Geodetic mass balance record with rigorous uncertainty estimates deducedfrom aerial photographs and lidar data – Case study from Drangaj?kull icecap, NW Iceland

摘要

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 Drangaj?kull 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 Ḃ? =??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 Ḃ??=?0.27?±?0.11?m?w.e.?a?1. There is a strikingdifference when Ḃ ?is calculatedseparately for the western and eastern halves of Drangaj?kull, 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.