Mass changes at the surface of a glacier dominate, in most cases, over internal and basal mass changes and form over a predefined period—usually the hydrological year or shorter—the so-called climatic glacier mass balance. It plays a crucial role in catchment hydrology and sea level rise. Furthermore, it is used to assess respective climate change impacts and is subjected to detection and attribution studies. In order to calibrate and validate high-resolution distributed glacier mass balance models, detailed information of glacier surface changes is needed (Klok and Oerlemans, 2002; Hock and Holmgren, 2005; Machguth et al., 2006).

The climatic mass balance information on the surface is often acquired with the traditional “direct glaciological method” (Kaser et al., 2003; Cuffey and Paterson, 2010; Cogley et al., 2011) by measuring the relative surface elevation changes at 10 to 50 selected locations (points) on the glacier. The measurements are transferred to mass changes in combination with density measurements of snow and ice and are then extrapolated to the glacier-wide surface. This “glaciological method” is laborious and resolves the complexity of spatial mass balance patterns only coarsely and is only grossly able to mirror the driving processes. On the contrary, the “geodetic method,” carried out from terrestrial or airborne platforms (Geist and Stotter, 2007; Fischer et al., 2016; Klug et al., 2018), allows for detecting comparatively high-resolution surface elevation changes relative to the surrounding bedrock. Again, obtained volume changes need measured, modeled, or assumed density information for conversion into mass changes. However, the geodetically measured glacier mass balance contains, beyond the climatic signal, the internal and basal changes in the ice column. In addition, it also contains effects of ice flow divergence, which is the elevation change component originating from the ice flux to maintain mass continuity (Cuffey and Paterson, 2010, Sect. 8.5.5). The ice flow divergence is omitted by integrating the elevation changes over the entire glacier area (Kuhn et al., 1999; Zemp et al., 2010; Klug et al., 2018). The effect of ice divergence on the point glacier mass balance may be neglected on glaciers with moderate to low ice flow dynamics and over short time periods such as daily up to monthly time intervals (Cuffey and Paterson, 2010). If, as on many mountain glaciers, internal and basal mass changes can also be neglected, the geodetically obtained mass changes can provide spatially and temporally distributed information on the climatic mass balance.

For most temperate and land-terminating glaciers, the representation of the snow cover dynamics poses the central deficiency in distributed mass balance models (Greuell and Bohm, 1998; Machguth et al., 2006; Carturan et al., 2012; Molg et al., 2012; Gurgiser et al., 2013; Ayala et al., 2015; Prinz et al., 2016). It crucially impacts the spatially distributed glacier surface mass balance by modulating accumulation and, subsequently, also ablation patterns. Data quantity and quality both from ground measurements and remote sensor systems have not yet been sufficient to reflect the actual snow cover processes on a glacier scale so far, which also limits the calibration and evaluation of distributed mass balance models (Machguth et al., 2006; Carturan et al., 2012; Gardner et al., 2013; Zemp et al., 2013).

A possible way to overcome this deficiency and acquire more information on surface elevation changes over the glacier is the measurement by a terrestrial laser scanner (TLS). A TLS emits a laser beam as the active sensing carrier. The distance between the sensor and the surface target is derived from the travel time of the laser beam and point clouds are created with a high point density ( > 1 points m⁻², depending on distance and scan settings) (Wehr and Lohr, 1999). Several studies have already proven that the total annual and seasonal mass balance can be acquired by TLS (Fischer et al., 2016; Wang et al., 2018; Xu et al., 2019). Since only the processes larger than the uncertainty of the TLS can be measured, an uncertainty assessment of the TLS is mandatory.

A permanent and automated TLS has been installed for monitoring the Hintereisferner (HEF) glacier (Ötztal Alps, Austria) in 2016. This TLS is able to capture 66.5% of the glacier area. Permanent TLS setups are known (Kromer et al., 2017; Vos et al., 2017; Anders et al., 2019; Deruyter et al., 2020; Campos et al., 2021) (Voordendag et al. (2021)), but not for studying glaciers and ranges longer than 2,500 m.

