Reanalysis of a 10-year record ( 2004 – 2013 ) of seasonal mass balances at Langenferner / Vedretta Lunga , Ortler Alps , Italy

Records of glacier mass balance represent important data in climate science and their uncertainties affect calculations of sea level rise and other societally relevant environmental projections. In order to reduce and quantify uncertainties in mass balance series obtained by direct glaciological measurements, we present a detailed reanalysis workflow which was applied to the 10-year record (2004 to 2013) of seasonal mass balance of Langenferner, a small glacier in the European Eastern Alps. The approach involves a methodological homogenization of available point values and the creation of pseudo-observations of point mass balance for years and locations without measurements by the application of a process-based model constrained by snow line observations. We examine the uncertainties related to the extrapolation of point data using a variety of methods and consequently present a more rigorous uncertainty assessment than is usually reported in the literature. Results reveal that the reanalyzed balance record considerably differs from the original one mainly for the first half of the observation period. For annual balances these misfits reach the order of > 300 kgm−2 and could primarily be attributed to a lack of measurements in the upper glacier part and to the use of outdated glacier outlines. For winter balances respective differences are smaller (up to 233 kgm−2) and they originate primarily from methodological inhomogeneities in the original series. Remaining random uncertainties in the reanalyzed series are mainly determined by the extrapolation of point data to the glacier scale and are on the order of ±79 kgm−2 for annual and ±52 kg m−2 for winter balances with values for single years/seasons reaching ±136 kgm−2. A comparison of the glaciological results to those obtained by the geodetic method for the period 2005 to 2013 based on airborne laser-scanning data reveals that no significant bias of the reanalyzed record is detectable.

of measurement points needed to derive glacier-wide mass balance was discussed by Fountain and Vecchia (1999) and Pelto (2000), Jansson (1999) investigated the uncertainties related to direct measurement techniques and the appropriate number of measurement points at Storglaciären. Several studies have attempted to quantify how different methods of extrapolating point measurements to the glacier scale affect the resultant glacier mass balance (e.g., Funk et al., 1997;Hock and Jensen, 1999;Sold et al., 2016), while others focused on statistical approaches to evaluate annual or seasonal glacier mass balance and their 10 associated confidence level (e.g., Lliboutry, 1974;Thibert and Vincent, 2009;Eckert et al., 2011).  provided a general concept for reanalyzing glacier mass balance series in the context of comparisons between directly measured and geodetically derived mass balance, which is commonly undertaken to cross-check the in-situ glaciological data (e.g., Funk et al., 1997;Østrem and Haakensen, 1999;Cox and March, 2004;Thibert et al., 2008;Cogley, 2009).
In addition, the use of subsidiary tools, such as distributed surface mass balance models, extensive accumulation measure- 15 ments and auxiliary imagery have become more commonly used components of mass balance (re-)analyses. Mass balance models have been used to extrapolate point measurements to the glacier scale (e.g., Huss et al., 2009Huss et al., , 2013Sold et al., 2016), to homogenize annual or seasonal mass balance with respect to the fixed date method (Huss et al., 2009), or to investigate the impact of changing glacier area and hypsometry to values of mean specific mass balance (Paul, 2010;Huss et al., 2012). Extensive accumulation measurements (e.g., Sold et al., 2016) provide detailed information on the intractable problem of spatial 20 variability of snow accumulation while additional optical imagery provides information on the evolving snow cover (e.g., Huss et al., 2013;Barandun et al., 2015;Kronenberg et al., 2016).
Despite the relatively high number of existing studies related to the reanalysis of glacier mass balance records, few of them (e.g., Thibert et al., 2008;Eckert et al., 2011) include a rigorous uncertainty analysis. Consequently, error assessment and reanalysis of glaciological data is of central interest to both the glaciological and climatological community (Zemp et al., , 25 2015. In this paper we present a reanalysis of the mass balance record of a small alpine glacier including a thorough uncertainty assessment. The example glacier is a particularly useful case as, like for many other glacier mass balance records, the measurement network has changed over time and the data record suffers from inconsistencies that must be tackled in order to create a consistent homogenized time series. Thus, developing a reanalyzed record and providing a detailed analysis of the uncertainty 30 associated with this record showcases a method that can be applied to glacier data-sets suffering from similar inconsistencies and provides insights into the reliability of existing glacier mass balance series for which such error analyses are no longer possible or practical. The reanalysis presented here involves: threatened by rapid glacier retreat and (ii) deemed to be not representative for the region due to the specific setting of the glacier (Kaser et al., 1995). Since the start of the program, the initially provisional measurement network has gradually evolved (Fig. 2) and hence, has changed substantially over time, especially in terms of spatial stake distribution, which poses a particular challenge for understanding the spatio-temporal variability of the glacier mass balance.
In fall 2002, a number of ablation stakes was installed in the lower part of Langenferner and systematic readings began Winter balance measurements have been carried out annually in the first half of May performing numerous snow depth 20 probings and four (or three) snow pits distributed over the glacier surface in each of which the bulk density of the snow pack was measured gravimetrically. While the number and location of the snow depth probings was not fixed throughout the observation period, the number and positions of the pits were more or less kept constant, except for the year 2009 when the large amount of winter accumulation resulted in omitting pit 3. Since the year 2013, the observational set-up includes two automatic weather stations (AWSs) on and near the glacier and in spring 2014 a run-off gauge was installed 3 km down-stream 25 of the glacier terminus. Seasonal and annual mass balances are regularly submitted to the World Glacier Monitoring Service (WGMS).

