Modelling the feedbacks between debris transport, ice flow and mass balance to predict the response to climate change of debris-covered glaciers in the Himalaya Ann V. Rowan 1 , Duncan J. Quincey 2 , David L. Egholm 3 , Neil F. Glasser 4 1 Department of Geography, University of Sheffield, Sheffield, S10 2TN, UK 2 School of Geography, University of Leeds, Leeds, LS2 9JT, UK 3 Department of Geoscience, Aarhus University, Aarhus C, Denmark. 4 Department of Geography and Earth Sciences, Aberystwyth University, Aberystwyth, SY23 3DB, UK Keywords: supraglacial debris; glacier dynamics; glacier modelling, Khumbu Glacier 1 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17
Transcript
Modelling the feedbacks between debris transport, ice flow and mass
balance to predict the response to climate change of debris-covered glaciers
in the Himalaya
Ann V. Rowan1, Duncan J. Quincey2, David L. Egholm3, Neil F. Glasser4
1Department of Geography, University of Sheffield, Sheffield, S10 2TN, UK2School of Geography, University of Leeds, Leeds, LS2 9JT, UK3Department of Geoscience, Aarhus University, Aarhus C, Denmark.4Department of Geography and Earth Sciences, Aberystwyth University, Aberystwyth, SY23
Many Himalayan glaciers are characterised in their lower reaches by surface debris cover,
which insulates the glacier surface from atmospheric warming and complicates the response
to climate change compared to glaciers with clean-ice surfaces. Debris-covered glaciers can
persist well below the altitude that would be sustainable for a clean-ice glacier, resulting in
much longer timescales of mass loss and meltwater production. The properties and evolution
of this supraglacial debris present a considerable challenge to understanding future glacier
change. Existing approaches to predicting variations in glacier volume and meltwater
production rely on numerical models that represent the processes governing glaciers with
clean-ice surfaces, and yield conflicting results. We developed a new numerical model that
couples the flow of ice and debris and includes important feedbacks between debris
accumulation and glacier mass-balance. To investigate the impact of debris transport on the
response of a glacier to recent and future climate change, we applied this model to an
excellent example of a large debris-covered Himalayan glacier—Khumbu Glacier in Nepal.
Our results demonstrate that supraglacial debris cover prolongs the response of the glacier to
warming and causes lowering of the glacier surface in situ, concealing the magnitude of mass
loss when compared with estimates based on glacierised area. Since the Little Ice Age,
Khumbu Glacier has lost 34% of its volume while its area has reduced by only 6%. We
predict a decrease in glacier volume of 8–10% by AD2100, and detachment of the debris-
covered tongue from the dynamic glacier within the next 150 years, which is likely to further
accelerate rates of glacier decay, and we would expect similar behaviour from other debris-
covered glaciers in the Himalaya.
1. Introduction
Glaciers in the Himalaya are rapidly losing mass (Bolch et al., 2012). However, data to
validate estimates of past, present and future glacier volumes are scarce, resulting in varying
estimates and predictions of glacier change (Cogley, 2011; Kääb et al., 2011). To improve
predictions of how Himalayan glaciers will decline through the 21st Century and the impact
on Asian water resources, we need to quantify the processes that drive glacier change
(Immerzeel et al., 2013; Pellicciotti et al., 2015; Ragettli et al., 2015). Changes in glacier
volume are driven by climate variations, specifically atmospheric warming and precipitation
variability, and modified by mass balance and ice flow (Bolch et al., 2012; Kääb et al., 2011;
Scherler et al., 2011). Clean-ice glaciers lose mass rapidly with atmospheric warming by
shrinking back to steeper hillslopes where they are fed by avalanching and can maintain an
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approximate equilibrium with climate. Debris-covered glaciers respond more slowly to
atmospheric warming because supraglacial debris insulates the ice surface and modifies ice
flow (Kirkbride and Deline, 2013; Pellicciotti et al., 2015; Østrem, 1959) (Fig. 1a). Debris-
covered glaciers lose mass by surface lowering rather than terminus recession (Hambrey et
al., 2008; Pellicciotti et al., 2015), and can persist at lower elevations than would be possible
for an equivalent clean-ice glacier (Anderson, 2000; Benn et al., 2012) even when
dramatically out of equilibrium with climate. As glaciers lose mass preferentially from areas
of clean ice, the debris-covered proportion of Himalayan glaciers will increase as glaciers
shrink (Bolch et al., 2008; Kirkbride and Deline, 2013; Thakuri et al., 2014). Therefore, the
future of the Himalayan cryosphere and Asian water resources depends on the impacts of
climate change on debris-covered glaciers.
