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Glacier thickness and volume estimation in the Upper Indus Basin using modeling and ground penetrating radar measurements

Published online by Cambridge University Press:  15 January 2024

Shakil Ahmad Romshoo Open the ORCID record for Shakil Ahmad Romshoo [Opens in a new window] ,
Tariq Abdullah ,
Ummer Ameen  and
Mustafa Hameed Bhat
Shakil Ahmad Romshoo*
Affiliation:
Department of Geoinformatics, School of Earth and Environmental Sciences, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India Islamic University of Science and Technology, Awantipora Kashmir, Jammu and Kashmir, 192122, India Centre of Excellence for Glacial Studies in the Western Himalaya, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India
Tariq Abdullah
Affiliation:
Centre of Excellence for Glacial Studies in the Western Himalaya, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India Department of Planning and Geomatics, Islamic University of Science and Technology, Awantipora Kashmir, Jammu and Kashmir, 192122, India
Ummer Ameen
Affiliation:
Department of Geoinformatics, School of Earth and Environmental Sciences, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India Centre of Excellence for Glacial Studies in the Western Himalaya, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India
Mustafa Hameed Bhat
Affiliation:
Department of Geoinformatics, School of Earth and Environmental Sciences, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India Centre of Excellence for Glacial Studies in the Western Himalaya, University of Kashmir, Hazratbal Srinagar, Kashmir, Jammu and Kashmir, 190006, India
*
Corresponding author: Shakil Ahmad Romshoo; Email: shakilrom@kashmiruniversity.ac.in
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Abstract

In the Himalaya, ice thickness data are limited, and field measurements are even scarcer. In this study, we employed the GlabTop model to estimate ice reserves in the Jhelum (1.9 ± 0.6 km3) and Drass (2.9 ± 0.9 km3) sub-basins of the Upper Indus Basin. Glacier ice thickness in the Jhelum ranged up to 187 ± 56 m with a mean of ~24 ± 7 m, while the Drass showed ice thickness up to 202 ± 60 m, with a mean of ~17 ± 5 m. Model results were validated using Ground Penetrating Radar measurements across four profiles in the ablation zone of the Kolahoi glacier in the Jhelum and nine profiles across the Machoi glacier in the Drass sub-basin. Despite underestimating ice-thickness by ~10%, the GlabTop model effectively captured glacier ice-thickness and spatial patterns in most of the profile locations where GPR measurements were taken. The validation showed high correlation coefficient of 0.98 and 0.87, low relative bias of ~ −13% and ~ −3% and a high Nash–Sutcliffe coefficient of 0.94 and 0.93 for the Kolahoi and Machoi glaciers, respectively, demonstrating the model's effectiveness. These ice-thickness estimates improve our understanding of glacio-hydrological, and glacial hazard processes over the Upper Indus Basin.

Keywords

Distributed ice-thickness modelingGlacier–volume and mass storageGPRUpper Indus Basin
Type
Article
Information
Annals of Glaciology , First View , pp. 1 - 11
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of International Glaciological Society

1. Introduction

The Himalaya has the largest glacier area outside the poles (Bolch and others, Reference Bolch2012; Sakai, Reference Sakai2019) sustaining lives and livelihood of millions of people downstream (Immerzeel and others, Reference Immerzeel, Van Beek and Bierkens2010; Tuladhar and others, Reference Tuladhar, Pasakhala, Maharjan and Mishra2021). Glaciers in the Himalaya and elsewhere in the world exert a complex influence on land surface and climate processes (Milner and others, Reference Milner2017; Johnson and Rupper, Reference Johnson and Rupper2020) and are anticipated to affect the regional hydrological regimes under the projected climate change (Romshoo and others, Reference Romshoo, Bashir and Rashid2020a; Chen and Yao, Reference Chen and Yao2021). The assessment of land system changes, changes in the local, and regional climate and hydrological regimes and glacial hazards requires an accurate estimate of glacier volume and ice thickness distribution (Huss and Hock, Reference Huss and Hock2018). However, despite far-reaching implications, glacier volume and ice thickness distribution estimates over the Himalayan region are limited largely due to technological limitations, remoteness, and challenging topography (Bolch and others, Reference Bolch2012) and the consequent limited field observations (Wagnon and others, Reference Wagnon2013; Zhang and others, Reference Zhang, Wang and Zhou2022). As a result, knowledge about the amount of water stored in these glaciers and their response to changing climate is limited. It is important to note that accelerated glacier melting and the consequent impacts on various dependent sectors have attracted the attention of researchers from all over the world to understand the response and behavior of the Himalayan glaciers (Cogley and others, Reference Cogley, Kargel, Kaser and Van Der Veen2010; Bhambri and others, Reference Bhambri, Bolch, Chaujar and Kulshreshtha2011; Gardelle and others, Reference Gardelle, Berthier, Arnaud and Kääb2013; Gardner and others, Reference Gardner2013; Kääb and others, Reference Kääb, Treichler, Nuth and Berthier2015; Brun and others, Reference Brun, Berthier, Wagnon, Kääb and Treichler2017; Salerno and others, Reference Salerno2017; Maurer and others, Reference Maurer, Schaefer, Rupper and Corley2019; Abdullah and others, Reference Abdullah, Romshoo and Rashid2020). However, most of these studies have investigated glacier retreat (Kamp and others, Reference Kamp, Byrne and Bolch2011; Pandey and others, Reference Pandey, Ghosh and Nathawat2011), mass balance (Ghosh and Pandey, Reference Ghosh and Pandey2013), glacier elevation changes (Abdullah and others, Reference Abdullah, Romshoo and Rashid2020; Romshoo and others, Reference Romshoo, Abdullah, Rashid and Bahuguna2022a), climate change impacts (Rashid and others, Reference Rashid, Romshoo and Abdullah2017) and only a few have studied glacier ice thickness or volume (Linsbauer and others, Reference Linsbauer2009; McNabb and others, Reference McNabb2012; Frey and others, Reference Frey2014; Gantayat and others, Reference Gantayat, Kulkarni and Srinivasan2014; Linsbauer and others, Reference Linsbauer2016; Farinotti and others, Reference Farinotti2017; Farinotti and others, Reference Farinotti2019; Sattar and others, Reference Sattar, Goswami, Kulkarni and Das2019; Pandit and Ramsankaran, Reference Pandit and Ramsankaran2020; Millan and others, Reference Millan, Mouginot, Rabatel and Morlighem2022; Nela and others, Reference Nela, Singh and Kulkarni2023). It is pertinent to mention that direct ice thickness measurements over the Himalayan region are available for only about 15 glaciers (Mishra and others, Reference Mishra2022).