Meteorological data
The mass balance model used in this study requires meteorological data as input. These data originate from AWSs (1851 to 3325 m a.s.l.) in the vicinity of the glacier (Fig. 1) and were provided by the HOB. Hourly values of air temperature, relative 30 humidity, and global radiation were taken from the station Sulden Madritsch, 2825 m a.s.l., located in an alpine rock cirque some 2.5 km north of Langenferner. The other three required meteorological input variables are wind speed, precipitation and atmospheric air pressure. Those data were not available at Sulden Madritsch for the entire study period. Consequently wind speed data was taken from the station at Schöntaufspitze, 3325 m a.s.l., 5 km north of Langenferner. Air pressure was down-4 The Cryosphere Discuss., doi:10.5194/tc-2016Discuss., doi:10.5194/tc- -286, 2017 Manuscript under review for journal The Cryosphere Published: 10 January 2017 c Author(s) 2017. CC-BY 3.0 License. scaled from ERA-Interim reanalysis data of the nearest surface grid point (47°N|11°E). Daily precipitation sums originate from the station at the dam of Zufritt Reservoir, 1851 m a.s.l. in the Martell Valley, approximately 11 km northeast of the glacier ( Fig. 1).
Since 2013 the Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck (ACINN) operates two AWSs at Langenferner. One station is drilled into the ice of the upper glacier part at an altitude of 3238 m a.s.l. and is designed to 5 measure all meteorological parameters needed to calculate the glacial surface energy balance. The second station was installed on solid rock ground close to the middle part of the glacier serving as a robust back up to bridge possible data gaps of the ice station. Data of those two stations were used to derive spatial gradients and transfer functions of meteorological data, as well as to optimize the radiation scheme of the applied mass balance model. data sets is 1.06 and 2.65 points per m 2 respectively  and the density of the 2011 data set is 2.84 points per m 2 . High resolution (1m) digital terrain models (DTMs) of the study area were calculated from the original ALS point data for all three data sets, where the mean value of all points lying in a raster cell was used as the elevation value for the cell and 15 cells without measurements were interpolated from surrounding grid cells.

Glacier outlines from ortho-images, ALS and GPS
Orthophotos from four acquisitions were used for updating the glacier area of Langenferner. Orthophotos for the years 2003, 2006 and 2008 were provided by the Autonomous Province of Bozen / Südtirol, while data for the year 2012 were available as a base-map within Esri-ArcGIS. The delineation of glacier area was done manually, which, for this small and well-known glacier, 20 ensures the maximum accuracy. Outlines for the years 2005, 2011 and 2013 were derived from ALS data using high resolution hill-shades and DEM-differencing (Abermann et al., 2010). ALS data also provided valuable information for the delineation of debris-covered glacier margins as areas which had undergone no change in surface elevation between two acquisition dates could be classified as ice-free while debris-covered ice was still subject to some lowering (Abermann et al., 2010). The glacier outline of 2010 was assessed from extensive differential GPS measurements in early October 2010. 25 In the uppermost part of the glacier the outlines are confined by ice divides which were derived applying a watershed algorithm to the ALS-DEM 2005. Although the glacier surface topography in this area changed during the observation period, the impacts on the glacier flow direction are negligible and the outlines of the uppermost glacier part were consequently kept constant throughout the study period.