The debris on glacier tongues is derived from surrounding hillslopes, transported englacially,
and resurfaces in the ablation zone (Fig. 1d). If the glacier develops a negative mass balance
then velocities decline and debris thickness at the ice surface increases (Fig. 1e). Additional
debris accumulates on the glacier surface from the collapse of hillslopes and moraine ridges
that become oversteepened as the glacier shrinks. From field observations of glaciers
worldwide, thin rock debris is known to enhance ablation of the glacier surface by reducing
albedo, and thick rock debris reduces ablation by insulating the glacier surface where
thickness exceeds 0.03 m (Fyffe et al., 2014; Mihalcea et al., 2008; Nicholson and Benn,
2006; Østrem, 1959). Debris layers on glaciers constrained by moraines are likely to thicken
over time (Kirkbride and Deline, 2013) (Fig. 1e), and spatial heterogeneity in debris thickness
results in differential ablation and the formation and decay of ice cliffs and supraglacial
ponds that enhance ablation locally (Reid and Brock, 2014). An outstanding challenge to
understanding the behaviour of debris-covered glaciers lies in quantifying the highly variable
distribution of debris across the glacier surface and between glaciers. Supraglacial debris
distribution and thickness are difficult to determine remotely and laborious to measure
directly (e.g. Mihalcea et al., 2008; Nicholson and Benn, 2006; Reid et al., 2012; Rounce and
McKinney, 2014), particularly over an area that is representative of more than one individual
glacier (Pellicciotti et al., 2015). A further challenge to predicting response of debris-covered
glaciers to climate change requires understanding not only the distribution of debris on a
glacier surface at present but also how this has varied in the past and will vary in the future.
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In the Himalaya, 14–18% of the total glacierised area is debris-covered (Kääb et al., 2011)
increasing to about 36% in the Everest region of Nepal where some of the longest debris-
covered glacier tongues in the world are found (Nuimura et al., 2012; Thakuri et al., 2014).
Where debris cover on an individual glacier exceeds 40% of the total area (Scherler et al.,
2011) mass loss is mainly by stagnation rather than recession (which requires a loss of mass
whilst maintaining flow towards the migrating terminus) (Immerzeel et al., 2013; Quincey et
al., 2009; Scherler et al., 2011), despite the reduction of the accumulation area relative to the
total glacier area (Anderson, 2000). For individual glaciers in the Himalaya, over 50% of the
glacier area is often debris covered (Ragettli et al., 2015) and this debris is generally
sufficiently thick to reduce rather than enhance ablation (Benn et al., 2012; Bolch et al., 2008;
Nicholson and Benn, 2006; Quincey et al., 2009). Moreover, where debris is thin in the upper
part of the ablation zones the effect on ablation is minimal, as the daytime air temperatures
are above zero and humidity is high (Inoue and Yoshida, 1980). The total glacierised area of
the Himalaya is dominated by a small number of large glaciers. In the Dudh Koshi Basin in
the Everest region, 70% of the glacierised area is comprised of just 40 of 278 glaciers, and
these large glaciers are generally debris covered (Thakuri et al., 2014). Since the Little Ice
Age (LIA; 0.5 ka) when glaciers in the Everest region last advanced (Owen et al., 2009;
Richards et al., 2000), these glaciers have developed a negative mass balance resulting in
overall mass loss (Kääb et al., 2011; Nuimura et al., 2012). Between 1962 and 2011, the
proportion of Everest region glaciers covered by rock debris increased has doubled (Thakuri
et al., 2014).
The future of debris-covered glaciers worldwide is uncertain due to the limitations of our
knowledge about the distribution of surface debris on glaciers at present and how this evolves
over time. Existing glacier models designed for clean-ice glaciers or static assumptions about
surface debris layers that describe only the present state of the glacier are difficult to
extrapolate under a changing climate. Here, we use a novel glacier model that includes the
self-consistent development of englacial and supraglacial debris and reproduces the
feedbacks among mass-balance, ice-flow and debris accumulation, to investigate how debris
modifies the behaviour of a large Himalayan glacier in response to climate change. As an
example of how many large debris-covered Himalayan glaciers respond to climate change,
we applied this model to Khumbu Glacier in the Everest region of Nepal over the period from
the Late Holocene (1 ka) through the present day to AD2200.
