Mountain glaciers and snow are crucial water resources for the surrounding river, lake, oasis, cropland and urban life in arid Central Asia [1
]. Glaciers’ ice volumes are usually estimated by Volume-Area (V-A) power law equations since there are few in situ measurements of ice volume using modern techniques, such as sounding echo, ground radar or gravity methods [2
]. The V-A scaling method is based on ice dynamics imposed by the climatic and topographic conditions in different glacierized regions, and has an inherent steady-state assumption [2
]. This assumption is often violated, with many glaciers being out of equilibrium [5
]. The volume estimation errors can exceed 50% for individual glaciers [6
]. Moreover, glaciers’ area change does not closely correspond to ice thickness changes (increase in the accumulation zone and decrease in the ablation zone), resulting in even larger errors, especially in estimating the ice volume changes by using glacier’s areas in different years [2
The glacier area is defined by the ice mass balance community as the extent in two horizontal dimensions (Figure 1
), i.e., the extent/outline of the glacier is projected onto the surface of an ellipsoid Earth surface, rather than the real topographic surface/the slope normal [7
]. The former is called 2D area (Figure 1
, A1), and the latter is called 3D area (Figure 1
, A2) in this study hereafter. Meanwhile, the ice/glacier thickness is defined as the vertical length (Figure 1
, T1) measured parallel to the vertical axis of the ellipsoid Earth surface and not normal to the glacier surface [7
]. Thus, the ice volume is the integral of the planar area and thickness. In contrast, the snow layer thickness (Figure 1
, T2) is usually measured perpendicularly relative to the slope normal of the snow/land surface [8
]. Both the glacier’s 2D area and thickness values are close to the true values for flat ice sheets and glaciers with gentle slope (<18°), while greater difference exists for glaciers with larger slopes, although the two pairs of definitions for area and thickness relative to horizontal normal (2D area) or slope normal (3D area) make no difference for calculating ice volume together (Figure 1
). The 3D area might be a better variable in the ice volume estimate using the V-A scaling method, since it considers the slope factor and reflects ice thickness changes. Moreover, glaciers’ 3D surface extent could be a better variable in modeling their surface melting and sublimation [9
Most glaciers in Central Tianshan lie in high mountainous areas over 3000 m a.s.l. These alpine glaciers often have complex catchments, divisions and large slopes. For example, one of the large glaciers, the Muzart Glacier near the Tumor Peak, is highly labile with fluctuating length, area, volume, and shape [1
], thus violating the steady state assumption of the V-A scaling method and leading to large uncertainties in the ice volume estimation.
Numerous studies have investigated glacier area changes in Central Tianshan based on satellite and airborne images and topographic data/DEM [1
]. Most studies analyze 2D planar areas, while few studies discuss the difference between glacier’s 2D areas and 3D areas [17
], partially due to the unavailability of topographic data with relatively high spatial resolution. Therefore, the primary objective of this study is to compute glaciers’ 2D and 3D areas and evaluate how the differences between them relate to changes in surface slope and elevation bands in the Muzart Glacier catchment and Central Tianshan.
5. Summary and Remark
This study utilizes the lastest relatively high-resolution global topographic data (ASTER GDEM V2) and CGI2 data to illustrate the large areal difference between glaciers’ 3D real surface extents and their projected 2D planar area in the Muzart Glacier catchment and Central Tianshan. Besides the CGI2 data, this study also extracts the glacier outlines from Landsat images in 2007 and 2013 by an object-based classification approach, which is validated using GeoEye high-resolution images and shows an accuracy of 89.3%. The extracted glacier outlines in 2007 also had an agreement of 89.3% with CGI2 data in the Muzart Glacier catchment. Most of the differences are in the lower-end of glaciers covered by debris.
The difference between 3D surface extents and 2D planar areas from those extracted glacier outlines in 2007 and 2013 (38.1%) are slightly larger than those of CGI2 (34.2%) in the Muzart Glacier catchment and were 27.9% on average in the entire Central Tianshan. The difference between 3D areas and 2D areas for the shrunk glaciers were slightly smaller than those of existing glaciers in the Muzart Glacier catchment (37.0%), and the entire Central Tianshan (27.6%) since many of the shrunk ones were located on the lower end of glaciers and had a smaller slope. Consequently, their relative shrinking rates from 2007 to 2013 were similar in both Muzart Glacier catchment (−7.8%, 30 km2) and Central Tianshan (−9.2%, 115 km2), although there was a large difference between 3D areas and 2D area of those shrunk glaciers. Those large areal differences remind us to re-consider glacier’s real topographic extent when discussing alpine glacier’s areal and volume changes, especially in calculating the glaciers surface energy balance and melting rates in the high Asian mountain glaciers with large surface slope and strong solar radiation.