Snow line from terrestrial photographs and satellite images
Information on snow cover extent was used to tune the mass balance model for individual points on the glacier. In order to map the evolution of the transient snowline at Langenferner during the ablation period, we made recourse of an extensive set of terrestrial and aerial images mainly recorded during the field campaigns on the glacier. We used photos from more than 70 field work campaigns, private visits and dated photographs from the internet. A small number of Landsat scenes from different 5 dates provided additional information on the snow cover extent on the glacier. These data were used to manually determine the approximate date when the snow of the previous winter had melted entirely at each given stake location. In most cases the date of snow melt could be determined with an estimated accuracy of ± five days, and in many cases probably even better.
3 Homogenization of data and methods

10
Besides a sparse and unevenly distributed measurement set-up during the first half of the study period affecting annual mass balances, the original record of winter balances was influenced by methodological inhomogeneities concerning the attribution of snow accumulation and ice ablation to the correct reference year or season. These problems have to be addressed in order to create a consistent and comparable record of annual and seasonal mass balance according to the fixed date system (e.g., Cogley et al., 2011).

Stratigraphic correction of snow measurements
Accumulation of snow or firn is measured by means of snow probings and snow pits. Both techniques record the entire snow pack down to a characteristic reference layer which is typically given by the ice surface at the end of the previous ablation season or the firn surface at the date of the last local mass minimum. Hence, there is a need to correct the snow depth measurements in spring for snow fallen during the previous hydrological year (i.e. before October, 1 st ) in order to obtain values corresponding 20 to the fixed date period. As part of the re-analysis process we accounted for this problem which was not considered in the original analyses up to the year 2008.

Ice ablation in the hydrological winter period
While incorrect attribution of summer snow can affect both annual and seasonal mass balance, ice ablation in late autumn (after September 30 th ) only affects the seasonal mass balances. In most years of the study period ice ablation during late autumn at 25 Langenferner was negligible since low elevated areas at the tongue are relatively small and receive only little insolation during that time of the year. Nevertheless, in October / November of the years 2004 and 2006 considerable melt took place in the middle and lower parts of Langenferner. While in the original analyses this issue was not considered, although stake data from late autumn field work were available, the point winter balances were corrected respectively during the reanalysis process.

Fixed date versus floating date
Measurements for the annual mass balance were always carried out very close to end of the hydrological year and, if necessary, stratigraphic corrections for snow cover were applied in order to meet the fixed date criteria. Original winter mass balances on the contrary were calculated following the floating date approach meaning that the water equivalent of the snow pack accumulated since the preceding summer was measured during a field campaign in the first half of May and no further corrections were 5 applied. In order to make the results of the seasonal balances comparable, we calculated the fixed date winter mass balance by scaling the measured and corrected point values of winter balance in order to obtain the water equivalent of snow at the end of the hydrological winter season (April 30 th ). This was done based on precipitation measurements at Zufritt Reservoir and on the ratio of accumulated precipitation during the measurement period (floating date) and during the hydrological winter season (fixed date) as follows: where b f ix and b f ld are the fixed date and floating date point values of winter balance and P f ix and P f ld are the precipitation sums recorded at Zufritt Reservoir during the fixed date and the floating date period respectively.