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2. Khumbu Glacier, Nepal
Khumbu Glacier is one of the largest debris-covered glaciers in the Everest region. The total
length of Khumbu Glacier is 15.7 km and the area is 26.5 km2. The Changri Nup and Changri
Shar Glaciers were tributaries of Khumbu Glacier during the LIA but have since detached
and have a combined area of 12.3 km2 (Fig. 2). The equilibrium line altitude (ELA) of
Khumbu Glacier estimated from mass balance measurements made in 1974 and 1976 is 5600
m, and located at the base of the icefall (Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue and
Yoshida, 1980) that links the accumulation area in the Western Cwm to the glacier tongue
(Fig. 1b). Atmospheric warming of about 0.9°C over the last 20 years (1994–2013) (Salerno
et al., 2014) has probably raised the ELA a further several hundred metres. The active part of
the glacier (the area exhibiting ice flow) has receded towards the base of the icefall since the
end of the LIA while the total glacier length has remained stable. Feature-tracking
observations of velocities define the length of the active glacier as 10.3 km (62% of the LIA
glacier length) (Fig. 2), and decaying ice at the terminus beneath debris several metres thick
indicates terminus recession of less than 1 km since the LIA (Bajracharya et al., 2014). We
therefore divide Khumbu Glacier into two parts based on observations of glacier dynamics;
(1) the active glacier where velocities range from 10 m to 70 m per year and the ice mass is
replenished from the accumulation zone, and (2) the decaying tongue that no longer exhibits
ice flow of more than a few metres per year. Similar behaviour is reproduced by our glacier
model and observed for many large glaciers in the Everest region (Quincey et al., 2009).
3. Methods
3.1 Bed topography
Measurements of ice thickness at Khumbu Glacier from previous studies used radio-echo
sounding (Gades et al., 2000) and gravity observations (Moribayashi, 1978). Ice thickness
measured along seven transects (Fig. 3) down-glacier from the icefall using radio-echo
sounding was 440 ± 20 m at 0.5 km below the icefall close to Everest Base Camp, decreasing
to less than 20 m at 4930 m at 2 km up-glacier of the terminus, although the latter value was
presented with some uncertainty (Gades et al., 2000). Results from gravity observations gave
an ice thickness of 110 m adjacent to Lobuche and 440 m adjacent to Gorak Shep
(Moribayashi, 1978). We estimated the thickness (h) of Khumbu Glacier and the Changri
Nup and Changri Shar tributaries at 35 regularly spaced transects perpendicular to the central
flowline of each glacier using the ASTER GDEM v2 Digital Elevation Model (DEM), the
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GLIMS outline for these glaciers (GLIMS et al., 2005) and an approximation of basal shear
stress (τb):
h = λ * (τb / f * ρ * g * sin(α))
where ρ is the density of glacier ice, g is acceleration due to gravity, and α is the slope of the
glacier surface derived from the DEM. The value used for τb was 150 kPa. We included a
variable shapefactor (f) to describe the aspect ratio of the cross-section of a valley glacier
following the method of Nye (1952), and a down-glacier thinning factor (λ) to describe the
long profile of the glacier:
λ = 1 – a * xb
where a is a constant accounting for the length of the glacier, x is the flowline distance from
the headwall and b describes where thinning first occurs along the flowline. Values for the
shapefactor and the down-glacier thinning factor were determined by empirical testing
against geophysical measurements. The ice thickness transects were interpolated within the
GLIMS outline to estimate ice thickness across the glacier. The model domain subglacial
bedrock topography was described by subtracting the estimated ice thickness from the DEM
then smoothing and resampling to 100-m grid spacing.
3.2 Glacier topography
The Little Ice Age surface of Khumbu Glacier was reconstructed from the elevation of lateral
and terminal moraine crests, which are well preserved close to the glacier (Fig. 1a). Long
profiles (Fig. 1b and 1c) were measured using a DEM with a 10-m grid spacing generated
from ALOS PRISM imagery acquired in 2006. Present-day glacier topography was
calculated perpendicular to the central flowline of the glacier by taking the mean of a 200-m
wide moving window over the centre of the glacier, and over the LIA lateral moraine by
taking the maximum of a 300-m wide moving window centered on the moraine crest. The
elevation of the lateral moraine crest was verified using a Garmin GPSmap 62s handheld unit
(Fig 1c).
3.3 Glacier dynamics
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Glacier velocities (i.e. surface displacements) were calculated using a Fourier-based cross-
correlation feature tracking method (Luckman et al., 2007). The images were first co-
registered with sub-pixel accuracy using large feature (128 x 128 pixels; 1920 m square) and
search (256 x 256 pixels; 3840 m square) windows focusing on non-glacierised areas. Glacier
displacements were then calculated using much finer feature and search windows of 48 x 48
pixels (720 m square) and 64 x 64 pixels (960 m square) respectively. Sufficiently robust
correlations were accepted on the strength of their signal-to-noise ratio (> 7.0) and matches
above an extreme threshold of 100 m a-1 were removed as blunders. The remaining
displacements were converted to annual velocities assuming no seasonal variability in flow.
Errors in the velocity data comprise mismatches associated with changing surface features
between images, and any inaccuracy in the image co-registration. Given that the glacier is
slow-flowing (and thus features do not change rapidly), and that the images were co-
registered to a fraction of a pixel, we estimate a maximum theoretical error of one pixel per
year (i.e. 15 m). Empirically measured displacements in stationary areas adjacent to the
glacier suggest the real error is around half this (i.e. 7–8 m a-1).
