TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-11-133-2017Brief communication: Thinning of debris-covered and debris-free glaciers in a warming climateBanerjeeArghaargha@iiserpune.ac.inEarth and Climate Science, Indian Institute of Science Education and Research, Pune, IndiaArgha Banerjee (argha@iiserpune.ac.in)18January201711113313816May201615June201620December201625December2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/11/133/2017/tc-11-133-2017.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/11/133/2017/tc-11-133-2017.pdf
Recent geodetic mass-balance measurements
reveal similar thinning rates on glaciers with or without debris cover in the
Himalaya–Karakoram region. This comes as a surprise as a thick debris cover
reduces the surface melting significantly due to its insulating effects. Here
we present arguments, supported by results from numerical flowline model
simulations of idealised glaciers, that a competition between the changes in
the surface mass-balance forcing and that of the emergence/submergence
velocities can lead to similar thinning rates on these two types of glaciers.
As the climate starts warming, the thinning rate on a debris-covered glacier
is initially smaller than that on a similar debris-free glacier.
Subsequently, the rate on the debris-covered glacier becomes comparable to
and then larger than that on the debris-free one. The time evolution of
glacier-averaged thinning rates after an initial warming is strongly
controlled by the time variation of the corresponding emergence velocity
profile.
Introduction
A knowledge gap related to debris-covered glacier dynamics affects our
understanding of the past and future of Himalayan glaciers in a changing
climate . The supraglacial debris cover present over the
ablation zone of a glacier induces qualitative changes in its dynamic
response due to a suppressed melt rate under a thick debris
layer , whereas a thin debris cover is
expected to accelerate melt due to its low albedo. While responding to a
warming climate, debris-covered glaciers exhibit a larger climate
sensitivity, a longer response time , a
decoupling of volume and length changes and the formation of a slow-flowing
stagnant downwasting tongue .
Despite several efforts to model and understand the dynamics of
debris-covered glaciers with various degrees of sophistication
, challenges still remain. This task is made more difficult by our
limited understanding of the time evolution of the debris extent
, the variability of debris thickness, and
common occurrences of highly dynamic supraglacial ponds and ice cliffs that
cause intense localised melting .
A curious fact that has emerged from large-scale remote-sensing measurements
of glaciers in the Himalayas and Karakoram during the first decade of the 21st
century is a similar magnitude of thinning of glacial ice irrespective of the
presence of supraglacial debris cover and this may seem counter-intuitive. A thick
debris cover, due to its insulating properties, significantly inhibits the
melting of the underlying ice – so much so that in the debris-covered part of
the glacier, the specific melt rate does not increase with decreasing
elevation. Rather, it saturates to some lower bound or even decreases
downglacier . On the other hand, on a debris-free
glacier the melt rate typically increases monotonically as elevation
decreases. Why then should both glacier types experience similar rates of
thinning as climate warms up?
Heuristic arguments were offered by various authors to reconcile with this
apparent paradox. suggested that the insulating effect of
the debris cover might be compensated for at the scale of the whole ablation
zone due to an enhanced melting from the thermokarst processes, namely
supraglacial ponds and ice cliffs that are often present on the
debris-covered glaciers. These features, due to an associated discontinuous
debris cover, experience large localised melting. Given that these features
typically contribute ∼ 10–20 % of the total melt (Sakai et al.,
2000; Reid and Brock, 2014), it is unlikely that they can lower the
glacier-wide mean melt rate on debris-covered glaciers sufficiently so that
it matches that on the debris-free glaciers. Field measurements by
seem to confirm this. It was also conjectured that a
reduction in ice flux from upstream areas to the stagnant tongue may be
behind the larger-than-expected thinning of debris-covered glacial ice
. too pointed out the
possible role of reduced flux into the low-slope slow-moving stagnant tongues
of large debris-covered glaciers. However, a quantification of this
flux effect is missing as of yet.
