# The surface energy balance

This page draws from the excellent review of glacier melt by Hock (2005) and the equally informative chapter on ‘Snow, Ice and Climate’ (Chapter 2) in Glaciers and Glaciation by Benn and Evans (2010). I highly recommend these resources if you want to dive deeper into the processes of glacier melting and the surface energy balance.

## What is the surface energy balance?

The balance of energy at the glacier surface control melting.

The term surface energy balance is specifically used to describe the balance between all surface energy inputs and outputs over a given interval of time. By calculating the surface energy balance, glaciologists can work out the change in temperature at a glacier surface and rate of glacier melt1-4.

The surface energy balance is the sum of all energy fluxes at the glacier surface, and is represented by the simple equation:

QM = SW + LW + QH + QE + QR

where QM is the energy available for melting SW is shortwave radiation, LW is longwave radiation, QH is sensible heat transfer, QE is latent heat transfer, QR is the energy supplied by rain.

This page will explain each component of the energy balance equation in order. But first, we need to understand how snow/ice is melted.

## The melting of snow and ice

For snow or ice to melt, its temperature must first be increased from sub-freezing (i.e. temperatures lower than 0°C) to the melting point, which is 0°C. Once at 0°C, further energy surplus will cause melting3.

For this reason, an air temperature of 0°C or warmer does not automatically result in melting. It may heat the glacier surface, but unless it raises the temperature of snow/ice to the melting point, no change in state will arise3.

The opposite transpires when there is an energy deficit at the glacier surface. This deficit either cools the ice further or forms new ice by freezing surface water or through the condensation of water vapour3,4.

### The energy needed to change state

The relationship between energy input (in the form of heat) and the change in temperature of a material is known as the specific heat capacity. The specific heat capacity is different for different materials. To warm 1 gram of ice at –10°C by 1°C requires an energy input of 2 joules3,4.

The melting of snow and ice requires an energy input of 334 joules per gram3,4. Conversely, 334 joules are released when water is frozen. The energy released during this change of state (as well as the consumption of energy in melting) is known as latent heat.

The energy required for evaporation, and that released by condensation, is much higher than for melting/freezing, being 2500 joules per gram.

## The surface energy balance

Now that we have the basics of the heating and melting of snow and ice, let’s break down the main components of the surface energy balance1-3.

QM = SW + LW + QH + QE + QR

We’ll start with the radiation emitted by the sun, otherwise called ‘shortwave’ radiation as it occurs at short wavelengths (0.2 – 4 micrometres). The shortwave radiation receipt varies from glacier to glacier depending on several factors.

#### Latitude

First, is latitude. The sun’s energy is focused over a much smaller area at the equator than at the poles, owing to the higher angle of the sun’s rays in the low latitudes. Therefore, more shortwave radiation is available per unit area for heating the Earth’s surface at the equator than at the poles3,4.

Some solar radiation is scattered by air/water molecules and other particles in the atmosphere as it moves towards Earth’s surface3,4. Because the distance between the sun and the poles is greater than between the sun and the equator, more energy is lost by the time it reaches the high latitudes, leaving less energy available for melting.

Shortwave radiation receipt tends to be highest at low latitude glaciers in high altitude mountain ranges (e.g. the Andes and Himalayas) where the sun angle is high and the thin, relatively cloudless air at high altitude limits the amount of solar energy lost by scattering5-7. In contrast, shortwave radiation receipts are often lower for mid- or high latitude glaciers in persistently cloudy (e.g. coastal) areas, such as Patagonia or Alaska.

#### Topography

Second, the local slope gradient and aspect impact the angle at which solar rays meet the land surface and, therefore, the amount of shortwave radiation received2,8. The terrain around a glacier may also play an important role, by shading the ice from direct solar radiation8,9.

#### Time of day

Shortwave radiation receipt also varies as the sun angle changes throughout the day, with a peak at midday when the sun angle is highest.