3.4 Numerical modelling of debris-covered glaciers
We used the ice model iSOSIA (Egholm et al., 2011) with a novel description of debris
transport that represented the self-consistent development of englacial and supraglacial debris
and reproduced the feedbacks amongst mass-balance, ice-flow and debris accumulation.
Debris was added to the glacier surface in the accumulation zone and transported through the
ice. When englacial debris reached the ablation zone, it emerged to form a debris layer that
was either transported off-glacier or thickened over time (Fig. 1d and e). Ablation beneath
supraglacial debris was calculated using an exponential function that gave a halving of
ablation beneath 0.5 m of debris and assuming minimal ablation beneath a debris layer with a
thickness exceeding 1.0 m, in line with values calculated for Ngozumpa Glacier (Nicholson
and Benn, 2006).
Transport of debris within and on top of the glacier was modelled as an advection problem
assuming that the ice passively transports the debris. Internal ice deformation and basal
sliding drive ice flow in iSOSIA and the depth-averaged flow velocity is therefore
u=ud+ub
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The velocity due to ice deformation, ud , is approximated as a tenth-order polynomial function
of ice thickness with coefficients that depend on ice surface slope and bed slope as well as
longitudinal stress and stress gradients (Egholm et al., 2011).
Basal sliding is assumed to scale with the basal shear stress according to the following
empirical sliding model (Bindschadler, 1983):
ub=B s τb
m
N e
where τ b is the basal shear stress, N e is the effective pressure at the bed, and Bs=4 × 10−4 m
y-1 Pa-1 and m=2 are constants.
The debris concentration, c, at any point within the ice was updated through time, t, using the
following equation:
∂ c∂ t
=−∇ ∙ {cu }
where u is the three-dimensional ice velocity vector. As a boundary condition to this
equation, we assumed that debris is fed to the surface of the glacier in the accumulation zone
and that csa=0.001 (the concentration of debris at the ice surface) is constant across the
accumulation area.
The debris transport was modelled using a three-dimensional grid. iSOSIA is a depth-
integrated 2D model, but for the purpose of tracking the three-dimensional debris transport,
the thickness of the ice was divided into 20 layers representing the vertical dimensional of the
3D grid structure. iSOSIA only computes depth-averaged velocity components. However, in
order to capture velocity variations at depth within the ice, we assumed that the horizontal ice
velocity caused by viscous ice deformation decays as a fourth-order polynomial down
through the ice, which is a standard assumption for most shallow ice approximations. We
calibrated the fourth-order polynomial to yield the correct depth-averaged velocity:
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u ( z )=54 [1−( z
h )4]u+ub
where u is the depth-averaged horizontal velocity and ub is basal sliding velocity. z is burial
depth below the ice surface and h is ice thickness. The internal vertical component of the ice
velocity, uv, was scaled linearly with accumulation/ablation at the surface (ms ¿and melting at
the glacier bed (mb ¿:
uv ( z )=h−zh
ms+zh
mb
The advection equation was integrated through time using explicit time stepping in
combination with a three-dimensional upwind finite difference scheme.
3.5 Experimental design
Simulations were made for the Khumbu Glacier catchment upstream of the base of the LIA
terminal moraine. Present-day (AD2000) mass balance was calculated across the catchment
and described by assuming linear temperature-dependent rates of accumulation and ablation
following those measured in 1974 and 1976 (Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue
and Yoshida, 1980), and an atmospheric lapse rate of –0.004°C m-1 calculated with a linear
regression of MODIS Terra Land Surface Temperature data covering the period 24/02/00 to
31/12/06 (NASA, 2001) for the Central Himalayan region. Extreme topography in the
Himalaya results in the majority of glacier mass gain by avalanching rather than direct
snowfall, and the avalanche contribution to the mass balance of Khumbu Glacier has been
estimated as 75% (Benn and Lehmkuhl, 2000). We removed snow and ice mass from slopes
exceeding 28° and increased accumulation on the glacier surface accordingly.
3.5.1 Initial Late Holocene simulation
Prior to the LIA maximum (0.5 ka), Khumbu Glacier had a slightly greater extent during the
Late Holocene (~1 ka) (Owen et al., 2009) and is likely to have reached the LIA extent by the
formation of large moraines that enclosed the LIA glacier and drove the ice mass to become
less extensive but thicker. Supraglacial debris thickened due to the reduction in debris export
to these moraines and the reduction in velocities promoted by warming temperatures and the
feedback with reduced ablation. As a starting point for our transient simulations of Khumbu
Glacier, we reconstructed the Late Holocene glacier from an ice-free domain using an ELA
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of 5325 m and an atmospheric lapse rate of –0.004°C m-1 over a 5000-year period (Fig. 4).
Minor recession between the LIA and Late Holocene maxima was imposed as an increase in
ELA of 50 m to 5375 m over 500 years.