The glacier thickness and volume are the basic and most important parameters for projecting the future glacier evolution (Le Meur and others, Reference Le Meur, Gerbaux, Schäfer and Vincent2007; Kaser and others, Reference Kaser, Großhauser and Marzeion2010; Gabbi and others, Reference Gabbi, Farinotti, Bauder and Maurer2012; Immerzeel and Bierkens, Reference Immerzeel and Bierkens2012; Farinotti and others, Reference Farinotti2019; Liang and Tian, Reference Liang and Tian2022), future water availability (Huss and others, Reference Huss, Farinotti, Bauder and Funk2008), and estimation of future sea-level rise (Gabbi and others, Reference Gabbi, Farinotti, Bauder and Maurer2012). Information about glacier thickness, besides being required for glacier, volume estimation, is also important for various glacio-hydrological studies (Huss and others, Reference Huss, Farinotti, Bauder and Funk2008), regional and local climate modeling (Kotlarski and others, Reference Kotlarski, Jacob, Podzun and Paul2010) and assessment of glacier hazards (Frey and others, Reference Frey2014). Due to the paucity of sufficient information, particularly about glacier thickness and volume (Haq and others, Reference Haq, Azam and Vincent2021), it is difficult to assess glacier dynamics and future glacier projections under climate change in the Himalaya (Jacob and others, Reference Jacob, Wahr, Pfeffer and Swenson2012).

The existing glacier volume estimates are largely based on a simple volume–area relation (Chen and Ohmura, Reference Chen and Ohmura1990; Bahr and others, Reference Bahr, Meier and Peckham1997) and slope-dependent glacier thickness estimation (Hoelzle and Haeberli, Reference Hoelzle and Haeberli1995). It is noteworthy that volume estimates based on volume–area scaling are inherently unstable, nonunique and sensitive to small changes in glacier boundaries (Bahr and others, Reference Bahr, Pfeffer and Kaser2012) and, the estimates quite often vary considerably between these methods. For example, Frey and others (Reference Frey2014) estimated the glacier volume over the Himalaya–Karakoram region to range from 2955 to 4737 km3 based on various approaches and the glacier mean thickness varies from 94–158 m in the Karakoram and 54–83 m in the Himalayan region (Frey and others, Reference Frey2014). Similarly, Bolch and others (Reference Bolch2012) reported glacier ice volume estimates over the Himalaya ranging from 2300 to 6500 km3 depending on the approach employed. On the other hand, Ohmura (Reference Ohmura2009) estimated glacier volume between 3800 and 4850 km3 over the Himalaya encompassing the parts of Pakistan, Nepal, Bhutan and India. Depending on the glacier inventory used, Cogley (Reference Cogley2011) estimated glacier volume in the range of 3600–7200 km3 for the Karakoram–Himalaya region. Recently, various spatially distributed glacier ice-thickness estimation models have been used to estimate glacier volume in the Himalaya and elsewhere (Linsbauer and others, Reference Linsbauer2009; McNabb and others, Reference McNabb2012; Gantayat and others, Reference Gantayat, Kulkarni and Srinivasan2014; Farinotti and others, Reference Farinotti2017, Reference Farinotti2019; Millan and others, Reference Millan, Mouginot, Rabatel and Morlighem2022) but there are significant differences in these estimates (Farinotti and others, Reference Farinotti2017; Farinotti and others, Reference Farinotti2019). Based on an ensemble of five distributed ice-thickness models, Farinotti and others (Reference Farinotti2019), for example, estimated glacier volume of the Jhelum (2.2 km3) and Drass (3.4 km3) sub-basins of the Upper Indus Basin. These simulated estimates usually lack validation from ground observations, particularly in the Upper Indus Basin (Haq and others, Reference Haq, Azam and Vincent2021).

Against this background, we simulated ice-thickness and volume of all the glaciers in the two sub-basins of the Upper Indus Basin; Jhelum and Drass using GlabTop distributed ice thickness model (Linsbauer and others, Reference Linsbauer, Paul and Haeberli2012) and validated the model estimates with field-based thickness estimates observed from several transects across two glaciers, one each from the Jhelum and Drass sub-basins of the Upper Indus Basin, employing 8 MHz GPR. We also used a different approach for ice-thickness estimates but the results did not look promising in comparison to field-based observations. In order to reduce the errors in the estimation of water stored in the Himalayan cryosphere, the purpose of this work was to establish a reliable approach based on simple parameterization for predicting ice thickness and volume estimates over a large region such as Himalaya. The knowledge of glacier thickness and volume is crucial for a wide range of applications, including predicting future water availability, assessing glacier hazards, glacio-hydrological investigations, estimating future sea-level rise and predicting future status and evolution of glaciers, that are rapidly melting due to climate change.

