Spatio-temporal variations in glacier surface velocity in the Himalayas

Glacier evolution with time provides important information about climate variability. Here we investigate glacier surface velocity in the Himalayas and analyse the patterns of glacier flow. We collect 220 scenes of Landsat-7 panchromatic images between 1999 and 2000, and Sentinel-2 panchromatic images between 2017 and 2018, to calculate surface velocities of 36,722 glaciers during these two periods. We then derive velocity changes between 1999 and 2018, based on which we perform a detailed analysis of motion of each individual glacier, and noted that the changes are spatially heterogeneous. Of 5 all the glaciers, 32% have speeded up, 24.5% have slowed down, and the rest 43.5% remained stable. The amplitude of glacier slowdown, as a result of glacier mass loss, is remarkably larger than that of speedup. At regional scales, we found that glacier surface velocity in winter has uniformly decreased in the western part of the Himalayas between 1999 and 2018, whilst increased in the eastern part; this contrasting difference may be associated with decadal changes in accumulation and/or melting under different climatic regimes. We also found that the overall trend of surface velocity exhibits seasonal variability: summer 10 velocity changes are positively correlated with mass loss, whereas winter velocity changes show a negative correlation. Our study suggests that glacier velocity changes in the Himalayas are more spatially and temporally heterogeneous than previously thought, emphasising complex interactions between glacier dynamics and environmental forcing.

Himalayan glaciers are experiencing significant thinning and mass loss, thereby affecting ice fluxes and river discharge. The thinning rate is also suggested to have accelerated in the past 40 years, which is possibly driven by atmospheric warming and 25 associated energy fluxes (Maurer et al., 2019). Recently, Dehecq et al. (2019) investigated the response of glacier flow to mass changes at regional scales. They estimated time-series glacier velocities from 2000 to 2016 using Landsat-7 optical satellite images (Dehecq et al., 2015), and found that the variability in velocity changes within a large region can be explained solely by changes in ice thickness, i.e. ice mass balance (Dehecq et al., 2019). Their study provides a novel way for estimating ice mass balance in the Himalayas as glacier velocity changes can be easily measured with satellite images. 30 Glacier surface velocity in summer has been heavily exploited, e.g. Dehecq et al. (2015) and Dehecq et al. (2019). Velocity estimates in Dehecq et al. (2019) show that glaciers in the Himalayas have experienced significant slowdown in the past two decades. However, seasonal variability of regional glacier motion remains unclear. The aim of this study is to explore the long-term winter velocity and its changes. We first derive glacier velocities for two periods, 1999periods, -2000periods, and 2017periods, -2018 and Sentinel-2 image pairs respectively. We chose Sentinel-2 over Landsat-7 for mapping present glacier 35 motion because it has been tested to have a better geometric and radiometric quality (Kääb et al., 2016). The uncertainties in the glacier velocities are estimated using the overlapping areas of adjacent image pairs. By differencing the Landsat-7 and Sentinel-2 derived velocities, we map velocity changes over nearly two decades, and combining the data with glacier mass balance, we show the complex patterns of glacier flow in the Himalayas.

40
The Himalaya front (Figure 1) stretches over 3,000 km from the west to the east, containing more than 36,000 glaciers of different sizes (Randolph Glacier Inventory, RGI 6.0). The topography increases rapidly across the front, from 200 m in the south to over 5,000 m in the north, entering the Tibetan Plateau. Evolution of glaciers in different parts of the Himalayas is affected by different climatic regimes. In the western part, snow accumulation is controlled by westerly atmospheric circulations, so Hindu Kush, Spiti Lahaul and Karakoram receive most accumulation during winter. In the eastern part, the Indian summer monsoon dominates the accumulation in West Nepal, East Nepal, Bhutan and Nyainqentanglha (Azam et al., 2016;Sun et al., 2017;Bookhagen and Burbank, 2010;Kääb et al., 2012;Fujita, 2008). The extreme topography creates additional complexity; precipitation at high-altitude regions has been suggested to be 2-10 times higher than that at low-altitude regions (Immerzeel et al., 2015). As a result, glaciers in the Himalayan front exhibit contrasting variabilities in evolution and mass balance (Kääb et al., 2012;Dehecq et al., 2019;Brun et al., 2017).

