An accurate and updated glacier area was important for both geodetic and glaciological mass-balance calculations (Zemp et al., 2013). Fresh snow cover probably led to an overestimate of glacier extent at the beginning of the ablation season. To reduce the influence of snow cover and to extract accurate glacier outlines, we mainly considered glacier extents at the end of the ablation season. Glacier boundary delineation was performed following Abermann et al. (2010). First three shade reliefs at the end of hydrological years 2015, 2016, and 2017 with an azimuth angle for illumination (300∘) were calculated based on multi-temporal high-resolution DEMs to show optimal visualization of contrasts in different aspects. We then delineated the glacier boundary directly by manually digitizing the strongest roughness in the shade reliefs (Fig. 2a). Area of Urumqi Glacier No. 1 was 1.555 km2 in 2015, 1.550 km2 in 2016 and 1.542 km2 in 2017. Glacier area reduction was primarily attributed to terminus retreat (Fig. 2b, c).

After multi-temporal registration, errors related to the spatial bias of the multi-temporal DEMs may be negligible. In addition to density conversion for converting TLS-derived glacier surface elevation changes to mass balance, uncertainties in the geodetic mass balances derived from the TLS may be related to (1) errors in point cloud data acquisition, including surface terrain and atmospheric conditions (moisture and wind) (Revuelto et al., 2014; Fischer et al., 2016) and (2) errors in data processing and DEM generation, e.g., registration (multi-station adjustment), point cloud compression, and filtering (smoothing terrain information) (Wheaton et al., 2010; Gabbud et al., 2015; Hartzell et al., 2015).

As mentioned in Sect. 3.1.2, dry and windless days were selected to perform the five scan campaigns. Instability of the TLS influences the registration of single scan positions from each data acquisition campaign, which includes small displacements of scan positions and the vibration of TLS. Each scan position was established on stable rock surfaces using reinforced concrete (the average drilling depth was greater than 80 cm) with a standardized GNSS-leveling point to avoid ground motion. In fieldwork, TLS is mounted using a tribrach on a tripod to level the instrument (Xu et al., 2017). Revuelto et al. (2014) found that the vibration of TLS can introduce considerable errors in measurements performed over large scales. In our experience, this issue is mainly relevant to wind, so windless weather conditions are important. Because the registration error cannot be distinguished from the positional uncertainties and the surface, it is difficult to assess registration-induced uncertainty; the error statistics are usually used to evaluate the registration error (Fey and Wichmann, 2017). RiSCAN PRO^® v 1.81 software reports error statistics of the MSA results (RIEGL Laser Measurement Systems, 2014b). The standard deviation of errors (σMSA) from the set of residuals obtained from registering the point cloud can be considered as an indication of registration quality (Gabbud et al., 2015; Fischer et al., 2016). Values of σMSA over stable terrain surrounding Urumqi Glacier No. 1 are listed in Table 2 for the four periods. Registration quality was higher at seasonal than at annual scales; the higher quality may be attributable to fresh snow cover, which makes the stable terrain smooth.

Despite four scan positions placed at the terminus of Urumqi Glacier No. 1, two undetected areas of the west branch exist (two green polygons in Fig. 5) due to flat terrain ranges from 4050 to 4100 m a.s.l. (Fig. 1a), where the emission laser cannot be received by the laser receiver. We filled these regions using the spatial interpolation method, which can induce potential errors in DEM creations. The lack of dense measured 3-D coordinates of the terrain limits us to assessing terrain-induced errors qualitatively. For precision, the undetected areas were not taken into account in calculating the geodetic mass balance; in fact, related errors were small as the relative proportions of the two areas over the entire glacier surface were minor (3.1 % for summer 2015, 3.2 % for 2015–2016, 3.6 % for summer 2016, and 4.6 % for 2016–2017, Fig. 5). Furthermore, a supraglacial river exists in the strong ablation season (June to September) due to glacier melting (Fig. 1c, d), which was detected by the TLS surveys. In order to preserve terrain information as much as possible, the octree algorithm built the topological relationship of scattered points to realize the compression of the point cloud. Point cloud filtering is also a significant post-processing step because of the dense ablation stake network, which is actually scanned by the device. Fortunately, a fine scan generates high-density points of the glacier surface terrain.