2. Study area

The Upper Indus Basin has an area of ~ 17 000 km2 and extends from the HinduKush through Karakoram to the western margins of the Tibetan Plateau (Immerzeel and others, Reference Immerzeel, Van Beek and Bierkens2010). With elevation ranging from 200 to 8600 m a.s.l., the Upper Indus Basin has a mean annual temperature of −1.3°C and mean annual precipitation of ~644 mm (Zou and others, Reference Zou2021). Around 10% of the Upper Indus Basin is covered by 11 711 glaciers and 80% of these glaciers are distributed in sub-basins of Hunza, Shigar and Shyok (Bajracharya and Basanta, Reference Bajracharya and Basanta2011). The study area in this research comprises of the Jhelum and Drass sub-basins of the Upper Indus Basin. The Jhelum sub-basin has ~ 150 glaciers covering an area of ~ 85 km2 (Romshoo and others, Reference Romshoo, Fayaz, Meraj and Bahuguna2020b). The basin has ~ 0.7% of its area covered by glaciers mainly confined to the Lidder and Sind watersheds (Romshoo and others, Reference Romshoo, Abdullah and Bhat2021). The Jhelum sub-basin has temperate type of climate dominated by the western disturbances (Dimri and Mohanty, Reference Dimri and Mohanty2009). The Drass sub-basin has a cold semiarid type of climate which is also dominated by the western disturbances and hosts 190 glaciers with an area of ~167 km2 (Romshoo and others, Reference Romshoo2022b). Both sub-basins receive precipitation in the form of snow largely during winter (Zaz and others, Reference Zaz, Romshoo, Krishnamoorthy and Viswanadhapalli2019; Romshoo and others, Reference Romshoo2022b). Most of the glaciers in both sub-basins are located in the elevation range 4500–5000 m a.s.l.

We selected the Kolahoi and Machoi glaciers in the Jhelum and Drass sub-basins, respectively, for the validation of the modeled ice thickness. The Kolahoi glacier (KG) with an area of ~11 km2 forms the largest glacier by area in Jhelum basin (Rashid and others, Reference Rashid, Romshoo and Abdullah2017). It has northerly aspect and lies between 34°07′ to 34°12′N latitude and 75°16′ to 75°23′E longitude (Fig. 1). The melt-waters emanating from the Kolahoi glacier in the form of west Lidder River, join the east Lidder River at Pahalgam, ~35 km from the present snout of the glacier and thereafter flows as Lidder River before discharging into the Jhelum River, one of the major tributaries of the Indus River. The glacier has mean altitude of ~ 4450 m a.s.l. and the slope varies from 7° to 60° with mean value of ~20°. The Machoi glacier (MG) is located in the Drass sub-basin, about 26 km from Sonamarg, the major tourist attraction in the Kashmir valley (Fig. 1). The glacier has an area of ~6 km2 and is the largest glacier in the Drass sub-basin (Romshoo and others, Reference Romshoo2022b). The Drass River originating from the melt-waters of the Machoi glacier joins the Suru River at the Kargil town (Pall and others, Reference Pall, Meraj and Romshoo2019). The glacier, facing north, has a mean altitude of ~4600 m a.s.l. and the slope ranges from 1°–60° with a mean value of 21°.

Fig. 1. Location map of the study region. (a) Jhelum and Drass sub-basins of the Upper Indus Basin. Location of various GPR profiles used for validation of the modeled ice thickness on (b) the Kolahoi glacier and (c) Machoi glacier.

3. Methods and data

3.1. Data sets

The glacier outlines and the branch lines were delineated manually from the snow- and cloud-free Landsat OLI Satellite imagery of October, 2016, complimented by the ASTER Global Digital Elevation Model (GDEM) V2 (Tachikawa and others, Reference Tachikawa2011). The Landsat OLI image has the spatial resolution of 30 m. The minimal seasonal snow-cover in the study area during the month of October facilitated easy discrimination of various glacier features on the satellite images (Rashid and Abdullah, Reference Rashid and Abdullah2016). The glacier topographic characteristics like elevation, slope and aspect were derived from the ASTER GDEM V2, with horizontal resolution of 30 m and vertical accuracy of 17 m (Tachikawa and others, Reference Tachikawa2011). The ASTER GDEM has been widely used in glaciological studies at different spatial scales worldwide to derive various topographic parameters such as elevation, slope and aspect (Vignon and others, Reference Vignon, Arnaud and Kaser2003; Bhambri and others, Reference Bhambri, Bolch, Chaujar and Kulshreshtha2011; Kamp and others, Reference Kamp, Byrne and Bolch2011; Wu and others, Reference Wu, Wang, Yang and Yang2014; Wang and Kääb, Reference Wang and Kääb2015; Haireti and others, Reference Haireti, Tateishi, Alsaaideh and Gharechelou2016; Lu and others, Reference Lu, Zhang, Shangguan and Yang2021). Therefore, we did not see the need to test different DEMs for determining the ice thickness and instead relied on the existing literature where ASTER GDEM has been used. GPR measurements (point measurement) were carried out over the Kolahoi and Machoi glaciers during 15–30 August 2018, along several transects.

