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Modelling the evolution of Vadret da Morteratsch, Switzerland, since the Little Ice Age and into the future


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We use a 3-D higher-order glacier flow model for Vadret da Morteratsch, Engadin, Switzerland, to simulate its strong retreat since the end of the Little Ice Age (LIA) and to project its future disintegration under a warming climate. The flow model, coupled to a 2-D energy-balance model, is initialized with the known maximum glacier extent during the LIA and subsequently forced with mean monthly precipitation and temperature records. To correctly reproduce the observed retreat of the glacier front for the period 1864–2010, additional mass-balance perturbations are required to account for uncertainties in the initial state, the mass-balance model and climate variations not captured by the ambient meteorological records. Changes in glacier volume and area are in good agreement with additional information from historical topographic maps. Under constant 2001–10 climate conditions, a strong retreat and mass loss continue and Vadret da Morteratsch disconnects from its main tributary, Vadret Pers, before 2020. The future glacier evolution is analysed in detail to understand the timing and rate of retreat, and to assess the role of ice dynamics. Assuming a linearly increasing warming of >3°C by 2100, only isolated and largely stagnant ice patches remain at high elevation.
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Modelling the evolution of Vadret da Morteratsch, Switzerland,
since the Little Ice Age and into the future
Harry ZEKOLLARI, Johannes Jakob FÜRST, Philippe HUYBRECHTS
Earth System Science and Departement Geografie, Vrije Universiteit Brussel, Brussels, Belgium
ABSTRACT. We use a 3-D higher-order glacier flow model for Vadret da Morteratsch, Engadin,
Switzerland, to simulate its strong retreat since the end of the Little Ice Age (LIA) and to project its future
disintegration under a warming climate. The flow model, coupled to a 2-D energy-balance model, is
initialized with the known maximum glacier extent during the LIA and subsequently forced with mean
monthly precipitation and temperature records. To correctly reproduce the observed retreat of the
glacier front for the period 1864–2010, additional mass-balance perturbations are required to account
for uncertainties in the initial state, the mass-balance model and climate variations not captured by the
ambient meteorological records. Changes in glacier volume and area are in good agreement with
additional information from historical topographic maps. Under constant 2001–10 climate conditions, a
strong retreat and mass loss continue and Vadret da Morteratsch disconnects from its main tributary,
Vadret Pers, before 2020. The future glacier evolution is analysed in detail to understand the timing and
rate of retreat, and to assess the role of ice dynamics. Assuming a linearly increasing warming of >3°C by
2100, only isolated and largely stagnant ice patches remain at high elevation.
KEYWORDS: energy balance, glacier flow, glacier fluctuations, ice dynamics, mountain glaciers
In recent decades, mountain glaciers worldwide have lost a
significant fraction of their volume in response to the global
temperature increase (Lemke and others, 2007). This volume
loss is crucial as glaciers are projected to be major contri-
butors to sea-level rise over the next century, with estimated
contributions of up to 25 cm (Kaser and others, 2006; Radić
and Hock, 2011; Marzeion and others, 2012; Radić and
others, 2014). In addition, these ice losses have an important
impact on the local water supply and the hydrological cycle
(Immerzeel and others, 2010, 2012; Kaser and others, 2010;
Farinotti and others, 2012), tourism (Elsasser and Bürki,
2002; Pütz and others, 2011) and risk management (Haeberli
and others, 1989; Frey and others, 2010; Werder and others,
2010). The rate of glacier retreat is, however, regionally
variable and depends on local factors such as mass balance,
glacier geometry, debris cover and orientation (Carrivick and
Chase, 2011). The resulting variety in glacier settings strongly
complicates general statements about the future evolution of
glaciers worldwide. Recent studies based on scaling argu-
ments have attempted to provide a global estimate of the
future mass loss of mountain glaciers (Radić and Hock, 2011;
Marzeion and others, 2012; Slangen and others, 2012; Radić
and others, 2014), but detailed studies of individual glaciers
remain essential to assess their reliability. In particular
process-based model studies of individual glaciers are
needed to improve our understanding of the factors control-
ling their evolution and to refine global estimates of future
sea-level rise from glaciers and ice caps.
Since the end of the Little Ice Age (LIA), alpine glaciers
have retreated significantly, a trend that has accelerated
over the last few decades and is expected to persist in the
coming century (Zemp and others, 2006; Braithwaite and
others, 2013). Individual rates of retreat and mean mass
balances differ strongly between alpine glaciers and show a
non-uniform pattern (Huss and others, 2010a; Lüthi and
others, 2010). To properly understand these differences,
several modelling studies were conducted focusing on the
retreat history. Such studies mainly relied on simple one-
dimensional (1-D) flowline models (e.g. Wallinga and Van
de Wal (1998) on Rhonegletscher, Switzerland; Zuo and
Oerlemans (1997) on Pasterzenkees, Austria) or 2-D models
based on the shallow ice approximation (SIA) (e.g. Le Meur
and Vincent (2003) on Glacier de Saint-Sorlin, France).
Recently, more complex 3-D flow models have successfully
been applied to model the past and future evolution of
glaciers such as Rhonegletscher (Jouvet and others, 2009)
and Grosser Aletschgletscher, Switzerland (Jouvet and
others, 2011; Jouvet and Funk, 2014).
Here we present a 3-D higher-order modelling study on
the transient behaviour of the Morteratsch glacier complex,
Switzerland, from the end of the LIA until 2100. Owing to its
relatively long response time, ‘the time a glacier takes to
complete most of its adjustment to a change in mass
balance’ (Cuffey and Paterson, 2010), the glacier’s past
evolution must be modelled before any future projections
can be made. Therefore the model is first dynamically
calibrated with the observed retreat since the LIA. The
Morteratsch glacier complex is well suited for such a study.
Indeed, it has been well monitored with a good temporal
and spatial data coverage based on topographic maps,
direct field evidence and other historical sources. Moreover,
both the surface-energy-balance model and the ice-dynam-
ics model have been well validated using data from more
than a decade of glaciological observations on surface mass
balance, ice thickness and flow velocity (Nemec and others,
2009; Zekollari and others, 2013).
2.1. Morteratsch glacier complex
The 16 km
glacier complex is located in southeastern
Switzerland (tongue at 46.43° N, 9.93° E in 2012) and
consists of two distinct glaciers: the main Vadret da
Journal of Glaciology, Vol. 60, No. 224, 2014 doi: 10.3189/2014JoG14J053 1155
Morteratsch (with a length of 6 km) and its tributary, Vadret
Pers (4.5 km) (Fig. 1). At present, the glacier front is at an
elevation of 2100 m, while the highest parts are 2000 m
higher and correspond to mountain tops such as Piz Bernina
(4049 m), Piz Zupo (3996 m) and Piz Palü (3905 m). These
peaks prevent direct insolation on the glacier by shadowing
for a large part of the year and therefore affect the surface
mass balance.
2.2. Field data
Starting in 2001, we have collected an elaborate dataset
on field observations. The ice thickness was measured
with different ground-penetrating radar (GPR) systems
and subsequently extrapolated over the entire glacier
assuming plastic flow along central flowlines. Based on
this, we estimate that the glacier volume in 2001 was
1.14 0.28 km
(Zekollari and others, 2013). Since 2001,
we have measured the annual mass balance with ablation
stakes, resulting in a dataset of 186 individual measurements
so far, which have also been used to deduce the surface
velocity of the glacier (error within the order of 1 m a
). We
also performed accumulation measurements with alumin-
ium poles. The absolute movement of all stakes is known
from GPS measurements (error within the order of 1 m in the
three dimensions). For sites near the ice front where
horizontal displacements are virtually nil, this directly
provides the thinning rate.
2.3. Ice-dynamic model
A 3-D isothermal ice-dynamic model (Fürst and others,
2011) with Blatter/Pattyn-type equations (Blatter, 1995;
Pattyn, 2003) is used, for which the rate factor for temperate
ice A0and sliding parameter Asl were tuned to match
observed surface velocities (Zekollari and others, 2013).
Nye’s generalization of Glen’s flow law is used to describe
the internal deformation (Glen, 1955; Nye, 1957):
ij ¼2_"ij,¼1
ð Þ1=n1,ð1Þ
where ij are the deviatoric stresses, nis the power-law
exponent (equal to 3 in this study) and _
"0is a small offset of
to prevent infinite effective viscosity () when the
strain rate is zero (following Pattyn, 2003). The effective
stress _"eis determined by the second invariant of the strain-
rate tensor:
2_"ij _"ij,ð2Þ
for which the components of the strain rate tensor "ij are
defined as
_"ij ¼1
 ,ð3Þ
and uiare the 3-D components of the velocity vector.
Equations (1–3) are simplified to obtain an LMLa (multi-
layer longitudinal stresses) higher-order model (Hindmarsh,
2004; Fürst and others, 2011). Assuming local cryostatic
equilibrium, bridging effects are neglected in the force
balance, and horizontal gradients in the vertical velocity
field are assumed to be negligible in comparison with
vertical gradients of horizontal velocity. Under these
approximations, the horizontal and vertical velocity fields
are decoupled, and the latter can be determined via mass
conservation. The basal drag
corresponds to the sum of
all basal resistive forces and is calculated following the
higher-order approximation (Weertman, 1964; Van der
Veen and Whillans, 1989):
ub¼  Asl 3
b, x¼xz bð Þ  2xx bð Þ þ yy bð Þ
 @b
@xxy bð Þ@b
b, y¼yz bð Þ  2yy bð Þ þ xx bð Þ
 @b
@yxy bð Þ@b
for which bis the bedrock elevation and ij are the
components of the stress tensor at the base. The best fit
between observed and modelled velocities (root-mean-
square error (RMSE) of 15.0 m a
) was obtained for a rate
factor A
of 1.6 10
and a sliding parameter A
12 10
(Zekollari and others, 2013). The
highest flow velocities are reached for Vadret da Morteratsch
and go up to 125 m a
(see fig. 7 in Zekollari and others,
2013). For Vadret Pers, both the rate factor A0and sliding
parameter Asl were doubled for a better match between
observed and modelled velocities and to avoid Vadret Pers
becoming too thick in transient simulations. Flow-law
parameters are kept constant in time. The model is run on
a 25 m horizontal resolution, and in the vertical the grid uses
21 non-equally spaced layers. The flow model is coupled to
a surface energy-balance model that determines the spatio-
temporal distribution of accumulation and ablation.
