Bolch, T., Kulkarni, A., Kääb, A., Huggel, C., Paul, F., Cogley, J. G., Frey, H., Kargel, J. S., Fujita, K., and Scheel, M.: The state and fate of Himalayan glaciers, Science, 336, 310–314,
https://doi.org/10.1126/science.1215828, 2012.
a
Brock, B. W., Mihalcea, C., Kirkbride, M. P., Diolaiuti, G., Cutler, M. E., and Smiraglia, C.: Meteorology and surface energy fluxes in the 2005–2007 ablation seasons at the Miage debris-covered glacier, Mont Blanc Massif, Italian Alps, J. Geophys. Res.-Atmos., 115, D09106,
https://doi.org/10.1029/2009JD013224, 2010.
a
Chand, M. B. and Kayastha, R. B.: Study of thermal properties of supraglacial debris and degree-day factors on Lirung Glacier, Nepal, Sciences in Cold and Arid Regions, 10, 357–368,
https://www.researchgate.net/publication/331398961 (last access: 30 June 2025), 2018.
a,
b,
c,
d,
e
Collier, E., Nicholson, L. I., Brock, B. W., Maussion, F., Essery, R., and Bush, A. B. G.: Representing moisture fluxes and phase changes in glacier debris cover using a reservoir approach, The Cryosphere, 8, 1429–1444,
https://doi.org/10.5194/tc-8-1429-2014, 2014.
a,
b
Conway, H. and Rasmussen, L. A.: Summer temperature profiles within supraglacial debris on Khumbu Glacier, Nepal, IAHS-AISH P., 264, 89–98, 2000.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k,
l,
m,
n,
o,
p,
q,
r,
s,
t,
u,
v,
w,
x,
y
Crank, J. and Nicolson, P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Math. Proc. Cambridge, 43, 50–67,
https://doi.org/10.1017/S0305004100023197, 1947.
a
Evatt, G. W., Abrahams, I. D., Heil, M., Mayer, C., Kingslake, J., Mitchell, S. L., Flowler, A. C., and Clark, C. D.: Glacial melt under a porous debris layer, J. Glaciol., 61, 825–836,
https://doi.org/10.3189/2015JoG14J235, 2015.
a,
b,
c,
d
Fontrodona-Bach, A., Groeneveld, L., Miles, E., McCarthy, M., Shaw, T., Melo Velasco, V., and Pellicciotti, F.: DebDab: A database of supraglacial debris thickness and physical properties, Earth Syst. Sci. Data Discuss. [preprint],
https://doi.org/10.5194/essd-2024-559, in review, 2025.
a,
b
Fourier, J.-B.-J.: The analytical theory of heat, Courier Corporation, ISBN 9781108001786/1108001785, 1955. a
Fyffe, C. L., Reid, T. D., Brock, B. W., Kirkbride, M. P., Diolaiuti, G., Smiraglia, C., and Diotri, F.: A distributed energy-balance melt model of an alpine debris-covered glacier, J. Glaciol., 60, 587–602,
https://doi.org/10.3189/2014JoG13J148, 2014.
a,
b,
c
Giese, A., Boone, A., Wagnon, P., and Hawley, R.: Incorporating moisture content in surface energy balance modeling of a debris-covered glacier, The Cryosphere, 14, 1555–1577,
https://doi.org/10.5194/tc-14-1555-2020, 2020.
a,
b
Haidong, H., Yongjing, D., and Shiyin, L.: A simple model to estimate ice ablation under a thick debris layer, J. Glaciol., 52, 528–536,
https://doi.org/10.3189/172756506781828395, 2006.
a
Inoue, J. and Yoshida, M.: Ablation and Heat Exchange over the Khumbu Glacier Glaciological Expedition of Nepal, Contribution No. 65 Project Report No. 4 on “Studies on Supraglacial Debris of the Khumbu Glacier”, Journal of the Japanese Society of Snow and Ice, 41, 26–33,
https://doi.org/10.5331/seppyo.41.Special_26, 1980.
a,
b
Juen, M., Mayer, C., Lambrecht, A., Wirbel, A., and Kueppers, U.: Thermal properties of a supraglacial debris layer with respect to lithology and grain size, Geogr. Ann. A, 95, 197–209,
https://doi.org/10.1111/geoa.12011, 2013.
a,
b,
c,
d,
e
Kayastha, R. B., Takeuchi, Y., Nakawo, M., and Ageta, Y.: Practical prediction of ice melting beneath various thickness of debris cover on Khumbu Glacier, Nepal, using a positive degree-day factor, IAHS-AISH P., 264, 7182,
https://iahs.info/uploads/dms/11683.71-81-264-Kayastha.pdf (last access: 30 June 2025), 2000. a
Kellerer-Pirklbauer, A., Lieb, G. K., Avian, M., and Gspurning, J.: The response of partially debris-covered valley glaciers to climate change: the example of the Pasterze Glacier (Austria) in the period 1964 to 2006, Geogr. Ann. A, 90, 269–285,
https://doi.org/10.1111/j.1468-0459.2008.00345.x, 2008.
a
Kirkbride, M. P. and Deline, P.: The formation of supraglacial debris covers by primary dispersal from transverse englacial debris bands, Earth Surf. Proc. Land., 38, 1779–1792,
https://doi.org/10.1002/esp.3416, 2013.
a,
b
Laha, S., Winter-Billington, A., Banerjee, A., Shankar, R., Nainwal, H. C., and Koppes, M.: Estimation of ice ablation on a debris-covered glacier from vertical debris-temperature profiles, J. Glaciol., 69, 1–12,
https://doi.org/10.1017/jog.2022.35, 2022.