3.2. Methodology

3.2.1. Ice thickness modeling

The distributed glacier ice thickness was estimated using the GlabTop model (Linsbauer and others, Reference Linsbauer, Paul and Haeberli2012; Paul and Linsbauer, Reference Paul and Linsbauer2012). The model uses glacier boundaries, glacier branch lines and a DEM as inputs to simulate glacier ice-thickness. The glacier boundaries and branch lines were manually digitized from the satellite images and the Digital Elevation Model, whereas the mean glacier slope was estimated from the ASTER GDEM. The GlabTop model is based on the parameterization scheme presented by Hoelzle and Haeberli, (Reference Hoelzle and Haeberli1995) using a constant value for the basal shear stress (τb). The GIS implementation of the GlabTop model (Paul and Linsbauer, Reference Paul and Linsbauer2012) used in the present study estimates the value for the basal shear stress τb as a function of elevation relief to derive ice-thickness along branch lines as follows:

(1)$$h = \displaystyle{{\tau _b} \over {\,f\rho gsin\alpha }}$$

where, h is the ice-thickness along the central branch lines, the shape factor f accounts for the friction of glacier body with the valley walls and is computed as the ratio of glacier cross sectional area and the product of its perimeter and the centre-line thickness, ρ is density of glacier ice (900 kg m−3), g is acceleration due to gravity (9.8 m s−2) and α is the mean glacier surface slope along the branch lines (α ≠ 0). In the present study we used a constant value of f = 0.8 and τ b = 120 kPa (Zou and others, Reference Zou2021). The technical details of the GlabTop model and its implementation in GIS are described in detail by Paul and Linsbauer (Reference Paul and Linsbauer2012) and Linsbauer and others (Reference Linsbauer, Paul and Haeberli2012), and are therefore only briefly summarized here. The GlabTop model calculates the ice-thickness at the points along the branch lines. The ice-thickness values between the base points were interpolated to produce a continuous thickness along the branch lines. The ice-thickness was calculated along 26 and 10 branch lines for the Kolahoi and Machoi glaciers, respectively. Spatial interpolation of the ice-thickness values along the branch lines was performed in ArcGIS (ESRI, 2008) using the ANUDEM interpolation scheme (Hutchinson, Reference Hutchinson1989) to generate spatially distributed ice thickness maps of both glaciers.

3.2.2. Field measurements

The field-based glacier ice-thickness measurements were carried out using 8 MHz Ground Penetrating Radar, a turnkey system developed by Blue System Integration Ltd (Mingo and Flowers, Reference Mingo and Flowers2010; https://www.bluesystem.about/ice-penetrating-radar.html). The system comprises of radar receiving unit, a set of antenna (Transmitter and Receiver), rigging components, and collapsible antenna protection tubing together with a ski-based sled system (Mingo and Flowers, Reference Mingo and Flowers2010). The IceRadar Embedded Processing Unit (EPU) is equipped with data acquisition electronics, GPS unit and a touch-screen embedded computer. The radar and GPS data are acquired and logged continuously at user defined intervals, besides, the radar data acquired is displayed real time in 1-D and 2-D radargrams. All the components are fitted within a water- and dust-proof rugged enclosure (Fig. 2).

Fig. 2. Ground Penetrating Radar (GPR) operation during glacier field survey; (a) Deployment of the ground penetrating ice-radar for surveys on the Kolahoi glacier; (b) The receiver, digitizer and embedded computer system are housed in a rugged water- and dust-proof enclosure. The receiving antenna is connected to the digitizer through a port drilled into the back of the case and (c) Transmitter and battery are housed in another case and mounted on skis during field survey. The transmitting antenna is threaded through ports drilled into case.

The mono pulse transmitter (Narod and Clarke, Reference Narod and Clarke1994) delivers 1100 V (±550 V) into a 50Ω resistively loaded dipole antenna at a rate of 512 Hz (Mingo and Flowers, Reference Mingo and Flowers2010). In the present study, 4 m half-length antenna i.e., 8 m each for receiving and transmitting, with a central frequency of 8 MHz, was used for glacier ice thickness measurements. With a wave speed of 168 m μs−1 in glacier ice and air speed of 300 m μs−1, the ice depth D is calculated as follows:

(2)$$D = \displaystyle{{\;1} \over 2}\left[{{168}^2\left({t + \displaystyle{d \over {300}}} \right)-d^2} \right]^{( 1/2) }\;, \;$$

where, d is the antenna separation and t is the two-wave travel time.

The IceRadar uses the National Instruments NI-5133 digitizer with a sampling rate up to 250 MSs−1, 100 MHz bandwidth, and 512 Hz PRF with 12-bit resolution (Mingo and Flowers, Reference Mingo and Flowers2010). A small, waterproof, rugged and USB-powered GARMIN NMEA 18 ×  GPS on-board is used for recording the coordinates at each measurement point. The GPR measurements were recorded once every five seconds. In this study, several glacier transects on the two glaciers were surveyed for the ice thickness (Fig. 1). IceRadar Analyzer version 4.2.6 software, as part of the IceRadar system, was used for data viewing, picking, analysis and export for generation of the ice-thickness data from the radargrams. The software allows applications of Dewow, Detrend, gain control and filtering of the radargram data.

3.2.3. Validation of the simulated ice thickness

The GPR measurements are stored as point features with the associated geolocation coordinates. Using the ‘Extract Multi Values to Points’ function in ArcGIS, ice-thickness values from the spatially distributed rasters were extracted for every GPR point measurement.