On the other hand, showed that a reduced
melt rate on a debris-covered glacier does not affect the volume response of
the glacier qualitatively, in stark contrast with its drastic effect on the
length response of the glacier. However, their model results (Fig. 3d of
) show a relatively larger thinning rate on the
debris-free glaciers in response to a rapid warming. Also, it was reported
that in the Pamir–Karakoram–Himalayas, depending on the region chosen,
geodetic measurement yielded decadal thinning rates of debris-covered ice
that were either larger or smaller than, or similar to that of debris-free
ice . The present scenario is summed up neatly by
, “This question of area-averaged melting rates over
debris-covered or clean glacier ablation areas remains unanswered”.
In this contribution, we analyse the rate of thinning on debris-covered and
debris-free glaciers in a warming climate using a one-dimensional flowline
model of idealised glaciers .
We conduct simple numerical experiments to investigate the role of the
magnitude of warming rate, the ice dynamics (i.e. the changes in the
flux-gradient profiles or equivalently that in emergence/submergence
velocities), and that of the surface mass-balance forcing in controlling the
thinning rates on these two glacier types.
Glacier response to instantaneous warming
An easy-to-analyse piece of this problem is the behaviour of a steady-state
debris-covered or debris-free glacier immediately after an instantaneous rise
of temperature (or equivalently that of the equilibrium line altitude, ELA).
In a steady state, the ice-thickness profile remains constant due to a stable
balance between the surface ablation (accumulation) rate and the emergence
(submergence) velocities. Dictated by mass conservation of incompressible
ice, the emergence or submergence rate equals the negative gradient of the
flux, F(x). After an instantaneous change in ELA, the surface mass-balance
values change, but the viscous ice flow takes a characteristic longer time to
relax. Therefore, the local thinning rate is initially just the difference in
specific mass balance, B(x), before and after the change in temperature.
However this is valid only over a timescale that is short compared to the
flow relaxation time.
Let us consider two idealised model glaciers. Glacier A does not have any
debris cover and has a linear mass-balance profile. Glacier B has a
supraglacial debris cover on its lower ablation zone where the ablation rate
saturates to a value of -2 m yr-1 (Fig. 1b). This idealised
mass-balance profile for the debris-covered glacier is motivated by data from
a Himalayan glacier . Similar simplified mass-balance
profiles have been used to analyse the response of the debris-covered
Himalayan glaciers . In a real
glacier, the possible variability of debris thickness and ephemeral
thermokarst features (ponds and ice cliffs) cause significant spatial
variation of the melt rate in the debris-covered parts of the glacier.
However, a relatively fast advection of these surface features would imply
that a long-term mean melt rate at a specific location is a well-defined
quantity. This justifies the simplified mass-balance profile employed here.
Further, the observed thinning rate values in the Himalayas are obtained for a
large set of glaciers so that the possible effects of specific details of
mass-balance profile of individual glaciers would be averaged out.
(a, b) The specific mass balance as a function of position
for the initial steady-states of glaciers A and B (red lines). Black arrows
denote the emergence velocities that balances the surface mass balance at
t=0. The blue lines are the surface mass-balance profiles a year after a
step change in ELA by 50 m (experiment 1). (c, d) The specific
mass-balance (red lines) and flux-gradient (blue lines) profiles after 1, 5,
25, 45, and 65 years. In (c) the curves are labelled with the
corresponding year. (e, f) The thinning rate profiles after 1, 5,
25, 45, and 65 years. Note the horizontal black thin lines at βΔE=0.35 m yr-1 (see text for details).
In Fig. 1a, b we show mass-balance profiles for the idealised model glaciers
before and after an instantaneous rise of ELA, ΔE=50 m. It is
assumed here that the mass-balance shape remains the same and changes only by
a shift of ELA. In practice the debris layer may thicken and the
debris-covered area may grow in a warming climate, affecting the shape of the
melt rate profile. However, it is known that above a debris thickness of
∼ 10 cm, the decrease in melt rate with a thickening debris layer is
small . Therefore such changes can safely be neglected as a
first approximation. The possible changes in supraglacial ponds/ice cliffs
are neglected at this level of approximation due to a relatively smaller
contribution of these features to the total melt, as discussed before. This
assumption of an invariant shape allows for the possible increase in debris
extent with warming as the upper boundary of the region with saturated
melt rate moves up with the ELA. Overall these simplifications allow us to
focus on the role of ice flow dynamics in controlling the downwasting of
glaciers in a warming climate.