The continuity equation is the link between ice dynamics
and the surface mass balance:
@t¼  r:
uHð Þ þ M,ð6Þ
where His the ice thickness,
uis the vertically averaged
horizontal velocity vector, ris the 2-D divergence operator
Fig. 1. Annual surface mass balance averaged over the period 2001–
10. The map uses the Swiss CH1903 coordinate system. The thick
black line delineates the Morteratsch glacier complex; the thin black
lines are surface-elevation contours at 200 m intervals (indicated
from 2200 to 3800 m). Note that only ice that flows into the glacier
complex is considered in the mask, and that isolated small glaciers,
such as Vadret da la Fortezza (situated between Vadret Pers (P) and
Vadret da Morteratsch (M)), are not taken into account. The highest
surrounding peaks are Piz Bernina (PB, 4049 m), Piz Zupo (PZ,
3996 m) and Piz Palü (PP, 3905 m). The inset in the upper right
corner shows the location of the glacier in Switzerland.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch1156
and Mis the surface mass balance. The higher-order
velocity field and changes in ice thickness are calculated
with a weekly time step (t= 0.02 years), while the mass
balance is updated annually. More details on parameter
choices, boundary conditions and numerical implemen-
tation are provided by Zekollari and others (2013) and Fürst
and others (2011).
2.4. Mass-balance model and climatic input
To compute the surface mass balance we use a 2-D energy-
balance model (Oerlemans, 2001) that has been calibrated
for the Morteratsch glacier complex (Nemec and others,
2009). The model is based on an equation for the cumu-
lative mass balance B(m w.e. a
) and accounts for the
shading effect of the surrounding mountains, the daily
temperature cycle, the timing of precipitation events, and
seasonal changes in snow thickness and albedo:
Bðtþ1Þ ¼ BðtÞ þ tmin 0,
  þPsolid ðtÞ:ð7Þ
Here L
is the latent heat of melting (3.34 10
J kg
the water density (1000 kg m
) and PsolidðtÞis the solid
precipitation. The time step t is 1 hour.
The net energy flux (W m
) at the surface is repre-
sented by
¼ ð1Þ  Qþc0þc1Tair,ð8Þ
where the first term on the right-hand side is the net
shortwave radiation received at the glacier surface, with
the transmissivity of the atmosphere and the surface
albedo. Q(W m
) is the incoming solar radiation, which
consists of a direct and an indirect (diffuse) term and is
corrected for the slope and orientation of the glacier surface
(Nemec and others, 2009). The term c
the sum of the net longwave radiation and the turbulent heat
exchange (Oerlemans, 2001). Here, c
= –45 W m
12 W m
,= 0.45 (Nemec and others, 2009) and T
the air temperature (°C). The parameter values, in particular
for , were obtained from a best fit of the energy-balance
model with our observed mass-balance measurements, and
are further informed by detailed observations from an
automatic weather station placed in the lower ablation area
(personal communication from J. Oerlemans, 2008). The
fraction of solid precipitation depends on the local air
temperature. Total precipitation is upscaled from nearby
weather stations using a fixed altitudinal gradient, and
accounts for the timing and intensity of precipitation events
informed by a daily precipitation series from a nearby valley
station for the period 1981–2006. As discussed in Nemec
and others (2009), available data do not allow a further
differentiation of snow accumulation with respect to wind
exposure, for example, making the precipitation treatment
probably the largest source of uncertainty in the calculation
of the net mass balance. The cumulative mass balance B
after a full balance year (1 October to 30 September) gives
the annual specific mass balance, M, needed in Eqn (6).
Meteorological data from surrounding weather stations
were used to calibrate the model to ablation and accumu-
lation measurements on both Morteratsch and Pers glaciers
for the period 2001–06 (Nemec and others, 2009). Most
measurements are available for the ablation zone, while for
the accumulation zone we rely on a handful of measure-
ments from aluminium poles, snow pits and a shallow ice
core that was drilled by a Swiss group under Piz Zupo
(Sodemann and others, 2006). The climatic input to drive the
mass-balance model consists of a monthly temperature
record from Segl Maria (46.44 ° N, 9.77 ° E, 1798 m a.s.l.)
since 1864 and monthly precipitation measurements from
Samedan (46.53 ° N, 9.88 ° E, 1705 m a.s.l.) extending back
to 1861 (Fig. 2). These data originate from the HISTALP
database (Auer and others, 2007) and were homogenized to
reduce errors such as the early instrumental warm-bias
(Frank and others, 2007; Böhm and others, 2010). The
modelled annual mass balance field-averaged over the
decade 2001–10, using the topography from a digital
elevation model (DEM) of 2001 (DHM25 from SwissTopo;
uncertainty 3–6 m), is shown in Figure 1. For this period, the
Morteratsch glacier complex has a mean specific mass
balance of –0.93 m w.e. a
and an accumulation-area ratio
(AAR) of 44%, clearly indicative of a glacier out of equi-
librium with the imposed climate due to a disproportionally
large snout characterized by high ablation. The associated
average equilibrium-line altitude (ELA) over this period is
3020 m for Vadret da Morteratsch, while for Vadret Pers it
is 3080 m. The higher ELA and generally more negative
surface mass balance for Vadret Pers are due to glacier
orientation. For a large part of the day, most of Vadret Pers is
directly exposed to the sun, whereas Vadret da Morteratsch is
Fig. 2. Annual precipitation measured in Samedan (1861–2010) and average summer temperature (May–September) as recorded in Segl
Maria (1864–2010), corrected for early instrumental warm-bias. The homogenized data come from the HISTALP database. The blue lines
represent annual values, and the red line represents the 20 year running mean.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch 1157
oriented to the north and receives more shading from the
high surrounding peaks (especially from Piz Zupo before
noon and from Piz Bernina in the afternoon).
2.5. Specific model set-up
Several rock outcrops exist around the ELA and within the
accumulation area of the glacier. Most of them are persistent
features since the LIA, as identified on topographical maps
(1 : 50 000) from 1851 (Maisch and others, 1999) and 1935
(DEM provided by F. Paul). These ice-free areas are very
steep, and consequently icefall and wind drift prevent
permanent snow or ice cover. Our glacier model does not
account for the details of this effect, so these parts are kept
ice-free in all simulations. However, it is reasonable to
assume that snow falling on these ice-free parts will
ultimately end up on the glacier and thus contribute to its
mass balance. In the model this is achieved by redistributing
the positive mass balance of these regions over an elevation
band down to 50 m below the specific ice-free part. An
additional issue related to keeping these zones ice-free is
that mass is lost when ice flows into these regions, which is
the case when the downward surface slope is directed
towards the outcrops. In reality this process coincides with
ice avalanches that fall on lower parts of the glacier. To take
this into account, a similar method to that for the snowfall is
used and the mass that flows into the ice-free zones is
redistributed over the same elevation bands as for the snow.
As the glacier geometry hardly changes in the accumulation
zone and to avoid ice flowing over ridges away from the
glacier (e.g. to the south, towards Italy), the glacier is not
allowed to expand laterally above 3000 m of elevation.
These modifications ensure that mass is conserved over the
glacier complex at all times.
2.6. Past glacier evolution (1850s to 2010)
An array of observational data is available to reconstruct the
retreat history of Morteratsch glacier since the LIA. These
data are required for the dynamical calibration of the ice-
flow model before any future projections.
2.6.1. Record of front position
The front position has been well known since 1878 and
serves as a first criterion to reconstruct the past evolution of
the glacier complex (Glaciological Reports, 1881–2010). As
the snout of Morteratsch glacier has a clear north–south
orientation, changes in glacier length follow almost exactly
the y-direction of the CH1903 coordinate system (Fig. 1).
Therefore the retreat of the front as found in the Glacio-
logical Reports (1881–2010) is considered to be in this
direction and moreover assumed to refer to the most
northerly position of the tongue. Note that for most Swiss
glaciers the retreat is not just in one direction, and often
corrections are needed as the cumulative length change
shows discrepancies with known front positions from
different sources (S. Wiesmann and A. Bauder, unpublished
2.6.2. LIA extent
The causes and timing of the LIA and the maximum extent of
alpine glaciers remain uncertain, as temperature records
show no clear cooling followed by a warming for this period
(Vincent and others, 2005; Mann and others, 2008; Böhm
and others, 2010). In the literature, it has been suggested
that an increase in winter accumulation between the 1760s
and 1830s may have caused the advance (Vincent and
others, 2005). A subsequent decrease in accumulation
should then have been responsible for the retreat from this
maximum extent (Vincent and others, 2005), perhaps
enhanced by a small increase in temperatures associated
with a positive phase of the Atlantic Multi-decadal Oscilla-
tion (AMO) index between 1850 and 1870 (Huss and others,
2010a). Other recurrent hypotheses link the 19th-century
glacier maximum to volcanic eruptions and aerosol forcing
(Crowley, 2000); Goosse and others, 2006; Painter and
others, 2013; Lüthi, 2014).
For the Morteratsch glacier complex, the maximum LIA
extent occurred between 1860 and 1865, somewhat later
than many (smaller) Swiss glaciers (Maisch and others,
1999; Oerlemans, 2007). The maximum LIA glacier extent is
well known from its end moraine and extends to
147 200 m (CH1903 y-coordinate), or 150 m further
north than its 1851 extent derived from topographic maps
(Maisch and others, 1999). Even for the LIA maximum
extent, Vadret da la Fortezza, situated between Vadret Pers
and Vadret da Morteratsch, did not coalesce with the main
glacier trunk as indicated by morainic and historical
evidence. Except for a very narrow lateral connection
through which almost no ice flows (as it is not along the
steepest gradient), Vadret da la Fortezza has always been an
isolated glacier. Therefore it is not considered part of the
Morteratsch glacier complex here.