Various studies (Soudarissanane, 2016; Friedli, 2020) have already stated the main sources for uncertainty in TLS point cloud data: 1) instrument and hardware limitations, 2) scanning geometry, 3) atmospheric conditions between TLS and target surface, 4) surface reflectance properties, and 5) post-processing including registration and georeferencing. Additionally, the rasterization of point clouds contributes to the uncertainty budget when working with a digital elevation model (DEM). Previous research assessed only selected uncertainty sources and at shorter distance ranges than the system at HEF (Soudarissanane, 2016; Friedli, 2020; Kuschnerus et al., 2021; Dong et al., 2020; Schaer et al., 2007). Here, we addressed the full spectrum of the main uncertainty sources of TLS point clouds and derived DEMs and at distances up to 4,500 m.

This paper aims to:

1) identify and quantify the main sources of uncertainty for measuring surface changes with a permanent long-range TLS system and

The findings contribute to a better understanding of requirements and limitations of permanent TLS systems for observing glacier surface dynamics.

The research area is the HEF (Figure 1), a valley glacier located in the Rofental catchment in the Ötztal Alps (Austria). The glacier has a length of approximately 6,300 m, ranging between the Weißkugel mountain peak (3,739 m a.s.l., green triangle in Figure 1C) and the glacier tongue at 2,460 m a.s.l. (2018). The glacier has been the key research site of the University of Innsbruck for glaciological studies since the early days of glacier research (Blumcke and Hess, 1899) and is now a part of the wider Open Air Laboratory Rofental (Strasser et al., 2018). Continuous long-term mass balance observations dating back to the year 1952/53 (Kuhn et al., 1999) and velocity and ice thickness change measurements since 1895 (Span et al., 1997) are available. The glacier is classified as one of the key “reference glaciers” by the World Glacier Monitoring Service (WGMS) (Zemp et al., 2009).

The catchment is instrumented with several permanently operated and automated weather stations and rain gauges. The most important station for this study is Im Hinteren Eis (IHE, 3,245 m a.s.l.), which is located on the orographic right side of the glacier on the ridge at the Austrian–Italian border (blue dot in Figure 1C) and was installed in September 2016. The main instrument at this location is the year-round permanently installed TLS, which was installed in September 2016 and is in operational use for monitoring surface elevation changes on the glacier since 2019. The TLS is mounted on a stable frame positioned in a small container. The scanning process was automated in 2020, along with the setup, as described in detail by Voordendag et al. (2021). The TLS is a RIEGL VZ-6000 (RIEGL, 2019a), which can scan up to 6,000 m. Due to its laser wavelength of 1,064 nm, the instrument is exceptionally capable of measuring snow and ice. To date, the RIEGL VZ-6000 at HEF is the only permanent installation of such a long-range system worldwide, but we are also aware of the permanently installed RIEGL VZ-2000 TLSs (ranging up to 2000 m) at coast lines (Vos et al., 2017; Anders et al., 2019; Deruyter et al., 2020) and in a boreal forest (Campos et al., 2021).

Furthermore, Im Hinteren Eis is equipped with an automatic weather station (AWS), which is located 50 m horizontally and 25 m vertically away from the TLS. The AWS provides all common meteorological data at a 1-min resolution and also includes a 3D sonic anemometer to measure turbulent fluxes. Last, two webcams are installed that take pictures of the glacier every 30 min1.

A second important measurement location is Station Hintereis (StHE, 3,026 m a.s.l.), built in 1966 and located at the orographic left side of the glacier (Strasser et al., 2018). This station presently hosts an AWS with a 10-min average of common meteorological variables.

We are mainly interested in the uncertainty of the gridded data, as they ease the comparison of scans to identify vertical changes at the glacier. The measurements are subjected to six potential uncertainty sources (Table 1). However, this study does not account for the surface reflectance properties, as RIEGL VZ-6000 delivers good reflectance from snow and ice surfaces. As we are mainly interested in surface elevation changes during the season where the glacier is covered in snow, we assume a good reflectance and a negligible respective influence on surface elevation changes (Kaasalainen et al., 2008; Fritzmann et al., 2011). Thus, five uncertainty sources remain, and they will be discussed individually in this study. The uncertainty sources σ in this study are calculated as uncertainties in vertical direction of a single laser pulse or gridded data and are given in meter.

