provide us with valu-
able insights in the dynamics of the ice cap. Our main find-
ings and their implications for the dynamics and modelling
of other Arctic ice caps are as follows:
1. RCM RACMO2.3 precipitation agrees well with field
observations, and so does the reconstructed SMB,
which is a valuable contribution to the model valida-
tion as much of the northernmost parts of Greenland
have few observations and mass balance measurements.
With our simple PDD melt–retention approach, using
downscaled RACMO2.3 precipitation, we were able to
reproduce the measured SMB and the modelled SMB
in good agreement with output from other RCMs, and
this for different periods in time. The simple PDD melt–
retention model allows for a direct coupling of the ice
topography and the SMB, which is crucial for the ice
cap dynamics.
2. For solving the ice dynamics and the ice flow in the
fast-flowing outlet glaciers, a higher-order solution is
needed. Compared to a local solution (SIA), this in-
fluences the steady-state volume in the order of 6–8 %,
and the area is also affected around 2–3% through the
SMB–elevation feedback. We also show that to repro-
duce the observed surface velocity patterns in outlet
glaciers a higher-order solution is needed as the con-
trast between the high and low velocities is overesti-
mated with a local solution (SIA). When modelling ice
caps with fast outlet glaciers a non-local velocity solu-
tion may be worthwhile depending on the focus of the
study and the availability of high-resolution field data.
To understand the large-scale dynamics of ice caps and
their long-term evolution, the focus should rather be on
an accurate representation of the SMB than on the ice
dynamics, and under most cases a SIA is justified. Run-
ning the model at a higher spatial resolution (250 m vs.
500 m) also mainly affects the outlet glaciers, but the
effect was found to be overall rather limited.
3. Under the 1961–1990 climatic conditions the ice cap
evolves to a steady state that is close to observations in
terms of ice cap geometry (extent and ice thickness),
ice temperature and surface velocities. This is in agree-
ment with output from RCMs and field observations that
indicate that few changes occurred during this period.
Given the long response time of the ice cap, a statement
about its equilibrium with the 1961–1990 climatic con-
ditions cannot be made, but likely the limited changes
result from an interplay between a long-term growth
trend, linked to Holocene cooling, and a short-term re-
treat trend, from the end of the LIA, linked to warming.
4. Englacial temperature measurements, modelled ice
thickness and temperatures in outlet glaciers suggest
that there is an important heating mechanism related to
infiltrating meltwater in the ablation area of the ice cap.
Without this additional heating source the measured
temperatures in the outlet glaciers cannot be repro-
duced, and the ice thickness is locally strongly overesti-
mated. In this study we provide additional evidence re-
lated to extensive warming through meltwater, a mecha-
nism that could be of large importance when modelling
the dynamics of Arctic ice caps, especially in a warming
climate, with more surface melt and a potential higher
meltwater supply to the base.
5. The SMB–elevation feedback is a crucial mechanism
for the ice cap evolution and stability. Due to this feed-
back the southern part of the ice cap is extremely sen-
sitive to a change in climatic conditions. This is clear
from its total disappearance when the 1961–1990 cli-
matic conditions are warmed by more than 0.85 ◦C. This
is in line with palaeorecords that suggest that the south-
ern part of the ice cap totally disappeared during the
Holocene Thermal Maximum. The northern part of the
ice cap is situated on a higher plateau, and the local ice
thickness is lower; this part is therefore less affected
by the SMB–elevation feedback and more stable. The
SMB–elevation feedback is also responsible for thresh-
olds in the system under certain conditions, where the
final steady state depends on the initial geometry, and
for which the ice flow from the northern plateaus to the
southern part of the ice cap is a crucial factor. This ice
flux also causes the response time of the ice cap to be
up to several thousands of years under some particu-
lar conditions. For cases where this ice feeder–supplier
mechanism is more limited the response time is typi-
cally around 1000 years, although this can be up to a
factor of 2 smaller under the influence of the SMB–
elevation feedback. These timescales are in agreement
The Cryosphere, 11, 805–825, 2017 www.the-cryosphere.net/11/805/2017/
H. Zekollari et al.: Dynamics and future evolution of Hans Tausen Iskappe 821
with palaeorecords that suggest that the ice cap (largely)
disappeared during the Holocene Thermal Maximum
and subsequently started to regrow some 3500–4000
years ago.
6. For limited SMB perturbations the ice cap evolves to a
steady state and does not have a runaway behaviour as is
occurring in some ice cap modelling studies, where the
ice cap has a tendency to grow far beyond the observed
state or evolves to a very small ice cap for the slight-
est perturbations. This is in part related to the specific
geometric setting, where the northern part, situated on
a higher plateau, delivers its mass surplus to the lower-
lying southern part. On the other hand, the fact that the
SMB is modelled explicitly ensures that for the highest
parts of the ice cap the SMB only changes little under
different climatic conditions (e.g. slightly increases un-
der colder conditions), as is the case in reality, avoiding
artefacts inherent to simple parameterizations of the el-
evation dependence of SMB.
7. In a moderately warming climate (up to 2–2.5 ◦C vs.
1961–1990) the projected mass loss may be partly at-
tenuated if precipitation sharply increases. A local ice
core drilled at the central dome suggests that precipi-
tation was higher during the Holocene Thermal Maxi-
mum, and this will likely also be the case in a warmer
climate, with more ice-free ocean conditions. Due to
their high elevation the local domes are almost unaf-
fected by a moderate temperature rise, and as a conse-
quence of a precipitation increase they could gain mass,
making the ice cap steeper, which is in line with recent
satellite observations. For warmer conditions (>3◦C
warming) the ice cap will (almost) fully disappear, even
under a higher-precipitation regime, within 350–400
years (1961–1990 +4◦C) to within less than 200 years
(1961–1990 +8◦C). This evolution is almost indepen-
dent of the modelled initial conditions. Taking into ac-
count the inherent uncertainty of the SMB model, there
is no need for a late Holocene transient run and detailed
future scenarios to understand the potential future ice
cap evolution and the potential for the precipitation to
mitigate this.
Data availability. All the data and results presented in this ar-
ticle are available upon request by email to the first au-
thor (harry.zekollari@vub.be). For the RACMO output, Brice
Noël (B.P.Y.Noel@uu.nl) or Michiel R. van den Broeke
(M.R.vandenBroeke@uu.nl) should be contacted.
Author contributions. Harry Zekollari and Philippe Huybrechts de-
signed the experiments, and Harry Zekollari performed the fully
coupled model simulations. Brice Noël, Willem Jan van de Berg
and Michiel R. Van den Broeke provided the RACMO3.2 model
simulations and developed the downscaling methods for this out-
put. Harry Zekollari and Philippe Huybrechts wrote the manuscript.
Brice Noël, Willem Jan van de Berg and Michiel R. Van den Broeke
read the manuscript and provided valuable comments.
Competing interests. The authors declare that they have no conflict
of interest.
Acknowledgements. We thank A. M. Solgaard, A. P. Ahlstrøm
and C. Hvidberg for their help in retrieving all data from field-
work and for providing documentation from the expedition in
the 1990s. The two anonymous reviewers are thanked for their
suggestions that improved the overall clarity of the manuscript.
Harry Zekollari wants to thank H. Goelzer for his generous
support with technical issues. Harry Zekollari holds a PhD fel-
lowship of the Research Foundation – Flanders (FWO-Vlaanderen).
Edited by: T. Mölg
Reviewed by: two anonymous referees
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