No better ways can be used to evaluate the uncertainty of DEMs without precise and well-distributed stable points (Bolch et al., 2017). The standard error (σΔhTLS‾) of elevation changes over stable terrain can be considered a criterion of the uncertainty of the entire glacier (Rolstad et al., 2009; Zemp et al., 2013). The standard deviation (σΔhTLS) of the stable terrain elevation changes is suitable for estimating the uncertainty of the DEM differences at the individual pixel scale (Fig. 3); in this case the standard error is defined as the standard deviation. However, the spatial auto-correlation must be considered when we calculate the uncertainty of the glacier-wide elevation changes. Thereby, the uncertainty of TLS-derived glacier-wide elevation changes (σΔhTLS‾) for individual glaciers was quantified using the geostatistical analysis methods of Rolstad et al. (2009) and written as 7σΔhTLS‾2=σΔhTLS2⋅15⋅ScorS, where σΔhTLS denotes the standard deviation of TLS-derived elevation changes over stable terrain. Scor is spatially correlated area. Given the high density (>1 point m-2) of the TLS data, we can probably assume that the number of independent items is about the number of glacier pixels (see Joerg et al., 2012). Here we therefore assume Scor=S. This leads to calculated values of σΔhTLS‾ ranging from ±0.16 to ±0.25 m (Table 2).

Uncertainty related to the density conversion for a single point (σρi) is determined by 8σρi=Δhice⋅σρice+Δhfirn⋅σρfirnΔhice+Δhfirn, where σρice and σfirn are uncertainties of ice and firn densities, which were assumed to be ±17 and ±50 kg m-3, respectively, following Klug et al. (2018). We then extrapolated single-point values to glacier-wide uncertainties (σρ) using the interpolation method on the ArcMAP 10.2 platform (Table 3). According to Huss et al. (2009), the uncertainties of the geodetic mass balance (σgeod) can be estimated using 9σgeod=±ΔhTLS‾⋅σρ2+ρ⋅σΔhTLS‾2, where ΔhTLS‾ is the average of TLS-derived glacier-wide elevation changes and the related uncertainty relies on the accuracy of the used DEMs.

There are additional sources of error in the glaciological measurements that lead to uncertainties in glaciological mass balance that are not easy to quantify (Dyurgerov, 2002). These uncertainties were classified into three groups: (i) errors in field observations, (ii) errors related to spatial extrapolation over the entire glacier, and (iii) errors due to non-updated glacier area. Note that the class (iii) uncertainties appeared to be negligible due to the short time intervals (2 consecutive years) in our study.

Point measurement uncertainties are prone to errors in stake readings and snow–firn density measurements (Jansson and Pettersson, 2007; Thibert et al., 2008; Huss et al., 2009), sinking or melting-out of stakes, and misidentification of the firn layer surface at the end of the last hydrological year (Zemp et al., 2010). Huss et al. (2009) demonstrated errors of ±0.1 and ±0.3 m w.e. for reading stakes in the ablation and accumulation areas, respectively. Zemp et al. (2010) determined an overall stochastic uncertainty at ±0.2 m w.e. a-1 for field measurements. Zemp et al. (2013) reanalyzed the mass balance of Hintereisferner, Austria, from 1953 to 2006 (six time intervals) and found an uncertainty of ±0.2 m w.e. a-1 for point mass balance. Beedle et al. (2014) suggested an error of point mass balance to be about ±0.1 m w.e. a-1 for accumulation area measurements. For Nigardsbreen (Norway) glacier, Andreassen et al. (2016) calculated a point measurement of ±0.25 m w.e. a-1 by summing false determination of the summer surface (±15 m w.e. a-1), subsidence of stakes (0.20 m w.e. a-1), errors in snow (0.05 m w.e. a-1), and firn (0.02 m w.e. a-1) density measurements. Following Thibert et al. (2008), here errors of ablation measured in ice (σaice) and firn (σafirn) are calculated using 0.14/Naice and 0.27/Nafirn, respectively, where Naice and Nafirn denote the number of ablation stakes and snow pits (if firn exists), respectively; errors in accumulation measurements (σc) are determined based on 0.21/Nc, where Nc is the number of snow pits.