3.5.2 Simulations of glacier change from the LIA to the present day
To simulate the LIA advance, maximum and recession, a slight recession was imposed
between the Late Holocene and the LIA maxima, equivalent to a rise in ELA of 50 m. The
ELA was then increased from 5375 m to 6000 m over 500 years with ablation adjusted as
described above in line with the development of supraglacial debris. The simulated ice
thicknesses were compared to the extent and thickness indicated by the LIA moraines and the
present-day glacier. This simulation was run to steady state to indicate how the glacier would
continue to change from the present day without a further change in climate. The response
time of Khumbu Glacier to reach equilibrium with the present-day ELA from the LIA was
1150 years, 500 years longer than the time elapsed between the LIA maximum and the
present day. 3.5.3 Simulations of glacier change from the present day to AD2200
Simulations of glacier change from the present day until AD2200 continued from the present-
day simulation where the glacier was out of balance with climate. We imposed a linear rise in
ELA over 100 years from AD2000 to AD2100 equivalent to predicted minimum and
maximum warming relative to 1986–2005 of 0.9°C and 1.6°C by 2080–2099 in line with
IPCC model ensemble predictions for this period (CMIP5 RCP 4.5 scenario) (Collins et al.,
2013). This simulation continued until AD2200 without any further change in climate to
investigate the continuing adjustment of the glacier over the following century.
4. Results
4.1 Glacier morphology and mass balance
Reconstruction of Khumbu Glacier using lateral and terminal moraine crests showed that
since the LIA, glacier area has decreased from 28.1 km2 to 26.5 km2 (a reduction of 6%). If
the glacier is considered only in terms of the measured active ice, then glacier area has
declined to 20.3 km2 (a reduction of 28%) (Fig. 2). These values exclude the change in
glacier area attributed to the dislocation of the Changri Nup and Changri Shar Glaciers that
were tributaries of Khumbu Glacier but detached after the LIA maximum (Fig. 2). The
volume of the currently active glacier is 1.7 x 109 m3 (50% of the LIA volume). The lack of
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dynamic behaviour in the tongue can be observed from the relict landslide material on the
true left of the glacier that has not moved between 2003 and 2014 (Fig. 1a).
Surface lowering between the LIA and the present day was greatest between 1.8 km and 3.2
km upglacier from the terminal moraine. Comparison of swath topographic profiles of the
glacier surface and the LIA lateral moraine crests (Fig. 1c) indicated mean surface lowering
across the debris-covered tongue of 25.5 ± 10.6 m, or 0.05 ± 0.02 m per year over 500 years
since the LIA. Over the same period, glacier volume decreased from 3.4 x 109 m3 to 2.3 x 109
m3 (66% of the LIA volume), a loss of 1.2 x 109 m3 and equivalent to 2.3 x 106 m3 per year.
Mean surface lowering observed between 1970 and 2007 across the ablation area was 13.9 ±
2.5 m (Bolch et al., 2011) suggesting that rates of mass loss have accelerated over the last 50
years compared to the last 500 years and consistent with the observed decrease in the active
glacier area (Quincey et al., 2009).
Using different methods, the ELA of Khumbu Glacier could be placed in a range from 5200
m to 5580 m by assuming that the integrated mass balance is zero (Benn and Lehmkuhl,
2000) (Fig. 5). Mass balance measurements made in 1974 and 1976 estimated an ELA of
5600 m and rates of accumulation and ablation between 2.0 m and –2.0 m water equivalent
(w.e.) per year (Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue and Yoshida, 1980).
Simulations using the lower range of ELA and assuming a net mass balance of zero produced
a glacier equivalent to the Late Holocene extent. Simulations of the present-day glacier
indicate that the ELA is likely to be several hundred meters higher between 5800 m and 6000
m (Fig. 5). However, methods for calculating ELA such as the accumulation-area ratio
(AAR) are difficult to apply to avalanche-fed, debris-covered glaciers for which AAR values
appear to be lower (around 0.1–0.4) than those for clean-ice glaciers (Anderson, 2000;
Banerjee and Shankar, 2014). Moreover, snowline altitude is not a reliable indicator of ELA
in high mountain environments, as avalanching, debris cover and high relief affect mass
balance such that ELA may differ by several hundred meters from the mean snowline (Benn
and Lehmkuhl, 2000). The range of ELA values calculated by previous studies and simulated
in this study for Khumbu Glacier (Benn and Lehmkuhl, 2000; Inoue, 1977; Inoue and
Yoshida, 1980) all fall within the vertical extent of the icefall (Fig. 5).
4.2 Glacier modelling
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The initial simulation representing the Late Holocene maximum, indicated by lateral and
terminal moraines located to the outside of the LIA moraines (Owen et al., 2009), was
computed from the ice-free domain using an ELA of 5325 m, equivalent to cooling of 2.7°C
relative to the present day over a 5000-year period until the glacier attained steady state.
