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Estimating Glacier Thickness and Volume:
A Case Study of the Nubra Basin,
Himalaya-Karakoram, India
Evangeline Sessford and J. Graham Cogley
41st annual Arctic Workshop: March 2-4, 2011 Montreal, Canada
Results
Introduction
The Himalaya and Karakoram (H-K) have been of great interest to glaciologists and the general public
in recent years, specifically due to claims that the Himalayan glaciers will disappear by 2035 (Cruz et
al., 2007). These claims have caused much controversy among glaciologists as present data from the
region are unsatisfactory. The Earth’s fresh water supply is greatly dependent on the presence of
glaciers, therefore it is crucial to have an understanding of how much fresh water is stored in the
world’s ice. In order to estimate the volume of fresh water currently on Earth and to make predictions it
is necessary to be able to estimate glacier thickness and volume without actual field measurements.
Often it is impossible to conduct field research when glaciers are situated in areas of political unrest
(such as the Nubra), or when the steep terrain and inconsistent weather pose hazardous conditions. This
study has been conducted to appraise two methods, Shallow Ice Approximation (SIA) and Volume Area
Scaling (VS), for estimating mean glacier thickness and glacier volume to determine if outcomes are
significantly different. Results are validated by applying the same methods to various mountain and
valley glaciers which have actual field measurements, and are compared to estimates made by Raina
and Srivastava (2008). Glacier data of the Nubra basin will contribute to the World Glacier Inventory
Extended Format (WGI-XF) and a more detailed evaluation of methods used in estimating mean
glacier thickness and glacier volume will be available for future studies.
SIA and VS make it possible to estimate glacier ice volume and mean glacier thickness for mountain
and valley glaciers without having field measurements. The results for the Nubra basin shown in Tables
1 and 2 are placed in context by Figures 3, 4 and 5, which illustrate method validation with 158
mountain and valley glaciers around the globe. On average estimates are low, though the outcome of
VS is systematically closer than SIA to the measured values.
Nubra Basin Results
This Study
Glacier Count
155
204
Total Glacier Area (km2)
1804.33
1536
Total Basin Area (km)
4346.51
4278
41.5
36
Total Area Glaciated (%)
Table 1: Results from this study and those of Raina and Srivastava (2008).
Nubra Basin Results
SIA
Total Volume (km3)
Volume Siachen Glacier (km3)
35.33 N
INDIA
34.66 N
N
108.36
942.09 942.09
253.55
Volume Area Scaling
The outcome of VS for all glaciers is a mean systematic error for volume of -6.8% and -11.5% for
mean thickness. Again, when broken down into surface area bins, error decreases (Figures 3 and 4).
Area (km2)
Area (km2)
0.1
0
<1
1 to < 5
5 to < 10
0.1
≥ 10
-0.2
-0.3
-0.4
-0.5
SIA
-0.6
VS
where h is the mean glacier thickness (m), τb, parameterized as a function of the elevation range with
an upper limit of 1.6 km for the latter, is the basal shear stress (kPa), ρ is the density of ice (kg m–3),
g is the acceleration of gravity (m s–2), and α is the mean glacier surface slope along the central
flowline (Paul and Svoboda, 2009).
V=Skh
[volume]
where V is volume (km3), S is area (km2) , k is a correction factor (which is π/4 for an assumed semielliptical glacier cross-section of a typical valley or mountain glacier; Paul and Svoboda, 2009), and
h is mean thickness along the longest flowline.
Volume Area Scaling (VS)
h = 28.5 S0.357
[mean thickness]
km2
where c is 28.5 when S has the units of
and can be interpreted as the estimated thickness
2
(metres) of a 1 km glacier while 1.357 is the scaling exponent γ (Chen and Ohmura, 1990).
V = 28.5 S1.357
[volume]
where the volume equation has been modified using the square of the residuals to determine the
scaling exponent 1.357 (Chen and Ohmura, 1990).
SIA and VS estimates of h and V were also made for a collection of glaciers with measured h and V.
Equations were subsequently used with measured data of other glaciers to validate results which
were categorized by glacier size. Methods were compared using systematic error of the residuals and
graphical representation. Data for measured glaciers, compiled by JGC, were originally obtained by
various scientists using radio echo sounding (ground-penetrating radar).
-0.3
SIA
VS
-0.6
1
Figure 4: Mean residuals of mean thickness estimates. Zero marks the value of measured
mean thickness.
100
Estimated Volume (km3)
0.1
Msrd
V = 0.0372S1.3008
R² = 0.9473
VS
V = 0.0285S1.357
R² = 1
0.01
Msrd
SIA
VS
SIA
V = 0.0133S1.4313
R² = 0.9824
0.001
0.01
0.1
Area
[mean thickness]
-0.2
-0.5
Figure 3: Mean residuals of volume estimates. Zero marks the value of measured volumes.
1
≥10
5 to < 10
-0.1
1
Volume (km3)
h = τb /(ρ g sin α)
1 to < 5
-0.4
-0.7
0.0001
0.0001
Glacier lengths, maximum elevations, minimum elevation and areas were determined from Soviet
military maps dating to the late 1970s. The 1:200,000-scale maps, in the transverse Mercator
projection and referenced to the Pulkovo 1942 datum, were imported into Golden Software
Didger®4.