Point mass balance modeling
A major shortcoming of the original mass balance record at Langenferner is the lack of observation points in the upper glacier 15 part during the first years of the study period. This affects the calculations of annual mass balance in the early observation years and the temporal consistency of the record. Therefore, the central aim of this study is to create a spatially and temporally consistent set of point annual mass balance. Due to the relatively short and inconsistent set of existing measurements, existing statistical approaches (e.g., Lliboutry, 1974;Thibert and Vincent, 2009;Eckert et al., 2011) are inapplicable. Instead we generate artificial measurement points in the poorly-represented upper glacier section by applying a physically based energy and 20 mass balance model (Mölg et al., 2012). The model was run in its point configuration as the purpose of this study is not to use a model for the spatial extrapolation of point measurements on the glacier wide scale as done in a number of other studies Barandun et al., 2015;Kronenberg et al., 2016;Sold et al., 2016), but is to reproduce a best possible estimate of annual balance values for point locations where ablation stakes were placed in the subsequent years. In this configuration, the model performance can be validated directly using data from available stake measurements. A spatially distributed model set 25 up would introduce larger errors regarding the mass balance at selected points, while the point model allows for a spatially flexible model tuning and strongly reduces errors due to shortcomings in the spatial extrapolation of meteorological variables (e.g., Carturan et al., 2015;Sauter and Galos, 2016;Shaw et al., 2016) and the choice of the optimal parameter setting (e.g., MacDougall and Flowers, 2011;Gurgiser et al., 2013). The application of a relatively complex physical model is justified by the dominant influence of micro-meteorological variability, local topographic factors and the resultant large spatial variability 30 of the surface mass balance, which can only be resolved in a sufficient way by a process based model. Furthermore, we aim at 7 The Cryosphere Discuss., doi:10.5194/tc-2016-286, 2017 Manuscript under review for journal The Cryosphere Published: 10 January 2017 c Author(s) 2017. CC-BY 3.0 License.
providing a set of homogenized point mass balances instead of glacier wide balances only, since point balances have proven to be valuable information sources for investigations on glacier-climate interactions (e.g., Huss and Bauder, 2009).

Transfer of meteorological variables
Meteorological variables (Section 2.2) were extrapolated to the glacier using spatial transfer functions. Those functions were obtained using data from the on-glacier weather station in the upper part of the glacier for the period July 2013 to August 5 2015, when measurements at all AWS were available. Air temperature from Sulden Madritsch was extrapolated to the glacier applying an altitudinal lapse rate of 6.5x10 −3 K/m and an offset of -0.56 K reflecting the different microclimates over rock (Sulden Madritsch) and the on-glacier station. Both values were derived from a linear regression between measurements at Madritsch and the glacier station during the summers 2013 and 2014. Relative humidity was corrected for saturation over ice for below-freezing temperatures but the data was not further modified since no clear spatial pattern was detectable in the 10 analysed data sets. Global radiation was used to calculate a cloud factor (e.g., Mölg et al., 2009b;Haberkorn et al., 2015) which was assumed to be spatially constant over the study area. This factor was used to drive the radiation scheme of the mass balance model which was optimized for the glacier using short-and long wave radiation data from the glacier. Wind speed from Schöntaufspitze was linearly scaled to match the observed wind speeds at the glacier station using a scaling factor of 0.67. ERA-Interim atmospheric air pressure was reduced to the altitude of the stake locations by the barometric equation, and 15 since the mass balance model is relatively insensitive to small changes in air pressure, the temporal resolution of one hour was achieved by linear interpolation of the six hourly reanalysis data. Daily precipitation sums measured at Zufritt Reservoir (1851 m a.s.l., 11 km from the glacier) were used to assess hourly precipitation at the glacier, whereby the daily sums were temporally redistributed according to the course of relative humidity during the measurement day. Precipitation was only assigned to time steps when humidity exceeded the threshold of 93 % and the amount for a single time step was then scaled according to the 20 magnitude of exceedance. If this threshold was not reached throughout the day but precipitation was measured, the threshold was lowered by steps of 5 %. This procedure was found to have a remarkable positive impact on the model performance. The sensitivity of modeled point mass balance to this correction can easily reach about ±100 kg m −2 on the annual scale compared to a model driven with daily precipitation sums equally distributed over 24 hours.

Monte Carlo optimization of model parameters 25
The mass balance model approach was set up as follows ( Fig. 3): first the model was pre-calibrated applying realistic values for the model parameters which were either taken from the literature or from direct meteorological observations in the study area. The first guess model precipitation P 0 model was generated applying a precipitation scaling factor Γ 0 to the measured and temporally re-distributed record of Zufritt P obs.red. in order to fit the model to the observed values of winter mass balance (Equation 2). This pre-calibration was done for the location of stake 22 (Fig. 4), a stake situated in the upper glacier part, near the center of the area where the point modeling was carried out. This stake was chosen as the relatively homogeneous terrain surrounding it makes it representative for a wider region of the glacier and it offers by far the highest number of stake readings in the upper region of Langenferner. It is hence the best choice for the optimization of model parameters, which was done applying a Monte-Carlo approach (e.g., Machguth et al., 2008;Mölg et al., 2012) performing 1000 model runs with different parameter 5 combinations in order to find the best model setting for the local conditions. The optimal parameter combination was then applied to all stake locations in the upper glacier. An individual Monte Carlo optimization for each stake was not possible due to the low number of available readings at some stakes.

