2.1 Time-dependent elevation from CryoSat-2 observations

We use observations from the SAR (synthetic aperture radar) Interferometric Radar Altimeter (SIRAL) on board the European Space Agency (ESA) CryoSat-2 satellite (Wingham et al., 2006). SIRAL is a beam-forming active microwave radar altimeter with a maximum imaging range of ∼ 15 km on the ground. The sensor emits time-limited Ku-band pulses aimed at reducing the footprint to ∼ 1.6 km within the beam. Over land ice, the sensor operates in synthetic aperture interferometric (SARIn) mode, which allows delay-Doppler processing to generate an along-track footprint of ∼ 380 m, while cross-track interferometry is used to extract key information about the position of the footprint centre. In practice however, footprint size will vary depending on properties such as surface slopes, scattering properties, and distance from the point of closest approach (POCA). CryoSat-2 orbits the Earth with a 369 d near-repeat period formed by the successive shift in a 30 d sub-cycle. The satellite has an inclination of 92^∘, offering improved coverage of the polar regions. We process level 1b, baseline C data and the corrected mispointing angle for aberration of light (Scagliola et al., 2018) supplied by the ESA ground segment using a swath processing algorithm (Gourmelen et al., 2018). Level 1b data are provided as a sequence of radar echoes along the satellite track, which translates into received power, interferometric phase, and coherence waveforms for each along-track location. The conventional level 1b data processing method consists of extracting single elevation measurements from the power signal in each waveform that corresponds to the POCA between the satellite and the ground. In contrast, swath altimetry exploits the full radar waveform to map a dense swath (∼ 5 km wide) of elevation measurements across the satellite ground track beyond POCA (Foresta et al., 2016, 2018; Gourmelen et al., 2018; Gray et al., 2013; Hawley et al., 2009), providing 1 to 2 orders of magnitude more elevation measurements compared with POCA and improving the sampling of topographic lows (Foresta et al., 2016). Because swath processing does not rely on retracking, it can retrieve elevation measurements also for atypical waveforms with no clearly defined leading edge such as those found over complex terrain and where retracking often fails to identify a reliable POCA. This makes the CryoSat-2 sensor at present the only radar altimeter able to survey glaciers at high resolution.

2.2 Rates of elevation change maps

Rates of elevation change and mass balance are based on ∼ 25 million swath elevation measurements in the GoA region and ∼ 8 million swath elevation measurements in HMA acquired from July 2010 to July 2019. The distribution of elevation measurements with altitude departs somewhat from the glaciers' hypsometry. Hypsometric representativeness of samples within spatial units is a key requirement for robust glacier trend estimates. A bias in the altitudinal distribution of observations can lead to a bias in the total rate of thinning when integrated over a larger domain as rate of thickness change is often strongly correlated with altitude. Therefore we derive a subset of the time-dependent elevation dataset, removing the impact of such point density biases by filtering out swath measurements so as to match the glacier hypsometry binned using 100 m elevation intervals (e.g. Treichler et al., 2019), and generate elevation change and mass change estimates from the reduced sample (Fig. S5). We remove data sequentially based on measurement uncertainty. This process reduces our sample size by 15 % for the GoA and by 30 % for HMA. We then follow a similar approach to Foresta et al. (2016) and Gourmelen et al. (2018); however the lower data density and the complexity of the terrain in the GoA region and in HMA require a slight adaptation of the methodology. We bin the elevation measurements into regions of 100 × 100 km, sufficiently large to contain the necessary number of measurements in each bin to ensure sufficient robustness and representativity. Due to the increased bin size (the pixel size used by Foresta et al., 2016, and Gourmelen et al., 2018, is 1000 m) and the variation in elevations within each bin, the topographic signature cannot simply be modelled and therefore needs to be removed using an auxiliary digital elevation model (DEM) (Kääb et al., 2012). We subtract the TanDEM-X 90 m DEM (German Aerospace Center (DLR), 2018), which has a near-complete coverage and is contemporaneous with the CryoSat-2 observations, from the swath elevation measurements. The remaining elevation differences (hereinafter referred to as elevDiff) are due to time-dependent elevation change that can be related to glacier thickness change as well as errors in the two datasets, temporal heterogeneity (TanDEM-X is a composite of acquisitions from different years), and differences in penetration between the reference DEM (X-band) and the swath elevation measurements. The errors related to the reference DEM will result in an increase in spread of the elevDiff measurements and are accounted for in the regression model discussed below.