As is clear from Fig. 1a, glacier A responds initially with a uniform
glacier-wide thinning rate,
〈dhdt〉A=βΔE, right after
the ELA change. Here β is the mass-balance gradient. For glacier B, a
uniform thinning operates only on the debris-free upper part of the glacier
and the lower part has not thinned at all (Fig. 1b). Thus, glacier B has a
lower mean thinning rate to start with that is given by
〈dhdt〉B=(1-fd)βΔE, where fd is the debris-covered fraction. Remarkably
these expressions do not involve the lengths of the glaciers. Also, the
initial lack of thinning on the debris-covered glacier is independent of the
actual value of the melt rate under the thick debris layer (assumed to be
2 m yr-1 here) and depends only on the general shape of the melt curve
(Fig. 1b).
A more general mass-balance profile for a debris-covered glacier than the one
considered above would involve a smaller or inverted mass-balance gradient in
the debris-covered parts . Even then, the mean
initial thinning rate on such a glacier would be less than that of a
corresponding debris-free one. This delayed thinning of the debris-covered
terminus is consistent with the formation of a slow-flowing stagnant tongue
with very little retreat as observed on debris-covered glaciers in the
Himalaya–Karakoram . This raises confidence in the
minimal description of such glaciers that is being used here. In case of an
inverted mass balance, a transient thickening of the lower ablation zone is
observed, though this is likely to be an artefact of the assumed fixed shape
of the mass-balance curve.
Thus, a debris-covered glacier starts with a lower value of mean thinning
rate compared to a debris-free one (as
〈dhdt〉A>〈dhdt〉B).
The ice fluxes then respond to the mass-balance change and subsequent
evolution of the flux-gradient profile, or equivalently that of the emergence
velocity profile alters the distribution and magnitude of the thinning rate.
Though the detailed spatial and temporal pattern of such changes are
difficult to predict, at some later stage the thinning rate on glacier B is
likely to become larger than that on glacier A. This is because (1) the
debris-covered glacier B has a larger climate sensitivity
compared to glacier A and thus loses more
mass for the same change in the ELA; (2) on glacier B, the lower ablation zone
responds to the perturbation with a delay. There must be an intermediate
crossover period as well, where the thinning rates on both the glaciers have
a similar magnitude within measurement errors.
Numerical investigations
To verify the above claims on the nature of the evolution of thinning rate on
glaciers A and B, we perform a set of numerical experiments with one-dimensional flowline
models of glaciers A and B. The model glaciers have a bedrock slope of 0.1 and
mass-balance gradient β=0.007 yr-1. See
for further details of the flowline model used.
Note that these glaciers are identical above the debris-covered region
(Fig. 1a, b). The initial steady states are prepared by running the models
with a fixed value of ELA for 500 (900) years for glacier A (B). The
steady-state lengths of the simulated glaciers are in the range 6–14 km.
Subsequently, the following ELA perturbations are switched on at t=0.
An instantaneous rise by 50 m.
A total rise of 50 m in steps of 5 m every 5 years.
A total rise of 30 m in steps of 1 m every 5 years.
In all three experiments the net warming is similar, but the rates and
durations of the ELA perturbations are different (1 – an instantaneous
warming; 2 – a rate of 10 m decade-1 for 50 years; 3 – a rate of
2 m decade-1 for 150 years). In experiment 3, we restrict the total
ELA rise to 30 m so as to limit the duration of the experiment to 150 years
to facilitate comparison with the other two experiments.
Results and discussionsInitial thinning rates
Just as argued in Sect. 2, mean thinning rate profiles obtained after a year
in experiment 1 show uniform thinning all over glacier A and in the upper
part of glacier B (Fig. 1e, f). In contrast, the debris-covered parts of
glacier B show no thinning. At this point, the flux gradient profile (same as
the negative of emergence velocity), dFdx, has
not changed significantly from the initial steady mass-balance profile B(x)
(Fig. 1c, d). Further, the initial thinning rates for glaciers A and B in
experiment 1 are quite accurately given by βΔE
(0.35 m yr-1) and (1-fd)βΔE
(0.22 m yr-1). All these results are consistent with our arguments as
outlined in Sect. 2. The thinning rate trends for finite warming rates follow
a similar pattern. However, the difference between the thinning rates
of glaciers A and B decreases for smaller warming rates (Fig. 2; experiments 2 and
3).