2.6.3. Retreat from the end of the LIA to present day
Up to the beginning of the frontal position record in 1878
(Glaciological Reports, 1881–2010), the glacier retreat from
the LIA maximum was only 75–100 m. Since then, the
glacier has continuously retreated, with only five excep-
tional years of standstill or a small advance. Vadret da
Morteratsch hardly reacted to the small climatic perturba-
tions that caused other Swiss glaciers to advance in the
1920s and 1980s (Glaciological Reports, 1881–2010),
probably because of its longer response time. In general,
the retreat history can be divided into four stages:
1. From the beginning of the length record until 1940 the
retreat rate is almost constant at 10–15 m a
. The glacier
retreats from its maximum LIA extent, which is too large
for the prevailing mass-balance and climatic conditions.
2. Subsequently a period of stronger retreat lasts from 1940
to 1965, during which the frontal retreat rates double to
30 m a
. This accelerated retreat possibly relates to an
increase in solar radiation (Huss and others, 2009) and
higher temperatures starting in the 1930s. The latter
result from anthropogenic greenhouse gas emissions and
a positive phase of the AMO index (Huss and others,
2010a). The faster retreat is verified for other Swiss
glaciers (Glaciological Reports, 1881–2010), but for
smaller glaciers the period is usually shorter (from
1940 until 1950–55).
3. Between 1965 and 1990, retreat rates decrease to a level
similar to that immediately after the LIA. This may relate
to an increase in aerosol concentrations (Ramanathan
and others, 2001), leading to lower atmospheric transmis-
sivity (Wild and others, 2005) and more cloud formation
(Krüger and Grassl, 2002). The resulting reduction in
incoming solar radiation had a positive influence on the
glacier mass balance (Huss and others, 2009).
Zekollari and others: Modelling the evolution of Vadret da Morteratsch1158
4. From the 1990s onwards this effect weakens, and warm-
ing due to a further increase in greenhouse gas concen-
trations dominates. Apart from the anthropogenic effect,
the positive phase of the AMO also contributed signifi-
cantly to the recent warming in the Alps and the associ-
ated more negative glacier mass balances (Knight and
others, 2005; Huss and others, 2010a). Glacier retreat
rates increased again to 30 m a
during the last decade.
To make realistic projections of the future glacier response,
it is important to simulate its flow history as the current
glacier is still responding to past changes in climate,
geometry and dynamics. To this end, the flow model is first
dynamically calibrated to correctly reproduce the observed
glacier retreat since the LIA.
3.1. LIA extent of the glacier
The initial condition of the simulation is a glacier in steady
state at the LIA extent. Although there is no reason to a priori
suspect a steady state around 1864, it is imposed to avoid an
unwanted model drift at the start of simulations. Figure 3
shows the corresponding geometry resulting from the flow
model. To obtain this glacier extent, the surface mass
balance was calculated with average climate conditions for
the period 1864–93, which is the first 30 year period for
which homogenized HISTALP data from nearby stations are
available. However, to obtain the desired glacier length it
was necessary to apply an additional mass-balance forcing of
+0.5 m w.e. a
, corresponding to an ELA lowering of 60 m.
This seems reasonable, as the mass balance over the glacier
was very likely more positive at the end of the LIA.
For the modelled LIA geometry the glacier volume is
2.25 km
and the thickest ice for central Morteratsch glacier
is found at 410 m. The ELA is 200 m lower than the 2001–
10 average at 2820 m for Vadret da Morteratsch and 2880
m for Vadret Pers. As a result of the steady-state configura-
tion the mean specific mass balance of the glacier complex,
which is the annual surface mass balance averaged over the
whole glacier, is equal to zero.
3.2. Evolution of the glacier from 1864 to 2010
From the balance year 1864/65 onwards, the surface mass
balance Bis calculated from the 2-D energy-balance model
driven by the Segl-Maria and Samedan temperature and
precipitation records. In the dynamic calibration process, a
mass-balance correction Bis iteratively applied to best
match the observed evolution of the frontal position
as follows:
Bðx,y,tÞ ¼ BSMBðx,y,tÞ þ BðtÞ:ð9Þ
Here Bis a function of location (x,y) and time t,B
calculated from the energy-balance model and BðtÞis
considered uniform over the glacier. The mass-balance
correction implicitly accounts for deviations from the initial
steady-state assumption, uncertainties in the mass-balance
model and errors in the climatic-forcing records. This cor-
rection varies in time and is necessary to reproduce the ob-
served retreat. This approach to generate the current glacier
imbalance is similar to Oerlemans (1997) in a study on
Nigardsbreen. Norway, and is applicable when the glacier-
length record exceeds the characteristic response time (Zuo
and Oerlemans, 1997; De Smedt and Pattyn, 2003).
Figure 4 shows the required mass-balance correction
BðtÞ, which was determined manually in order to
reproduce the main frontal retreat trends. It can conveni-
ently be expressed as four piecewise linear sections
representing different periods between 1864 and 1960.
The initial Bis kept constant at +0.5 m w.e. a
until 1905.
Without keeping this positive mass-balance correction, the
modelled retreat would have been too strong. After 1905,
B had to decrease to 0.1 m w.e. a
by 1930 to capture the
Fig. 3. Modelled steady-state thickness field for a glacier with the
same length as indicated by the LIA moraine. The contours are
spaced 50 m apart. The thick black line indicates the ELA. White
areas are either ice-free or contain ice that does not contribute to
the flow of the glacier complex.
Fig. 4. Modelled and observed glacier length evolution of Vadret da
Morteratsch between 1878 and 2010. An additional mass-balance
correction (shown in blue) is required for a better match of the
modelled frontal retreat with the observations and is set to zero
after 1960.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch 1159
accelerated retreat starting in the 1930s. A further positive
mass-balance correction of maximally +0.5 m w.e. a
centred around 1945 was required to correctly simulate
the smaller glacier retreat rates during the 1970s and 1980s.
In this paper we can only speculate about the reasons why a
surface-mass-balance model driven by HISTALP data alone
is not able to produce a correct glacier retreat. Apparently,
the glacier’s mass balance is affected by additional features
not captured well in the ambient climate records, as noted
earlier, for example in a study on Glacier d’Argentière,
France (Huybrechts and others, 1989), and a recent study
by Lüthi (2014). Possibly this is related to variations in
aerosol content (Huss and others, 2009; Painter and others,
2013). The absence of a mass-balance correction after 1960
to correctly simulate the glacier retreat of the last 50 years
does, however, lend credibility to the dynamic calibration
as performed here. It clearly suggests that the effect of the
initial steady-state assumption has faded by 2010 and that
the surface-mass-balance model driven by unbiased HIS-
TALP data over recent decades produces a basically correct
forcing for the glacier flow model.
Other sources of information have been used to validate
the glacier model. Huss and others (2010b) reconstructed
the evolution of the Morteratsch glacier volume between
1900 and 2008 based on mass-balance modelling and
absolute volume differences derived from four DEMs for
1935, 1955, 1985 and 2008. Overall, there is a good
agreement between the results of Huss and others (2010b)
and our volume change reconstructions (Fig. 5), especially
after 1960 when the mass-balance correction is no longer
applied. In both cases, the same general trends are captured,
including two phases of higher volume-loss rates. Interest-
ingly, these two phases (1925–1960 and from 1980
onwards) precede the associated periods of accelerated
frontal retreat by 5–10 years. This is because glacier
volume is known to adapt faster to climatic changes than
glacier length (e.g. Oerlemans, 2001; Adhikari and others,
2011). This can also be inferred from the evolution of glacier
area shown in Figure 5, which mainly reflects length
changes at the snout. Huss and others (2010b) derived a
volume loss of 0.61 km
between 1935 and 2008, compared
with 0.58 km
from our ice-dynamic model. For the more
recent period between 1985 and 2008, the volume losses
are respectively 0.305 km
and 0.316 km
. Fischer and
others (2014), also based on DEM differencing, obtain a
volume loss of 0.30 km
between 1991/92 and 2008/09,
while we obtain 0.27 km
for this period.
The recent increase in mass loss and the subsequent
accelerated frontal retreat has its counterpart in the long-term
mean specific mass balance of the Morteratsch glacier com-
plex. Centred around 1980, the 20 year average annual sur-
face mass balance of the glacier is around –0.21 m w.e. a
while only 20 years later, in 2000, this value lowers to
–0.82 m w.e. a
. From the meteorological records shown in
Figure 2, it is clear that the recent glacier retreat is primarily
driven by higher summer temperatures.
Additionally, the modelled 2001 glacier state is com-
pared with the observed glacier geometry (Zekollari and
others, 2013). As shown in Figure 6, there is overall quite
good agreement between the modelled surface topography
and that from the DEM. As the bedrock is kept constant in
the modelling, good agreement also applies to the ice
thickness. The highest ice thickness of 350 m is found for
central Vadret da Morteratsch in both fields. The maximal
ice thickness for Vadret Pers is equally 250 m in both cases.
The total ice volume obtained from the transient model run
in 2001 (1.41 km
) is, however, situated at the high end of
the range inferred from available radar observations
(1.14 0.28 km
) (Zekollari and others, 2013). This may
reflect shortcomings in the assumptions made to generalize
the radio-echo sounding lines over the whole glacier to
reconstruct ice thickness, as well as in the flow parameters
used in the ice-dynamic model. The largest discrepancies
between observed and modelled ice thickness occur for the
tongue, the confluence area and the accumulation area of
Morteratsch glacier. However, the last zone lacks mean-
ingful ice thickness and velocity measurements. One
explanation is that the flow model assumption for the ice
in the accumulation area is too stiff, because flow par-
ameters were derived from a calibration between glacier
geometry and measured surface velocities in the ablation
zone. Alternatively, the reconstructed ice thickness in the
accumulation zone, inferred from the concept of plastic
flow with a constant yield stress, may be an underestimate.
Quite possibly the real ice thickness in the accumulation
zone and the real ice volume in 2001 are much closer to the
modelled estimate of 1.41 km
A final comparison can be made between the surface
mass balance predicted by the energy-balance model and
the actual stake readings from our observations. RMSEs for
individual balance years vary between 0.5 and
1.0 m w.e. a
and are similar to those obtained during the
model calibration by construction (Nemec and others,
2009). The largest discrepancies are found in the lower
part of the glacier for the warmest years. However, the
deviations have a stochastic component and did not prevent
the model from correctly reproducing the recent glacier
evolution as discussed above.
