Rock and sediment debris often cover part or all of a glacier’s surface, where it plays an important role in surface energy balance and the rate of glacier ablation.
The relationship between debris thickness and glacier melting
Measurements taken at the surface of glaciers show there to be a strong relationship between the thickness of debris and the rate of ice melting1,2.
Where debris covering the ice surface is thin, the rate of melting rises. The rate of melting continues to rise until the debris layer reaches around 2 cm thick. Where debris cover is thicker than 2 cm, the rate of melting falls exponentially1.
This relationship is explained by both the albedo effect and the insulation effect.
Albedo (usually denoted by the Greek letter ‘α’) is the term used for the proportion of incoming shortwave (solar) radiation that is reflected by a surface3. The albedo of a surface can be determined using the following simple equation:
α = SWout / SWin
where α is albedo, SWout is outgoing shortwave radiation (i.e. the amount reflected by a surface), and SWin is incoming shortwave radiation (i.e. the amount received by a surface).
|Slightly dirty ice||0.26–0.33|
|from: Paterson (1994)|
The albedo of dirty and debris-covered ice (i.e. the parts of a glacier’s surface littered with bare rock and sediment) is lower than that of clean ice or snow (see table above) and, as a consequence, they absorb more incoming shortwave radiation4. This increases the amount of energy that is available for melting.
The second effect of debris on ice surface melting is insulation. Surface debris forms a barrier between the glacier and the atmosphere, reducing the amount of energy that reaches the ice surface and, therefore, insulating the ice from melting3.
Which effect is most important?
That depends – as you may have guessed – on the thickness of debris at the glacier surface. The albedo effect has a greater influence on ablation rates where the debris cover is sparse or absent, whereas the insulation effect is more important where the debris cover is thick3.
Calculating the impact of surface debris on ice melt
The influence of surface debris on ice melt can be assessed by calculating how much heat is transferred vertically through a debris layer to the top of the glacier. This heat transfer is known as the conductive heat flux (Qc) and can be estimated by a simple equation5:
Qc = k (Ts – Ti) / hd
where k is the thermal conductivity of the debris layer (i.e. the ability of the debris to conduct heat, which varies depending on rock type), Ts and Ti are the temperature at the top and base of the debris layer, and hd is the debris layer thickness.
The above equation is handy as it provides a simple method of calculating the conductive heat flux, which can then be used to calculate ice melt rates (using the equation below) beneath debris cover. However, it makes several assumptions.
Most importantly, the equation assumes that the change in temperature between the top and base of the debris layer is linear (i.e. that the temperature changes at an even rate).
In nature, however, this temperature gradient is rarely stable, but is always changing in response to fluctuations in the receipt of energy at the surface6. In short, it is non-linear. This means that the above equation may not always give a reliable estimate of the passage of heat through a debris layer and, thus, melt rate.
However, as the difference in temperature between the top and base of a debris layer is linear when averaged out over the course of a day, it is possible to get around this problem by using daily mean surface temperature data (which can be accessed from local weather stations) to calculate ice melt rates6.
Using daily mean surface temperatures, the equation above gives the daily average heat flux through a debris layer, which can be used to calculate ice melt rate (M) using the following simple equation:
M = M/Lf(M > 0)
where M is the energy flux available for melting (i.e. the daily average heat flux from above) and Lf is latent heat given off by melting.
Why should we care about the effect of debris on glacier ablation?
Many of the world’s alpine glaciers are covered by debris to some extent7, and this debris (as explained above) affects the rate of ice melting1,2,5. This, in turn, impacts the overall mass balance of glaciers, as well as the landforms produced at ice margins7.
Understanding the relationships between surface debris and glacier melting is also important for accurately predicting how debris-covered glaciers in regions such the Himalayas, Andes, and Southern Alps of New Zealand, will react to climate change, and whether changes in the patterns of ice melting will threaten communities living downstream (e.g. flooding)8.
 Østrem, G. 1959. Ice melting under a thin layer of moraine, and the existence of ice cores in moraine ridges. Geografiska Annaler Series A, 41, 228–230.
 Kayastha, R.B., Takeuchi, Y., Nakawo, M. and Ageta, Y., 2000. 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, 71-81.
 Benn, D.I., and Evans, D.J.A., 2010. Glaciers and Glaciation. Hodder-Arnold, London.
 Paterson, W.S.B., 1994. Physics of glaciers. Butterworth-Heinemann.
 Nakawo, M. and Young, G.J., 1981. Field experiments to determine the effect of a debris layer on ablation of glacier ice. Annals of Glaciology, 2, 85-91.
 Nicholson, L. and Benn, D.I., 2006. Calculating ice melt beneath a debris layer using meteorological data. Journal of Glaciology, 52, 463-470.
 Benn, D.I., Kirkbride, M.P., Owen, L.A. and Brazier, V., 2003. Glaciated valley landsystems. In Evans, D.J.A. (ed.) Glacial Landsystems, pp. 372-406.
 Benn, D.I., Bolch, T., Hands, K., Gulley, J., Luckman, A., Nicholson, L.I., Quincey, D., Thompson, S., Toumi, R. and Wiseman, S., 2012. Response of debris-covered glaciers in the Mount Everest region to recent warming, and implications for outburst flood hazards. Earth-Science Reviews, 114, 156-174.