Rates of elevation change are then calculated for each 100 × 100 km bin individually based on elevDiff measurements from July 2010 to July 2019. In order to achieve the most robust trends, we considered several fitting methods, including ordinary least squares, robust regression (e.g. Kääb et al., 2012, 2015), weighted regression (e.g. Berthier et al., 2016; Foresta et al., 2018; Gourmelen et al., 2018), random sample consensus (RANSAC), and the Theil–Sen estimator (e.g. Shean et al., 2020). We found that the best results were achieved with a weighted regression model of the elevDiff measurements, similar to the methods of Gourmelen et al. (2018). However, whilst their weights are calculated only according to the power attribute, here we assign each observation a weight based on power and coherence; i.e. measurements with high power and low coherence within the sample will have lower weights assigned (see Sect. S1.1 in the Supplement). We exclude solutions that display extremely large variability across various regression models, considering them to be unstable results (see Sect. S1.2). When fitting the model, we iteratively exclude measurements that are more than 3σ from the mean distance to the fitted line until no more outliers are present (e.g. Foresta et al., 2016, 2018). We discard bins that did not fulfil a set of quality criteria based on elevation change uncertainties, temporal completeness, interannual changes, and stability of regression results (see Sect. S1.2). The remaining bins covered more than 96 % of the total glacierized area in the GoA region and 88 % in HMA. To estimate values for the gaps in our dh/dt map, we use the altitudinal distribution of elevation change rates on a sub-regional level (Moholdt et al., 2010a, b; Nilsson et al., 2015), applying the hypsometric averaging methods described in Sect. S1.3.

2.3 Mass balance and contribution to sea level rise

To obtain volume changes we use the glacierized area of the Randolph Glacier Inventory (RGI 6.0) (RGI Consortium, 2017). We assume a standard bulk density of 850 ± 60 kg m⁻³ (Huss, 2013) to convert volume changes to equivalent mass changes. This assumption is considered appropriate for a wide range of conditions and longer-term trends; however, this factor can differ significantly for shorter-term periods (< 3 years) (Huss, 2013). To obtain a region-wide mass balance, mass changes in each individual bin are summed up. To generate the contribution to sea level rise (SLR), we assume an area of the ocean of 361.8×10⁶ km² and consider total contributions from all glaciers and then only those glaciers within exorheic basins in High Mountain Asia, based on the HydroSHEDS dataset (Lehner et al., 2006).

2.4 Time series of surface elevation changes

CryoSat-2's monthly repeat cycle provides the opportunity to monitor seasonal as well as multiannual trends of surface elevation. We therefore generate time series with a monthly step (30 d) and a 3-month (90 d) moving window using the median of all the elevDiff observations (residuals from the reference DEM) within a time period with reference to the first month. Time series are generated at the bin size level (100 × 100 km), at the sub-regional level (using the RGI sub-regions), and for the full study region. The time series of the 100 × 100 km bins are also used as an additional check of the dh/dt quality (see Sect. S1.2), whilst we exploit the sub-regional and regional time series to analyse spatio-temporal variability in thickness change across both the GoA and HMA regions. To generate region-wide time series for HMA and the GoA, we use an area-weighted mean of the sub-regional time series. Note that, as opposed to the linear rates, the regional and sub-regional time series displayed in this publication start in January 2011 (with the earliest data from November 2010 using the 90 d window) since we retrieve fewer swath measurements for the first few months of CryoSat-2's life cycle, impacting the quality of the time series pre-2011. The time series in this paper end in April 2019, with the latest data from June 2019 due to the 90 d window.

2.5 Uncertainty assessment

The error budget of mass change has three uncertainty sources, which are assumed to be independent and uncorrelated: uncertainty in time-dependent elevation change (σ_Δh), uncertainty in glacierized area A (σ_A), and uncertainty in mass–volume conversion (σ_p).