During this period, debris accumulated within the glacier but was exported to form the
extensive Late Holocene moraines (Fig. 4b). A small amount of recession after the Late
Holocene maximum was forced with a 50 m increase in ELA over a 500-year period, and
followed by a transient simulation through the LIA to the present day, then a further rise in
ELA to simulate warming to AD2100 and through the following century.
4.2.1 The Little Ice Age to the present day
Recession from the LIA to the present day was simulated by imposing a rise in ELA from
5375 m to 6000 m. Khumbu Glacier initially advanced to the LIA maximum for 150 years
despite the rise in ELA as decreasing velocity in the tongue (Table 1) resulted in thickening
supraglacial debris (Fig. 6e) leading to mass loss by lowering of the glacier surface
accompanied by minimal recession of the terminus (Fig 6b and Table 1). Prior to this, the
expanding glacier efficiently transported debris to the ice margins where the effect on
ablation was minimal (Fig. 6d). The large LIA moraines suggest that debris export from the
glacier to the ice margins declined because the glacier was impounded following the
construction of these moraines. The simulation from the LIA to the present day reproduced
this observation and resulted in the formation of a thick debris layer (Fig. 6b and 6d). The
simulated glacier surface was compared to the extent and elevation of the lateral and terminal
LIA moraines (Fig. 6a and 6e). After the LIA maximum, and despite the reduction in ablation
beneath supraglacial debris, the simulated glacier lost mass by surface lowering that produced
minor recession at the terminus. The glacier simulated 500 years after LIA maximum was
compared to the extent and elevation of the present-day glacier surface (Fig. 6h). Simulated
present day velocities (Table 1 and Fig. 7) reproduced the pattern and the absolute values
measured (Fig. 2). The active part of the glacier shrunk to the observed active ice extent but
did not reach steady state.
The LIA maximum was followed by rapid mass loss for about 500 years, then a slower rate
of mass loss over the subsequent 1000 years until the glacier reached equilibrium with
present-day climate, indicating that Khumbu Glacier is out of balance with climate at present.
This simulation was run to steady state to calculate the glacier response to warming between
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the LIA and the present day with no further change in climate. Khumbu Glacier will continue
to respond to post-LIA warming until about AD2500 and will lose a further 0.4 x 10 9 km3
(18%) of ice without any further change in climate.
4.2.2 The present day to AD2200
To predict the volume of Khumbu Glacier at the end of the 21 st and 22nd Centuries, we
imposed a linear rise in ELA from the present day over 100 years in line with IPCC warming
scenarios for AD2100 (Collins et al., 2013). Simulations of future glacier change under IPCC
minimum and maximum warming scenarios for AD2100 were driven by an increase in ELA
of 225 m to 6225 m (equivalent to warming of 0.9°C) and 400 m to 6400 m (equivalent to
warming of 1.6°C) over a 100-year period. These simulations were allowed to continue
without a further change in climate until AD2200. Warming of 0.9°C will result in mass loss
of 0.17 x 109 km3 and warming of 1.6°C will result in mass loss of 0.21 x 109 km3 (Fig. 9a
and 9c) resulting in a decrease in the volume of Khumbu Glacier of between 8% and 10% by
AD2100 (Table 1). Simulated mass loss was greatest close to the base of the icefall, where
ablation exceeded that occurring further down-glacier beneath thicker supraglacial debris and
also up-glacier in the Western Cwm accumulation area. Furthermore, our results indicate that
the debris-covered tongue of Khumbu Glacier could physically detach at the base of the
icefall within 150 years and persist in situ while the active glacier recedes (Fig. 9b and 9d).
The surface debris layer will expand and thicken across the glacier tongue from the present
day, and will reach about 1.5 m thickness at the base of the icefall (Fig. 9e). After the
physical detachment of the debris-covered tongue from the active glacier, a debris layer will
start to develop on the tongue of the active glacier at the upper part of the icefall (Fig. 9f).
4.2.3 Comparison with simulations that do not transport debris
To verify the effect of supraglacial debris on glacier change, the LIA maximum and recession
were simulated; (1) without the modification of ablation beneath the debris layer, that is,
assuming that Khumbu Glacier has a clean rather than debris-covered surface, and (2) with
ablation reduced by 50% to compare the impact of a uniform reduction in ablation as is
sometimes used when clean-ice glacier models are applied to debris-covered glaciers. In both
experiments, mass loss from the clean-ice glacier exceeded that from the debris-covered
glacier, even with a reduction in ablation, and was accompanied by significant terminus
recession (Fig. 8). Our results highlight that debris-covered glaciers respond to climate
change less rapidly than clean-ice glaciers and that using models designed for clean-ice
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glaciers applied with a uniform modification of ablation rate does not reliably simulate the
evolution of a debris-covered glacier.
