Journal cover Journal topic
The Cryosphere An interactive open-access journal of the European Geosciences Union
The Cryosphere, 10, 159-177, 2016
https://doi.org/10.5194/tc-10-159-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
19 Jan 2016
Geodetic mass balance record with rigorous uncertainty estimates deduced from aerial photographs and lidar data – Case study from Drangajökull ice cap, NW Iceland
E. Magnússon1, J. Muñoz-Cobo Belart1, F. Pálsson1, H. Ágústsson2, and P. Crochet2 1Institute of Earth Sciences, University of Iceland, Sturlugata 7, 101 Reykjavík, Iceland
2Icelandic Meteorological Office, Bústaðavegi 7–9, 108 Reykjavík, Iceland
Abstract. In this paper we describe how recent high-resolution digital elevationmodels (DEMs) can be used to extract glacier surface DEMs from old aerialphotographs and to evaluate the uncertainty of the mass balance recordderived from the DEMs. We present a case study for Drangajökull ice cap,NW Iceland. This ice cap covered an area of 144 km2 when it wassurveyed with airborne lidar in 2011. Aerial photographs spanning all ormost of the ice cap are available from survey flights in 1946, 1960, 1975,1985, 1994 and 2005. All ground control points used to constrain theorientation of the aerial photographs were obtained from the high-resolutionlidar DEM. The lidar DEM was also used to estimate errors of the extractedphotogrammetric DEMs in ice- and snow-free areas, at nunataks and outside theglacier margin. The derived errors of each DEM were used to constrain aspherical semivariogram model, which along with the derived errors in ice- and snow-free areas were used as inputs into 1000 sequential Gaussiansimulations (SGSims). The simulations were used to estimate the possible biasin the entire glaciated part of the DEM and the 95 % confidence level ofthis bias. This results in bias correction varying in magnitude between 0.03 m (in 1975) and 1.66 m (in 1946) and uncertaintyvalues between ±0.21 m (in 2005) and ±1.58 m (in 1946). Error estimation methods based onmore simple proxies would typically yield 2–4 times larger error estimates.The aerial photographs used were acquired between late June and earlyOctober. An additional seasonal bias correction was therefore estimated using adegree-day model to obtain the volume change between the start of 2glaciological years (1 October).This correction was largest for the 1960 DEM, corresponding to an average elevation change of −3.5 m or approx. three-quarters of the volume change between the 1960 and the 1975 DEMs.The total uncertainty of the derived mass balance record is dominated by uncertainty in the volume changes caused by uncertainties of the SGSim bias correction,the seasonal bias correction and the interpolation of glacier surface where data are lacking.The record shows a glacier-wide mass balance rate of   = −0.26 ± 0.04 m w.e. a−1 for the entire study period(1946–2011). We observe significant decadal variability including periods ofmass gain, peaking in 1985–1994 with   = 0.27 ± 0.11 m w.e. a−1. There is a strikingdifference when  is calculatedseparately for the western and eastern halves of Drangajökull, with areduction of eastern part on average  ∼  3 times faster than thewestern part. Our study emphasizes the need for applying rigorousgeostatistical methods for obtaining uncertainty estimates of geodetic massbalance, the importance of seasonal corrections of DEMs from glaciers withhigh mass turnover and the risk of extrapolating mass balance record fromone glacier to another even over short distances.

Citation: Magnússon, E., Muñoz-Cobo Belart, J., Pálsson, F., Ágústsson, H., and Crochet, P.: Geodetic mass balance record with rigorous uncertainty estimates deduced from aerial photographs and lidar data – Case study from Drangajökull ice cap, NW Iceland, The Cryosphere, 10, 159-177, https://doi.org/10.5194/tc-10-159-2016, 2016.
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Short summary
We demonstrate the opportunities given by high resolution digital elevation models (DEMs) to improve procedures for obtaining mass balance records from archives of aerial photographs. We also describe a geostatistical approach to estimate uncertainty of elevation changes derived by differencing DEMs. This method is more statistically robust than other described in the literature. Our study highlights a common tendency of overestimating this uncertainty, downgrading geodetic mass balance records.
We demonstrate the opportunities given by high resolution digital elevation models (DEMs) to...
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