The class (ii) errors originate from extrapolating observed values to unmeasured areas, insufficient spatial distribution of measured sites, and the interpolation method. Hock and Jensen (1999) evaluated the error of the interpolation method at about ±0.1 m w.e. a-1 for mean specific mass balances. Huss et al. (2009) computed and compared mean specific net balance with randomly reduced annual stake datasets and found that the error was ±0.12 m w.e. a-1. For Urumqi Glacier No. 1, we found that the differences between specific net mass balance at individual sites and in-situ-measured point mass balance at corresponding sites were in the range of 0–0.04 m w.e. a-1 with an average value of 0.01 m w.e. a-1; namely the error of spatial interpolation in the measured area is small. Firn basin and glacier tongue terrain of the west branch are very steep and the upper eastern elevation of the east branch is also precipitous, resulting in no in situ measurements available in these inaccessible areas. Therefore the error mainly originates from unmeasured areas (e.g., accumulation areas), but the lack of measured data in the accumulation areas limits us to quantify relevant uncertainties. We conservatively assume that the corresponding uncertainty σextra was ±0.1 m w.e. a-1 (see Andreassen et al., 2016).

Taking into account the abovementioned factors, the uncertainty of the glaciological mass balance σglac is calculated as 10σglac=σaice2+σafirn2+σc2+σextra2. Resulting values of σglac are listed in Table 3.

The high-accuracy and high-resolution DEMs allowed a detailed insight into the glacier surface elevation changes. Distributed elevation change patterns are generally similar for the four periods; i.e., both branches are characterized by a lower-elevation thinning of 1–3.5 m. Elevation changes are more positive and show smaller lowering to pronounced thickening in the upper-elevation parts except for the west branch in the mass-balance year 2016–2017 (Fig. 4a, c, e). These altitudinal change patterns are in good agreement with the long-term glaciological measurements.

Compared to the mass-balance year 2015–2016, areas of clearer increase were observed in the upper eastern parts of the east branch in the mass-balance year 2016–2017, but ice losses in the lower-elevation parts and glacier thickening in the upper reaches of the west branch were greater in the previous mass-balance year (Fig. 4c, g). Surface lowering in summer 2015 mainly occurred in the ablation areas of the east branch (Fig. 4a), and glacier surface ablation was significantly greater in summer 2016 than in the first summer (Fig. 4e). For a completed mass-balance year 2015–2016, glacier thinning areas and values in summer were obviously bigger than the whole year, which may be related to fresh snow covering the glacier at the beginning of ablation season. In addition, there were some curves of pronounced glacier surface lowering in the ablation areas during summer periods, which were related to supraglacial river (Fig. 1c, d). An area of minor thinning is detected at the lower lift (northerly) edge of the east branch, which may be associated with debris cover (Fig. 1c).

TLS-derived glacier-wide mass balances (Table 3) and their spatial distributions (Fig. 5b, d, f, h) were calculated by multiplying the spatially distributed glacier surface elevation changes (Fig. 4a, c, e, g) with the corresponding distributed density conversion (Fig. 5a, c, e, g). The thicker snow and firn covered the whole glacier surface at the beginning of May each year and the ablation area was bare ice or covered by a thin snow layer at the end of the ablation season according to field observations (Liu et al., 1997; Xie and Liu, 2010), so the changes in ice and firn–snow thickness are observed during the summer months. However, firn and snow densities are far smaller than glacier ice density. These result in annual single-point density conversion ρi being bigger and the glacier-wide annual density conversions were accordingly higher than the summer ones (Table 3). From the density conversions, we can conclude that the summer geodetic mass balance was highly affected by the snow and firn, and the magnitude of the altitudinal variability in the summer mass balance significantly changed when compared to elevation changes (Fig. 4a, e), whereas the spatially distributed patterns between elevation changes and mass balances showed good performances. These suggest that the density conversions vary for all of the studied periods and a constant value used as the conversion is clearly inappropriate. Here in-situ-measured densities from snow pits improved the accuracy of TLS-derived geodetic mass-balance calculations and therefore provided an exceptional level of detail on glacier-wide mass balance.

Urumqi Glacier No. 1 experienced negative surface elevation changes and mass balances for all of the four investigated periods (Table 3). Summer elevation lowering and mass loss were slightly greater than annual decreases, which may be related to the climatic conditions observed at Daxigou Meteorological Station (see Sect. 2). In the mass-balance year 2015–2016, calculated glacier-wide geodetic mass balance was -0.72±0.17 m w.e., which was slightly more negative than in the second mass-balance year. Summer and annual mass balances of the west branch were more negative compared to the corresponding values of the east branch, except for summer 2016 when the mass loss of the east branch was greatest.