4.1. Climatic-forcing scenarios
With the past evolution of the glacier well constrained, the
simulations can be extended into the future. To force the
future mass balance we use climatic scenarios inspired by
Fig. 5. Reconstructed cumulative volume change (relative to 2008)
and area change (2 year running mean) for the Morteratsch glacier
complex between 1864 and 2010. The reconstruction by Huss and
others (2010b) is based on mass-balance modelling, constrained by
four fixed points derived from DEM differencing.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch1160
the CH2011 (2011) projections for the 21st century over
Switzerland. These are based on output from global climate
models (GCMs) that are coupled to European-scale regional
climate models (RCMs). CH2011 considers three Inter-
governmental Panel on Climate Change (IPCC) scenarios, of
which two are non-intervention scenarios (A2 and A1B) and
a third is a climate-stabilization scenario (RCP3D, emissions
cut by 50% in 2050 compared with 1990). With respect to
1980–2009, the different GCM/RCM combinations and
scenarios result in a mean temperature increase in 2070–
99 in the range of +0.8 to +2°C (RCP3PD scenario) and 2.7°
C to +5.0°C (A2 scenario). For the Alpine region, the
warming in all RCMs is most pronounced in the summer
months. Also the change in precipitation shows a seasonal
character, with wetter winters (between +0% and +30%
precipitation) and drier summers (–30% to 0%). This is in
line with the results of the PRUDENCE project (Prediction of
Regional scenarios and Uncertainties for Defining European
Climate change risks and Effects; Christensen and Christen-
sen, 2007). Based on these climate projections, we construct
nine schematic warming scenarios that broadly cover the
range of CH2011 scenarios. We opted for schematic
scenarios as the interest is in the main future climatic trends
and not in a specific scenario-model set-up. As a control we
also consider three scenarios with no temperature increase.
The nine warming scenarios consist of a combination of
three linear warming trends (+1.0°C, +2.5°C and +4.0°C of
mean annual warming between 2010 and 2100) and three
precipitation trends (neutral, wet and dry). The changes are
applied with respect to the 2001–10 averages of the monthly
mean temperature and precipitation data. For all scenarios,
the summer (June–July–August) warming lies 25% of the
annually averaged warming above the warming of the other
seasons: for example, the +4.0°C scenario corresponds to a
temperature increase of +4.75°C for the summer and +3.75°
C for the other seasons. The wet scenario accounts for a
linear 30% increase of winter precipitation by 2100, an
increase of 15% for spring and autumn and no change in
summer precipitation. In the dry scenario the summer
precipitation linearly decreases by 30%, the spring and
autumn by 15% and the winter precipitation remains
unchanged. For the neutral precipitation scenario, future
precipitation rates are kept constant at their 2001–10 level.
4.2. Projections of ice volume and ice extent
Figure 7 and Table 1 summarize the projected evolution of
glacier volume. Under all scenarios a strong mass loss is
expected. This includes the no-warming scenario, in which
the glacier still loses between 24.4% and 33.4% of its
volume by 2100 depending on whether precipitation
Fig. 6. Ice thickness distribution in 2001, derived from field measurements (Zekollari and others, 2013) (a) and from the transient model run
(b). The contours represent the difference in ice thickness (m) between the two methods.
Fig. 7. Future evolution of ice volume under different climate
scenarios. The black line represents the reconstructed evolution
over the past 50 years. The line colour denotes the temperature
scenario, while the line style indicates the precipitation scenario.
For a particular colour, the thick solid line represents the ‘neutral’
precipitation scenario, the thin dashed line represents the ‘wet’
scenario and the thin solid line the ‘dry’ scenario.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch 1161
rates increase, decrease or remain stable. This provides a
clear manifestation of the current imbalance of Morteratsch
glacier and of the time needed to equilibrate towards 2001–
10 mass-balance conditions. For the highest warming
scenario considered here (+4.0°C), ice volume by 2100 is
reduced by 80% relative to 2010. For all warming
scenarios, ice loss continues beyond the 21st century. On
the other hand, up to 2020 the glacier evolution does not
depend on any particular scenario and is almost entirely
conditioned by past climatic changes, in particular the post-
1970 warming. Strikingly the effect of precipitation changes
is small compared with the effect of temperature changes.
Even the adopted increase in precipitation of the wet
scenario is not sufficient to counterbalance further glacier
retreat for the no-warming case. This relates to the fact that
the annual mass balance of Alpine glaciers is mainly driven
by their summer balance (Vincent and others, 2004;
Zekollari and Huybrechts, 2014).
The corresponding glacier geometries are shown in
Figure 8. By 2030 the glacier has retreated by 1 km
compared with 2010, and Vadret Pers is no longer a
tributary of Vadret da Morteratsch. The separation of the two
glaciers occurs in the model before 2020. The imminent
disconnection of the two glaciers is clearly supported by
field observations since 2000 and may perhaps take place as
early as 2015 if a remaining frontal ice patch of unknown
thickness connecting both glaciers melts completely. For
both glacier tongues, the frontal thinning and retreat is
almost entirely driven by the local surface mass balance as
there is virtually no mass supply from upstream as flow
velocities in the tongue area approach zero (Zekollari and
others, 2013). Typical ablation rates at the tongue of
Morteratsch glacier are 7–8 m w.e. a
for the period 2001–
10, and so are observed ice-thinning rates. For the highest-
warming scenario (+4.0°C by 2100), the mean ELA has risen
by 40–80 m by 2030 to 3100 m for Vadret da Morteratsch
and 3120 m for Vadret Pers.
After 2050, the effect from considering different scenarios
becomes evident. By 2065, the retreat is stronger for Vadret
Pers than for Vadret da Morteratsch, mostly due to thinner
ice, a higher ELA and a more negative mass balance in the
frontal area. In the +4.0°C warming scenario, the ELA for
Vadret Pers rises to 3330 m by 2065, while for Vadret da
Morteratsch it rises to 3315 m. Towards the end of the
century the ELA rises to 3520 m for Vadret da Morteratsch
and 3500 m for Vadret Pers. This reflects a similar exposure
and orientation of the respective glacier sections in this
elevation band. Glacier retreat continues up to the end of
the 21st century. By 2100, there is a clear distinction
between the different scenarios considered. For the two
highest-warming scenarios, only ice at high elevations
remains and the glacier complex starts to disintegrate into
disconnected ice patches. Despite its slightly more negative
mass balance, the tongue of Vadret da Morteratsch extends
further north than that of Vadret Pers because of its higher
ice thickness which takes longer to completely waste away.
Three-dimensional views of the various model simula-
tions discussed above are displayed in Figure 9. In the
scenarios with the strongest retreat, it is likely that proglacial
lakes will form in bedrock depressions (Zekollari and others,
2013). Their effect is not taken into account here, but can
potentially accelerate the glacier retreat by hydrostatic lifting
of the glacier front. The formation of future proglacial lakes
is also important from a natural-hazards perspective, as
some of them form behind natural moraine dams that can
easily break, potentially causing serious damage from flash
flooding downstream (Haeberli and others, 1989; Frey and
others, 2010). Judging from the glacier bed exposed so far,
the lake that may form in the central Morteratsch area is,
however, probably dammed by hard rock rather than by soft
sediment, and so may not be subject to potential failure.
4.3. Climate–geometry imbalance
Further insight into the future time-dependent response and
glacier imbalance is provided by the time evolution of the
mean specific mass balance. Figure 10 displays the spatially
averaged annual surface mass balance for all future
warming experiments with constant (2001–10 average)
precipitation. The mean specific mass balance is a measure
for the annual rate of mass loss and is a complex function of
both the climate state and the actual glacier hypsometry
(area–elevation distribution). For constant 2001–10 climate
forcing (no-warming scenario), the expected quasi-expo-
nential decay of the glacier imbalance is confirmed. It is
caused by geometric adjustment that mainly entails loss of
an excess glacier tongue that can no longer be supplied with
sufficient ice mass from a reduced accumulation area.
By the end of the 21st century, the glacier is still out of
equilibrium with the 2001–10 climate, although an asymp-
totic evolution towards a zero mean specific mass balance is
evident. The eventual steady state corresponds to a volume
loss with respect to 2010 of between 25% and 35%,
depending on the precipitation scenario, and a frontal
retreat of almost 2 km for Vadret da Morteratsch and 1.5 km
for Vadret Pers (see also Figs 7–9). In this experiment, the
associated AAR steadily increases from 44% for the period
2001–10 to 57% in 2065 and 58% in 2100.
From the no-warming case, one can also derive a first
estimate of the volume response time of Morteratsch glacier,
as the time period during which a fraction of (1 –e
) or 63%
of the imbalance in 2010 of –0.82 m w.e. a
, derived from
the 2001–10 mean climatology, has been overcome. This
timescale corresponds to 32 years but is not considered a
clean measure of the response time of the current glacier as
it also contains a contribution from the cumulated imbal-
ance prior to the 2001–10 period.
For the other warming scenarios, the evolution of the
mean specific mass balance results from an interplay
between geometric adjustment and a continuously decreas-
ing surface mass balance. In the +4°C scenario the effect of
further warming initially dominates and the imbalance
increases until 2052. After that period, the loss of surface
area is more pronounced and this increases the mean
specific mass balance faster than the warming decreases it.
Table 1. Relative ice volume loss in 2100 compared to 2010 for the
different climatic scenarios
Temperature Precipitation
Dry Neutral Wet
°C % % %
+0.0 –33.4 –29.3 –24.4
+1.0 –51.3 –48.2 –44.5
+2.5 –70.2 –68.7 –67.1
+4.0 –81.8 –80.9 –79.8
Zekollari and others: Modelling the evolution of Vadret da Morteratsch1162
The complex evolution of the imbalance in a changing
climate illustrates the difficulty of deducing a climatic signal
from changes in glacier geometry. For this purpose the
reference surface mass balance, the mass balance on a fixed
surface at a certain reference date (Elsberg and others, 2001;
Huss and others, 2012), should be used. Over the 21st
century, the glacier’s reference surface mass in our
experiments is found to increase continuously for all
warming scenarios (i.e. it becomes less negative).