5. Discussion
We validated our glacier model simulations by comparison with observations of ice
thickness, velocities and mass balance measured for Khumbu Glacier. The agreement
between these observations and our simulations was generally good, and is discussed here
along with the uncertainties associated with the application of the glacier model.
5.1 Validation of glacier model simulations
We validated the LIA simulation by comparison of the simulated ice thickness with the
position of the glacier margins indicated by contemporary lateral and terminal moraines. The
LIA simulations were designed to give the best fit to Khumbu Glacier in each case, and
tended to under-fit the Changri Nup and Changri Shar Glaciers. The simulated LIA debris
distribution was comparable to the present day extent of supraglacial debris. We consider that
after the LIA, the supraglacial debris layer would have thickened due to exhumation of debris
by ablation resulting in some change in the extent of debris cover, which is represented in our
model. The addition of debris to the glacier surface by rock avalanching from the surrounding
hillslopes is not represented by our glacier model, but is unlikely to add large volumes of
debris across the whole glacier surface, particularly when velocities are low.
The present-day simulation was validated by comparison with observations of; (1) ice
thickness using measurements from geophysical surveys as described above, (2) velocities
measured using feature-tracking observations between 2013 and 2014 (Fig. 2), and (3) mean
surface elevation change and geodetic mass balance measured using multi-temporal digital
terrain models derived from satellite imagery (Bolch et al., 2011). Although there is excellent
agreement between estimated and simulated ice thicknesses, and measured and simulated
velocities and mass balance, there are differences in the estimated and simulated volume of
the present-day glacier due to differences in glacier extent. Furthermore, as there are no
measurements with which to constrain ice thickness in the accumulation area, this estimate of
ice thickness is based solely on the slope of the glacier surface. We consider the ice
thicknesses simulated using our model to be more accurate than those calculated using a
static assumption of basal shear stress as the glacier model represents the dynamics of mass
transfer. Calculation of bed topography beneath present-day glaciers and ice sheets remains
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an outstanding challenge in glaciology, and one that is difficult to resolve in the absence of
data describing the basal properties of the glacier.
5.1.1 Comparison of observed and simulated ice thickness
Maximum present-day ice thickness estimated using an approximation of basal shear stress
(Fig. 3) was 388 m and the mean flowline ice thickness was 168 m. The mean estimated ice
thickness along the flowline of Khumbu Glacier was 125 m in the accumulation area above
the base of the icefall and 190 m for the debris-covered tongue below the icefall. Simulated
ice thicknesses were in good agreement with these data, particularly in the ablation area (Fig.
6g and 6h). The maximum simulated present-day ice thickness was 345 m and the mean
flowline ice thickness was 168 m. The mean simulated ice thickness along the flowline of
Khumbu Glacier was 88 m in the accumulation area above the base of the icefall and 210 m
for the debris-covered tongue below the icefall.
5.1.2 Comparison of observed and simulated velocities
The simulated present-day maximum flowline velocity was 59 m per year and the mean was
9 m per year. The mean simulated velocity above the base of the icefall was 24 m per year,
and the mean velocity of the debris-covered tongue below the icefall was 2 m per year. These
simulated velocities are in good agreement with those measured using feature-tracking
observations between 2013 and 2014 (Fig. 2), which give a present-day maximum flowline
velocity of 67 m per year, and a mean of 16 m per year. The mean measured velocity above
the base of the icefall was 25 m per year, and the mean velocity of the debris-covered tongue
below the icefall was 9 m per year (although the latter value is within uncertainty due to the
15-m grid spacing of the imagery used for the feature-tracking measurements).
5.1.3 Comparison of observed and simulated mass balance
The decrease in the elevation of the simulated glacier surface over the 40 years prior to the
present day was close to zero at the terminus and increased to 8–10 m in the upper part of the
ablation area, showing good agreement both in terms of the absolute values and the
distribution of surface lowering to that observed from 1970 to 2007 (Bolch et al., 2011).
Integrated mass balance for the simulated present-day glacier was –0.22 m w.e. per year,
slightly lower than but not dissimilar to geodetic mass balance values estimated between
1970 and 2007 as of –0.27 ± 0.08 m w.e. per year (Bolch et al., 2011) and between 1992 and
2008 as –0.45 ± 0.52 m w.e. per year (Nuimura et al., 2012).
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5.3 Uncertainties associated with glacier modelling
We used a simple approach to represent the relationship between climate and mass balance,
to avoid introducing additional uncertainties to our simulations by making assumptions about
the response of meteorological parameters such as monsoon intensity to climate change.