TLS-derived geodetic elevation changes at individual stakes closely matched the glaciological elevation change (changes in stake height) of individual stakes from in situ measurements, and the difference (ΔhTLS-Δhglac) in surface elevation changes was close to zero for most of the point measurements (Fig. 4a, c, e, g). The correlation coefficients (R2) between the glaciological elevation change at the ablation stakes and TLS-derived geodetic elevation change at corresponding points were more than 0.90 (Fig. 4b, d, f, h). Note that the location and number of ablation stakes varied slightly over time due to stake melt-out; thus we selected the best-monitored single-point results to objectively assess the accuracy of the geodetic elevation changes. The majority of the point elevation changes from TLS measurements were slightly positive compared to the glaciological ones, except for summer 2016. During summer 2016 and mass-balance years 2015–2016 and 2016–2017, the mean values of ΔhTLS-Δhglac were 0.18, 0.25, and 0.14 m, respectively, which are systematically less than the corresponding uncertainties (σΔhTLS‾) of the glacier-wide elevation differences. The varying tendencies of the glaciological mass balances coincided with the geodetic ones (Fig. 6, Table 3). In 2016–2017, the difference (ΔB=Bglac-Bgeod) in glacier-wide mass balances of Urumqi Glacier No. 1 between the glaciological and geodetic methods was close to zero. Significant differences between the two methods were detected in summer 2015 for Urumqi Glacier No. 1 and the east branch, with ΔB=-0.24 m w.e. and ΔB=-0.27 m w.e., respectively. In the other three periods, the differences were much less than the uncertainties of ΔB, which were calculated based on the law of error propagation (±σgeod2+σglac2). Overall, the differences of Urumqi Glacier No. 1 were slightly smaller than those of the two branches (Fig. 6). In order to calculate the statistical significance between the two methods and validate the geodetic against the glaciological mass balance, the reduced discrepancy (δ) between the two methods was calculated following Zemp et al. (2013, Eqs. 19–21); the results of δ range from -1.14 to 0.58. As δ falls within the 95 % (δ<1.96) and 90 % (δ<1.64) confidence intervals, good agreement between the glaciological and geodetic methods can be considered satisfactory.

Spatially distributed differences between glacier-wide glaciological and geodetic mass balances were calculated to give the spatial deviations. Over most parts of the glacier surface, especially for the areas near the best-monitored points, deviations were small, indicating both methods showed very close spatial results. Pronounced differences mainly occurred on the steep slopes where in situ measurements were missing (Fig. 7a, d, g, j). The mass-balance elevation distribution derived from the two methods remained similar despite the presence of differences in magnitude, i.e., mass balance increased with rising altitude (Fig. 7b, c, e, f, h, i, k, m). The geodetic results were more positive in lower-elevation regions and more negative in the higher glacier parts in general compared with the glaciological mass balance, which was probably related to glacier dynamic processes (discussed in Sect. 6.4). The dotted (glaciological) and solid (geodetic) lines met where the glacier mass balances were close to zero; this meant that the equilibrium-line altitudes (ELAs) derived from the two methods matched closely, especially in mass-balance year 2015–2016 and summer 2016 (Fig. 7e, f, h, i), but the biggest shift between the two methods was detected in summer 2015 for the east branch, which may be related to survey data differences between the glaciological and geodetic observations (see details in Sect. 6.5). This reflects that the TLS can therefore be considered an effective tool to calculate ELA.

The important factors for scanning high-quality point cloud data are visual angles of the scan positions and atmospheric conditions. A dry and windless atmosphere is a prerequisite for high-quality data acquisition. Good visual angles can easily be achieved for very small cirque glaciers. Generally, the area and length of reference glaciers are greater, with a huge variation in altitude. The maximum working distance (6 km) of Riegl VZ^®-6000 is specified for flat targets with size in excess of the laser beam diameter, perpendicular angle of incidence, and atmospheric visibility in excess of 23 km. In bright sunlight the operational range may be considerably shorter than under an overcast sky (RIEGL Laser Measurement Systems, 2014a). However, glaciers generally have complicated surface terrain and the requirement of perpendicular angle of incidence is not always met, so the unscanned regions usually have flat terrain (Fig. 1d). It is very difficult for us to get a dry and windless atmosphere under an overcast sky around a glacier. In these situations, more than one scan position must be set in order to scan as much of the glacier surface area as possible. However, this, in turn, can create errors in data registration. The average error originating in MSA (σMSA) of the investigated periods was ±0.16 m (Table 2). Actually, σMSA is highly dependent on the overlap percentage of point clouds from each scan position of the same survey data and the accuracy of global 3-D coordinates of each scan position. In our fieldwork, the overlap percentage of point clouds from the four scan positions was more than 30 %, which met the requirements of data registration (CH/Z 3017-2015, 2015). Note that we did not get better results with more scan positions since this would probably decrease the quality of the MSA. We should find the best visual angles to obtain the maximum scan range with the fewest scan positions. Higher elevation favors better angles, but it is not always easy for us to access higher parts and place the instrument. For the ideal distribution, scan positions should be located in different elevation bands and directions, and we can also mount a steadying bar on a tripod to raise the altitude of the TLS.