The rate of elevation change uncertainty for each 100 × 100 km bin is based on the standard error of the regression model. We conservatively use a factor of 5 (Berthier et al., 2014; Brun et al., 2017) for uncertainties in areas without coverage of swath measurements:

where g is the proportional coverage of glacierized area at 400 m postings, u is (1−g), and σ_Δz is the standard error of the regression. To retrieve the uncertainty in extrapolated bins, we calculate the differences in all non-extrapolated bins between elevation changes using the plane fit approach and elevation changes using the hypsometric averaging method. The standard deviation of these differences is the uncertainty in elevation change (σ_Δh) for all extrapolated bins. We retrieve an uncertainty in elevation change for extrapolated bins of 0.34 and 0.47 m yr⁻¹, respectively, for High Mountain Asia and the Gulf of Alaska. To account for errors due to temporal changes in glacier extents and polygon digitization (Shean et al., 2020), we use an error of 10 % (σ_A=0.1A) in the glacierized area A in a bin, even though the reported uncertainty in the RGI is ∼ 8 % (Pfeffer et al., 2014). Assuming independence between the two error components (σ_A, σ_Δh), volume change uncertainty (σ_ΔV) of a bin is

where Δh is the elevation change rate of the respective bin. To generate the region-wide volume uncertainty (σΔVtot), we combine all the values (including extrapolated bins) in quadrature. We use a density uncertainty of σ_p=60 kg m⁻³ and a density mass conversion of p= 850 kg m⁻³ (Huss, 2013). The total mass balance uncertainty is

where ΔV_tot is the total volume change for the region.

3.1 Spatial coverage and elevation sampling

Using the theoretical pulse-limited footprint size of CryoSat-2, we derive a total spatial coverage of glaciated regions of 55 % in the GoA and 32 % in HMA, respectively. These values are the combined result of the absence of recorded returns due to orbit separation and onboard-tracking limitation (Dehecq et al., 2013) as well as data quality. Given that it is estimated that 40 % of HMA glaciers are not sampled due to onboard-tracking limitations (Dehecq et al., 2013) we estimate that with an appropriate onboard-tracking system, the rate coverage for HMA would be as high as 50 %. These values are within the high end of the range of observational methods (Zemp et al., 2019) whilst generally lower than the coverage provided by high-resolution sensors (Brun et al., 2017; Shean et al., 2020). As expected from the relatively large footprint of radar altimeters, we observe a positive correlation between spatial coverage and glacier size; we do however observe coverage over all glacier sizes (Fig. S6).

We observe a bias in the total number of swath measurements towards higher altitudes (e.g. Fig. S5), which can be attributed to the onboard tracking tending to favour elevations closest to the satellite. However, a comparison of the glacier hypsometry and the spatial coverage of our data (Fig. S4) shows that we still achieve good coverage at low elevations in both regions. In addition, we interpolate missing data based on the relationship between elevation and elevation changes and therefore still capture the changes in the lower reaches of the HMA and GoA glaciers.

Figure 2Specific glacier mass balance (m w.e. yr⁻¹) in High Mountain Asia (HMA) for the period of July 2010 to July 2019 on a 100 × 100 km grid. The size of the circles is scaled by the total glacierized area within a 100 × 100 km bin.

Figure 3Specific glacier mass balance (m w.e. yr⁻¹) in the Gulf of Alaska (GoA) for the period of July 2010 to July 2019 on a 100 × 100 km grid. The size of the circles is scaled by the total glacierized area within a cell. Note that our total mass change estimate of −76.3 ± 5.7 Gt yr⁻¹ (−0.89 ± 0.07 m w.e. yr⁻¹) only includes glaciers from the RGI region 1 (Alaska). Including also the northern Rocky Mountains and the Mackenzie and Selwyn mountains, we retrieve a mass change of -77.7±5.7 Gt yr⁻¹.

