Terminus data for: Multi-decadal retreat of Greenland’s marine-terminating glaciers

The details are included in the manuscript and elements of the 'Ice-front change mapping' section are copied here, with minor edits: We mapped the change in ice-front position between image pairs using the ‘box method’ of Moon and Joughin (2008) and Howat and others (2010). On each image, we manually digitized (with a computer mouse) the outline of a polygon bounded on the down-glacier edge by the ice front, on each lateral side by parallel lines approximating the glacier margins, and on the upstream side by an arbitrary straight line placed inland of the minimum observed front position. This polygon was overlain on the second image, and the ice-front border of the polygon was adjusted to the new front position. The difference in the area of the polygon between successive images is the area change of the front, and the average retreat distance is obtained by dividing the area of retreat by the polygon width. This procedure yields a less arbitrary measure of front position change than the change along a center line, and captures spatially asymmetric retreat and advance. The primary sources of error in this measurement are (1) errors in manual selection of the front position, (2) image co-registration error due to terrain and other factors and (3) uncertainty in feature locations due to pixel resolution. The first source is difficult to quantify, but is likely substantially reduced by the averaging inherent in the ‘box method’, since the front position is sampled in many locations along the front, rather than at a single point (Moon and Joughin, 2008). In some cases, the front was difficult to locate unambiguously due to the presence of semi-detached icebergs. In these cases, separate maximum and minimum positions (i.e. including and excluding the icebergs) were mapped to provide a range in estimates, which typically resulted in a difference of <0.1 km a–1 for a few glaciers. One exception, however, was Zachariæ Isstrøm on the northwest coast, which underwent a break-up of its poorly defined front between 2000 and 2005 as noted by Moon and Joughin (2008). The change in front position due to this break-up can vary by 1.5–2.5 km, giving a rate uncertainty of 150–250ma–1, depending on where the front is placed. Since the total retreat was ~1.8 km, however, this uncertainty is only 8–14% of the rate of change. Additionally, this single retreat does not have an appreciable effect on the uncertainty of the average changes in the northeast subsample for 2000–10, due to the large number of observations (N = 35). The second and third sources of uncertainty are quantified by, first, measuring the offset of stationary features near sea level to determine the co-registration error. Second, the square of this error is summed with the pixel resolution and multiplied by the number of pixels on the perimeter of the polygon representing the front area difference between successive images. The RMS co-registration error is 94 m for warp-registered MSS imagery, 65m for TM imagery and 36 m for ETM+ imagery. This yields a standard error of 300 m (or ~23 m a–1) for front position changes between 1972 and 1985, and 90 m (~9 m a–1) for position changes between 2000 and 2010, with other time combinations falling between these. Since the error for individual position change measurements is likely to be spatially and temporally random, uncertainties of typically +/-2–3 m a–1, and never more than+/-10 m a–1 for all mean and median change estimates. References: Howat, I. M., J. E. Box, Y. Ahn, A. Herrington, and E. M. McFadden (2010), Seasonal variability in the dynamics of marine-terminating outlet glaciers in Greenland, Journal of Glaciology, 56(198), 601–613. Moon, T., and I. Joughin (2008), Changes in ice front position on Greenland's outlet glaciers from 1992 to 2007, J Geophys Res-Earth, 113(F2), F02022, doi:10.1029/2007JF000927.

详细内容已收录于论文手稿中，以下节选自"冰前端（ice-front）变化制图"章节并经少量编辑：
我们采用Moon与Joughin（2008）以及Howat等人（2010）提出的"框法（box method）"，对影像对间的冰前端位置变化进行了制图。
在每幅影像上，我们通过鼠标手动数字化勾勒多边形轮廓：该多边形的冰川下游边界由冰前端划定，两侧边界为近似冰川边缘的平行线，上游边界则为置于观测到的最小前端位置内陆侧的任意直线。
将该多边形叠加至第二幅影像后，调整多边形的冰前端边界以匹配新的前端位置。
相邻影像间多边形面积的差值即为前端的面积变化量，通过将退缩面积除以多边形宽度，即可得到平均退缩距离。
相较于沿中心线的变化量计算方法，该流程得到的前端位置变化量主观性更低，且可捕捉空间上不对称的退缩与前进过程。
该测量过程的主要误差来源包括：(1) 人工选取前端位置时产生的误差；(2) 由地形及其他因素导致的影像配准（co-registration）误差；(3) 由像素分辨率引发的地物位置不确定性。
第一种误差来源难以量化，但由于"框法"天然具备平均效应——沿冰前端在多个位置采样前端位置，而非仅选取单点——因此该误差大概率会被大幅降低（Moon与Joughin，2008）。
在部分场景中，由于存在半脱离的冰山，冰前端的位置难以被明确界定。对此，我们分别绘制了包含与不包含冰山的最大、最小前端位置，以给出估算值的区间范围；对于少数冰川而言，该方式通常会导致年变化差值小于0.1 km·a⁻¹。
但西北海岸的扎卡里亚艾斯特罗姆冰川（Zachariæ Isstrøm）是个例外，正如Moon与Joughin（2008）所述，该冰川在2000至2005年间发生了前端边界模糊的崩解事件。
此次崩解导致的前端位置变化量可达到1.5~2.5 km，根据前端位置选取的不同，其速率不确定性可达150~250 m·a⁻¹。
但由于总退缩量约为1.8 km，该不确定性仅占变化速率的8%~14%。
此外，由于观测样本量较大（N=35），此次单次退缩事件对2000至2010年东北部子样本的平均变化量不确定性未产生显著影响。
第二、第三种不确定性来源的量化方式如下：首先，通过测量近海平面固定地物的偏移量来确定影像配准误差；其次，将该误差的平方与像素分辨率相加后，乘以代表相邻影像间前端面积差值的多边形周长所对应的像素数。
经扭曲配准的MSS影像的均方根（RMS）配准误差为94 m，TM影像为65 m，ETM+影像为36 m。
以此计算，1972至1985年间冰前端位置变化的标准误差为300 m（约合23 m·a⁻¹），2000至2010年间则为90 m（约合9 m·a⁻¹），其余时间组合的误差值介于二者之间。
由于单次位置变化测量的误差在空间与时间上均呈随机分布，所有均值与中位数变化估算值的不确定性通常为±2~3 m·a⁻¹，最高不超过±10 m·a⁻¹。
参考文献：
Howat, I. M., J. E. Box, Y. Ahn, A. Herrington, and E. M. McFadden (2010), Seasonal variability in the dynamics of marine-terminating outlet glaciers（海洋终止型出口冰川） in Greenland, Journal of Glaciology, 56(198), 601–613.
Moon, T., and I. Joughin (2008), Changes in ice front position on Greenland's outlet glaciers（出口冰川） from 1992 to 2007, J Geophys Res-Earth, 113(F2), F02022, doi:10.1029/2007JF000927.