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Measurement And Modelling Notes

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How would you go about measuring the net mass balance of a 10,000 km2 Arctic ice cap which terminates in the sea?
10,000 km2 is at the very top of the size range of Arctic ice caps. Detailed measurement programs of mass balance are relatively rare for Arctic glaciers, and those that are available mostly relate to smaller glaciers (around 10km 2) terminating on land, and not to larger ice caps above 100km2 (Dowdeswell & Hagen, 2004). Observation of such an ice cap would therefore be quite scientifically valuable. Precedents include the Hans Tausen Ice Cap in Greenland (4000 km2) and the Austfonna Ice Cap (8000 km2) in Svalbard (Dowdeswell & Hagen, 2004). The equation for calculating total mass balance is V / a = Ma Mm Mc ± Mb (Hagen & Reeh, 2004). There are two main approaches for measuring the mass balance of ice masses, which quantify the left and right sides of this equation respectively: (1) the cartographic method, directly measuring the change in volume by monitoring the changes in surface elevation through remote sensing or (2) the direct glaciological method, seperately measuring each element of accumulation and ablation through local measurements (Reeh, 2006; Hagen & Reeh, 2004). The direct glaciological method is more resource-intensive than the cartographic method, but is potentially more accurate (Hagen & Reeh, 2004). Since a 10,000 km 2 ice sheet is sufficiently small for direct glaciological methods to be feasible but big enough that remote sensing may be preferable, both methods will be considered here. Cartographic method The basis of the cartographic method is that the change in volume can be estimated by comparing the topographic changes in an ice mass between different years. Topographic changes can be measured using photography, airborne laser altimetry, or satellite radar altimetry (Hagen & Reeh, 2004), however the accuracy of current satellite radar altimetry is not sufficient for an ice cap of this size, so air-based methods would be required (Dowdeswell & Hagen, 2004). Of the two methods, aerial photography has been more commonly used in the past, but laser altimetry is far more accurate (down to ± 10 cm compared with ± 1-2 m for photography) (Bamber &
Kwok, 2004). Either could potentially be used here. Hagen & Reeh (2004) describe the process of measuring mass balance using this method. An aerial survey using photography or laser altimetry is made at the same point late in the ablation cycle in different years, and the data is used to create digital elevation models (DEMs) showing the change in topography over the period, which can be converted to the volume change in water equivalent to yield the net mass balance figure. Cartographic estimation of mass balance based on remote sensing is often used

for very large ice masses such as the Greenland Ice Sheet (Hagen & Reeh, 2004). Airborne surveying would be a good option for mass balance studies on an ice cap of this size, although it is more suitable for longer spans of time than for annual measurements due to its lesser accuracy. Surveys done at intervals of a few years could provide a continuing indicator of the health of the ice mass (Paterson, 2002). Direct Glaciological Method In this method mass balance is determined by seperately estimating each variable on the right side of the mass balance equation V / a = Ma Mm Mc ± Mb. These represent annual surface accumulation (Ma), annual surface losses (Mm), annual loss from iceberg calving (Mc) and annual balance at the bottom (melting or freeze-on of ice) (Mb) (Hagen & Reeh, 2004). Surface accumulation and loss can be directly measured using stakes inserted into the ice, snow or firn; these are read at the end of the accumulation period (April-May) and at the end of the ablation period (September-October). The resulting depth data is transformed into water equivalent units using density measurements from pit studies, ice cores or crevasse statigraphy at a range of elevations (Østrem & Stanley, 1969; Hagen & Reeh, 2004). Typically stakes are placed in a dense array covering a glacier to produce a large number of local mass balance measurements which are then integrated to give a net mass balance figure (Dyurgerov, 2002). This presents a problem on such a large ice cap where it is impossible to take such measurements over the entire area (Hagen & Reeh, 2004). The solution to this is to make mass balance measurements either in detail on a small section off the ice cap or at a series of local points, then extrapolate these measurements to estimate the mass balance of the overall ice mass. The Hans Tausen ice cap study, for instance, inferred overall mass balance from detailed measurement of a 15 km outlet glacier. In the Austfonna study, spot masurements at a series of elevations were extrapolated over the whole area of the ice cap based on a digital elevation model to estimate overall mass balance. (Dowdeswell & Hagen, 2004). Such an inferential approach is not necessarily inaccurate; recent studies suggests it is possible to calculate mass balance accurately using relatively few measurements (Dyurgerov, 2002). The next element to measure is loss through iceberg calving. This can be calculated based on glacial velocity and ice thickness. These are measurable using aerial or terrestrial photogrammetry, as well as satellite radar altimetry and airborne ice-penetrating radar measurements. Calving by ice caps is usually a very slow process, but experiences periodic surges which makes it important to consider long-term as well as annual calving data (Hagen & Reeh, 2004; Dowdeswell & Hagen, 2004). The final element is bottom mass balance, which includes both basal melting

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