Methods

1. Estimating Glacier Thickness and Volume: A Case Study of the Nubra Basin, Himalaya-Karakoram, IndiaEvangeline Sessford and J. Graham Cogley41st annual Arctic Workshop: March 2-4, 2011 Montreal, Canada Results Introduction 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. 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. 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). 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 toestimates 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. Table 1: Results from this study and those of Raina and Srivastava (2008). Study Area 77E Table 2: Results from this study and those of Raina and Srivastava (2008). PAKISTAN The Nubra basin lies in the northernmost region of India, bordering the Pakistani-Indian 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. 35.33 N INDIA 34.66 N Figure 3: Mean residuals of volume estimates. Zero marks the value of measured volumes. Figure 4: Mean residuals of mean thickness estimates. Zero marks the value of measured mean thickness. N 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. Methods • 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. • Shallow Ice Approximation (SIA) • h = τb /(ρ g sin α) [mean thickness] • 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 = S k h [volume] • where V is volume (km3), S is area (km2) , k is a correction factor (which is π/4 for an assumed semi-elliptical 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] • where c is 28.5 when S has the units of km2 and can be interpreted as the estimated thickness (metres) of a 1 km2 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). Figure 6: Estimated and measured volumes of 158 mountain and valley glaciers. 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. 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. 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. Raina, V.K., Srivastava, D. (2008): Glacier Atlas of India.Geological Society of India, Bangalore. N Figure 2: Section of Nubra basin indicating map type and program used.