The uncertainty that applies to a single-point measurement originates from the laser pulse source, the medium of the laser beam, and/or the target surface. The laser pulse source is the TLS, which has to deal with instrument and hardware limitations (Soudarissanane, 2016) (σ _instrument , Sect. 3.3). Atmospheric perturbations due to fluctuations and changes in air pressure, air temperature, and relative humidity along the path of the laser beam influence the velocity and pathway of the laser pulse in the medium (Friedli, 2020) and thus the calculated distance of a laser pulse (σ _atm , Sect. 3.4). The target surface is the footprint of the laser beam (Schaer et al., 2007; Sheng, 2008) and is elaborated as the scanning geometry in this study (σ _geo , Sect. 3.5). These three uncertainty sources are assumed to be random, independent uncertainties. The assumption of the independence of these uncertainty sources is a simplification, as they are all affected by the distance from the TLS to the surface R (800–4,500 m), which is several orders of magnitudes larger than these uncertainties (see Sect. 3.3–3.5). So, the influence of a small uncertainty in R, say R ± δR, is negligibly small on σ _instrument , σ _atm , and σ _geo , and R can be seen as an independent constant, which differs for every single laser pulse. After this simplification, the error propagation law for addition is applied in Eq. 1 to calculate the total error propagation of a single laser pulse. σ point = σ instrument 2 + σ geo 2 + σ atm 2 (1)

Subsequently, the acquired point clouds are gridded to DEMs by taking the mean of all the points in the 1-m grid cell. The number of points per grid cell is called the point density and decreases with the distance from the TLS. Likewise, if the point density increases, the uncertainty decreases, as the mean is taken over a higher number of points. The point density can be adjusted by changing the scan settings, but in our study, the angular step width of the TLS is set to 0.01° and not changed. The point density ρ _point can be seen as a repeated measurement and thus, due to the error propagation, the uncertainty of σ _point must be divided by the square-root of the number of measurements (Joerg et al., 2012) to get the uncertainty of every grid cell σ _gridcell (Eq. 2). σ gridcell = σ point ρ point (2)

The calculated σ _gridcell does not yet include the uncertainty caused by the registration (see Sect. 3.2). The registration of the point clouds introduces a systematic error and is a rigid transformation and translation applied to the point clouds. Opposed to the other random uncertainty sources, the registration uncertainty depends on the method the user applies to the data, independent of the previously calculated σ _gridcell (Joerg et al., 2012; Fey and Wichmann, 2016). Therefore, the variable σ _reg is added to Eq. 2 to acquire Eq. 3. σ total = σ point ρ point + σ reg (3)

The registration uncertainty cannot be distinguished from the other uncertainty sources (Fey and Wichmann, 2016), and is therefore first assessed in Sect. 3.2.

The aim of the installation of the TLS is to measure glacier surface changes at HEF. This section discusses a series of different phenomena that involve glacier surface changes with their appurtenant time scales, albeit having different magnitudes and can possibly be detected with a TLS.

The ability to measure the annual geodetic mass balance with a TLS has already been proven in other studies (Fischer et al., 2016; Wang et al., 2018; Xu et al., 2019). The geodetic method is comparable to the glaciological method under the assumption that we integrate over all the processes that lead to elevation changes at any single point of the glacier over the total glacier area (Kuhn et al., 1999; Zemp et al., 2010; Klug et al., 2018). The geodetic mass balances derived from the automatically registered TLS data were compared to the glaciological mass balances for the hydrological years (between 1 October and 30 September) 2016/17 to 2019/20 for HEF. Differences of −117 kg·m⁻² (mean) and 162 kg·m⁻² (root-mean-square error) were found. This is within in the glaciological mass balance uncertainty, which is quantified at ±210 kg·m⁻² for HEF (Klug et al., 2018). Thus, reanalysis (Zemp et al., 2013) or better registration is not needed and also shows the applicability of the automatically registered TLS data for yearly mass balance measurements at HEF.