#### The albedo effect

Only some of the shortwave radiation that reaches Earth’s surface is absorbed. A portion is also reflected. This is known as albedo. The energy available for melting, therefore, is the difference between incoming and outgoing radiation3,4.

The amount of energy reflected depends on the surface material10. Clean ice or snow reflect more solar radiation than dirty or debris-covered ice, leaving less energy for melting.

QM = SW + LW + QH + QE + QR

Longwave radiation, so-called because it occurs at the ‘long’ wavelengths of 4 to 120 micrometres, is emitted from both the land surface and atmosphere. Glaciers also emit longwave radiation, so the net energy available for melting is the difference between that received and that emitted by ice3,4.

The main sources of incoming longwave radiation are the valley walls that surround glaciers and water vapour (as well as CO2 and ozone) in the atmosphere11,12. Heat emitted from warm rockwalls increase the energy available for melting, particularly around the glacier sides. As water vapour absorbs and emits longwave radiation, it is most important where the air is humid, and weather cloudy3,4.

For most glaciers, the most important components of the surface energy are the combined flux of shortwave (solar) and longwave radiation, which may supply over 75% of the energy for melting1,3,12.

### Sensible heat transfer

QM = SW + LW + QH + QE + QR

Sensible heat is the thermal energy passed directly from one material to another, in this case, from the atmosphere to a glacier (or vice versa). It is called sensible heat as it we can sense or feel it (a cold breeze, for example).

The amount of sensible heat transferred from the atmosphere to a glacier depends on the temperature gradient near the glacier surface (i.e. the difference in temperature between the ice and air above it) and wind speed3,12.

The higher the temperature gradient and the faster the wind speed, the more sensible heat is transferred to a glacier.

There are several examples of such weather conditions. The first are Föhn winds, which are dry, strong winds that blow down the leeside of mountains, warming the air, and glacier surface, as they descend. The second are valley winds, which are warm, low-level winds that are drawn up alpine valleys as the air over mountain ranges heats up during the day.

### Latent heat transfer

QM = SW + LW + QH + QE + QR

Latent heat is the energy consumed or released during a change of state at the ice surface; condensation (vapour to liquid), evaporation (liquid to vapour), deposition (vapour to solid) and sublimation (solid to vapour).

Like sensible heat above, these processes depend on wind speed over the glacier and the humidity of the air at and above the ice. For this reason, sensible and latent heat transfers are often grouped together and termed the turbulent fluxes3,13.

Where the air is above the glacier is more humid than at the surface, evaporation or sublimation will occur. In contrast, where the air is above the glacier is less humid (drier) than at the surface, condensation or deposition will occur. This change in state, releases energy for warming or melting ice.

Winds are important in latent heat transfer as they can stir up the air at the ice surface (which is often humid) and mix it with the air above.

Latent heat fluxes are important at high-altitude mountain glaciers that experience cold and dry weather conditions, where sublimation occurs14. However, they can also be important in the energy balance of maritime glaciers15.

### The energy supplied by rain

QM = SW + LW + QH + QE + QR

Rainfall that falls on the surface of a glacier, although generally a minor component of the overall energy balance (except for short periods, e.g. during warm fronts or storms16), can supply energy for melting.

Rain will cool to the temperature of the surface snow or ice and ultimately, freeze. This releases latent heat that contributes to heating or melting ice. If the glacier surface is already at the melting point, then rain will add to melting directly.

## How is glacier melt modelled?

So, we have covered the main components of glacier surface energy balance, but how is glacier melt actually modelled? Well, there are two main types of model for this purpose3.

First, are point models, where the energy balance is estimated at a single point on a glacier surface. Usually, this is at the site of a weather station.

Second, are distributed models, where the energy balance is estimated across an area1,2,3. This method has become more common in recent years as satellite datasets (such as digital elevation models) and computer power have improved.

Distributed models are used to investigate how the individual energy balance components influence ice melting over different parts of a glacier. Detailed information of this nature is needed to better understand how glacier ablation trends will react to climate and weather changes, and to predict how glacier mass balance will change in the future.