Evolution of thinning rates after ELA perturbations are applied to a
model debris-covered glacier (solid line) and a debris-free glacier (dotted
line). The warming rate profiles for each of the experiments are described in
Sect. 3.
Time evolution of the thinning rates
A thinning of ice in the ablation zone takes place when the local melt rate
overcomes the local emergence velocity. Data from experiment 1 show that
the initial profile of the thinning rate gets modified at later times, largely
due to a changing profile of dFdx (Fig. 1e, f).
After the initial rapid change, the competing term of mass-balance rate
varies weakly with time due to a feedback from the changing ice thickness.
Therefore, the evolution of the spatial distribution and the mean value of
the thinning rate are mostly dynamically controlled by a changing
emergence velocity profile. While this is in general true for both
glaciers types, emergence velocity profile on the lower ablation zone of the
debris-covered glacier shows a delayed response (Fig. 1f), which
leads to a low glacier-averaged initial thinning rate for these glaciers.
Consistent with arguments given in Sect. 2, the mean thinning rate on glacier
B has a lower magnitude initially. Subsequently the thinning rate matches and
then overtakes that of glacier A (Fig. 2). This illustrates that, depending on
the stage of response, a debris-covered glacier can have a smaller, larger or
similar mean thinning rate compared to that of a corresponding debris-free
glacier. As expected, similar trends are obtained in experiments with finite
warming rates. However, at the limit of a very low rate of warming, the
differences between the thinning rates on the two glaciers are small (Fig. 2;
experiment 3). The crossover time seems to be controlled by the rate of
warming.
While we have considered the glacier-wide thinning rate, the same conclusions
are obtained if one compares only the lower part of the two glaciers as they
are identical in their upper parts. The thinning rate, when measured on a
regional scale, is an average over glaciers having a different size, shape,
bedrock profile, and even a different history of warming. Clearly, in the light of the
above discussion, this may lead to larger, smaller, or similar mean thinning
rates in the debris-covered glaciers compared to the debris-free
glaciers from the same region, in agreement with observations by
.
Conclusions
We provide very general arguments that debris-covered glaciers, while
responding to a warming climate, can have smaller, larger or similar thinning
rates compared to corresponding debris-free glaciers. The thinning of glaciers
is controlled by a competition between a changing mass balance and the
emergence velocity profile. A debris-covered glacier starts with a smaller
glacier-averaged thinning rate, but overtakes that of a debris-free glacier
at later stages of evolution. The initial difference in the corresponding
thinning rates depend on the balance gradient and the debris-covered
fraction. The changes in local melt rates control the thinning of glacial ice
immediately after an instantaneous warming, whereas a stronger variation of
the corresponding emergence velocity profile dictates the evolution of the
thinning of ice at subsequent stages. Our arguments are validated against
results from flowline model simulations of idealised glaciers.
Acknowledgements
This work is supported by DST-SERB grant no SB.DGH-71.2013 and DST-INSPIRE
Faculty award (IFA-12-EAS-04). Edited by:
G. Hilmar Gudmundsson Reviewed by: three anonymous referees
ReferencesAnderson, L. S. and Anderson, R. S.: Modeling debris-covered glaciers:
response to steady debris deposition, The Cryosphere, 10, 1105–1124,
10.5194/tc-10-1105-2016, 2016.
Banerjee, A. and Azam, M. F.: Temperature reconstruction from glacier length
fluctuations in the Himalaya, Ann. Glaciol., 57 (71), 189–198, 2016.
Banerjee, A. and Shankar, R.: On the response of Himalayan glaciers to
climate change, J. Glaciol., 59, 480–490, 2013.
Benn, D. I., Bolch, T., Hands, K., Gulley, J., Luckman, A., Nicholson, L. I.,
Quincey, D., Thompson, S., Toumi, R., and Wiseman, S.: Response of
debris-covered glaciers in the Mount Everest region to recent warming, and
implications for outburst flood hazards, Earth-Sci. Rev., 114, 156–174,
2012.