Model tuning for individual stakes and years
Large uncertainties in process-based studies of glacier mass balance are commonly related to accumulation and its spatial 10 distribution: altitudinal precipitation gradient, redistribution of snow due to wind and its large influence on spatial accumulation patterns, the temporal evolution of surface albedo and hence net radiation, etc. (e.g., Gurgiser et al., 2013;Machguth et al., 2008). In order to minimize uncertainties related to the unsatisfactory representation of local accumulation in the mass balance model, we made recourse of a calibration procedure which integrates available snow information. Therefor, the mass balance model with the optimized parameter setting was tuned by replacing Γ 0 in equation 2 by the individual (for stake i and year a) 15 scaling factor Γ i,a which accounts for all site-specific properties related to accumulation. This tuning procedure was performed for every stake and year individually and in a way that the observed date of the emergence of the ice surface at the respective location was correctly reproduced by the model. An automated iterative approach ensured that the modeled date did not differ by more than one day from the observed date. Note that this approach is not applicable in years with a persisting snow cover at the stake location. But during the first observation years ( calculate the total mass change ∆M by spatial integration of the specific mass change b over the area S based on the following equation: The mean specific mass balance B is then calculated as follows: For comparisons with the geodetic method there is the need for direct glaciological balances over the geodetic survey period. These are calculated summing up the annual glaciological mass changes (∆M a ) from the beginning (t 0 ) to the end (t 1 ) of the period of record (P oR) and dividing the result by the average glacier area S through that period (equation 6).

Contour Line based extrapolations
The contour line method (e.g., Østrem and Brugman, 1991) is an often used approach for the determination of glacier mass balance. It is based on manually derived lines of equal mass balance based on point measurements and has the advantage that the spatial pattern of surface mass change is relatively well reflected in the analysis if the method is applied thoroughly. The manual generation of contour lines often incorporates the integration of further observational information such as the position of the 20 snowline, date of ice emergence at individual locations, meteorological conditions on the glacier and other expert knowledge such as typical spatial patterns etc. This kind of information is difficult to capture in a purely objective or mathematical sense, nevertheless it often enhances the quality of the results and the spatial resolution of mass balance information.
Mass balance contour lines are then used to derive areas of equal mass balance where the mean value of the contour lines is assigned to the area between the lines. However, for this study we applied the contour line method in two different ways: 25 Once in its purely traditional form creating areas of equal mass balance between the lines of 250 kg m −2 equidistance, and once applying the Esri-ArcGIS interpolation tool topo to raster, which is based on the ANUDEM algorithm (e.g., Hutchinson, 2008;Hutchinson et al., 2011), to the hand drawn and digitized contour lines and the set of reanalyzed point values. The latter method results in mass balance rasters with a 1x1 m resolution which were subsequently spatially integrated to obtain the mean specific mass balance (Equations 3 and 4).

Automatic extrapolations
In contrast to the contour line based analyses, automatic extrapolation methods avoid subjective influences, are fast and relatively simple to apply but are subject to restrictions in realistically reproducing the spatial distribution of surface mass balance.
We apply three fully automatic extrapolation procedures: years. The total volume change ∆V was calculated by integrating the elevation change ∆h at the individual pixel k of length r of the co-registered DEMs as follows : Subsequently the derived volume change is converted to a geodetic mass balance over the period of record following equation 8: where ρ denotes a mean glacier density of 850±60 kg m −3 as proposed by Huss (2013) and S is the mean glacier area at the two acquisition dates calculated as the mean of the extents at the beginning and the end (S t0 and S t1 ) of the P oR.