3.2 Elevation changes and mass balance in High Mountain Asia

The total HMA mass balance between 2010 and 2019 was −28.0 ± 3.0 Gt yr⁻¹ (−0.29 ± 0.03 m w.e. yr⁻¹), or −18.3 ± 2.3 Gt yr⁻¹ (−0.38 ± 0.03 m w.e. yr⁻¹) when including only exorheic basins. This mass loss corresponds to 0.078 ± 0.008 mm yr⁻¹ SLE, or 0.051 ± 0.006 mm yr⁻¹ when including only exorheic basins, and a cumulative loss of 4.2 % of the total ice volume in High Mountain Asia during the study period (Farinotti et al., 2019). Our maps of surface elevation change show a heterogeneous pattern in the Himalayan range, with a cluster of slightly positive and near-balance trends in the Kunlun and Karakoram ranges (Fig. 2), the so-called “Karakoram anomaly” (Gardelle et al., 2012; Hewitt, 2005). Another striking feature is the gradient from moderate thinning in Spiti–Lahaul and western Himalaya (−0.25 ± 0.09 m w.e. yr⁻¹) to increasingly negative surface elevation changes along the central (−0.43 ± 0.14 m w.e. yr⁻¹) and eastern (−0.56 ± 0.16 m w.e. yr⁻¹) Himalayan mountain range, with the Nyainqêntanglha Mountains and Hengduan Shan (−0.98 ± 0.22 m w.e. yr⁻¹) showing the highest negative trends (Table 1).

We display the altitudinal distribution of elevation changes in Fig. 6 and a comparison with Brun et al. (2017) in Fig. S7. While some variability exists along the profiles, in particular over regions and elevation ranges containing fewer glaciers that can reflect a less robust solution and/or spatial variability in glacier response, trends between elevation and ice thickness change are clearly visible. In general, we observe decreasing negative trends with increasing altitudes, which is an expected pattern (Brun et al., 2017; Gardelle et al., 2013). We find the steepest gradient (Fig. 6, S7, Table S4) in the Nyainqêntanglha or Hengduan Shan, which is in line with the findings of Brun et al. (2017). We also observe lower or even inverse gradients in Bhutan or eastern Himalaya, Spiti–Lahaul or western Himalaya, Karakoram or western Kunlun, and Pamir (Figs. 6, S7, Table S4), which have been reported previously and been related to debris thickness (Bisset et al., 2020; Brun et al., 2017).

Table 2Gulf of Alaska (GoA) mass balance trends from July 2010 to July 2019, aggregated on the Randolph Glacier Inventory (RGI 6.0) sub-regions.

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We show temporal variability in surface elevation change for the whole HMA region (Fig. 4), the RGI second-order regions (Figs. 5, S1), and the regions by Brun et al. (2017) (Fig. S2). The monthly time series show sustained multiannual trends across almost all of the sub-regions until 2015–2016 and decreased loss or even mass gain from 2016–2017 onwards (Figs. 5, S2), which is also reflected in the full HMA time series (Fig. 4) and consistent with previous observations (Ciracì et al., 2020). The Karakoram region in particular displays thinning from 2011 to 2014–2015 before abating and thickening again from 2016–2017. This shift in thinning rates post-2015 is also clearly seen in Bhutan or eastern Himalaya, Kunlun (west and east), Tien Shan, Pamir Alay or Hissar Alay, and Nyainqêntanglha or Hengduan Shan (Figs. 5, S1, S2).

Figure 4Monthly surface elevation change time series for High Mountain Asia (a) and the Gulf of Alaska (GoA) region (b). The grey lines display the elevation change time series with the uncertainty envelope. The red line displays a 12-month moving average.

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Figure 5High Mountain Asia (HMA) 30 d elevation change time series in the RGI 6.0 second-order regions. The coloured line displays the time series with the uncertainty envelope (y axis: elevation change [m]; x axis: time [30 d steps]). The numbers describe the elevation change with uncertainties in m yr⁻¹.