a,
b,
c,
d,
e,
f,
g,
h,
i,
j,
k
Mattson, L. E.: Ablation on debris covered glaciers: an example from the Rakhiot Glacier, Punjab, Himalaya, Intern. Assoc. Hydrol. Sci., 218, 289–296, 1993.
a,
b
Mihalcea, C., Mayer, C., Diolaiuti, G., Lambrecht, A., Smiraglia, C., and Tartari, G.: Ice ablation and meteorological conditions on the debris-covered area of Baltoro glacier, Karakoram, Pakistan, Ann. Glaciol., 43, 292–300,
https://doi.org/10.3189/172756406781812104, 2006.
a
Miles, E. S., Steiner, J., Buri, P., Immerzeel, W., and Pellicciotti, F.: Controls on the relative melt rates of debris-covered glacier surfaces, Environ. Res. Lett., 17, 064004,
https://doi.org/10.1088/1748-9326/ac6966, 2022.
a
Minora, U., Senese, A., Bocchiola, D., Soncini, A., D'Agata, C., Ambrosini, R., Mayer, C., Lambrecht, A., Vuillermoz, E., and Smiraglia, C.: A simple model to evaluate ice melt over the ablation area of glaciers in the Central Karakoram National Park, Pakistan, Ann. Glaciol., 56, 202–216,
https://doi.org/10.3189/2015AoG70A206, 2015.
a
Nicholson, L.: Modelling melt beneath supraglacial debris: implications for the climatic response of debris-covered glaciers, University of St. Andrews (United Kingdom),
https://research-repository.st-andrews.ac.uk/handle/10023/10264 (last access: 30 June 2025), 2005. a
Nicholson, L. and Benn, D. I.: Calculating ice melt beneath a debris layer using meteorological data, J. Glaciol., 52, 463–470,
https://doi.org/10.3189/172756506781828584, 2006.
a,
b,
c,
d,
e
Nicholson, L. and Benn, D. I.: Properties of natural supraglacial debris in relation to modelling sub-debris ice ablation, Earth Surf. Proc. Land., 38, 490–501,
https://doi.org/10.1002/esp.3299, 2012.
a,
b,
c,
d,
e,
f
Nicholson, L., Wirbel, A., Mayer, C., and Lambrecht, A.: The challenge of non-stationary feedbacks in modeling the response of debris-covered glaciers to climate forcing, Front. Earth Sci., 9, 662695,
https://doi.org/10.3389/feart.2021.662695, 2021.
a
Petersen, E., Hock, R., Fochesatto, G. J., and Anderson, L. S.: The Significance of Convection in Supraglacial Debris Revealed Through Novel Analysis of Thermistor Profiles, J. Geophys. Res.-Earth, 127, e2021JF006520,
https://doi.org/10.1029/2021JF006520, 2022.
a,
b,
c,
d,
e,
f
Reznichenko, N., Davies, T., Shulmeister, J., and McSaveney, M.: Effects of debris on ice-surface melting rates: an experimental study, J. Glaciol., 56, 384–394,
https://doi.org/10.3189/002214310792447725, 2010.
a,
b
Rounce, D. R., Quincey, D. J., and McKinney, D. C.: Debris-covered glacier energy balance model for Imja–Lhotse Shar Glacier in the Everest region of Nepal, The Cryosphere, 9, 2295–2310,
https://doi.org/10.5194/tc-9-2295-2015, 2015.
a,
b,
c,
d,
e
Rounce, D. R., Hock, R., Maussion, F., Hugonnet, R., Kochtitzky, W., Huss, M., Berthier, E., Brinkerhoff, D., Compagno, L., Copland, L., Farinotti, D., Menounos, B., and McNabb, R. W.: Global glacier change in the 21st century: Every increase in temperature matters, Science, 379, 78–83,
https://doi.org/10.1126/science.abo1324, 2023.
a
Rowan, A. V., Nicholson, L. I., Quincey, D. J., Gibson, M. J., Irvine-Fynn, T. D., Watson, C. S., Wagnon, P., Rounce, D. R., Thompson, S. S., Porter, P. R., and Neil, F.: Seasonally stable temperature gradients through supraglacial debris in the Everest region of Nepal, Central Himalaya, J. Glaciol., 67, 170–181,
https://doi.org/10.1017/jog.2020.100, 2021.
a,
b,
c,
d,
e,
f,
g,
h
Scherler, D., Wulf, H., and Gorelick, N.: Global assessment of supraglacial debris-cover extents, Geophys. Res. Lett., 45, 11798–11805,
https://doi.org/10.1029/2018GL080158, 2018.
a,
b
Thakuri, S., Salerno, F., Smiraglia, C., Bolch, T., D'Agata, C., Viviano, G., and Tartari, G.: Tracing glacier changes since the 1960s on the south slope of Mt. Everest (central Southern Himalaya) using optical satellite imagery, The Cryosphere, 8, 1297–1315,
https://doi.org/10.5194/tc-8-1297-2014, 2014.
a
Tielidze, L. G., Bolch, T., Wheate, R. D., Kutuzov, S. S., Lavrentiev, I. I., and Zemp, M.: Supra-glacial debris cover changes in the Greater Caucasus from 1986 to 2014, The Cryosphere, 14, 585–598,
https://doi.org/10.5194/tc-14-585-2020, 2020.
a
Zhang, T. and Osterkamp, T.: Considerations in determining thermal diffusivity from temperature time series using finite difference methods, Cold Reg. Sci. Technol., 23, 333–341,
https://doi.org/10.1016/0165-232X(94)00021-O, 1995.
a
