标题：Geodetic mass balance record with rigorous uncertainty estimates deduced from aerial photographs and lidar data – Case study from Drangajökull ice cap, NW Iceland
摘要：In this paper we describe how recent high-resolution digital elevation models (DEMs) can be used to extract glacier surface DEMs from old aerial photographs and to evaluate the uncertainty of the mass balance record derived 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 was surveyed with airborne lidar in 2011. Aerial photographs spanning all or most of the ice cap are available from survey flights in 1946, 1960, 1975, 1985, 1994 and 2005. All ground control points used to constrain the orientation of the aerial photographs were obtained from the high-resolution lidar DEM. The lidar DEM was also used to estimate errors of the extracted photogrammetric DEMs in ice- and snow-free areas, at nunataks and outside the glacier margin. The derived errors of each DEM were used to constrain a spherical semivariogram model, which along with the derived errors in ice- and snow-free areas were used as inputs into 1000 sequential Gaussian simulations (SGSims). The simulations were used to estimate the possible bias in the entire glaciated part of the DEM and the 95 % confidence level of this bias. This results in bias correction varying in magnitude between 0.03 m (in 1975) and 1.66 m (in 1946) and uncertainty values between ±0.21 m (in 2005) and ±1.58 m (in 1946). Error estimation methods based on more simple proxies would typically yield 2–4 times larger error estimates. The aerial photographs used were acquired between late June and early October. An additional seasonal bias correction was therefore estimated using a degree-day model to obtain the volume change between the start of 2 glaciological 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 of mass gain, peaking in 1985–1994 with Ḃ = 0.27 ± 0.11 m w.e. a−1. There is a striking difference when Ḃ is calculated separately for the western and eastern halves of Drangajökull, with a reduction of eastern part on average ∼ 3 times faster than the western part. Our study emphasizes the need for applying rigorous geostatistical methods for obtaining uncertainty estimates of geodetic mass balance, the importance of seasonal corrections of DEMs from glaciers with high mass turnover and the risk of extrapolating mass balance record from one glacier to another even over short distances.