Measurements were exported to Microsoft Excel®2007 and equations for estimating mean ice
thickness and volume were implemented.
The constants given below apply only to mountain and valley glaciers, not to ice caps.
<1
0
-0.1
0.001
Shallow Ice Approximation (SIA)
4.
128.6 309.52
Shallow Ice Approximation
On average, SIA has a systematic error (estimated minus measured) of -52.9% for volume and -42.9%
for mean thickness. However, when subdivided into area classes the mean systematic error of volume
decreases with area (Figure 3); the same can be seen in Figure 4 for mean glacier thickness.
10
Methods
3.
199.45
100
Figure 1: Map of India and zoomed image of the Nubra
basin outlined in blue. The black line indicates the
approximate line of control between India and Pakistan.
2.
174.01 394.47
Residual
The Nubra basin lies in the northernmost
region of India, bordering the PakistaniIndian Line of Control, and is drained by
the Nubra River, a tributary of the Shyok
River. The Nubra River is fed by 155
glaciers (this study). Glaciers cover
41.5% (1804.33 km2) of the Nubra basin
(4346.51 km2). The largest of the glaciers
is the Siachen Glacier (942 km2), a
northwest-southeast trending glacier at
the head of the river and its main source.
All glaciers lie at an elevation between
3600 masl (the tongue of Siachen
Glacier) and 6980 masl (the maximum
elevation on Siachen Glacier) (this
study). All the glaciers in the Nubra basin
are either valley or mountain glaciers. It
is important to note that there are no ice
caps.
Raina and Srivastava
(2008)
VS
Table 2: Results from this study and those of Raina and Srivastava (2008).
Residual
PAKISTAN
1.
Surface Area Siachen (km2)
Study Area
77E
Raina and Srivastava
(2008)
1
10
100
1000
10
1
0.1
0.01
Msrd
SIA
VS
0.001
0.0001
0.0001
0.001
0.01
0.1
1
Figure 5: Estimated and measured volumes of 158 mountain and valley glaciers.
Discussion
Shallow Ice Approximation
SIA estimates of glacier mean thickness and volume presumably have larger systematic error than VS
due to their dependence on shear stress and slope. The derivation of the parameters for estimating shear
stress in terms of elevation range is uncertain, and their accuracy is unknown. If the estimated shear
stress is too low, then by the domino effect the volume and mean thickness estimates will also be too
low. The upper limit of 1.6 km on the elevation range for estimating shear stress, imposed for numerical
reasons, suggests that SIA mean thickness estimates for larger glaciers are probably unrealistic.
Volume Area Scaling
Although VS appears to estimate mean glacier thickness and volume with greater accuracy than SIA,
the factor c of 28.5 m, representing mean thickness for a glacier with 1 km2 surface area, was derived
from a sample of only 61 glaciers and is likely to be quite uncertain. With 95 % confidence a sample of
74 of the glaciers measured in this study has been analyzed using a normal distribution Z-test and found
to have a mean area of 0.98 km2, not significantly different from 1 km2. The same test was performed
on the mean thicknesses of the same sample, and it was found with 95 % confidence that there is
sufficient evidence to justify rejection of the claim that a typical mean thickness for a 1 km2 glacier is
28.5 m. A better estimate from the data of this study (Figure 5) is c = 37.2 ± 15.7 m. Therefore the VS
equation probably needs to be re-evaluated.
Comparison to The Glacier Atlas of India
Although the glacier count differs between the studies it does not impact the volume outcomes
significantly (Table 1 and 2). The reason may be that Raina and Srivastava considered tributary glaciers
as distinct glaciers. The accuracy of glacier volume estimates in the atlas is doubtful as the only
reference to data acquisition is to some Himalayan mountain glaciers in the Mount Everest region.
References
Cruz, R.V., H. Harasawa, M. Lal, S. Wu, Y. Anokhin, B. Punsalmaa, Y. Honda, M. Jafari, C. Li and N.
Huu Ninh (2007): Asia, in: Parry, M.L., O.F. Canziani, J.P. Palutikof, P.J. van der Linden and C.E. Hanson,
eds., Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the
Fourth Assessment Report of the Intergovernmental Panel on Climate Change, 469-506. Cambridge
University Press, Cambridge, UK.
Paul, F., Svoboda, F. (2009): A new glacier inventory on Southern Baffin Island, Canada, from
ASTER data: II. Data analysis, glacier change and application, Annals of Glaciology, 50,
22–31.
Figure 2: Section of Nubra basin indicating map type and program used.
100
Figure 6: Estimated and measured volumes of 158 mountain and valley glaciers.
Chen, J., Ohmura, A. (1990): Estimation of alpine glacier water resources and their change
since the 1870s, International Association of Hydrological Sciences Publication,
Hydrology in Mountainous Regions, 193, 127-135.
N
10
Measured Volume (km3)
(km2)
Raina, V.K., Srivastava, D. (2008): Glacier Atlas of India. Geological Society of India,
Bangalore.