50
In this study, we focus primarily on surface velocity changes of the Himalayan glaciers at decadal scales. Satellite optical images were used to generate glacier velocity maps at different times. We collected 40 pairs of Landsat-7 Level-1T data between 1999 and 2000 to calculate glacier velocity during this period. Each panchromatic Landsat-7 Level-1T image covers an area of 185 km × 170 km, with a spatial resolution of 15 m. 70 panchromatic Sentinel-2A/B Level-1C image pairs were obtained to calculate glacier velocity between 2017 and 2018. Each Sentinel-2 Level-1C image has a footprint of 100 km × 100 55 km and a spatial resolution of 10 m. Dehecq et al. (2019) analysed velocity changes in summer. We are interested to explore whether glacier velocities exhibit seasonal variations, so all the 110 pairs of Landsat-7 and Sentinel-2 images used in this study were acquired during winter, centred around December. We also collected glacier geometry data including length, area, slope and thickness from RGI 6.0 and Farinotti et al. (2019), along with satellite-derived glacier elevation changes from Brun et al. (2017), for a comprehensive analysis of glacier velocity changes and the possible driving factors.

Methods and results
We estimated glacier velocities by applying cross-correlation using the COSI-Corr software package (freely available from www.tectonics.caltech.edu/slip_history/spot_coseis/index.html). Optical correlation is implemented in the frequency domain with an accuracy ∼1/10 of the input pixel size (Leprince et al., 2007;Ayoub et al., 2009). We used a correlation window of 64 pixels × 64 pixels as a first step, followed by 32 pixels × 32 pixels for a second run, with a step of 16 pixels × 16 pixels 65 (160 m) for Sentinel-2A/B data and 10 pixels × 10 pixels (150 m) for Landsat-7 data. The resulting east-west and northsouth components of the displacement were filtered using the non-local means algorithm (Ayoub et al., 2009). We then used their analysis of glacier velocity changes mainly on regions, we conducted our analysis based on individual glacier. For each glacier, we computed its velocity and the associated change by averaging all the pixel values that cover the glacier. A total of 36,722 glaciers were included in our study. As shown in Table 1, 43.5% of the glaciers remain stable during 1999-2018 (the difference between Landsat-7 and Sentinel-2 velocities is no more than 3 m yr −1 ), 32.0% speeded up (velocity changes > 3 m yr −1 ), and the rest 24.5% slowed down (velocity changes < − 3 m yr −1 ). Although speedup glaciers outnumber 80 slowdown glaciers, the average amplitude of glacier speedup (6.3 m yr −1 ) is much smaller than slowdown (−12.3 m yr −1 ).

Relationship between glacier surface velocity and geometry
We analyse glacier surface velocity in combination with glacier geometry data including area, length, slope and thickness. We  during winter (0∼1 m yr −1 decade −1 ) are considerably smaller than the changes during summer (1∼6 m yr −1 decade −1 ) (see Figure 4 and Table 1), possibly due to strong spatio-temporal variations in melting in the Himalayas. From the winter velocity changes, we also observed a contrasting difference between the western (slowdown) and eastern (speedup) parts of the Himalayan front, indicating heterogeneous changes in accumulation and/or melting under different climatic regimes.