In order to ascertain the accuracy of the simulated ice-thickness estimates, statistical tests including Correlation Coefficient (CC, Benesty and others, Reference Benesty, Chen, Huang and Cohen2009), Relative Bias (RB) (Gumindoga and others, Reference Gumindoga, Rientjes, Haile, Makurira and Reggiani2016) and the Nash–Sutcliffe Coefficient (NSC, Nash and Sutcliffe, Reference Nash and Sutcliffe1970) were used. A CC value of +1 indicates a perfect positive fit, −1 value indicates a perfect negative fit whereas 0 value indicates no correlation at all. The CC is calculated as follows:

(3)$$CC = \displaystyle{{\mathop \sum \nolimits^ \left({Obs-\mathop {Obs}\limits^{{\_}{\_}{\_}{\_}{\_}{\_}} } \right)\left({Sim-\mathop {Sim}\limits^{{\_}{\_}{\_}{\_}{\_}} } \right)} \over {\sqrt {\mathop \sum \nolimits_i^n \left({Obs-\mathop {Obs}\limits^{{\_}{\_}{\_}{\_}{\_}{\_}} } \right)} \sqrt {\mathop \sum \nolimits_{i = 1}^n \left({Sim-\mathop {Sim}\limits^{{\_}{\_}{\_}{\_}{\_}{\_}} } \right)} }}\;, \;$$

The performance of a model, on the basis of RB, is generally categorized into three basic classes: underestimation (bias ≤10%), overestimation (bias >10%), and approximately equal (−10 to 10%) (Brown, Reference Brown2006). RB is calculated by using the following equation:

(4)$$RB = \left[{\displaystyle{{\mathop \sum \nolimits_{i = 1}^n ( {Sim_i-Obs_i} ) } \over {\mathop \sum \nolimits_{i = 1}^n Obs_i}}} \right]\times 100\;, \;$$

The Nash–Sutcliffe Coefficient (NSC) (Nash and Sutcliffe, Reference Nash and Sutcliffe1970), also known as the coefficient of efficiency, is a good indicator for predicting efficiency of a model and varies from minus ∞ to 1, with 1 being the perfect skill and values close to 1 indicate high model efficiency. The NSC is calculated as follows:

(5)$$NSC = 1-\displaystyle{{\mathop \sum \nolimits_{i = 1}^n {( {Obs_i-Sim_i} ) }^2} \over {\mathop \sum \nolimits_{i = 1}^n {( {Obs_i-\overline {Obs} } ) }^2}}\;, \;$$

where, n is the total number of pairs of simulated (Sim) and observed (Obs) ice thickness values, i is the i th value of the simulated and observed ice thickness values, $\overline {Sim}$ and $\overline {Obs\;}$ are mean values of modeled and observed glacier ice thickness, respectively.

3.2.4. Error estimation

We estimated uncertainty in the glacier-area estimates, field observed ice-thickness measurements, simulated ice-thickness estimates and glacier-volume estimates using various approaches. The uncertainty in glacier area was found to be equal to 0.2 and 0.1 km2 for Kolahoi and Machoi glaciers, respectively, obtained using the following equation (Braun and others, Reference Braun2019):

(6)$$\delta A = \displaystyle{{Rp/A} \over {Rp/A_P}}\;\;\times \;0.03\;, \;$$

where, Rp/A is the glacier perimeter–area ratio and Rp/A P is a constant equal to 5.03 km–1 (Paul and others, Reference Paul2013). Several other studies have used the same approach to determine uncertainty in glacier area delineation from remote sensing data (Malz and others, Reference Malz2018; Farías-Barahona and others, Reference Farías-Barahona2020). The uncertainty observed in glacier area in this study is in line with the error estimates reported in previous studies over the region (Abdullah and others, Reference Abdullah, Romshoo and Rashid2020; Romshoo and others, Reference Romshoo, Fayaz, Meraj and Bahuguna2020b, Reference Romshoo, Abdullah, Rashid and Bahuguna2022a).

For determining uncertainty of the GlabTop simulated ice thickness, we relied on the error estimation analysis done by Linsbauer and others (Reference Linsbauer, Paul and Haeberli2012) who calculated the model uncertainty by systematic variation in the values of the input parameters including shear stress (τ: ± 30%), glacier slope (α: ± 10%) and shape factor (f: ± 12.5%). The study reported an uncertainty of ±30%, and the same has been considered in other studies like Paul and Linsbauer (Reference Paul and Linsbauer2012) and Ramsankaran and others (Reference Ramsankaran, Pandit and Azam2018).

Similarly, we considered an overall uncertainty of ±5% for the GPR measurements (Fischer and Kuhn, Reference Fischer and Kuhn2013), which is due to the uncertainty of the signal velocity in a glacier, uncertainty in the antenna separation, uncertainty in the interpretation of multiple reflections, the accuracy of the oscilloscope readings (Fischer and Kuhn, Reference Fischer and Kuhn2013), and errors caused by off-nadir reflections as we did not perform off-nadir reflection corrections (Plewes and Hubbard, Reference Plewes and Hubbard2011; Björnsson and Pálsson, Reference Björnsson and Pálsson2020).

The uncertainty in the total glacier volume u(V)/V depends on the ice-thickness (h) and glacier area (A) and was calculated using the error propagation method (Ramsankaran and others, Reference Ramsankaran, Pandit and Azam2018), which is described as follows:

(7)$$\displaystyle{{u( V ) } \over V} = \sqrt {{\left[{\displaystyle{{u( A ) } \over A}} \right]}^2 + {\left[{\displaystyle{{u( h ) } \over h}} \right]}^2} , \;$$

where, u(A) and u(h) are uncertainties in glacier area and ice thickness, respectively.