5.1. Comparison with other studies
Comparable studies simulating the future 3-D geometry of a
mountain glacier have been performed by other researchers.
Using a distributed accumulation and temperature-index
melt model driven by RCMs to estimate ice-thickness
changes, Huss and others (2010b) attempted to project the
future evolution of the Morteratsch glacier complex. In their
modelling, similar climate scenarios were used but ice
Fig. 8. Simulated glacier extent and ice thickness for different temperature scenarios (vs 2010) and time periods, assuming neutral
precipitation. The ice-thickness scale is the same as that used in Figure 6. The thick black line delineates the DEM glacier outline in 2001,
while the thin lines delineate 50 m ice-thickness intervals.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch 1163
dynamics was not considered. Instead, they imposed a
distributed ice-thickness change based on the observation
that elevation changes of retreating glaciers are normally
largest near the glacier terminus. Since Huss and others
(2010b) also carried out a model calibration over the 20th
century, there is reasonable agreement between their
projections and ours concerning the evolution of glacier
length, area and volume until 2030. Beyond 2030, however,
Huss and others (2010b) produce a more fragmented glacier
retreat with more isolated patches of ice in the deeper
bedrock depressions, which are largely absent from our
work as analysed further below.
The relative volume loss of the Morteratsch glacier
complex over the 21st century is generally smaller than
that of other large Swiss glaciers (Huss and others, 2010b;
Farinotti and others, 2012; Salzmann and others, 2012). This
difference depends on several factors, such as the sensitivity
of the mass balance and differences in climatic scenarios,
but is mainly dictated by the specific hypsometry of the
glacier in question. Morteratsch glacier stands out in having
a comparably large areal fraction in the elevation band
between 3500 and 4000 m, which will remain in the
accumulation zone even for a warming of +4°C. In another
3-D ice-dynamic simulation, Jouvet and others (2009) find
that Rhonegletscher almost entirely disappears by 2100 in
their ‘median’ scenario (in between our +2.5°C and +4.0°C
scenarios), but that is mainly because Rhonegletscher has its
Fig. 9. 3-D view of the glacier from the north-northwest for different settings, scenarios and times. The domain ranges from 789 500 m to
796 000 m in the x-direction and from 137 500 m to 148 000 m in the y-direction following the CH1903 coordinate system. Blue areas
denote local bedrock depressions that may hold proglacial lakes after the glacier has retreated.
Fig. 10. Future evolution of mean specific mass balance for the dif-
ferent climate scenarios, assuming average 2001–10 precipitation.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch1164
highest point at 3600 m, eliminating an accumulation area
of sufficient size. In another study with the same ice-
dynamic model, Jouvet and others (2011) reported dramatic
ice losses for Grosser Aletschgletscher by 2100. In their
‘ENSmed’ scenario, close to our +4.0°C scenario, <10% of
the 1999 ice volume remains by 2100, less than the 15%
remaining for Morteratsch glacier. For Glacier de Saint-
Sorlin (2700–3400 m) Le Meur and others (2007) modelled a
total disappearance of the glacier by the end of the 21st
century under the IPCC’s SRESB1 scenario. Again, these
differences reflect different area–elevation distributions. A
common feature of all these studies, however, is the near
disappearance of even the largest Alpine glaciers by the end
of the 21st century, albeit for a higher-than-average
warming scenario.
5.2. The role of ice dynamics
To further investigate the role of ice dynamics in our
projections, we considered two additional experiments.
These test the role of ice dynamics in different set-ups
following the work of Huybrechts and De Wolde (1999).
The dynamic response is the one discussed so far in which
there is a full coupling between the mass balance and the
ice flow. In the static response, the ice flow is kept constant
at the year 2010 state (constant flux divergence in Eqn (6))
but changes in ice thickness can still feed back on the mass
balance through the mass-balance elevation gradient. For
the fixed-geometry response, the ice flow is also kept
constant, and additionally changes in glacier geometry
cannot feed back on the mass balance (through the mass-
balance elevation gradient). Here only perturbations with
respect to the 2001–10 mass balance, which are solely
climate-driven, are integrated forward in time. This set-up
enables us to distinguish between the role of ice dynamics
on the one hand and the effect of the height–mass-balance
feedback on the other hand.
Figure 11 shows the results. For both the no-warming
and the +4°C scenarios the differences in total volume loss
by 2100 are within 10% of each other for all three cases.
This clearly shows that the dominant response is from
changes in the surface mass balance, not from ice dynam-
ics. The static and fixed-geometry cases are most closely
aligned, indicating that due to the limited ice thicknesses
the height–mass-balance feedback does not play an import-
ant role in the future response of an alpine mountain
glacier. This is different from the response of ice sheets
(Huybrechts and De Wolde, 1999), which have a much
larger ice thickness.
As time evolves, the inclusion of ice dynamics is found to
speed up the total volume loss, and this effect is much more
pronounced in the +4°C scenario than in the no-warming
scenario. Moreover, keeping the flux-divergence term con-
stant in the static response has an opposite effect on the
accumulation and ablation zones. This is demonstrated in
Figure 12. Including ice dynamics increases the mass loss in
the ablation zone and enhances the retreat of the glacier
tongue. This is because the flux-divergence term can adjust
to the thinning margin (it becomes less positive) so that less
mass is transported to the same position in the tongue area.
Fig. 11. Future evolution of glacier volume under different model
set-ups addressing the role of ice dynamics. The upper curves are
for the no-warming scenario and the lower curves for the +4.0°C
warming scenario.
Fig. 12. Glacier geometry in 2100 in the +4.0°C scenario in an experiment including ice-dynamic adjustment (dynamic response, left panel)
and excluding ice-dynamic adjustment (static response, right panel). The view is from the north-northwest and coordinates are given in the
CH1903 system.
Zekollari and others: Modelling the evolution of Vadret da Morteratsch 1165
This is not the case for the static experiment in which the
ice-transport term is fixed. In the accumulation zone, on
the other hand, excluding ice-dynamic adjustment (static
response) increases mass loss and enhances local thinning,
so that the glacier disintegrates more easily into separate ice
patches than in the dynamic response.
Since the end of the LIA, Morteratsch glacier has almost
continuously retreated, a trend which recently intensified
due to anthropogenic warming and will persist in the future
under all scenarios considered here. We were able to
reconstruct the past evolution of the glacier in good
agreement with field data. However, this required imposing
an additional mass-balance bias on top of the surface mass
balance calculated with an energy-balance model forced by
climatic data from nearby meteorological stations. Appar-
ently, past mass-balance changes were influenced by other
processes not well captured in the ambient climate records.
The absence of any artificial mass-balance correction after
1960, together with a correctly simulated glacier retreat,
lends credibility to the dynamic calibration as performed
here. It also indicates that the initial steady-state assumption
made for the start of the simulation in 1864 has basically
been forgotten by today.
The decadal mean specific mass balance between 2001
and 2010 is found to be –0.93 m w.e. a
, indicative of the
strong disequilibrium between the current glacier geometry
and today’s climate conditions. The e-folding volume-
response time scale could be estimated at 30 years.
Consequently, the evolution of the glacier in the coming
decades is already defined by its past evolution. Irrespective
of any scenario considered here, the glacier is found to
retreat further by almost 1 km by 2030, and Vadret da
Morteratsch disconnects from its main tributary, Vadret
Pers, before 2020. Even if the present-day climate were to
be maintained, Morteratsch glacier is committed to retreat
until at least the end of the 21st century, when it comes near
to a new steady state with a volume loss of 25–35% and a
frontal retreat of 2 km compared with the present day. A
realistic increase in precipitation can attenuate the future
retreat, but cannot stop it. For the two highest warming
scenarios (+2.5°C and +4.0°C), in 2100 only ice at high
elevations remains and the glacier starts to disintegrate into
disconnected ice patches. Glacier retreat is almost entirely
mass-balance driven; however, ice-dynamic adjustment is
found to accelerate the volume loss by 10%, producing a
less-fragmented ice distribution. If Vadret Pers and Vadret
da Morteratsch retreat by >3 km, proglacial lakes are likely
to form in bedrock depressions, and this may speed up the
retreat under certain circumstances.
Compared with other well-studied Swiss glaciers that
have been subjected to similar modelling studies, the 21st-
century relative length changes and mass loss of the
Morteratsch glacier complex seem to be less dramatic. This
can be attributed to its relatively large size and high
elevation, especially the large fraction of its area above
3500 m that will probably remain above the ELA, even for a
warming of +4°C. Nevertheless, it is clear that the climatic
warming realized so far already has a profound effect on
Alpine glacierized environments and will commit us to a
substantial further ice loss for the next century, even when
future warming could be stabilized at relatively low levels.
We thank everyone who helped with data collection in the
field. We also thank the Zentralanstalt für Meteorologie und
Geodynamik (ZAMG) and MeteoSwiss for providing the
HISTALP data. We are very grateful to Frank Paul and
Matthias Huss for providing DEM data and reconstructed
mass-balance series. Thoughtful comments by two anony-
mous reviewers and G. Jouvet helped to improve the
manuscript. Financial support was provided by projects
funded by the Belgian Science Policy Office (BELSPO)
within its Research Program on Science for a Sustainable
Development (projects MILMO, ASTER and iCLIPS). Harry
Zekollari holds a PhD fellowship of the Research Founda-
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Zekollari and others: Modelling the evolution of Vadret da Morteratsch1168
... At present, the two glaciers cover an area of about 15 km 2 with a volume of ca. 1 km 3 , making it the largest continuous ice area in the Bernina region. Vadret da Morteratsch reached its maximum Little Ice Age (LIA) extent between 1860 and 1865 (Zekollari et al., 2014). Since 1878, the glacier front has retreated more than 3 km and is nowadays located at an altitude of 2200 m above sea level (a.s.l.). ...