3.3 Glacier elevation changes and mass balance in the Gulf of Alaska

In general, we find much higher mass losses in the Gulf of Alaska than in High Mountain Asia. Over an area of ∼ 86 000 km², including all 26 490 glaciers in the RGI region 1 except northern Alaska, we estimate a total mass balance of −76.3 ± 5.7 Gt yr⁻¹ (−0.89 ± 0.07 m w.e. yr⁻¹), contributing −0.211 ± 0.016 mm yr⁻¹ to global sea level rise, corresponding to a cumulative loss of 4.3 % of the total ice volume during the study period (Farinotti et al., 2019). Surface elevation change maps (Fig. 3) display an expected pattern, with more negative trends towards lower elevations close to the coast. Note that some of the lower rates observed in the Saint Elias Mountains are likely the result of the presence of accumulation areas of large glaciers, e.g. Hubbard and Bering glaciers in these particular grid cells. We present sub-regional estimates aggregated in the RGI 6.0 second-order regions in Table 2. The largest mass loss is seen in the northern Coast Ranges (−1.08 ± 0.09 m w.e. yr⁻¹, −24.8 ± 2.1 Gt yr⁻¹) and Saint Elias Mountains (−1.03 ± 0.10 m w.e. yr⁻¹, −34.1 ± 3.4 Gt yr⁻¹), especially in the Yukutat and Glacier Bay region, which is in line with the spatial patterns of Luthcke et al. (2008) and Luthcke et al. (2013). The lowest thinning rates are observed in the Alaska Range mountains (-0.41±0.05 m w.e. yr⁻¹), which is also in agreement with other studies (Berthier et al., 2010; Luthcke et al., 2008). We observe a clear correlation between surface elevation changes and altitude (Fig. 11, Table S2), with the highest negative trends at low altitudes in the Saint Elias Mountains and Coast Ranges.

We display temporal variability in surface elevation change for the whole GoA region (Fig. 4), the RGI sub-regions (Figs. 9, S3), and for different elevation bands within sub-regions (Fig. 10). Figure 9 shows negative trends across all the sub-regions. The four coastal sub-regions – Alaska Pena, western Chugach Mountains, Saint Elias Mountains, and Coast Ranges – display a seasonal oscillation, with an annual surface elevation maximum in spring and annual surface elevation minimum in autumn. In contrast, the seasonal cycle of the Alaska Range mountains is shifted, with the thickness maximum in winter, which is also somewhat visible in the time series by Luthcke et al. (2008). A very noticeable feature within the full GoA time series is the acceleration of thinning from 2013 to 2014 onwards (Fig. 4). We record an acceleration of thinning from −0.06 ± 0.33 m yr⁻¹ (January 2011 to January 2013) to −1.1 ± 0.06 m yr⁻¹ (January 2013 to January 2019). We observe this almost consistently across the five sub-regions, but this is most pronounced in the Saint Elias Mountains, the western Chugach Mountains, and the Coast Ranges.

Figure 6Altitudinal distribution of elevation changes and glacier hypsometry functions in High Mountain Asia (HMA) in RGI 6.0 sub-regions between 2010 and 2019. The lines show elevation change rates with uncertainty envelopes plotted against 100 m elevation bands (left y axis). The bars display the glacier hypsometry (right y axis).

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4.1 Uncertainty

While our uncertainty methods follow existing approaches, and our error bounds are similar in magnitude to Brun et al. (2017), Kääb et al. (2012), and Shean et al. (2020) but lower than GRACE-based estimates, several additional potential sources of errors could impact the results. Radar altimetry – delay-Doppler radar in particular – has been shown to be sensitive to surface slopes, in particular to slopes in the direction of the satellite's flight path. In regions like HMA and GoA, this impact will also be seen in the performance of the onboard tracker as, for large slopes, the system is expected to “lose lock”. While we observe a decreased coverage compared to other, less mountainous, glaciated regions, we also demonstrate here that measurements do cover the entire elevation range of glaciers in the HMA and GoA regions, allowing us to match the glaciers' hypsometry. We also do not observe significant coverage bias as a function of glacier orientation with respect to the satellite's track path. The spatial coverage is such that we demonstrably resolve spatial, altitudinal, and temporal evolution of glacier elevation.

It is a well-known observation that microwave pulses scatter from the surface as well as the subsurface, which can lead to elevation change bias in regions of historically anomalous melt events (Nilsson et al., 2015) or at a seasonal timescale (Gray et al., 2019). Over most regions however, it has been shown that surface elevation change from CryoSat over annual and pluri-annual timescale is consistent with in situ, airborne, and meteorological observations (Gourmelen et al., 2018; Gray et al., 2015, 2019; McMillan et al., 2014a; Zheng et al., 2018). Using static glacier masks can also lead to errors in regions of rapid dynamic changes. In general, these limitations are known, and efforts are currently underway in the community to improve uncertainty analysis and develop new glacier outline products (RAGMAC, 2019).