Systematic shifts of DEMs in the horizontal and vertical directions can also increase the uncertainty of DEM differencing (Nuth and Kääb, 2011), so multi-temporal registration of two consecutive scan campaigns is predicted for the TLS-derived geodetic elevation changes to be accurate. The mean uncertainty of elevation changes was ±0.22 m (Table 2), which was slightly smaller than in the TLS datasets used for other glacier thinning measurements (e.g., López-Moreno et al., 2016). This may be attributable to the use of accurate global 3-D coordinates of each scan position and a sufficient number of stable terrains (Fig. 3). In addition, fixed scan positions also reduce multi-temporal registration error and enhance the accuracy of glacier-wide elevation changes. So the quality of point cloud data and DEM differencing is encouraging.

It is obvious that the quality of TLS-derived geodetic mass balances relies on the accuracy of glacier surface elevation changes and density conversion of volume-to-mass changes. With regard to density conversion, our approaches account for the changes in ice and firn–snow thickness as well as the corresponding densities to calculate more accurate values of density (Table 3). The annual values for ρ were in the range of 763–865 kg m-3, which was in line with the average density of 850±60 kg m-3 recommended by Huss (2013), whereas, ρ of the west branch declined to 763 kg m-3 in the mass-balance year 2015–2016, largely because of the presence of fresh snow cover at the time of the glaciological measurements. For the same reason, the summer values concurred with the recommended density. Calculated uncertainties in the geodetic mass balances ranged from ±0.13 to ±0.20 m w.e., with an average value of ±0.16 m w.e. for the investigated periods (Table 3), and were slightly greater than the other geodetic mass balance measured base on the same TLS device (e.g., Fischer et al., 2016). This may be related to multiple scan positions and a larger scanning range, but the uncertainties are smaller than those derived from remote sensing imagery (e.g., Holzer et al., 2015; Barandun et al., 2018).

Dense spatially measured sites cover the glacier surface (the average density is about 28 stakes km-2 from 2015 to 2017), except for the inaccessible areas, to measure the glaciological mass balance (Fig. 1a). The mean uncertainty of σglac was ±0.12 m w.e. and mainly originated from spatial extrapolation of point measurements. This value is smaller than most recent studies (e.g., Andreassen et al., 2016; Thomson et al., 2017; Klug et al., 2018). This is probably due to a relatively smaller area and accompanying higher density of point measurements of Urumqi Glacier No. 1 than in aforementioned studies. Thus the TLS device yields accurate geodetic results and the quality of the glaciological mass balances is also very good. Nonetheless, uncertainties in field measurements and interpolation can potentially contribute the deviations between glaciological and geodetic mass balances. The obvious deviations in the spatially distributed differences were found at the firn basin of the west branch and the upper right edge elevations of the east branch. Two unscanned areas also present big deviations (Fig. 7a, d, g, j). Remarkable differences in the east branch in summer 2015 induce the poorest match between glaciological and geodetic mass-balance elevation distribution (Fig. 7c); this can be explained by the lack of well-measured point data (Fig. 7a).

The glaciological method cannot measure internal and basal mass balances, but these processes are implicitly captured by the repeated geodetic surveys. We need to provide a rough estimate of internal and basal mass balances of Urumqi Glacier No. 1 to detect their contributions to the differences between glaciological and geodetic mass balances.

