Geometry and scale-dependence of an Arctic glacier

Glaciers and ice caps outside the Greenland and Antarctic ice sheets comprise approximately 4% of the area and around 0.5% of the volume of land ice. If they were to melt completely, they would raise global sea levels by approximately 0.5 m. Small glaciers and ice caps are more responsive to climate change than large ice sheets, and the melting of such small ice masses is believed to have contributed 0.2 to 0.4 mm yr^-1 to global sea level changes during the 20th century, compared with 0.15 mm yr^-1 for Greenland, 0.2 mm yr^-1 for West Antarctica and possible balance, though with large uncertainties, for East Antarctica. Small ice masses will also continue to make a significant contribution to sea level rises during the 21^st century. The range of uncertainty in these estimates is large, and part of this stems from the paucity of measurements of glacier mass balance globally, especially at high latitudes. However, part of the uncertainty also relates to the extrapolation of sparse, point-based direct measurements of glacier mass balance, or of point measurements of height change between known time intervals, to give areal estimates of total melt. Such extrapolations usually assume that the measured mass balance is applicable to some elevation range across the glacier, implicitly assuming that only height will determine mass balance, and effectively neglecting any spatial variability in mass balance within given elevation bands. Recent research has cast some doubt on the validity of these assumptions.

Knowledge of the surface roughness of a glacier, interpreted as small-scale topographic variation, is also important for a number of reasons. The surface roughness is an important control on turbulent heat exchange between the glacier surface and the atmosphere, and hence on the surface energy balance, and ultimately, the mass balance. The size of the roughness elements that are significant in this regard is typically of the order of 0.1 m. Glacier albedo has also been shown to vary at small spatial scales, and given the anisotropic reflectance of ice and snow surfaces at high solar zenith angles, typical for high latitude ice masses, small scale topographic variation, and the resulting variation in the local incidence angle of the solar beam, may also play a role in glacier surface energy balance via the flux of short-wave radiation at the surface.

Surface roughness also modulates the response of an imaging radar to the surface of a glacier. In situations where surface scattering dominates over volume scattering, which, in the context of a glacier, means where the surface is either free of snow or the snow cover is sufficiently wet, the backscattering coefficient is controlled by three factors: the local incidence angle, the dielectric constant of the surface, and the roughness at a scale comparable with the radar wavelength. The local incidence angle is determined by the larger-scale topography (slope and aspect) of the surface and the viewing geometry of the radar. In the case of a snow-covered surface the dielectric constant is determined by the density and liquid water content of the snow, while in the case of a bare ice surface it is simply that of ice itself. Thus, knowledge of the radar backscattering coefficient and the incidence angle has the potential to yield information on the surface roughness of a bare ice surface, and of a combination of surface roughness and snowpack parameters in the case of a snow-covered surface.

A particularly interesting possibility is that the surface roughness properties retrieved from a radar image can be related to those relevant to the thermodynamic and optical properties of the surface. The idea of seeking a link between radar backscatter and surface roughness, as it affects aeolian processes, has been investigated for desert and vegetated surfaces but not, as far as we are aware, for glacier surfaces. Furthermore, it is not obvious at what spatial scale the roughness properties should be described. In the case of radar imagery the relevant scale is less than that of the spatial resolution, while for aerodynamic interactions the answer is not clear. Models of surface roughness usually assume that it can be characterised by some definite horizontal and vertical scale, while there is increasing evidence that many natural surfaces, including those of glaciers, should be described as consisting of a spectrum of scales.

It is thus particularly important to develop detailed and accurate characterisations of the surface geometry of glaciers over a wide range of spatial scales. This presents a considerable technical challenge. Recently, changes in surface elevation of glaciers have begun to be made by comparing digital elevation models (DEMs) compiled at different times. Suitable DEMs can be constructed from a number of types of data, including GPS survey, stereophotography, radar interferometry, spaceborne radar altimetry and laser profiling or LiDAR. In particular, recent technological improvements in airborne LiDAR technology have substantially enhanced the available precision, horizontal resolution and data rate. We have been working with airborne LiDAR data from the glacier Midre Lovénbreen on Svalbard since 2003, supported by detailed field data, to develop these ideas.

Midre Lovénbreen from the air.

Reduced-resolution version of slope-shaded DEM of Midre Lovénbreen compiled from LiDAR data collected in July 2005.

Full-resolution extract of the slope-shaded DEM of Midre Lovénbreen, showing the glacier's snout. The graticule spacing is 200 m; the grid interval of the LiDAR data is 2 m and the vertical accuracy is around 15 cm.

Comparing the surface roughness of Midre Lovénbreen at a range of scales: top and middle, using in situ measurements; bottom: using LiDAR data.

Results obtained to date have elucidated the scale-dependence of the surface geometry of the glacier and have been used to develop improved understandings of glacier energy balance and radar imaging. Work on mass balance is in progress.

Publications

• Arnold, N.S. and Rees, W.G. (2004). Self-similarity in glacier surface characteristics. Journal of Glaciology 49 167 547-554.
• Arnold, N.S., Rees, W.G., Devereux, B.J. and Amable, G.S. (2006). Evaluating the potential of high-resolution airborne LiDAR data in glaciology. International Journal of Remote Sensing 27, 1233-1251.
• Rees, W.G. and Arnold, N.S. (2006) Scale-dependent roughness of a glacier surface: implications for radar backscatter and aerodynamic roughness modelling. Journal of Glaciology 52, 177, 214-222.
• 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 111 F02011, doi 10.1029/2005JF000426 (15 pp).