Although the time series generally reflect the actual change in surface elevation, there are a number of limitations that are important to keep in mind when interpreting the results from radar altimetry. For the reasons stated above, scattering properties can induce elevation biases at a seasonal timescale (Gray et al., 2019). In addition, integrating changes over large regions can lead to spatial heterogeneity in the successive time steps, in particular when the data volume becomes too low. These limitations may explain some of the observed patterns and in particular the few cases where seasonal variability is larger than what is expected from our knowledge of SMB (surface mass balance) in the regions.

4.2 High Mountain Asia

4.2.1 Temporal variability

The seasonal and annual time series variability reflects the influence of atmospheric circulations and precipitation seasonality in High Mountain Asia on ice thickness change. Sub-regions dominated by winter accumulation (generally westerly regimes), such as the Hindu Kush, western Himalaya, and the Pamir region (Pohl et al., 2015; Yao et al., 2012), show the typical seasonal pattern with mass accumulation during winter and early spring and mass losses in the summer and autumn months (Fig. 5).

Contrarily, sub-regions such as central Himalaya, eastern Himalaya, and Hengduan Shan show a more heterogeneous seasonal pattern. The elevation change time series of these three sub-regions indicate that the annual cycle has two maxima, with a first maximum in winter and a second and smaller peak in summer (Figs. 5, S1). Receiving summer accumulation through the Indian monsoon, these sub-regions generally have a precipitation maximum in July or August; however they are also defined by a high variability in precipitation regimes (Maussion et al., 2014) and a high temperature range (Sakai and Fujita, 2017), resulting in glaciers with varying types over very short distances (Maussion et al., 2014). The impact of this variability becomes evident when compared to the more periodic seasonal patterns of the Hindu Kush, western Himalayas, and Pamir time series. This also stands in contrast with the inner Tibetan Plateau, dominated by a more continental climate, where glaciers exhibit almost no intra-annual cycle.

In general, the heterogeneity of the time series reflects the sensitivity of mountain glaciers to meteorological patterns and changes and emphasizes that glaciers in High Mountain Asia cannot be considered to be one entity with uniform temporal variability and sensitivity to changes.

Figure 7High Mountain Asia (HMA) specific mass balance trends on a sub-regional level (using the sub-regions of Brun et al., 2017) in comparison with DEM differencing and ICESat studies. It is important to note that Shean et al. (2020) cover the time period of 2000 to 2018, Brun et al. (2017) cover the time period of 2000 to 2016, and Kääb et al. (2015) cover the time period 2003 to 2008, whilst this study covers the time period of July 2010 to July 2019. We have complemented the data from Kääb et al. (2015) with ICESat data from Brun et al. (2017) for the sub-regions Kunlun, inner TP (Tibetan Plateau), Tien Shan and Pamir Alay, which extended the estimates of Kääb et al. (2015) using the same method.

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4.2.3 Comparison of sub-regional mass balances with previous work

Our higher regional mass loss when comparing to the two DEM differencing studies by Brun et al. (2017) and Shean et al. (2020) is mostly due to differences in the south-eastern Himalaya – especially Nyainqêntanglha or Hengduan Shan – and in the Pamir regions. We used the regions by Brun et al. (2017), the RGI 6.0 second-order regions, and the HiMAP (Hindu Kush Himalayan Monitoring and Assessment Programme) regions (Bolch et al., 2019) to compare our results with other estimates (Figs. 7, S8, S9 and Tables S1, S2). For a full discussion of regional differences between estimates of recent studies, refer to Bolch et al. (2019). Our results are in line with general findings by Bolch et al. (2019) in the sense that we obtain similar results in sub-regions where there is a good agreement in general between studies, such as Tien Shan, Karakoram, western Nepal (western Himalaya), and Hindu Kush. For Nyainqêntanglha (named Hengduan Shan and southern and eastern Tibet in the RGI sub-region masks) – one of the most controversial regions – Shean et al. (2020) and Brun et al. (2017) report significantly less negative mass trends (−0.50 ± 0.15 and −0.62 ± 0.23 m w.e. yr⁻¹) than our estimates of −0.97 ± 0.19 m w.e. yr⁻¹, whilst in situ measurements (−0.94 m w.e. yr⁻¹ by Yao et al., 2012, based on the Parlung glaciers between 2006 and 2010) and ICESat studies (Kääb et al., 2015; Treichler et al., 2019) find higher negative rates for the survey time period of 2003 to 2008. We also record higher mass losses in eastern Himalaya/Bhutan, adjacent to the Nyainqêntanglha Mountains. The differences in Nyainqêntanglha and eastern Himalaya between our estimates and the ones of Brun et al. (2017) and Shean et al. (2020) (time periods 2000–2016 and 2000–2018) fit in with the generally observed acceleration of mass loss in South East Asia over the past decades (Maurer et al., 2019; Zemp et al., 2019). Some studies suggest the weakening of the Indian summer monsoon as the primary source of increased thinning (Salerno et al., 2015), whilst other studies find no widespread precipitation decrease in monsoonal regimes, which could account for all of these changes and attribute the temperature sensitivity of glaciers in monsoon-dominated regions as the main driver (Maurer et al., 2019). In fact, glaciers in Hengduan Shan, Nyainqêntanglha, and eastern Himalaya have been found to exhibit the highest sensitivity towards temperature in the whole HMA region (Sakai and Fujita, 2017).