The glacier mass balance can likewise be measured over seasons (Gabbud et al., 2015; Xu et al., 2019; Li et al., 2021), months, weeks, and potentially days with a TLS, given snow density information is available. This is especially interesting during the melt season, where melt evolves quickly, and snow is distributed as patches over the glacier. This can be useful validation data for atmospheric (Goger et al., 2022), snow cover (Mernild et al., 2006), or distributed mass balance models (Klok and Oerlemans, 2002; Hock and Holmgren, 2005; Machguth et al., 2006) and has magnitudes between centimeters and meters. Additionally, with daily measurements, the glacier loss day can be determined, which is the day in the hydrological year when the volume and, with similar snow distribution patterns, the mass is the same as that on 1 October. This means that after this date, the glacier will only lose mass in the present climate conditions.

On shorter time scales, the process with a magnitude of centimeters to meters at the glacier is snowfall. During snowfall events, snow is not evenly distributed over the glacier but is mostly driven by orographic precipitation in winter and by two precipitation processes that are mainly terrain and wind-driven, namely, 1) snowfall enhancement caused by the interaction with the local flow field and local cloud formation processes (Mott et al., 2014) and 2) pure particle flow interaction (preferential deposition of snowfall) (Lehning et al., 2008). After snowfall, the snow is redistributed over the glacier. These snow drift phenomena have a vertical spatial scale of < 1 m (Filhol and Sturm, 2015) and a horizontal spatial scale of 1–100 m (Marsh et al., 2020). Depending on the atmospheric conditions, snow drifts and settles after snowfall (Mott et al., 2018). During the day, snow fall and redistribution are still hard to model, but the TLS data can be a useful tool to validate models that take them into account. Snow fall, redistribution, and snow settling are difficult to distinguish from each other as they happen simultaneously, so these are partly combined in the investigation of snow distribution.

Last, special cases of snow redistribution are avalanches. Avalanches can occur within seconds but have magnitudes up to meters in the vertical direction and runout lengths of meters to kilometers. The avalanches are clearly visible in webcam pictures at HEF, yet the DEMs give quantitative information, which is of interest for the snow avalanche community as the input for model calibration (Prokop et al., 2008; Schaffhauser et al., 2008; Hancock et al., 2020).

Our study shows the possibility to investigate the mentioned phenomena. First, on longer time scales, processes with magnitudes in the order of meters can be detected with the automatically registered data.

Second, this automated registration is also helpful to select case studies and to qualify days when glacier surface changes have occurred. Subsequently, the scans taken at these days can be post-processed with RiSCAN PRO, delivering an uncertainty of the TLS data of ±0.10 m. Moreover, the grid size in this study is set to 1 m, but to achieve the best combination between accuracy and spatial horizontal resolution, the grid size can also be set an order of magnitude larger. A coarser horizontal resolution increases the amount of measurements per grid cell and hence leads to a smaller contribution of the instrument and hardware limitations to the uncertainty budget as these are evened out in the data. Eventually, this leads to a more accurate automatically registered DEM, which is still usable in the generally coarser models, though having a lower horizontal spatial resolution.

Nevertheless, it is known that snow drift mainly occurs at mountain crests to leeward slopes (Mott et al., 2018), and these areas have an insufficient coverage and a rather low point density (1–2 points m⁻²) in the data of HEF. Therefore, future research could benefit from the coverage of the glacier accumulation zone with airborne laser scanning (ALS), which has already been done in the past at HEF at annual and seasonal temporal resolution (Helfricht et al., 2014; Klug et al., 2018). These studies can be improved with more frequent acquisitions, which might be feasible with uncrewed aerial vehicles (UAVs) (Zieher et al., 2019).

The uncertainty sources discussed in this study were separately assessed in previous studies and in different contexts. The scanning geometry has been evaluated for a TLS on short ranges (≤50 m) inside a building (Soudarissanane et al., 2011). The focus in this study was on point cloud quality, when incidence angles are unfavorable and scanning ranges are long. Similar to our study, Soudarissanane et al. (2011) found that larger incidence angles lead to larger noise levels and a higher uncertainty in the position of the laser beam. Likewise, the extent of the footprint for an ALS acquisition was investigated (Schaer et al., 2007). The estimation of the uncertainty of the footprint in our study is based on the study by Schaer et al. (2007) (Eq. 18), even though the scanning geometry in an ALS acquisition is more favorable due its more perpendicular and closer range ( < 1,000 m) to the surface than the permanent TLS setup. On the other hand, TLS has no positioning errors related to the GPS/INS navigation of the airborne carrier.