... −0.8 m of water equivalent per year (Fischer et al., 2015). The SMB stake measurements served to calibrate a mass balance model (Nemec et al., 2009) which was coupled to a higher-order ice flow model to simulate the future evolution of the glacier complex (Zekollari et al., 2014) and to study its response time (Zekollari and Huybrechts, 2015). Furthermore, the ice thickness in the ablation area has previously been measured twice (Zekollari et al., 2013;Langhammer et al., 2019). ...
... Hutter and Morland, 1984) but also on the surrounding geometry, typically over scales corresponding to several times the local ice thickness (accounted for in higher-order and full Stokes models; see e.g. Zekollari et al., 2014, where such a model was applied for this glacier complex). Local gradients of the ice thickness and the velocity are often magnified when they are determined on a numerical grid with a central difference scheme. ...
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The surface mass balance (SMB) of a glacier provides the link between the glacier and the local climate. For this reason, it is intensively studied and monitored. However, major efforts are required to determine the point SMB at a sufficient number of locations to capture the heterogeneity of the SMB pattern. Furthermore, because of the time-consuming and costly nature of these measurements, detailed SMB measurements are carried out on only a limited number of glaciers. In this study, we investigate how to accurately determine the SMB in the ablation zone of Vadret da Morteratsch and Vadret Pers (Engadin, Switzerland) using the continuity equation method, based on the expression of conservation of mass for glacier flow with constant density. An elaborate dataset (spanning the 2017–2020 period) of high-resolution data derived from unoccupied aerial vehicle (UAV) measurements (surface elevation changes and surface velocities) is combined with reconstructed ice thickness fields (based on radar measurements). To determine the performance of the method, we compare modelled SMB with measured SMB values at the position of stakes. Our results indicate that with annual UAV surveys, it is possible to obtain SMB estimates with a mean absolute error smaller than 0.5 m of ice equivalent per year. Yet, our study demonstrates that to obtain these accuracies, it is necessary to consider the ice flow over spatial scales of several times the local ice thickness, accomplished in this study by applying an exponential decay filter. Furthermore, our study highlights the crucial importance of the ice thickness, which must be sufficiently well known in order to accurately apply the method. The latter currently seems to complicate the application of the continuity equation method to derive detailed SMB patterns on regional to global scales.
... Here, we investigate the thermal regime of the Grigoriev ice cap and the Sary-Tor glacier, both located in the inner Tien Shan, Kyrgyzstan (central Asia), using a threedimensional (3D) higher-order (HO) thermomechanical ice flow model coupled to a simplified 2D surface energy mass balance model. The selected ice flow model has been successfully applied at different scales, ranging from a mediumsized mountain glacier in the Alps (Zekollari et al., 2013(Zekollari et al., , 2014Zekollari and Huybrechts, 2015), and a medium-sized ice cap in Greenland (Zekollari et al., 2017) to the entire Greenland ice sheet (Fürst et al., , 2015. To date, most of the 3D glacier and ice cap model studies have been performed assuming an isothermal state of the ice mass (e.g. ...
... To date, most of the 3D glacier and ice cap model studies have been performed assuming an isothermal state of the ice mass (e.g. Jouvet et al., 2011;Zekollari et al., 2014). Only a few studies have been performed by applying a 3D thermomechanical ice flow model including variations in englacial temperatures for glaciers (Zwinger et al., 2007;Zwinger and Moore, 2009;Zhao et al., 2014;Rowan et al., 2015;Li et al., 2017;Gilbert et al., 2017Gilbert et al., , 2020 and ice caps (Flowers et al., 2007;Schäfer et al., 2015;Zekollari et al., 2017). ...
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The thermal regime of glaciers and ice caps represents the internal distribution of ice temperatures. An accurate knowledge of the thermal regime of glaciers and ice caps is important to understand their dynamics and response to climate change and to model their evolution. Although the assumption is that most ice masses in the Tien Shan are poly-thermal, this has not been examined in appropriate detail so far. In this research, we investigate the thermal regime of the Grigoriev ice cap and the Sary-Tor glacier, both located in the inner Tien Shan in Kyrgyzstan, using a 3D higher-order thermomechanical ice flow model. Input data and boundary conditions are inferred from a surface energy mass balance model, a historical air temperature and precipitation series , ice thickness measurements and reconstructions, and digital elevation models. Calibration and validation of the englacial temperatures are performed using historical borehole measurements on the Grigoriev ice cap and radar measurements for the Sary-Tor glacier. The results of this study reveal a polythermal structure of the Sary-Tor glacier and a cold structure of the Grigoriev ice cap. The difference is related to the larger amount of snow (insulation) and refreezing meltwater (release of latent heat) for the Sary-Tor glacier, resulting in higher surface layer temperature, especially in the accumulation area, which is subsequently advected downstream. Further, ice velocities are much lower for the Grig-oriev ice cap, with consequent lower horizontal advection rates. A detailed analysis concerning the influence of temperature and precipitation changes at the surface reveals that the thermal structure of both ice bodies is not constant over time, with recent climate change causing increasing ice temperatures in higher areas. The selected ice masses are representative examples of the (inner) Tien Shan glaciers and ice caps. Therefore, our findings and the calibrated parameters can be generalised, allowing improved understanding of the dynamics and future evolution of other glaciers and ice caps in the region.
... Het terugtrekken en zeker het verdwijnen van deze gletsjer heeft drastische gevolgen voor het toerisme, veruit de belangrijkste bron van inkomsten van Pontresina. De aanvoer van smeltwater en de veiligheid in het gebied zijn andere aangelegenheden die negatief beïnvloed kunnen worden door de krimp: een kleinere gletsjer betekent minder ijs voor zomerse smelt enerzijds, en anderzijds verhoogt het afsmelten van de gletsjer het risico op ijslawines en vloedgolven van water uit glaciale meren, zogenaamde "glacial lake outburst floods" oftewel GLOF's (Zekollari et al., 2014). Globaal gezien dragen krimpende gletsjers bij aan de stijging van de zeespiegel. ...
... De data voor de tussenliggende jaren worden berekend door uit te gaan van een lineaire trend. De scenario's die hier toegepast worden, zijn eerder al gehanteerd door Zekollari et al. (2014) in hun onderzoek naar de evolutie van het VdM gletsjercomplex. Het betreft telkens drie temperatuur-en neerslagtrends, gecombineerd goed voor negen reeksen die in lijn liggen met de scenario's voor Zwitserland van CH2011 (2011). ...
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Het opzet van dit onderzoek is het kwantificeren van het effect van een positieve massabalansperturbatie op de Vadret da Morteratsch (VdM), een gletsjer in de Zwitserse Alpen. Net als verschillende andere gletsjers in de regio en verspreid over de Aarde, is de evolutie van de VdM over de afgelopen eeuw getekend door een gestage achteruitgang, het resultaat van een verlies aan massa als gevolg van klimaatopwarming. De staat van de gletsjer werd geprojecteerd over het vervolg van de 21ste eeuw a.d.h.v. een numeriek model, aangedreven door data bepaald met verschillende klimaatscenario’s. Het verloop van de VdM werd gesimuleerd zowel met als zonder perturbatie, die men in rekening brengt als het toevoegen van sneeuw, en zodanig ook een albedofeedback teweegbrengt. In het geval van een geringe opwarming kan de massabalans op nul stellen voorkomen dat de gletsjer terugtrekt tot in een omvangrijke depressie in het gesteente, waar de achteruitgang anders in versnelling komt. Om dit te realiseren bij een extremere klimaatverandering heeft men aanzienlijk meer artificiële sneeuw nodig, die de depressie opgevuld houdt (en zodoende de mogelijke vorming van een glaciaal meer belet) maar de terugtrekking van de gletsjer voorbij dit gebied niet stopt. Bijkomend werd nagegaan of er jaarlijks voldoende smeltwater beschikbaar is voor het maken van de kunstsneeuw, aangenomen dat men dit als bron gebruikt. Rond het produceren van de additionele accumulatie bestaan belangrijke problemen, die hier slechts kwalitatief benaderd werden. Hoewel de impact van een perturbatie d.m.v. kunstsneeuw significant is, blijven vele vragen nog onbeantwoord.
... The stake's elevation changes with time due to the melting of ice and glacial downward flow [56][57][58] . During seven years, the total elevation change is around 253 m for stake 1, 210 m for stake 2, and 183 m for stake 3 (kindly refer Statistical Analysis under Results and Discussion for Stake 1, 2 and 3 description). ...
... To understand the relation between meteorological parameters and surface mass balance perturbation, the MLRA approach has been used by considering Eq. (4) 57,77 . This correlation analysis requires the abandonment of the effect of measurement of different meteorological parameters in other units (here, the temperature in degree C and precipitation in mm w.e.). ...
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In the present study, we analyze a field-based seven-year data series of surface mass-balance measurements collected during 2011/12 to 2017/18 on Naradu Glacier, western Himalaya, India. The average annual specific mass balance for the said period is − 0.85 m w.e. with the maximum ablation of − 1.15 m w.e. The analysis shows that the topographic features, south and southeast aspects and slopes between 7 to 24 degrees are the reasons behind the maximum ablation from a particular zone. The causes of surface mass balance variability have been analyzed through multiple linear regression analyses (MLRA) by taking temperature and precipitation as predictors. The MLRA demonstrates that 71% of the observed surface mass balance variance can be explained by temperature and precipitation. It clearly illustrates the importance of summer temperature, which alone explains 64% variance of surface mass balance. The seasonal analysis shows that most of the surface mass balance variability is described by summer temperature and winter precipitation as two predictor variables. Among monthly combinations, surface mass balance variance is best characterized by June temperature and September precipitation.
... Since then, ice retreat has increased to nearly 3 km, about 65% of which has occurred since 1950 (GLAMOS, 1881(GLAMOS, -2019. In contrast to MM, retreat at MOR since the late 1800s has only been interrupted by a standstill in the 1980s but not by any significant advances, highlighting a longer volume response time at MOR of c. 32 years (Zekollari et al., 2014). MOR is a benchmark site for glaciological research (Klok and Oerlemans, 2002;Nemec et al., 2009;Zekollari and Huybrechts, 2018) and has more recently also become a key site for geoengineering investigations (Oerlemans et al., 2017). ...