Contrasting estimates have also been published for the Pamir and Pamir Alay mountains (Hissar Alay), where high (Kääb et al., 2015), moderate (this study; Ciracì et al., 2020; Gardner et al., 2013), and slight mass losses (Brun et al., 2017; Shean et al., 2020) and even mass gains (Gardelle et al., 2013) have been reported. Part of the discrepancy can be attributed to time variability in mass loss (Brun et al., 2017) and driven by fluctuation in winter precipitation (Smith and Bookhagen, 2018). CryoSat time series indeed suggest increased mass loss from January 2015 onwards, which could account for the higher mass loss estimates in comparison to the DEM differencing studies covering the last 2 decades (Brun et al., 2017; Gardelle et al., 2013; Shean et al., 2020).

Figure 8Estimates of mass balance [Gt yr⁻¹] as published in different studies for High Mountain Asia (a) and Alaska (b).

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The spatial thinning pattern in the Kunlun–Karakoram area (Fig. 2) confirms the suggestion of previous studies (Brun et al., 2017; Gardner et al., 2013; Kääb et al., 2015) that the so-called “Karakoram anomaly” (Gardelle et al., 2012; Hewitt, 2005) stretches up to western Kunlun Shan, which is now considered the centre of the anomaly. We record less mass gain in Kunlun (+0.01 ± 0.05 m w.e. yr⁻¹, +0.06 ± 0.05 m w.e. yr⁻¹ in the western part of Kunlun) than previous studies, indicating that the Karakoram anomaly might not persist long-term (Farinotti et al., 2020; Rounce et al., 2020). This observation is also reflected in the elevation change profile of the Kunlun regions, where Brun et al. (2017) find constant thickening at almost all elevations during the survey time period of 2000 to 2016, whilst we record thinning at lower elevations (see Fig. S7). These findings suggest a shift towards negative mass balance at lower elevations in the Kunlun region in comparison to the previous decade. However, our time series suggests increased mass gain from 2016 in western Kunlun and also mass gain in the Karakoram (Fig. 5). At the same time, we also observe decreased thinning rates in inner Tibet and eastern Kunlun. These changes could be a short-term trend; however, it displays the limitation of all mentioned studies (including this study) when deriving linear trends in a region like High Mountain Asia with large interannual climate variability and associated glacier changes.

We generally find better agreements with Shean et al. (2020), the study including an additional 2+ years (2017 and 2018) in comparison to Brun et al. (2017) and thus more closely aligned with our time period. This potentially indicates that a large part of the disagreements could be related to interannual variability and survey time period.

Figure 9Gulf of Alaska (GoA) monthly elevation change time series on a sub-regional level. The coloured lines display the time series with the uncertainty envelope (y axis: elevation change [m]; x axis: time [30 d steps]). The numbers describe the elevation change with uncertainties in m yr⁻¹.