The instrument and hardware limitations of TLS systems are also assessed in other studies (Lichti and Licht, 2006; Griebel et al., 2015), but they use different systems. The radial stripes found in our study have only been mentioned by Kuschnerus et al. (2021), but the cause of the stripes was not investigated.

The uncertainty caused by the atmosphere has previously been modeled in an idealized situation by Friedli (2020). This study investigated the velocity difference and refraction of the laser beam due to atmospheric conditions. The differences in the laser beam found by Friedli (2020) range between −0.11 and 0.27 m at a longest simulated distance of 1,841 m and, thus, an order of magnitude smaller than that found in our study. Friedli (2020) also stated that the change strongly depends on the temperature profile in the boundary layer. We assumed a linear temperature profile in the last 10 m of the laser beam path based on the simulated temperature at 2 m and the surface temperature. Different temperature profiles for these last meters of the laser beam path have also been tried, but no significant influences on the laser beam properties were found. Furthermore, our setting is not an idealized situation, and the temperature changes at one point in time are smaller than that in an idealized situation. In our study, the refraction of the laser beam has not been investigated, as the interpolation of the derivative of the refractive index perpendicular to the path d n ( s ) d q (Eq. 11) is not accurate in a simulation with a horizontal grid spacing of 48 m. The maximum change in the refraction angle found by Friedli (2020) is 6.3 mgon, but this strongly depends on the distance and temperature profile in the boundary layer. The refraction angle change of 6.3 mgon equals 0.0057°, which is approximately the same order of magnitude as the uncertainty added by the instrument and hardware limitations. Under the assumption that the boundary layer temperature profile is weak on a snow-covered glacier, the contribution of the angle of refraction is likely less strong than that found by Friedli (2020) and makes the laser beam hit the surface within the calculated footprint. This also validates neglecting the influence of refraction of the laser beam in our study.

Eventually, our study is able to enhance the results of Friedli (2020), as the data of the atmospheric variables are based on a high-resolution simulation and variable over time. Therewith, we show the novelty of our study, where the uncertainties as assessed by different studies are combined and applied to an actual permanent long-range TLS system.

The potential of the permanent long-range TLS system at HEF for detecting glaciologically relevant surface elevation changes has been assessed. Five uncertainty sources are analyzed: the registration method, the influence of the instrument and hardware limitations of the TLS, the effect of atmospheric conditions on the laser beam, the scanning geometry, and the uncertainty caused by rasterization. The uncertainty sources are investigated separately, showing a strong dependence on the distance from the TLS to the surface. The registration method is tested with an automated ICP approach (ICP _HEF) and with commonly used RiSCAN PRO software (ICP _RiSCAN). This results in an average vertical accuracy of the TLS data of ±0.50 m with ICP _HEF and ±0.10 m with ICP _RiSCAN at grids of 100 by 100 m. The precision of the inclination sensors of the scanner cause an uncertainty between 0.09 and 0.64 m. The influence of the atmosphere on the velocity of the laser beam strongly depends on air temperature and to a lesser extent on RH and air pressure, but only has an order of magnitude of millimeters. The contribution of the scanning geometry to the uncertainty budget is approximated between 0.02 and 0.25 m. The instrument and hardware limitations cause the largest uncertainty to the TLS data. The total uncertainty with the point density of the TLS taken into account is between 0.01 m at the area between the TLS and StHE and 0.66 m in the areas close to Weißkugel.

For the annual and seasonal mass balance, the automated approach has proven to be sufficient, as the decimeter-range uncertainty is comparable to the uncertainty of the glaciological mass balance method. Phenomena smaller than a few decimeters, such as snowfall and snow distribution, can be studied after increasing the registration accuracy with post-processing. The uncertainty of the TLS system is an order of magnitude smaller than the processes of interest. Thus, snow drift phenomena with a vertical spatial scale > 0.10 m and a horizontal spatial scale of 1–100 m can still be investigated with the data at hand. This also shows the suitability of the system setup to validate high-resolution atmospheric models that compute snow (re)distribution by wind.