Spatially integrated geodetic glacier mass balance and its uncertainty based on geostatistical analysis: application to the western Svartisen ice cap, Norway

Estimates of glacier mass balance using geodetic methods can differ significantly from estimates using direct glaciological field-based measurements. To determine if such differences are real or methodological, there is a need to improve uncertainty estimates in both methods. In this paper, we focus on the uncertainty of geodetic methods and describe a geostatistical technique that takes into account the spatial correlation of the elevation differences when calculating spatially averaged elevation changes. We apply this method to the western Svartisen ice cap, Norway, using elevation differences from the surrounding bedrock derived from stereophotogrammetry. We show that the uncertainty is not only dependent on the standard error of the individual elevation differences but is also dependent on the size of the averaging area and the scale of the spatial correlation. To assess if the geostatistical analysis made over bedrock is applicable to glacier surfaces, we use concurrent photogrammetrical and laser scanning data from bedrock and a range of glacier surfaces to evaluate the dependency of the geostatistical analysis on the surface type. The estimated geodetic mass balance, and its uncertainty, is -2.6 +/- 0.9 m w.e. for the period 1968-85, and -2.0 +/- 2.2 m w.e. for 1985-2002.