The spatial distribution of glacier depth and assessment of glacial-stored water is essential information to manage water resources in North India. Glacier ice thickness can be estimated using ground penetrating radar (GPR), and this technique has been used to estimate depth of few glaciers such as the Dokriani Bamak, Patseo and Chotta Shigri (Gergan et al. 1999; Singh et al. 2010, 2012). An attempt was also made to measure the ice thickness of Samudra Tapu but failed due to the limitations of the instrument (Singh et al. 2010). The ice thickness of the Dokriani and the Chotta Shigri glaciers measured by GPR ranged from 15 to 120 m and 110 to 150 m, respectively. The depth of the Patseo glacier was estimated at 40 m. But these in situ measurements are clearly limited in number, and moreover, these records are point measurements and do not cover the entire glacier.
Alternatively, glacier volume is estimated through glacier parameters such as area, length and slope. Various scaling methods estimate volume by developing empirical relationships between volume and glacier parameters (Chen and Omura 1990; Bahr 1997; Liu and Sharma 1998; Arendt et al. 2006; Cuffey and Paterson
2010). However, glacier-stored water in the Indian Himalayas estimated by
Fig. 2 Glacier outline from the inventory of the International Centre for Integrated Mountain Development (ICIMOD), Randolph Glacier Inventory (RGI) and the interpretation of glacier extents from the present study overlaid on Landsat imagery of 2014 of Naradu Garang in the Baspa basin, Himachal Pradesh
different scaling methods shows large variability (Fig. 3). Also, these methods have their own limitations. Few volume-scaling methods are developed for glaciers of different geomorphological settings than those of glaciers in the Indian Himalayas and hence, are inherently not free of uncertainties. Error in delineating glacier boundary can magnify the error in volume estimates that are deduced from volume area scaling method. Moreover, scaling methods estimate only the amount of glacier-stored water and not the spatial distribution of thickness.
To address this limitation, a method based upon surface velocity and flow law of ice was developed to estimate the ice thickness distribution (Gantayat et al. 2014). In this approach, surface velocity fields were estimated using remote sensing data, and then ice thickness is determined using flow law of ice (Eqs. 1 and 2). The methodology is applied to the Gangotri Glacier (Figs. 4 and 5).
Fig. 3 Estimation of glacier-stored volume in the Indian Himalaya using Randolph Glacier Inventory (RGI), and various scaling methods show large variability
Fig. 4 Surface velocity field of the Gangotri Glacier, varying from 85 to 5 ma 1. Maximum velocity at higher reaches and minimum velocities along the glacier boundary were observed. The two large white dots represent the sites where surface velocity was validated using field measurements. Source Gantayat et al. (2014)
Fig. 5 The model thickness of ice was varying from 40 to 540 m, and maximum thickness was observed in the central part of the main trunk, whereas the thickness at the snout is estimated to be in the range of 40-65 m. Source Gantayat et al. (2014)
where Us and Ub are surface and basal velocities, respectively. In the absence of basal velocity, Ub is assumed to be 25 % of the surface velocity (Swaroop et al. 2003). Glen’s flow law exponent, n, is assumed to be 3, H is ice thickness and A is a creep parameter. s is basal stress. p is the ice density, g is acceleration due to gravity and f is a scale factor, i.e. the ratio between the driving stress and basal stress along a glacier, and f is assumed to be 0.8 (Haeberli and Hoelzle 1995). Slope a is estimated from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEM elevation contours, at 100-m intervals. This gives depth for each area between successive 100-m contours which are all plotted together to provide an ice-thickness distribution for the entire glacier. The total ice volume was estimated to be around 1.8 ± 0.5 km3 (Gantayat et al. 2014). This compares well with the estimates of Gabbi et al. (2012) and Farinotti et al. (2009), as 1.36 ± 0.07 and 1.96 km3, respectively.