Urumqi Glacier No. 1 is a small and cold glacier. Basal sliding and bed deformation of the glacier are negligible since the temperature at the glacier bed is below the melting point of ice, so the glacier has low ice velocity and dynamics and hardly any subglacial water systems (Huang, 1999; Xie and Liu, 2010; Wang et al., 2017). Previous studies have suggested that internal ablation of polythermal glaciers is negligible as the ice motion is small (e.g., Albrecht et al., 2000; Zemp et al., 2010). In addition, internal melt caused by changes in potential energy due to glacier dynamics is negligible as the glacier dynamics themselves are insignificant. Thus, internal ablation of Urumqi Glacier No. 1 is weak, and mainly comes from the released potential energy of descending water: 11Bpe=QmgLfs¯ρwater⋅h¯ELA-hterm2, where Qm denotes annual discharge of flowing water, g is the gravitational acceleration, and Lf is the latent heat of fusion. Glacier mass loss mainly comes from ablation area and we assume meltwater originates at half the vertical from the glacier terminus to ELA, so h¯ELA and hterm are average ELA (4152 m) and the altitude of the glacier terminus (3775 m), respectively, and s¯ is the average glacier area between 2015 and 2017. The cumulative measured glacier surface ablation over the two years was used to determine annual discharge and the value of Qm was estimated to be about 1.4×109 kg a-1. Equation (11) gives Bpe=-0.005 m w.e. a-1. Internal accumulation results from refreezing percolating water or the freezing of capillary-trapped water in cold snow and firn, which plays a significant role in cold and continental climates, such as Storglaciären, Sweden (Zemp et al., 2010), and Castle Creek Glacier, Canada (Beedle et al., 2014). Urumqi Glacier No. 1 is a cold glacier in a continental climate setting with no measurements of internal accumulation, so we conservatively estimate internal accumulation to be about 4 % of the winter mass balance and the resulting value was about 0.01 m w.e. a-1. Final calculated internal mass balance of Urumqi Glacier No. 1 was about 0.005 m w.e. a-1.

Basal ablation is generally attributed to frictional heat of basal sliding and geothermal heating for mountain glaciers (Thibert et al., 2008; Thomson et al., 2017; Galos et al., 2017). Basal ablation caused by frictional heat is very small since there is hardly any basal sliding of Urumqi Glacier No. 1. Here we mainly consider the contribution of basal ablation from geothermal heat (Bgt), which is estimated using 12Bgt=qtLfρwater, where q=0.059 W m-2 is the geothermal heat flux (Huang, 1999), and t is the mass-balance period; here we primarily consider annual scale and basal ablation to be about 0.005 m w.e. a-1. The calculated internal and basal ablation totaled -0.01 m w.e. a-1.

Finally the total value of internal and basal mass balances was close to zero, which is far less than the difference (ΔB) between the two methods. This suggests that the contribution of annual internal and basal processes is negligible and does not affect the differences between the two methods.

Geodetic measurements of glacier surface elevation changes include glacier surface mass balance and vertical velocity components (Kaser et al., 2003; Geist et al., 2005). Vertical velocity (ws) is downward (submergence) and causes dynamic thinning of the glacier in the accumulation area. Vertical velocity is upward (emergence) and results in dynamic thickening of the glacier. This dynamic process results in the general difference between the elevation-distributed mass changes stated above. To discuss the influences of vertical velocity component, here ws depends on the kinematic boundary condition at the Urumqi Glacier No. 1 surface as basal sliding and bed deformation of the glacier are negligible (see Pettersson et al., 2007; Cuffey and Paterson, 2010): 13h˙=b˙ρ+ws-us∂S∂x-vs∂S∂y, in which h˙ is the rate of glacier surface elevation changes, and us and vs are the components of horizontal ice velocity at the glacier surface s (Cuffey and Paterson, 2010). We neglect the advection of the glacier surface topography induced by horizontal ice flux due to the low reduced horizontal velocity (Wang et al., 2017) and short time intervals of this study. Then changes in h˙ equal the sum of b˙ρ and ws (Beedle et al., 2014) and can be expressed as 14h˙ρ-b˙=wsρ. Glacier dynamic thinning and thickening can be detected by subtracting the glaciological mass balances from the geodetic ones. For most of the study periods, positive difference values (thickening) dominate in the lower elevations, especially the glacier tongue, and negative difference values (thinning) mainly occur in the higher parts (Fig. 7a, d, g, j). Positive values across the east branch in summer 2015 may be related to different survey dates between the geodetic and glaciological methods.

Applying a reciprocal density conversion to the mass-balance differences provides estimates of the submergence and emergence velocities. Here we defined the term submergence as negative vertical velocity and emergence as positive vertical velocity. Variation tendency of the estimated velocities at ablation stakes were found to match the in-situ-measured ones, especially for the east branch (Fig. 8). Relatively bigger differences in the west branch were detected in the mass-balance year 2016–2017 (Fig. 8b, d), which may be due to an avalanche in the upper part during the summer 2017. The firn basin terrain of the west branch is very steep and is adverse to mass accumulation, which can also be validated in terms of TLS-derived glacier surface elevation changes (Fig. 4g). Thus pronounced misalignment of mass-balance elevation distribution curves between the two methods occurred. Considering the errors of estimate and in situ measurements, submergence and emergence velocities can be estimated using the TLS-derived DEMs and glaciological mass balance. The difference in mass-balance elevation distribution can be largely explained by glacier dynamic thinning at higher elevations and dynamic thickening at lower elevations.