Gardelle, J., Berthier, E., and Arnaud, Y.: Slight mass gain of Karakoram
glaciers in the early twenty-first century, Nat. Geosci., 5, 322–325, 2012.Gardelle, J., Berthier, E., Arnaud, Y., and Kääb, A.: Region-wide glacier
mass balances over the Pamir-Karakoram-Himalaya during 1999–2011, The
Cryosphere, 7, 1263–1286, 10.5194/tc-7-1263-2013, 2013.Juen, M., Mayer, C., Lambrecht, A., Han, H., and Liu, S.: Impact of varying
debris cover thickness on ablation: a case study for Koxkar Glacier in the
Tien Shan, The Cryosphere, 8, 377–386, 10.5194/tc-8-377-2014, 2014.
Kääb, A., Berthier, E., Nuth, C., Gardelle, J., and Arnaud, Y.:
Contrasting patterns of early twenty-first-century glacier mass change in the
Himalayas, Nature, 488, 495–498, 2012.
Mattson, L. E., Gardner, J. S., and Young, G. J.: Ablation on debris covered
glaciers: an example from the Rakhiot Glacier, Punjab, Himalaya, IAHS Publ.
218 (Symposium at Kathmandu 1992 – Snow and Glacier Hydrology), 289–296,
1993.
Miles, E. S., Pellicciotti, F., Willis, I. C., Steiner, J. F., Buri, P., and
Arnold, N. S.: Refined energy-balance modelling of a supraglacial pond,
Langtang Khola, Nepal, Ann. Glaciol., 57 (71), 29–40, 2016.
Naito, N., Nakawo, M., Kadota, T., and Raymond, C. F.: Numerical simulation
of recent shrinkage of Khumbu Glacier, Nepal Himalayas. IAHS Publ. 264,
Symposium at Seattle 2000 – Debris-Covered Glaciers, 245–254, 2000.
Nakawo, M. and Young, G. J.: Estimation of glacier ablation under a debris
layer from surface temperature and meteorological variables, J. Glaciol., 28,
29–34, 1982.
Nuimura, T., Fujita, K., Yamaguchi, S., and Sharma, R. R.: Elevation changes
of glaciers revealed by multitemporal digital elevation models calibrated by
GPS survey in the Khumbu region, Nepal Himalaya, 1992–2008, J. Glaciol., 58,
648–656, 2012.
Reid, T. D. and Brock, B. W.: Assessing ice-cliff backwasting and its
contribution to total ablation of debris-covered Miage glacier, Mont Blanc
massif, Italy, J. Glaciol., 60, 3–13, 2014.
Rowan, A. V., Egholm, D. L., Quincey, D. J., and Glasser, N. F.: Modelling
the feedbacks between mass balance, ice flow and debris transport to predict
the response to climate change of debris-covered glaciers in the Himalaya,
Earth Planet. Sci. Lett., 430, 427–438, 2015.
Sakai, A., Takeuchi, N., Fujita, K., and Nakawo, M.: Role of supraglacial
ponds in the ablation process of a debris-covered glacier in the Nepal
Himalayas, IAHS Publ. 265, 119–132, 2000.Scherler, D., Bookhagen, B., and Strecker, M. R.: Spatially variable response
of Himalayan glaciers to climate change affected by debris cover, Nat.
Geosci., 4, 156–159, 10.1038/ngeo1068, 2011.
Steiner, J. F., Pellicciotti, F., Buri, P., Miles, E. S., Immerzeel, W. W.,
and Reid, T. D.: Modelling ice-cliff backwasting on a debris-covered glacier
in the Nepalese Himalaya, J. Glaciol., 61, 889–907, 2015.Vacco, D. A., Alley, R. B., and Pollard, D.: Glacial advance and stagnation
caused by rock avalanches, Earth Planet. Sci. Lett., 294, 123–130, 2010.
Vincent, C., Wagnon, P., Shea, J. M., Immerzeel, W. W., Kraaijenbrink, P.,
Shrestha, D., Soruco, A., Arnaud, Y., Brun, F., Berthier, E., and Sherpa, S.
F.: Reduced melt on debris-covered glaciers: investigations from Changri Nup
Glacier, Nepal, The Cryosphere, 10, 1845–1858, 10.5194/tc-10-1845-2016,
2016.