Corrections for snow cover and survey date
The results of the geodetic surveys were corrected for differences in snow cover between the acquisition dates as follows: where ∆M geod.corr denotes the geodetically derived mass change corrected for snow cover differences between the two acquisition dates t 0 and t 1 , ∆M geod is the uncorrected mass change, h s denotes the mean snow depth (at dates t 0 and t 1 respectively), ρ the bulk glacier density and ρ s the mean snow density at the acquisition dates t 0 and t 1 . Despite the short time difference between direct and geodetic measurements, we applied a correction of the measured snow 5 depths due to relatively warm weather conditions in this period. Therefor, the (optimized but untuned) mass balance model was initialized at all ablation stakes and a few additional locations using the measured snow depths and densities of September 30 th as initial condition. In 2013, extensive direct measurements were carried out simultaneously to the ALS campaign on September 23 rd in order to quantify the high amount of snow and firn in this year.
Survey date corrections were based on modeled mass change during the periods between ALS survey and direct measure-

Annual glacier topographies and outlines
Changes in glacier area and topography may have significant impacts on the mass balance of mountain glaciers through various feed-backs (e.g., Paul, 2010;Huss et al., 2012) and since respective data is used as input for glacier models, they constitute glaciological key information. Hence, there is a need to frequently update topographic reference data used in mass balance calculations (e.g., Zemp et al., , 2015. Langenferner was subject to remarkable hypsometry changes during the study 20 period ( Fig. 4 and 6). While glacier outlines for the current study could be directly derived from ortho-photos or ALS data for all years except for 2004, 2007 and 2009, data on glacier topography is only available through the three ALS campaigns.
In order to minimize the effect of outdated area and hypsometry we calculated annual glacier outlines and topographies by combining the available set of related data with the fields of reanalyzed annual surface mass balance. For that we consider the change in surface elevation ∆h at one location (pixel) k of the glacier over the time period t as the result of the following terms: where ∆h surf k,t denotes the surface elevation change related to surface mass balance, ∆h dyn k,t represents the surface change due to glacier dynamics and ∆h basal k,t is the surface change related basal (and internal) processes. As the latter term is assumed to be relatively small on the glacier wide scale (e.g., Cuffey and Paterson, 2010), it is neglected. The rasters of spatially ∆h dyn k,t for the respective period can be calculated as follows: where h k,t0 and h k,t1 are the surface elevations at the pixel k given by the DEMs taken at date t 0 and t 1 respectively and t1 t0 ∆h surf k,t refers to the temporally integrated elevation change due to surface mass balance. Due to the absence of data on the temporal evolution of glacier flow velocity, we assume the rate of ∆h dyn k to be temporally constant during the observation 5 period. This simplifies the calculation of the annual ∆h dyn k,a to: where d P oR is the duration of the observation period in years. The result is a raster of ∆h dyn k,a which can be applied to all the observation years. The surface elevation of a certain year h k,a can finally be calculated by adding the surface elevation change due to surface mass balance in the respective year a and the annual change related to glacier dynamics to the surface elevation 10 of the previous year h k,a−1 (Equation 13).
The DEM taken at the end of the observation period serves as a boundary condition for surface elevation at areas which become ice-free during the observation period in a way that all raster cells in those areas showing a surface height smaller than the surface of the ice free topography are set back to the value of the latter. Glacier outlines were derived by identifying ice-free 15 pixels as having undergone no change in surface elevation.
Note that the term ∆h dyn k,a represents all the differences between the direct surface measurements and geodetically detected surface changes. These are not only differences which can be associated which glacier dynamics, but also shortcomings in the spatial extrapolation of surface mass balance measurements and changes due to internal or basal processes. This problem does not affect the temporally-integrated topography change, but may lead to additional errors regarding annual surface 20 topographies. Nevertheless, this simple method provides a possibility to annually update the reference area and topography used in the mass balance calculations and hence represents a useful tool for areas with large changes in surface elevation.

Uncertainty Assessment
In order to enhance the value of the reanalyzed mass balance record, a detailed error assessment was performed following the recommendations of . We categorized potential errors in the measurements and analyses into random (σ) 25 and systematic ( ) errors. In the subsequent sections we discuss the origin of such errors related to the methods applied and explain how they were assessed. Thereby we primarily focus on random uncertainties, since systematic errors are difficult to quantify in the absence of an absolute reference for validation. In order to detect an eventually significant systematic bias in the reanalyzed record of annual balance, we finally perform a comparison of directly measured mass changes to those obtained

Uncertainties of glaciological measurements
Uncertainties in glaciological mass balances may originate from various sources and can be categorized into errors in point measurements, errors related to spatial extrapolations of point measurements and errors due to inaccurate or outdated glacier extents . The random error of the mean specific mass balance for an individual year (σ glac.total.a ) can consequently be formulated as follows: where σ glac.point.a is the error due to uncertainties on the point scale, σ glac.spatial.a represents errors related to spatial extrapolations and σ glac.ref.a accounts for uncertainties due to inaccurate glacier outlines.