Linking surface velocity changes with glacier mass balance
To further investigate the driving factors of glacier velocity changes, we use the empirical power law relation between glacier surface velocity V and driving stress τ (Glen, 1952(Glen, , 1955Weertman, 1957;Goldsby and Kohlstedt, 2001): where A and m are positive constants, related to ice rheology, bed topography and flow mechanisms (ice deformation and basal sliding) (Glen, 1952(Glen, , 1955. m has been estimated to vary from 1 (flow over soft sediments, MacAyeal 1989) to 4 (high Taking the derivative of V with respect to τ , we have: Combining Equations (1) and (2), we have: Assuming that changes in the driving stress (dτ ) are induced by mass balance (dM ) and ignoring other factors, as proposed by Dehecq et al. (2019), i.e. dτ = C 1 dM + C 2 , we have: where C 1 and C 2 are assumed constant, relating the driving stress and mass balance. Dehecq et al. (2019) analysed velocity changes and mass balance data, and found that at regional scales, summer velocity changes are positively correlated with mass 135 balance: dV V ∼ 1.25dM (see Figure 6). To test whether velocity changes exhibit any seasonal variability, we applied Equation (4) to analyse the winter velocity estimates. We calculated the average values of velocity V and its change dV for each of the glaciers, based on which we determined the overall dV and V for each subregion. Measurements of glacier mass balance (dM ) were taken from Brun et al. (2017). Although Brun et al. (2017)'s estimates of glacier mass balance did not take seasonal variability into account, earlier 140 study by Kääb et al. (2012) has shown that the long-term trend of dM is consistent between seasons (the amplitude differs slightly). Therefore, using the average long-term trend of dM should not affect the linear relationship between dV and dM . As shown in Figure 6, glacier velocity changes dV V are negatively correlated with mass balance ( dV V ∼ −0.96dM ), suggesting that ice mass loss promotes glacier motion in winter. This is in contrasting difference with summer velocity changes in the study by Dehecq et al. (2019), which states that mass loss drives glacier slowdown. Such seasonal variability indicates different 145 mechanisms of glacier mass loss in the Himalayas. In summer, mass loss is dominated by decrease in precipitation, which will reduce gravitational driving stress, resulting in the long-term glacier slowdown (Dehecq et al., 2019); in winter, mass loss is likely to be controlled by increased melting, which will reduce basal frictional stress and hence promote glacier motion.
In this study, we used Landsat-7 and Sentinel-2 optical imagery to investigate glacier surface velocity and the associated 150 changes in the Himalayas. We analysed flow patterns of individual glacier along the range front and found that glacier velocity changes exhibit an evident heterogeneity at different spatial scales. Of all the 36,722 glaciers, 32% have experienced speedup, 24.5% have slowed down, and the rest 43.5% remained stable. At regional scales, the amplitude of velocity changes is significantly larger in summer (Dehecq et al., 2019) than that in winter (this study). The decreasing velocities in winter between 1999 and 2018 in the western part of the Himalayas, in contrast to the increasing velocities in the eastern part, may be caused 155 by changes in accumulation and/or melting under different climatic regimes. We also observed that glacier velocity changes in winter are controlled by mass balance, as suggested by Dehecq et al. (2019), but unlike summer velocity changes that are positively correlated with mass balance, winter velocity changes show a negative correlation. Our study suggests that glacier velocity changes in the Himalayas are more spatially and temporally heterogeneous than previously thought, emphasising complex interactions between glacier dynamics and environmental forcing. Landsat-7 images were downloaded from https://earthexplorer.usgs.gov/; Sentinel-2 images were downloaded from https://scihub.esa.int/.
The RANDOLPH GLACIER INVENTORY (RGI 6.0) is freely available from https://www.gtn-g.ch/data_catalogue_rgi/. Table 1. Statistics of glacier velocity changes in the Himalayas. Stable glaciers are defined as the amplitude of differences between Landsat-7 and Sentinel-2 velocities, i.e. velocity changes between 1999 and 2018, ≤ 3 m yr −1 . Velocity changes > 3 m yr −1 are regarded as speedup, and < − 3 m yr −1 slowdown. The overall changes were calculated by averaging all the glaciers within each subregion, in order to be comparable with the results in Dehecq et al. (2019).

Number of glaciers Speedup Slowdown Stable
Speedup (