Therefore, our results indicate the sensitivity and response of a large debris-covered
Himalayan glacier to climate change of the order of the Late Holocene period (1 ka to
present). We tested the sensitivity of Khumbu Glacier to mass balance parameter values
through the LIA maximum to the present day and the impact of these uncertainties on our
projections for AD2100. From the Late Holocene simulation, we used a range of present-day
ELA values between 5925 m and 6075 m. This 150 m variation in ELA resulted in a
difference in present day ice volume of 0.3 x 109 m3 (14% of present-day volume) with no
change in glacier length beyond the cellsize of the model domain (100 m). We tested a range
of atmospheric lapse rates from –0.003°C m-1 to –0.006°C m-1 maintaining the same ELA,
which resulted in a difference in ice volume of 0.4 x 109 m3 (19%) and no change in glacier
length. We tested a range of values for maximum accumulation and ablation that represented
an uncertainty in these values of ±10%, which resulted in a difference in present day ice
volume of 4.0 x 106 m3 (0.2%) with no change in glacier length. Finally we examined the
uncertainty in accumulation resulting from the application of a calculation to remove
snowfall from slopes susceptible to avalanching. A simulation using the same description of
mass balance as the present-day simulation that did not include a calculation for avalanching
and downslope distribution of snow on the glacier surface resulted in a much larger glacier
(4.9 x 109 m3; 227% of present-day volume) due to unrealistically high accumulation of snow
on steep slopes at high altitude. The simulated glacier extents were similar between these two
experiments indicating the importance of including the impact of avalanching on mass
balance when building numerical models of mountain glaciers.
We note that the simulated present-day ice thickness in the upper parts of the Changri Nup
and Changri Shar Glaciers is limited, suggesting both that the upper, clean-ice sections of
these glaciers have lost considerable volume since the LIA, but also that the mass balance
parameters used for Khumbu Glacier may not precisely represent the mass balance of these
tributaries. Although our numerical model captures the dynamics and hypsometry of
mountain glaciers, the interaction of high topography with atmospheric circulation systems
will affect mass balance and future studies could use energy balance modelling to capture
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these variables. However, energy balance modelling requires long-term meteorological data
knowledge of spatially variable parameters such as albedo, and reliable multi-annual
measurements of mass balance for verification. At present, these data are relatively scarce for
nearly all Himalayan glaciers, even those as well studied as Khumbu Glacier. Other factors
that are not captured by our model that may affect how glaciers respond to climate change
include; (1) the impact of atmospheric warming on the timing, phase and intensity of
monsoon precipitation (Salerno et al., 2014), (2) differential ablation across decaying debris-
covered glaciers driven by the formation and decay of ice cliffs and supraglacial ponds
(Immerzeel et al., 2013; Reid and Brock, 2014), and, (3) the physical properties of the debris
layer, particularly variations in water content and grain size (Collier et al., 2014).
6. Conclusions
Our results demonstrate that predictions of glacier change in the Himalaya based on
assumptions about clean-ice glaciers or static measurements from debris-covered glaciers that
do not capture the feedbacks amongst debris transport, mass balance and ice dynamics are
unlikely to give reliable results when applied to simulate past and future glacier change. The
development of supraglacial debris across the surface of Khumbu Glacier in Nepal promoted
a reversed mass balance profile across the ablation area resulting in greatest mass loss where
debris is thin or absent close to the icefall and least mass loss down-glacier towards the
terminus. This reduction in ablation across the debris-covered section of the glacier reduced
ice flow and led to thickening of the supraglacial debris layer. Khumbu Glacier extends to a
lower altitude (4870 m compared to 5160 m) and greater length (15.7 km compared to 10.3
km) than would be possible without the surface debris layer. We predict a loss of ice volume
equivalent to 8–10% of the present-day glacier by AD2100 with only minor change in glacier
area and length and detachment of the debris-covered tongue from the upper active part of the
glacier before AD2200, and would expect regional atmospheric warming to result in a similar
response for other glaciers in the Everest region over the same period.
For as long as snow is delivered to high altitudes, small avalanche-fed glaciers will survive in
the Himalaya for many centuries, but will represent only fragments of the present-day
systems. The abandoned debris-covered tongues of formerly large valley glaciers will persist
for a longer period than equivalent clean-ice glaciers, but these debris-covered tongues are
losing mass at rates that have accelerated over the last 40 years as observed from the vertical
difference in the glacier surfaces between Little Ice Age moraine crests and comparison with
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multi-temporal topographic data from the 1970s to the present day. Process-based glacier
models such as that presented here that represent the transient processes governing the
behaviour of mountain glaciers, supported by detailed direct and remotely-sensed
observations of debris-covered Himalayan glaciers, are needed to accurately predict glacier
change in the Himalaya and inform assessments of glaciological and hydrological change.
Acknowledgements We thank S. Brocklehurst for critical discussion and reading of the
manuscript. Some of this research was undertaken while A.V.R. was supported by a Climate
Change Consortium of Wales (C3W) postdoctoral research fellowship at Aberystwyth
University. The glacier model simulations were performed on the Iceberg High-Performance
Computer at the University of Sheffield. ASTER GDEM is a product of METI and NASA.
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