In fact, the vertical velocity of Urumqi Glacier No. 1 is small (Fig. 8). We now discuss the errors of glacier surface elevation changes versus dynamic thinning and thickening. Differences in glacier surface elevation changes derived from the TLS and glaciological measurements were close to zero for the vast majority of the ablation stakes, and corresponding errors in the differences were mostly larger than the difference themselves (Fig. 9). Compared with the errors of measurements, dynamic thinning and thickening of the glacier were minor and negligible. So Riegl VZ^®-6000 TLS can be considered an effective tool to measure the mass balance of Urumqi Glacier No. 1.

Although glacier thinning and thickening were negligible, other factors such as meteorological conditions and glacier surface terrain may cause mass-balance differences between the two methods. Figure 9 shows daily meteorological records provided by Daxigou Meteorological Station from 25 April 2015 to 28 August 2017. Positive temperature and more than 75 % of the annual total precipitation amount occurred during the summer months; this probably resulted in summer mass balances that were slightly more negative than annual ones (Table 3). Although the reduced discrepancies between TLS-derived geodetic and glaciological mass balances fall within the 95 %, a bigger difference (ΔB) between the two datasets is detectable for the east branch, and the difference is caused by survey date differences. The glaciological measurements of east branch were performed 5 d before the TLS surveys (28 August–2 September 2015). The total precipitation was 67 mm and daily mean temperatures were close to zero. The daily minimum temperatures were also all below 0 ∘C during the 5 d (Fig. 9). The climatic conditions may be responsible for the larger mass-balance differences of the east branch. In addition, light snow occurred before the last TLS surveys (28 August 2017), possibly resulting in the noticeable increase in the upper eastern parts of the east branch (Fig. 5h).

The differences in mass balance between the two methods were possibly related to the effect of glacier surface terrain. The presence of two minimal unscanned areas in TLS surveys is due to the flat terrain of the west branch surface (two green polygons in Fig. 5). The geodetic mass-balance calculations did not include these unscanned areas; this cloud potentially increased the difference between the two methods. Furthermore, these undetected regions located in the ablation area and higher wastage than the surroundings were observed according to glaciological measurements. This may imply that the geodetic mass balances of the west branch were more positive than the glaciological ones (Table 3), and a discrepancy in mass-balance elevation distributions of the west branch was observed at 4000–4150 m a.s.l. Nevertheless, the geodetic method is able to cover the majority of the glacier surface and take the terrain characteristics into account, whereas the glaciological measurements cannot capture all the topographic features despite a dense spatial coverage of in situ observations being applied. Furthermore, in situ observations are missing in the firn basin and glacier tongue terrain of the west branch and eastern elevations of the east branch because of the presence of precipitous terrains in these inaccessible regions (green color in Fig. 11a). The eastern elevations of the east branch are dominated by the northwest aspect, and the firn basin has aspects from north to northwest (Fig. 11b). Aspects are likely to influence the glacier surface albedo and thereby control the surface change patterns (see Yue et al., 2017).

This study presents the application of multi-temporal Riegl VZ^®-6000 TLS point clouds in mass-balance monitoring of Urumqi Glacier No. 1. The long-range TLS can provide DEMs of high temporal spatial resolution and accuracy to allow more detailed insight into glacier evolution (e.g., Gabbud et al., 2015). To take advantage of this and provide more-precise glacier surface elevation changes, it is worth remembering that fixed scan positions are highly important between consecutive scans when using our approach. We should also note that not all glaciers in China are as easily accessible as Urumqi Glacier No. 1. For many large glaciers, it is not always easy to fix scan positions using reinforced concrete with a standard GNSS-leveling point, but we can mark stable bedrock outcrop as a scan site. Another advantage of this type of TLS is the long scanning range, and such an instrument could allow most of the glacier surface to be scanned from one or several scan positions, especially for remote and inaccessible glacier areas (e.g., crevasses, steep ice, debris cover). Therefore the instrument provides a quantitative evolution in spatial coverage compared to glaciological in situ measurements, which can be seen as a beneficial complement to glaciological mass balance, particularly for calibrating inaccessible areas. TLS surveys can also provide updated glacier boundary and surface DEMs. In addition, we can paste several retro-reflective targets (e.g., reflective foils, corner cube reflectors, and retro-reflective paintings) to the surface of each stake and the targets can be easily surveyed and identified since each of them has a high directivity of the reflected laser radiation; then the location of stakes can be determined. All of these parameters are favorable for glaciological mass-balance calculations. A combination of glaciological and TLS observations may yield optimum results. TLS-derived geodetic results can validate the distributed glacier mass-balance models as the TLS can provide measurements of high spatial and temporal resolution, especially in the strong ablation season. The instrument can be used to investigate daily or sub-daily ablation (e.g., Haut Glacier d'Arolla, Switzerland; Gabbud et al., 2015), which can completely meet the requirements of time resolution for glacier mass-balance models.