The term ‘Little Ice Age’ (LIA) is classically used to define a period of repeated and extensive glacier advances during the last millennium. In the meanwhile, this term is also used to address the period of relatively low temperatures between the Medieval Climate Anomaly (MCA), or Medieval Warm Period, and present-day warming. The end of the LIA is generally set to the mid or late 1800s CE, however, the published onset dates of the LIA are more variable from the mid 1200s to the late 1500s. At Mont Miné and Morteratsch glaciers, Swiss Alps, we sampled and subsequently analysed detrital as well as in situ tree remnants from the early LIA period. At both glaciers, trees with lifespans of up to about 400 years were buried at various lateral moraine sites. The corresponding advance of both glaciers can be traced from the 1280s until the 1310s. At Morteratsch glacier, this early LIA advance phase culminated likely around 1375 CE. Evidence collected at both glaciers indicates that the ice surfaces were at least c. 12–15 m from the lateral moraine crests deposited during the maximum extent of the LIA. This suggests a similar (though very slightly weaker) magnitude than later LIA advances at our sites. The advances of Mont Miné and Morteratsch glaciers coincide with relatively cool summer temperatures from the late 1200s to the late 1300s. Taken together, the onset of the Little Ice Age in the Alps can be considered to be c. 1260 CE. The Little Ice Age was not a uniform period, but had several phases as can be derived from the records of Alpine glaciers and summer temperatures. We propose a subdivision of the LIA in the European Alps into an early (1260–1380 CE), an intermediate (1380–1575 CE) and a main (1575–1860 CE) phase.
... GloGEMflow was extensively evaluated over the European Alps by relying on observed mass balances, surface velocities, and glacier changes and by comparing the simulated glacier changes to those from high-resolution 3D modelling studies that focus on individual glaciers (e.g. Jouvet et al., 2009;Zekollari et al., 2014). The simulated glacier extents under the CH2018 CC scenarios considered in this study were transformed from the GloGEMflow 1D model grid to the 2D model grid (at both 100 and 500 m resolution) by ensuring that the area and volume were conserved for each elevation band. ...
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River ecosystems are highly sensitive to climate change and projected future increase in air temperature is expected to increase the stress for these ecosystems. Rivers are also an important socioeconomic factor impact-ing, amongst others, agriculture, tourism, electricity production , and drinking water supply and quality. In addition to changes in water availability, climate change will impact river temperature. This study presents a detailed analysis of river temperature and discharge evolution over the 21st century in Switzerland. In total, 12 catchments are studied, situated both on the lowland Swiss Plateau and in the Alpine regions. The impact of climate change is assessed using a chain of physics-based models forced with the most recent climate change scenarios for Switzerland including low-, mid-, and high-emission pathways. The suitability of such models is discussed in detail and recommendations for future improvements are provided. The model chain is shown to provide robust results, while remaining limitations are identified. These are mechanisms missing in the model to correctly simulate water temperature in Alpine catchments during the summer season. A clear warming of river water is modelled during the 21st century. At the end of the century (2080-2090), the median annual river temperature increase ranges between +0.9 °C for low-emission and +3.5 °C for high-emission scenarios for both lowland and Alpine catchments. At the seasonal scale, the warming on the lowland and in the Alpine regions exhibits different patterns. For the lowland the summer warming is stronger than the one in winter but is still moderate. In Alpine catchments, only a very limited warming is expected in winter. The period of maximum discharge in Alpine catchments, currently occurring during midsummer , will shift to earlier in the year by a few weeks (low emission) or almost 2 months (high emission) by the end of the century. In addition, a noticeable soil warming is expected in Alpine regions due to glacier and snow cover decrease. All results of this study are provided with the corresponding source code used for this paper.
... In the Pyrenees, Rico et al. (2017) assessed a decline of the glacier area by 88% between 1850 and 2016, with a rapid wastage since the 1980s, confirming the recently accelerated shrinkage trend. Small glaciers in temperate and southern Europe are likely to completely disappear, and even large valley glaciers will have lost much of their current volume by the end of the century (Jouvet et al. 2009;Linsbauer et al. 2013;Zekollari et al. 2014Zekollari et al. , 2019. ...
This review summarizes current understanding of drivers for change and of the impact of accelerating global changes on mountains, encompassing effects of climate change and globalization. Mountain regions with complex human–environment systems are known to exhibit a distinct vulnerability to the current fundamental shift in the Earth System driven by human activities. We examine indicators of the mountain cryosphere and hydrosphere, of mountain biodiversity, and of land use and land cover patterns, and show that mountain environments in the Anthropocene are changing on all continents at an unprecedented rate. Rates of climate warming in the world’s mountains substantially exceed the global mean, with dramatic effects on cryosphere, hydrosphere, and biosphere. Current climatic changes result in significantly declining snow-covered areas, widespread decreases in area, length, and volume of glaciers and related hydrological changes, and widespread permafrost degradation. Complex adaptations of mountain biota to novel constellations of bioclimatic and other site conditions are reflected in upslope migration and range shifts, treeline dynamics, invasion of non-native species, phenological shifts, and changes in primary production. Changes in mountain biodiversity are associated with modified structure, species composition, and functioning of alpine ecosystems, and compromise ecosystem services. Human systems have been negatively impacted by recent environmental changes, with both inhabitants of mountain regions as well as people living in surrounding lowlands being affected. Simultaneously, accelerating processes of economic globalization cause adaptation strategies in mountain communities as expressed clearly in changing land use systems and mobility patterns, and in increasing marginalization of peripheral mountains and highlands. The current state of the world’s mountains clearly indicates that global efforts to date have been insufficient to make significant progress towards implementing the Sustainable Development Goals of the 2030 Agenda for Sustainable Development, adopted by all United Nations member states.
Mountain glaciers are at risk of rapid retreat, which requires an accurate prediction of their melt and evolution. However, there is a great deal of hassle with mountain glacier melt modelling at a regional scale. Most advanced physical process-based models require an ample amount of high-resolution measurements, while widely-used empirical models suffer from parameter transferability. We developed a glacier melt, mass balance, and evolution modelling framework using three temperature index melt modelling approaches. We performed 24 model scenarios to examine the response of 19 empirical parameters to the effects of: (1) two time periods, for understanding how parameter response can vary with time period considered for the simulation; (2) two glaciers located at the eastern slopes of the Canadian Rocky Mountains, for understanding the effects of glaciers hydro-climate and geographic setting; and (3) two levels of complexity in the model structure including melt and mass balance models coupled with (complex) and without (simple) glacier evolution modules. The results showed that the best optimal melt parameter sets vary temporally and spatially for both simple and complex models, indicating that they are not transferable from one period to another and across glaciers. The variations of ice melt parameters are greater than the snowmelt parameters. The spatiotemporal variations of parameters are resulted from the geographical and local climatic settings and energy balance components, including albedo parameterization on the glacier surface, the altitudinal variations of the glaciers, and the slope and aspects to which glaciers are exposed. For all models, the most sensitive parameter is temperature Lapse rate (LR), but with increasing model complexity, the parameter responses vary depending on the melt model structure and input data. Our study provides important information for modelling glacier melts and evolution at a regional scale.
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Glaciers play a crucial role in the Earth System: they are important water suppliers to lower‐lying areas during hot and dry periods, and they are major contributors to the observed present‐day sea‐level rise. Glaciers can also act as a source of natural hazards and have a major touristic value. Given their societal importance, there is large scientific interest in better understanding and accurately simulating the temporal evolution of glaciers, both in the past and in the future. Here, we give an overview of the state of the art of simulating the evolution of individual glaciers over decadal to centennial time scales with ice‐dynamical models. We hereby highlight recent advances in the field and emphasize how these go hand‐in‐hand with an increasing availability of on‐site and remotely sensed observations. We also focus on the gap between simplified studies that use parameterizations, typically used for regional and global projections, and detailed assessments for individual glaciers, and explain how recent advances now allow including ice dynamics when modeling glaciers at larger spatial scales. Finally, we provide concrete recommendations concerning the steps and factors to be considered when modeling the evolution of glaciers. We suggest paying particular attention to the model initialization, analyzing how related uncertainties in model input influence the modeled glacier evolution and strongly recommend evaluating the simulated glacier evolution against independent data.
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Mountain glaciers have response times that govern retreat due to anthropogenic climate change. We use geometric attributes to estimate individual response times for 383 glaciers in the Cascade mountain range of Washington State, USA. Approximately 90% of estimated response times are between 10 and 60 years, with many large glaciers on the short end of this distribution. A simple model of glacier dynamics shows that this range of response times entails consequential differences in recent and ongoing glacier changes: glaciers with decadal response times have nearly kept pace with anthropogenic warming, but those with multi-decadal response times are far from equilibrium, and their additional committed retreat stands well beyond natural variability. These differences have implications for changes in glacier runoff. A simple calculation highlights that transient peaks in area-integrated melt, either at the onset of forcing or due to variations in forcing, depend on the glacier's response time and degree of disequilibrium. We conclude that differences in individual response times should be considered when assessing the state of a population of glaciers and modeling their future response. These differences in response can arise simply from a range of different glacier geometries, and the same basic principles can be expected in other regions as well.
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Since the mid-1980s, glaciers in the European Alps have shown widespread and accelerating mass losses. This article presents glacier-specific changes in surface elevation, volume and mass balance for all glaciers in the Swiss Alps from 1980 to 2010. Together with glacier outlines from the 1973 inventory, the DHM25 Level 1 Digital Elevation Models (DEMs) for which the source data over glacierized areas was acquired from 1961 to 1991 are compared to the swissALTI3D DEMs from 2008–2011 combined with the new Swiss Glacier Inventory SGI2010. Due to the significant differences in acquisition date of the source data used, resulting mass changes are temporally homogenized to directly compare individual glaciers or glacierized catchments. Along with an in-depth accuracy assessment, results are validated against volume changes from independent photogrammetrically derived DEMs of single glaciers. Observed volume changes are largest between 2700–2800 m a.s.l. and remarkable even above 3500 m a.s.l. The mean geodetic mass balance is −0.62 ± 0.03 m w.e. yr−1 for the entire Swiss Alps over the reference period 1980–2010. For the main hydrological catchments, it ranges from −0.52 to −1.07 m w.e. yr−1. The overall volume loss calculated from the DEM differencing is −22.51 ± 0.97 km3.