4.3 Gulf of Alaska

4.3.2 Comparison of total mass balance with previous work

Our total mass budget of −76.3 ± 5.7 Gt yr⁻¹ (−0.89 ± 0.07 m w.e. yr⁻¹) agrees with existing estimates, including those using GRACE (−76 ± 4, −72.5 ± 8, and −69 ± 11 Gt yr⁻¹ by Sasgen et al., 2012, Ciracì et al., 2020, and Luthcke et al., 2013) and ICESat (−65 ± 12 Gt yr⁻¹ by Arendt et al., 2013) as well as a study from airborne altimetry (−75 ± 11 Gt yr⁻¹ by Larsen et al., 2015) and a consensus estimate combining glaciological and geodetic observations (−73 ± 17 Gt yr⁻¹, or −0.85 ± 0.19 m w.e. yr⁻¹ by Zemp et al., 2019) (Fig. 8b). Our result is significantly more negative than two GRACE studies, with estimates of −53 ± 14 Gt yr⁻¹ (Wouters et al., 2019) and -42±6 Gt yr⁻¹ (Jacob et al., 2012). Besides the variations in methodologies and data between these studies, also differences in study area extents, glacier masks, and volume-to-mass conversion factors contribute to the spread of total mass change results. Our estimates correspond to the RGI region 1 (excluding northern Alaska) to make the results more comparable for future studies. In general, our total mass balance is more negative than most other studies' findings, reflecting the increased thinning rates we show in the sub-regional time series from 2013–2014.

Figure 10Gulf of Alaska (GoA) monthly surface elevation change time series with uncertainty envelopes at different elevation bands aggregated on the RGI 6.0 second-order regions. The different colours represent the elevation bands (> 3000, 2000–3000, 1000–2000, 0–2000 m).

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4.3.3 Comparison of sub-regional mass balances with previous work

Since there is no prevalent sub-region mask used by more recent studies, we cannot directly compare and validate our results on a sub-regional level. Mass balance or surface elevation change estimates that overlap with our time period are either spatially not resolved (e.g. Gardner et al., 2013; Zemp et al., 2019), presented on a glacier-to-glacier basis (e.g. Larsen et al., 2015), or GRACE mascon extents (e.g. Luthcke et al., 2008, 2013).

Figure 11Altitudinal distribution of elevation changes and glacier hypsometry functions in the Gulf of Alaska (GoA) in RGI 6.0 sub-regions between 2010 and 2019. The lines show elevation change rates with uncertainty envelopes plotted against 100 m elevation bands (left y axis). The bars display the glacier hypsometry (right y axis).

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Figure 12 displays a comparison with the 1962–2006 estimates of Berthier et al. (2010), providing insights into changes in thinning rates since this time period. Our results are consistently more negative; however the general pattern with the lowest changes discovered in the Alaska Range and the highest rates taking place in the Coast Ranges is in agreement with Berthier et al. (2010). We see the largest differences along the east coast − particularly in the Saint Elias mountains − which are also the areas where the lowering of mean surface elevations after 2013–2014 has been most pronounced (see Figs. 9, S3). In comparison to the study by Berthier et al. (2010), which is based on sequential digital elevation models over the time period from 1962 to 2006, we observe similar elevation changes at the lowest altitudes but less steep gradients in sub-regions along the east coast (Fig. 11, Table S2). This is particularly pronounced in the Saint Elias Mountains, where Berthier et al. (2010) show near-balance at around 1000 m a.s.l., whilst our estimates suggest a surface elevation change of −1.5 m yr⁻¹ at the same altitude. These findings indicate a propagation of thinning upstream compared to the time period 1962–2006. In contrast, whilst on the Alaska Peninsula elevation changes have increased at lower altitudes, the limit of the thinning area has stayed the same since the survey time period of Berthier et al. (2010).

In the western Chugach Mountains, Alaska Range, and Alaska Peninsula, we observe a decrease in thinning rates towards the lowest elevations of these sub-regions, which can be attributed to the effect of debris cover and the temporal evolution of glacier extent during the study period, one of the limitations of using static glacier masks. This characteristic has been observed, although more pronounced and across all sub-regions, by Berthier et al. (2010) and Arendt et al. (2002).

Figure 12Gulf of Alaska (GoA) specific mass balance trends, aggregated on the sub-regions by Berthier et al. (2010). The figure compares our results (July 2010 to July 2019) to the estimates of Berthier et al. (2010), covering the time period 1962 to 2006.

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