## Why study glacier energy balance?

To sum up – why should we care about the surface energy balance of glaciers and ice sheets?

Well, mainly because it allows glaciologists to understand current – and, therefore, predict future – trends in glacier melting.

At the global scale, this information can help us estimate the glacier contribution to sea-level rise with climate change.

At the regional scale, this information helps to predict river discharge and geomorphic activity downstream of mountain glaciers, where huge numbers of people rely on glacial freshwater for drinking, the irrigation of crops, and hydroelectric power. It is also important for the forecasting of floods and the safety of downstream communities.

## References

[1] Arnold, N.S., Willis, I.C., Sharp, M.J., Richards, K.S. and Lawson, W.J., 1996. A distributed surface energy-balance model for a small valley glacier. I. Development and testing for Haut Glacier d’Arolla, Valais, Switzerland. Journal of Glaciology42, 77-89.

[2] Hock, R. and Holmgren, B., 2005. A distributed surface energy-balance model for complex topography and its application to Storglaciären, Sweden. Journal of Glaciology51, 25-36.

[3] Hock, R., 2005. Glacier melt: a review of processes and their modelling. Progress in Physical Geography29, 362-391.

[4] Benn, D.I., and Evans, D.J.A., 2010. Glaciers and Glaciation. Hodder-Arnold, London.

[5] Benn, D.I., Wiseman, S. and Hands, K.A., 2001. Growth and drainage of supraglacial lakes on debris-mantled Ngozumpa Glacier, Khumbu Himal, Nepal. Journal of Glaciology47, 626-638.

[6] Mölg, T., Hardy, D.R. and Kaser, G., 2003. Solar‐radiation‐maintained glacier recession on Kilimanjaro drawn from combined ice‐radiation geometry modeling. Journal of Geophysical Research: Atmospheres108 (D23).

[7] Pellicciotti, F., Helbing, J., Rivera, A., Favier, V., Corripio, J., Araos, J., Sicart, J.E. and Carenzo, M., 2008. A study of the energy balance and melt regime on Juncal Norte Glacier, semi‐arid Andes of central Chile, using melt models of different complexity. Hydrological Processes22, 3980-3997.

[8] Arnold, N.S., Rees, W.G., Hodson, A.J. and Kohler, J., 2006. Topographic controls on the surface energy balance of a high Arctic valley glacier. Journal of Geophysical Research: Earth Surface111 (F2).

[9] Olson, M. and Rupper, S., 2019. Impacts of topographic shading on direct solar radiation for valley glaciers in complex topography. The Cryosphere13, 29-40.

[10] Paterson, W.S.B., 1994. Physics of glaciers. Butterworth-Heinemann.

[11] Brock, B.W., Willis, I.C., Sharp, M.J. and Arnold, N.S., 2000. Modelling seasonal and spatial variations in the surface energy balance of Haut Glacier d’Arolla, Switzerland. Annals of Glaciology31, 53-62.

[12] Oerlemans, J. and Klok, E.J., 2002. Energy balance of a glacier surface: analysis of automatic weather station data from the Morteratschgletscher, Switzerland. Arctic, Antarctic, and Alpine Research34, 477-485.

[13] Morris, E.M., 1989. Turbulent transfer over snow and ice. Journal of Hydrology105, 205-223.

[14] Cullen, N.J., Mölg, T., Kaser, G., Steffen, K. and Hardy, D.R., 2007. Energy-balance model validation on the top of Kilimanjaro, Tanzania, using eddy covariance data. Annals of Glaciology46, 227-233.

[15] Conway, J.P. and Cullen, N.J., 2013. Constraining turbulent heat flux parameterization over a temperate maritime glacier in New Zealand. Annals of Glaciology54, 41-51.

[16] Hay, J.E. and Fitzharris, B.B., 1988. A comparison of the energy-balance and bulk-aerodynamic approaches for estimating glacier melt. Journal of Glaciology34, 145-153.