4. Results

4.1. Ice thickness simulations of the Kolahoi and Machoi glaciers

The estimated, spatially distributed ice thickness of the Kolahoi and Machoi glaciers are presented in Figure 3. The modeled ice-thickness of the Kolahoi Glacier ranges up to 158 ± 47 m with a mean value of 79 ± 24 m. Ice-thickness up to 135 ± 41 m was modeled in the flatter parts of the glacier ablation zone. With an area 10.9 ± 0.2 km2, the total ice volume was determined to be 0.9 ± 0.3 km3 based on the GlabTop model.

Fig. 3. GlabTop simulated spatially distributed ice thickness of (a) the Kolahoi glacier and (b) the Machoi glacier. Dashed lines show the central branch lines used in the ice thickness modeling.

Mean ice thickness of the Machoi glacier was 81 ± 24 m ranging up to 162 ± 48 m and the maximum ice-thickness was found in the ablation zone near the Equilibrium Line. The ablation zone of the Machoi glacier has in general thicker ice compared to the accumulation zone. The ice thickness drops from ~60 ± 18 m to ~45 ± 13 m above the ice falls, which coincides with the ELA of the glacier. Based on the GlabTop model, the Machoi glacier stores ~0.44 ± 0.2 km3 of ice within an area of 5.9 ± 0.1 km2.

4.2. Validation of ice thickness simulations

The simulated glacier thickness over the two glaciers was validated with the observed GPR ice thickness measurements carried out on the two glaciers.

4.2.1. Kolahoi glacier

The modeled ice thickness across all the four profiles matches quite well with the observed GPR measurements. A representative radargram of the Kolahoi glacier GPR measurements is provided in the supplementary figure (Fig. S1). The GlabTop model in general underestimated the ice-thickness when compared with the GPR measurements (Fig. 4) with an average RB of −10%, CC of 0.96 and NSC of 0.94 across the four profiles. The lowest RB was observed in the Profile 1 (KP1) in the lower ablation zone (Fig. 4) with a mean observed ice thickness of 92 ± 5 m against the mean simulated ice thickness of 86 ± 26 m. Comparison of the observed and simulated ice thickness along KP1 revealed a good agreement, indicated by the high correlation coefficient of 0.97 and a low relative bias of −6%. The NSC value of 0.93 also indicates effectiveness of the GlabTop for simulating glacier ice thickness.

Fig. 4. GlabTop Simulated and GPR observed ice-thickness estimates of four profiles of the Kolahoi glacier. The line graphs have been smoothed using the exponential smoothing filter with smoothing factor of 0.3 in the Excel software. The profiles are numbered from terminus towards accumulation zone of the glacier and were taken across the width of the glacier.

Despite RB of −13% with KP4, highest among the four profiles, the model performed well in capturing the spatial patterns of the ice thickness transect, which is evident by high values of CC and NSC for KP4 (Table 1).

Table 1. Simulated and GPR-observed ice-thickness data along transects on the Kolahoi and Machoi glaciers and statistical evaluation of the relationship between simulated and GPR-observed ice thickness estimates.

4.2.2. Machoi glacier

For Machoi Glacier, modeled ice thickness across all the profiles matches well with the GPR measurements. The simulated ice-thickness of the glacier was validated against nine GPR profiles taken in the ablation zone of the glacier (Fig. 1). A representative radargram of the Glacier is provided as supplementary figure (Fig. S2). The RB between the field-observed and simulated ice thickness was found to be between +6% and ~ −11% with a mean value of ~ −3% (Table 1), indicating good agreement between the two. A high CC value 0.92 and NSC of 0.90 for the nine profiles further corroborates the effectiveness of the GlabTop model (Fig. 5, Table 1).

Fig. 5. GlabTop simulated and GPR-observed ice-thickness estimates of nine profiles on the Machoi glacier. The lines graphs have been smoothed using the exponential smoothing function with a smoothing factor of 0.3 in Excel software. The profiles are numbered from terminus towards accumulation zone of the glacier and were taken across the width of the glacier.

The thickest ice was observed in Profile MP4 with a mean simulated ice-thickness of 91 ± 16 m, which is in good agreement with the mean observed ice-thickness of 96 ± 5 m with a low RB of −6% only. With a slight overestimation of ~ 2%, the lowest bias was observed for the Profile MP5. For Profile MP7, the RB of −11%, was the highest among the nine profiles.

4.3. Ice-reserves of the Jhelum and Drass sub-basins

Given the good agreement between the simulated and observed ice thickness, we estimated the glacier ice-reserves of the Jhelum and Drass sub-basins in the Upper Indus Basin using the GlabTop model. The model simulations revealed that the ice thickness of glaciers in the Jhelum basin ranges up to 187 ± 56 m with a mean ~24 ± 7 m (Fig. 6). The glaciers in the Jhelum basin cover an area of ~ 85 ± 11 km2, and hold a glacier volume of ~2 km3 corresponding to an ice-reserve of 1.8 ± 0.6 Gt. The investigation further revealed that 85% of the ice-reserves in the Jhelum are concentrated in the elevation zone 4000–4800 m a.s.l., whereas only 10% of the total ice volume is located between 3300 m and 4000 m a.s.l. (Fig. 6). The simulated ice thickness as well as the altitude distribution of glacier area and ice mass in the Jhelum basin are shown in Figure 6.

