3 | DATA AND METHODOLOGY
3.1 | Data (Glacier inventory and digital elevation
model)
Spatial data included the digital elevation model (DEM) and PGI, SUPARCO
released the available latest PGI database in cooperation with ITPCAS,
previous studies rely on the old version of the glacier database mostly,
therefore the accumulated glacier area was too large. PGI was originated
from Landsat-8 (30 m) imagery that acquired from 2013 to 2015. The
potential error in the glacial boundary estimated measurement
(Eb ), in case of the debris-covered is 2.6%, whereas for the
clean glacier area is 1.9%, with the calculated adjustment error is
below 0.35%. Similarly, to assess the average error (θ ), the PGI
was compared with the boundaries delineated through some high-resolution
multispectral images of Pleiades and SPOT-5, 6 & 7. In total, 32
glaciers were randomly selected for this comparison, the result shows
less than 9% difference in the debris-covered outlines, on the other
hand, the θ -value in clean glacier outline is found less than 5%
(SUPARCO & ITPCAS, 2015). We counted smaller glacier area because of
the improved mapping accuracy, and PGI excluded glaciers with an area
that less than 0.01 km2. Meanwhile, we used the
Chinese Glacier Inventory version 2.0 (CGI2.0)
(http://data.tpdc.ac.cn/) and
GLIMS Randolph Glacier Inventory version 6.0 (RGI6.0)
(http://www.glims.org/RGI/) as
the supplemental database to determine glacier outline of a small part
of Shyok and Kharmong sub-basins that PGI uncovered (Guo et al., 2015).
The quality of GlabTop2-modeled ice thickness largely depends on DEM,
and we derived the topographic inputs from the free Shuttle Radar
Topography Mission Digital Elevation Model (SRTM-C DEM)
(http://dds.cr.usgs.gov/srtm/version2_1/SRTM1), which has a high
spatial resolution of 1 arc-second (approximately 30 m). SRTM-C DEM was
released in 2011 by NASA and NGA and acquired using a radar
interferometry technique. We can collect the most accurate glacier
surface elevation because it can penetrate many meters into snow firm
efficiently and has been used successfully over 80% of the earth’s land
surface between 60°N and 56°S latitude interval. In the subsequent
study, we mosaiced the SRTM-C DEM, and projected it to Universal
Transverse Mercator Projection (UTM43N) and World Geodetic System 1984
ellipsoidal elevation (WGS84), all GPS data were kept the unified
projections.
3.2 | Methodology
3.2.1 | Ground-penetrating radar and GPS field
investigation
In the 1980s, the Lanzhou
Institute of Glaciology and Geocryology, Chinese Academy of Science
conducted the B-1 GPR work on the Antarctic Nelson, Urumqi glacier No.
1, and Hailuogou glacier (Su, Ding & Liu, 1984; Zhang, Zhu, Qian, Chen
& Shen, 1985). A direct
comparison between the GPR-surveyed ice depth with the results derived
from the hot water drilling technique indicated that radar results were
usually within ± 5% deviation (Liu,
2012), it was verified
by the precise ice core drilling
data down to the bedrock in the ablation area of the Hailuogou
glacier,
the B-1 GPR were quite satisfied with an error below 5 m (Wang, Li, Shen
& Huang, 1996). In this study, we used an impulse B-1 modified GPR
system with a separate transmitter and receiver antenna separated by a
fixed distance of 5 or 10 m, the low frequency (approximately 2–220
MHz) is much more suitable for probing mountain glaciers, this GPR has a
standard offset geometry with point measuring mode with a 5-MHz
resistively loaded dipole antenna length of 10 m and wavelength of 33.8
nm. On the two-dimensional radar graphic, we derived ice thickness
(h ) from the vertical axis radar wave and calculated the two-way
travel time by the following equation:
\(h=\frac{\sqrt{v^{2}t^{2}-x^{2}}}{2}\) (1)
where t refers to the two-way travel time of radar wave, xrefers to the distance between transmitter and receiver antenna, andv refers to the velocity of radar signal in the glacier.
The speed of electromagnetic wave
propagation in the ice was assessed to be 0.169-0.171 m
ns-1, we set it to be 0.169 ± 0.002 m
ns-1, ensuring the relative error was within the
accuracy demands of glaciology research.
During the actual operation process, firstly, we adjusted a start point
of echo wave to check the whole wave shape was displayed on the GPR
screen, then measured the t -value between the direct wave arrival
through the air and the reflections from the ice bedrock, finally, we
determined the h -value of measured points by identifying the ice
and bedrock interface in the radar graphic. Glacier surface elevation of
GPR points was surveyed simultaneously by a differential global
positioning system (DGPS) device (SF-3050 GNSS, NavCom Technology, Inc.,
accuracy < 0.05 m) and a portable GPS
(Shtech, accuracy≤ ± 1 m).
The accuracy of ice thickness was
decided by two factors: one is the measuring system, another is the
property of ice and bedrock, the accuracy of travel time was determined
to be ± 10 ns (1.6 m) from the oscilloscope trace. In our study, Batura
glacier, the maximum error was ± 2.4 m (the highest thickness
measurement 201 m), within the quoted error at ± 5%.
3.2.2 | Description of GlabTop2
Model
GlabTop2 is a grid-based and slope-dependent ice thickness estimate
model, Linsbauer et al. (2009) established and developed it based on the
flow mechanics of the relationship between average basal shear stress
(τ ) with shape factor (f ) (Nye, 1952; Paterson, 1970),
the detailed formula explanation
of GlabTop2 were depicted as follows:
\(h=\frac{\tau}{\text{fρg\ }\sin(\alpha)}\) (2)
\begin{equation}
H\leq 1.6\ km,\tau=0.005+1.598H-0.435{H}^{2}\nonumber \\
\end{equation}\(H>1.6\ \text{km},\ \ \tau=150\ kPa\) (3)
\(f=\frac{w}{h_{m}}\) (4)
where the quantity of τ is
under a perfect-plasticity assumption for the flow rheology. τ is
parameterized with the glacier vertical elevation range (ΔH )
(Haeberli & Hölzle, 1995). The f -values depends on the aspect
ratio of half-width (w ) to the
midpoints’ depth on central
flowline (hm ) along the glacier cross-section, it
is usually set to 0.8 for all glaciers (Paterson, 1994). ρ refers
to the ice density (900 kg m-3),g refers to
the gravitational acceleration (9.81 m s-2), andα refers to the surface slope. A detailed working flow chart for
processing data, GPR diagram, and GlabTop2 illustration schematic were
presented in Figure 2. GlabTop2 calculated ice thickness for selection
of a set of randomly picked DEM cells within the glacierized area, then
interpolated to the entire mask, which was fully automated and required
only glacier mask, DEM, and surface slope as inputs. It is indispensable
for solving the problem of the non-measured area (Farinotti, 2017; Frey
et al., 2014), and the prospect is considerable by using GPR-measured
ice thickness to modify the GlabTop2 results.
FIGURE 2 (a) Working flow chart for processing data, (b) GPR
(Liu, 2012), and (c) GlabTop2 illustration schematic (Frey et al., 2014)