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Since the mid-1980s, glaciers in the European Alps have shown widespread and accelerating mass losses. This article presents glacier-specific changes in surface elevation, volume and mass balance for all glaciers in the Swiss Alps from 1980 to 2010. Together with glacier outlines from the 1973 inventory, the DHM25 Level 1 Digital Elevation Models (DEMs) for which the source data over glacierized areas was acquired from 1961 to 1991 are compared to the swissALTI3D DEMs from 2008– 2011 combined with the new Swiss Glacier Inventory SGI2010. Due to the significant differences in acquisition date of the source data used, resulting mass changes are temporally homogenized to directly compare individual glaciers or glacierized catchments. Along with an in-depth accuracy assessment, results are validated against volume changes from independent photogrammetrically derived DEMs of single glaciers. Observed volume changes are largest between 2700–2800 m a.s.l. and remarkable even above 3500 m a.s.l. The mean geodetic mass balance is –0.62±0.03 m w.e. yr–1 for the entire Swiss Alps over the reference period 1980–2010. For the main hydrological catchments, it ranges from –0.52 m w.e. yr–1 to –1.07 m w.e. yr–1. The overall volume loss calculated from the DEM differencing is –22.51±0.97 km3.
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Mountain glaciers sample a combination of climate parameters - temperature, precipitation and radiation - by their rate of volume accumulation and loss. Flow dynamics acts as transfer function which maps volume changes to a length response of the glacier terminus. Long histories of terminus positions have been assembled for several glaciers in the Alps. Here I analyze terminus position histories from an ensemble of seven glaciers in the Alps with a macroscopic model of glacier dynamics to derive a history of glacier equilibrium line altitude (ELA) for the time span 400-2010 C.E. The resulting climatic reconstruction depends only on records of glacier variations. The reconstructed ELA history is similar to recent reconstructions of Alpine summer temperature and Atlantic Meridional Oscillation (AMO) index. Most reconstructed low-ELA periods coincide with large explosive volcano eruptions, hinting to mass balance reduction by volcanic radiative cooling. The glacier advances during the LIA, and the retreat after 1860 are thus explained by temperature and volcanic cooling alone.
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We have reconstructed the ice thickness distribution of the Morteratsch glacier complex, Switzerland, and used this to simulate its flow with a higher-order 3-D model. Ice thickness was measured along transects with a ground-penetrating radar and further extended over the entire glacier using the plastic flow assumption and a distance-weighted interpolation technique. We find a maximum ice thickness of 350±52.5 m for the central trunk of Vadret da Morteratsch, resulting from a bedrock overdeepening. The average thickness of the glacier complex is 72.2±18.0 m, which corresponds to a total ice volume of 1.14±0.28 km3. The flow of the glacier is modelled by tuning the rate factor and the sliding parameters taking into account higher-order terms in the force balance. The observed velocities can be reproduced closely (root-mean-square error of 15.0 m a–1, R 2 = 0.93) by adopting a sliding factor of 12 × 10–16 m7 N–3 a–1 and a rate factor of 1.6 × 10–16 Pa–3 a–1. In this setting, ice deformation accounts for 70% of the surface velocity and basal sliding for the remaining 30%. The modelled velocity field reaches values up to 125 m a–1, but also indicates an almost stagnant front and confluence area, which are crucial for understanding the ongoing glacier retreat.
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We present estimates of sea-level change caused by the global surface mass balance of glaciers, based on the reconstruction and projection of the surface mass balance of all the individual glaciers of the world, excluding the ice sheets in Greenland and Antarctica. The model is validated using a leave-one-glacier-out cross-validation scheme against 3997 observed surface mass balances of 255 glaciers, and against 756 geodetically observed, temporally integrated volume and surface area changes of 341 glaciers. When forced with observed monthly precipitation and temperature data, the glaciers of the world are reconstructed to have lost mass corresponding to 114 ± 5 mm sea-level equivalent (SLE) between 1902 and 2009. Using projected temperature and precipitation anomalies from 15 coupled general circulation models from the Coupled Model Intercomparison Project phase 5 (CMIP5) ensemble, they are projected to lose an additional 148 ± 35 mm SLE (scenario RCP26), 166 ± 42 mm SLE (scenario RCP45), 175 ± 40 mm SLE (scenario RCP60), or 217 ± 47 mm SLE (scenario RCP85) during the 21st century. Based on the extended RCP scenarios, glaciers are projected to approach a new equilibrium towards the end of the 23rd century, after having lost either 248 ± 66 mm SLE (scenario RCP26), 313 ± 50 mm SLE (scenario RCP45), or 424 ± 46 mm SLE (scenario RCP85). Up until approximately 2100, ensemble uncertainty within each scenario is the biggest source of uncertainty for the future glacier mass loss; after that, the difference between the scenarios takes over as the biggest source of uncertainty. Ice mass loss rates are projected to peak 2040 ∼ 2050 (RCP26), 2050 ∼ 2060 (RCP45), 2070 ∼ 2090 (RCP60), or 2070 ∼ 2100 (RCP85).
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A large component of present-day sea-level rise is due to the melt of glaciers other than the ice sheets. Recent projections of their contribution to global sea-level rise for the twenty-first century range between 70 and 180 mm, but bear significant uncertainty due to poor glacier inventory and lack of hypsometric data. Here, we aim to update the projections and improve quantification of their uncertainties by using a recently released global inventory containing outlines of almost every glacier in the world. We model volume change for each glacier in response to transient spatially-differentiated temperature and precipitation projections from 14 global climate models with two emission scenarios (RCP4.5 and RCP8.5) prepared for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. The multi-model mean suggests sea-level rise of 155 ± 41 mm (RCP4.5) and 216 ± 44 mm (RCP8.5) over the period 2006–2100, reducing the current global glacier volume by 29 or 41 %. The largest contributors to projected global volume loss are the glaciers in the Canadian and Russian Arctic, Alaska, and glaciers peripheral to the Antarctic and Greenland ice sheets. Although small contributors to global volume loss, glaciers in Central Europe, low-latitude South America, Caucasus, North Asia, and Western Canada and US are projected to lose more than 80 % of their volume by 2100. However, large uncertainties in the projections remain due to the choice of global climate model and emission scenario. With a series of sensitivity tests we quantify additional uncertainties due to the calibration of our model with sparsely observed glacier mass changes. This gives an upper bound for the uncertainty range of ±84 mm sea-level rise by 2100 for each projection.
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Significance The end of the Little Ice Age in the European Alps has long been a paradox to glaciology and climatology. Glaciers in the Alps began to retreat abruptly in the mid-19th century, but reconstructions of temperature and precipitation indicate that glaciers should have instead advanced into the 20th century. We observe that industrial black carbon in snow began to increase markedly in the mid-19th century and show with simulations that the associated increases in absorbed sunlight by black carbon in snow and snowmelt were of sufficient magnitude to cause this scale of glacier retreat. This hypothesis offers a physically based explanation for the glacier retreat that maintains consistency with the temperature and precipitation reconstructions.
Polycrystalline blocks of ice have been tested under compressive stresses in the range from 1 to 10 bars at temperatures from -13 degrees C to the melting-point. Under these conditions ice creeps in a manner similar to that shown by metals at high temperatures; there is a transient creep component and also a continuing or quasi-viscous component. The relation between the minimum observed flow rate $\dot{\epsilon}$, the applied stress $\sigma $ and the absolute temperature T is $\dot{\epsilon}$ = B exp (-Q/RT) $\sigma ^{n}$, where R is the gas constant, and B, n and Q are constants; the value of n is about 3$\cdot $2, that of Q is 32 kcal/mole, and that of B is 7 $\times $ 10$^{24}$ if the stress is measured in bars and the strain rate in years$^{-1}$. At the higher stresses a third, accelerating stage of creep was observed; on the basis of the appearance and behaviour of sections cut from the specimens, this acceleration was attributed to recrystallization. The effect of changing the load during a test has also been studied; for large reductions creep recovery was observed. The results of these tests are discussed in connexion with previous work on metals and ice, and also with measurements of glacier flow.
In this paper we reconstruct the space–time trajectory beneath the surface of Aletschgletscher, Switzerland, of the corpses of three mountaineers that disappeared in March 1926 and reappeared at the glacier surface in June 2012. Our method integrates the time-dependent velocity field of an existing full-Stokes glacier model, starting at the point where the corpses were found at the glacier surface. Our main result is that we were able to localize the immersion location where the brothers presumably died. As a second result, the upstream end point of the computed trajectory emerges very close to the glacier surface in 1926, giving a new and global validation of the glacier model in space and time. Testing the sensitivity of the immersion location obtained with respect to the model and other uncertainties indicates an area of 0.6% of the entire glacier area where the accident could have occurred. Our result suggests that death was not caused by an avalanche or a fall into a crevasse; instead, it is likely that the mountaineers became disoriented in prolonged severe weather conditions and froze to death.
We estimate temperature sensitivity of observed mass balance for glaciers in the European Alps to compare with our earlier estimates from modelling. We treat 1961–90 as our reference period and compare mass balance for 1991–2010 with this reference period. There are eight Alpine glaciers with long enough records. The mean mass balance for the eight glaciers is close to zero for the reference period, very negative for 1991–2010 and highly negative in the exceptionally warm year 2003. Mass-balance changes are compared with 1991–2010 temperature anomalies to give an average temperature sensitivity of approximately –0.7 AE 0.2 m w.e.a–1 K–1 for the eight glaciers. There is considerable variation between individual glaciers, with higher sensitivity for western glaciers and lower sensitivity for eastern glaciers. Temperature sensitivity for the eight glaciers is strongly correlated with the standard deviation of observed mass balance, which from earlier work is known to be correlated with winter balance. The mean temperature sensitivity for observed mass balance is in reasonable agreement with values from earlier models, but changes in glacier hypsometry during 1991–2010 may have further increased observed mass loss.