Fig. 6. Spatial distribution of the simulated ice thickness of glaciers in the Jhelum basin. The inset graph depicts glacier area and ice storage in different elevation zones of the sub-basin. (a) and (b) provide zoomed-in views of the glacier ice-thickness distribution.

Similarly, with a glaciated area of 167 ± 17 km2, the Drass sub-basin has an ice reserve of 2.7 ± 0.9 Gt (Fig. 7). The ice thickness in the Drass sub-basin ranges up to 202 ± 60 m with a mean of ~17 ± 5 m. Around 96% of the total ice mass in the Drass sub-basin is stored in the elevation range 4200–5100 m a.s.l. The simulated ice thickness as well as the altitude distribution of glacier area and ice mass in the Drass sub-basin are shown in Figure 7.

Fig. 7. Spatial distribution of the simulated ice thickness of the glaciers in the Drass sub-basin. The inset graph depicts glacier area and ice storage in different elevation zones of the sub-basin. (a) and (b) provide zoomed-in views of the glacier ice-thickness distribution.

5. Discussion

A comparison of the simulated and field-observed ice-thickness revealed an underestimation of 16% (averaged over four profiles) and ~3% (averaged over nine profiles) for the Kolahoi and Machoi Glaciers, respectively (Table 1). These differences are well within the uncertainty range (±30%) of the GlabTop model (Paul and Linsbauer, Reference Paul and Linsbauer2012). Similar differences have been reported in previous studies using GlabTop-based ice-thickness simulations. For instance, Petrakov and others (Reference Petrakov2016) reported a 16% underestimation in GlabTop ice-thickness estimates over the Tien Shan region. Similarly, Ramsankaran and others (Reference Ramsankaran, Pandit and Azam2018) found an uncertainty of ±14% in GlabTop model ice-thickness estimates when compared to field measurements on the Chotta Shigri glacier in the western Himalaya. The average difference between the field measurements and GlabTop-based ice-thickness estimates found in this study are consistent with the ±15 m range reported by Azam and others (Reference Azam2012).

The robustness and accuracy of the GlabTop model in simulating glacier ice thickness are substantiated by various statistical tests employed in this study. The small deviation of the simulated ice-thickness with respect to the field-based measurements from the two glaciers is supported by high correlation coefficients, low relative biases and a robust Nash–Sutcliffe Efficiency for both the Kolahoi and Machoi glaciers. These findings indicate that the model is efficient for simulating glacier ice thickness (Table 1). The model consistently captured the general ice-thickness pattern, and the magnitudes across all surveyed profiles over the two glaciers. The widely-available input parameters required by GlabTop compared with other available models, which required data such as mass balance and velocity (Gardner and others, Reference Gardner2013; Vincent and others, Reference Vincent2013; Ramsankaran and others, Reference Ramsankaran, Pandit and Azam2018), is an advantage of the GlabTop model for computing distributed ice-thickness over the data-scarce Himalaya.

Furthermore, the reliability of the GlabTop model for estimating glacier volume in the Himalayan region has been previously reported by Linsbauer and others (Reference Linsbauer, Frey, Haeberli and Machguth2014) and Frey and others (Reference Frey2014). A recent study by Zou and others (Reference Zou2021) further demonstrated the reliability of GlabTop for ice-thickness estimation over a part of the Upper Indus Basin. It is noteworthy that we also explored a velocity-based approach to estimate ice thickness, where we used the by laminar flow equation to relate glacier surface velocity and ice thickness (Cuffey and Paterson, Reference Cuffey and Paterson2010; Gantayat and others, Reference Gantayat, Kulkarni and Srinivasan2014). However, in comparison to the GPR measurements, this velocity-based model performed poorly in simulating glacier ice thickness, showing an average relative bias of −28%. Consequently, we have not included the results from this approach in this study.

The average ice-thickness in the Jhelum (24 m) and Drass (17 m) sub-basins is lower than the reported average ice thickness for the entire Upper Indus Basin (~75 m) by Zou and others (Reference Zou2021). This difference can be attributed to the distribution of ice thickness at high altitudes, probably influenced by steep headwalls that hinder snow accumulation and glacier formation at these elevations (Nagai and others, Reference Nagai, Fujita, Sakai, Nuimura and Tadono2016; Zou and others, Reference Zou2021). However, both this study and Zou and others (Reference Zou2021) found a good agreement between modeled and GPR-based ice thickness. As expected, the larger glaciers have thicker ice in both sub-basins, while ice tends to thinner on steeper slopes at higher altitudes compared to ice on more gentle slopes at lower altitudes, consistent with the findings by Salerno and others (Reference Salerno2017) and Hoelzle and Haeberli (Reference Hoelzle and Haeberli1995). It is noteworthy that the glacier volume estimates for the Jhelum and Drass sub-basins presented in this study are respectively 13 and 17% lower than those provided by Farinotti and others (Reference Farinotti2019). The volume estimates of the Jhelum sub-basin by Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022) are 2.3 km3, or ~17% higher than results presented in this study. Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022), furthermore, estimated the volume of the Drass sub-basin glaciers to be 5.5 km3, nearly double the volume estimate of this study. Additionally, Zou and others (Reference Zou2021) estimated the ice volume in the Drass sub-basin as 7.6 km3, or 150% higher than the result of this study. The differences between our study and previous studies can be attributed to the different approaches employed. For instance, Farinotti and others (Reference Farinotti2017, Reference Farinotti2019) averaged their ice-thickness estimates from multiple models, while Millan and others (Reference Millan, Mouginot, Rabatel and Morlighem2022) relied on a velocity-based approach. Additionally, disparities may arise from differences in model input parameters, including the glacier boundaries, delineation errors, and the extent and number of glacier branch lines. These differences probably account for the discrepancies observed in the ice-thickness estimates between our study and that of Zou and others (Reference Zou2021).