One drawback of the TLS surveys is the presence of data voids (unscanned areas), even for very small glaciers (e.g., Fischer et al., 2016). This is due to limited scanning angle and complex glacial terrain. An emerging low-cost unmanned aerial vehicle (UAV) has the potential to avoid data voids in glaciological monitoring with the good surveying angle of UAV. Immerzeel et al. (2014) showed that UAV combined with a structure from motion (SFM) workflow provide a powerful tool for monitoring mass balance and surface velocity of a Himalayan glacier with high spatial accuracy. From our field experiment at Urumqi Glacier No. 1, rarefied air and frequent blustery wind around glaciers usually reduce the power of UAV, and rock outcrops result in difficult operations of such instruments. Hence we mainly consider using UAV to survey unscanned area. Integration of UAV- and TLS-acquired data can provide the whole glacier surface terrain of interest. Other technology such as terrestrial photogrammetry also has the ability to estimate mass balance, and the quality of photogrammetric estimation is similar to the quality of TLS (e.g., Piermattei et al., 2015; Fugazza et al., 2018). However, the reliability of UAV and terrestrial photogrammetry in glacial environments is more dependent on the natural features (i.e., characteristic image objects) of the surveyed surfaces compared with TLS. The cost of TLS is higher than UAV and ground-based photogrammetric surveys.

From our experience, the monitoring tool is potentially applicable to other glaciers provided that these glaciers have a small to medium size and relatively steep terrain. According to the second Chinese glacier inventory (Guo et al., 2015), ∼83 and ∼70 % of the total number of glaciers in China have an area smaller than 1 and 0.5 km2, respectively, and only ∼3 % have an area larger than 5 km2. Riegl VZ^®-6000 TLS has been proven successful in monitoring mass balance of very small glaciers (area smaller than 0.5 km2) in the Swiss Alps (Fischer et al., 2016). Hence it should be possible to measure most glaciers using the TLS. Furthermore, if we assume that these glaciers with an area ≤1.6 km2 (approximate area of Urumqi Glacier No. 1) and a mean surface slope greater than 23.4∘ (mean slope of Urumqi Glacier No. 1) have a good visibility to be monitored using the TLS, the proportion of theoretical appropriate glaciers is ∼58.5 %, which is evenly distributed at different mountains (Fig. 12). However, it is not always easy for us to monitor all of the appropriate glaciers as some of them are located in remote areas (i.e., far away from the road). Now we have selected some benchmark glaciers with easily accessible locations for future application of TLS measurements. The TLS system thus has a huge potential for glacier mass-balance monitoring in China.

Nevertheless, TLS measurements and point cloud data post-processing are challenges for a broader application. One disadvantage of the TLS is that it requires specific knowledge, skills, and experience for its use and data processing. Other limitations of the TLS are related to suitable scan positions for obtaining good visual angles of the glacier surface and stable scan positions for multi-temporal registration of repeated scans for change detection. In addition, the uncertainties of density conversion still remain at seasonal and annual scales as in-situ-measured densities of all benchmark sites are difficult to obtain (very few glaciers in China have as detailed of observations as Urumqi Glacier No. 1). A day with little snow in the accumulation area and no snow in the ablation area (i.e., snow line is clearly distinguished) should be chosen to perform TLS measurements. We may use a built-in camera of the TLS to create high-resolution panorama images of a glacier (RIEGL Laser Measurement Systems, 2014a). Then firn–snow and bare ice areas (i.e., snow line) can be determined (e.g., Barandun et al., 2018). An area-weighting approach can be used to estimate density because the lack of in-situ-measured densities makes the volume-weighting approach difficult to extensively use. A density assumption over time intervals (≥5 years) based on physical models is also important as most glaciers in northwest China are cold and multi-thermal.