Additionally, we computed the glacier volume across the study area using the volume–area scaling approach (Bahr and others, Reference Bahr, Meier and Peckham1997) and found 3.8 km3 for the Jhelum and 7.5 km3 for Drass sub-basins. These values are considerably higher (97% for Jhelum and 150% for Drass) than our results (Supplementary Fig S3).

6. Conclusions

The lack of ice-thickness measurements has led to significant uncertainty regarding the total glacier ice volume in the Upper Indus Basin and consequently, projections of changes in glacier mass and volume under a changing climate. This study is the first reporting of ice- thickness measurements for two glaciers in the Jhelum and Drass sub-basins of the Upper Indus Basin. The study found that the GlabTop model generally performs well in modeling the spatial distribution of glacier ice thickness, albeit typically underestimating the thickness by on the order of 10% on average. The model proved robust in modeling the ice thickness along almost all selected field transects for GPR-based measurements on the two glaciers, as demonstrated by the statistical evaluation of the simulated ice-thickness profiles. The relative bias between observed and simulated ice thickness for the Kolahoi and Machoi glaciers was −11% and ~ 2%, respectively, falling within acceptable error limits.

These improved estimates of glacier ice thickness and volume are essential for accurate projections of glacier-melt contributions to sea-level rise, the impact on streamflow, and informed water resource management under a changing climate. This is particularly important for policymaking for food, energy and water security in the Indus basin, where waters are shared among neighboring countries across political boundaries.

Supplementary material

The supplementary material for this article can be found at https://doi.org/10.1017/aog.2024.2.

Data

The Landsat data satellite images are free available from USGS via the https://earthexplorer.usgs.gov/ portal, whereas, the ASTER GDEM is available from the Ministry of Economy, Trade, and Industry (METI) of Japan and the United States National Aeronautics and Space Administration (NASA) via https://search.earthdata.nasa.gov/search/ portal. The GPR-based ice-thickness measurements on the Kolahoi and Machoi glaciers and the modeled ice-thickness for the two sub-basins are available at https://doi.org/10.5281/zenodo.8176635

Acknowledgement

The research work was carried out as part of the sponsored research project titled ‘Centre of Excellence for Glacial Studies in Western Himalaya’, which is funded by the Department of Science and Technology (DST), Government of India. The financial assistance provided by the Department under the project to complete the research is gratefully acknowledged. The authors are also grateful to Linsbauer and others (Reference Linsbauer, Paul and Haeberli2012) for the GlabTop model. The authors express gratitude to the Scientific Editor and three anonymous reviewers for their valuable comments and suggestions on earlier versions of the manuscript, which has greatly improved its content and structure. The authors also thank Laurent Mingo from Blue System Integration Ltd, for his advice on GPR operation and radargram interpretation.

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Fig. 1. Location map of the study region. (a) Jhelum and Drass sub-basins of the Upper Indus Basin. Location of various GPR profiles used for validation of the modeled ice thickness on (b) the Kolahoi glacier and (c) Machoi glacier.

Figure 1

Fig. 2. Ground Penetrating Radar (GPR) operation during glacier field survey; (a) Deployment of the ground penetrating ice-radar for surveys on the Kolahoi glacier; (b) The receiver, digitizer and embedded computer system are housed in a rugged water- and dust-proof enclosure. The receiving antenna is connected to the digitizer through a port drilled into the back of the case and (c) Transmitter and battery are housed in another case and mounted on skis during field survey. The transmitting antenna is threaded through ports drilled into case.

Figure 2

Fig. 3. GlabTop simulated spatially distributed ice thickness of (a) the Kolahoi glacier and (b) the Machoi glacier. Dashed lines show the central branch lines used in the ice thickness modeling.

Figure 3

Fig. 4. GlabTop Simulated and GPR observed ice-thickness estimates of four profiles of the Kolahoi glacier. The line graphs have been smoothed using the exponential smoothing filter with smoothing factor of 0.3 in the Excel software. The profiles are numbered from terminus towards accumulation zone of the glacier and were taken across the width of the glacier.

Figure 4

Table 1. Simulated and GPR-observed ice-thickness data along transects on the Kolahoi and Machoi glaciers and statistical evaluation of the relationship between simulated and GPR-observed ice thickness estimates.

Figure 5

Fig. 5. GlabTop simulated and GPR-observed ice-thickness estimates of nine profiles on the Machoi glacier. The lines graphs have been smoothed using the exponential smoothing function with a smoothing factor of 0.3 in Excel software. The profiles are numbered from terminus towards accumulation zone of the glacier and were taken across the width of the glacier.

Figure 6

Fig. 6. Spatial distribution of the simulated ice thickness of glaciers in the Jhelum basin. The inset graph depicts glacier area and ice storage in different elevation zones of the sub-basin. (a) and (b) provide zoomed-in views of the glacier ice-thickness distribution.

Figure 7

Fig. 7. Spatial distribution of the simulated ice thickness of the glaciers in the Drass sub-basin. The inset graph depicts glacier area and ice storage in different elevation zones of the sub-basin. (a) and (b) provide zoomed-in views of the glacier ice-thickness distribution.

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