Uncertainties related to point measurements
Random errors on the point scale mainly originate from inaccurate readings. This involves ablation and accumulation measure-  For accumulation measurements the error potential is generally higher. Snow pits with measurements of snow depth and density offer the highest accuracy (≈ 50kg m −2 ). But the number of snow pits is often kept low, as they are labor intensive and time-consuming. Snow probings are somewhat less accurate since they are affected by instrument tilt, by uncertainties in the spatial extrapolation of snow density and by possible difficulties in the determination of last summer's reference surface. The latter effect can lead to large errors on the point scale but is assumed to play a minor role in this study since most "outliers" 20 could be identified due to the high number of probings in combination with snow pit information.
However, the impact of uncertainties in point measurements on glacier wide calculations depends on the amount of point measurements and their spatial distribution. To quantify this problem, we applied a bootstrap approach (e.g., Efron, 1979) in which random errors according to a defined normal distribution were applied to all available individual point measurements before calculating the glacier wide balance 5.000 times for each case using the inverse distance weighting method for extrapo- 25 lation. The respective annual uncertainties are then given by the standard deviation of the 5.000 runs and range from 11 to 26 kg m −2 for annual balances and from 7 to 16 kg m −2 for winter balances.

Uncertainties in the extrapolation of point measurements
Similar to the above problem, uncertainties related to the applied extrapolation method are also dependent on the number and distribution of point measurements, as well as to spatial balance patterns of the individual year or season. We assessed those

Uncertainties in geodetic mass balances
Uncertainties in the geodetic mass balance are mainly related to two problems: (i) errors in the used DEMs and (ii) uncertainties related to the conversion of the observed surface elevation changes to changes in mass. The over-all random error of the corrected geodetic mass balances can be expressed as: 15 σ geod.corr = σ 2 geod.total + σ 2 dc + σ 2 sc + σ 2 sd , where σ geod.total refers to the remaining uncertainties related to geodetic measurements after all applied corrections such as co-registration etc., σ dc is the error related to density conversion, σ sc refers to the error due to snow cover and σ sd is the remaining error due to different survey dates compared to the glaciological method. Note that equation 15 differs from equation 18 in  in two points: Firstly we split the uncertainties related to bulk glacier density and those 20 introduced by differences in snow cover between the two survey dates. This is done because the available set of data allows for a sound quantification of snow cover. Secondly, we do not include the impacts of basal and internal processes since they neither represent an error in geodetic mass balance calculations nor could they be quantified in a sufficient matter in the frame of the current study. Nevertheless we discuss those effects in section 5.6.

25
In order to minimize systematic errors in the geodetic analyses, a co-registration of the three ALS data sets was performed including the roofs of three mountain huts in the vicinity of Langenferner. Thereby no significant dependence of the errors to slope and aspect of the surface could be detected. The remaining uncertainty potential related to vertical errors after coregistration and due to spatial auto-correlation for the individual survey periods σ geod.total was estimated as 0.15 m. This value is based on tests over reference areas not involved in the co-registration and can be regarded as a quite solid upper threshold of

Uncertainties related to glacier density
In our study uncertainties related to unknown mean glacier density are reflected by the applied density range of 850±60 kg m −3 (Huss, 2013). Based on the knowledge about the study area, such as the typical size of the accumulation area and the absence of large crevasse zones, we estimate the real near surface glacier density in the absence of seasonal snow to be in the range of 850 to 880 kg m −3 .

Uncertainties due to snow cover and survey date differences
Uncertainties due to differences in snow cover at the two acquisition dates are difficult to estimate but we assume that they are quite small after we applied respective corrections (section 3.4.1). Similar is true for uncertainties related to different acquisition dates between geodetic and glaciological surveys. Especially for the two longer periods (2005 to 2013 and 2005 to 2011), due to the drastic mass loss both errors are at least one order of magnitude smaller than the uncertainties related to the 10 used bulk glacier density and are hence of minor importance. However, the respective errors for both problems were estimated as 100 kg m −2 for all (sub-) periods.

Method comparison
In order to check the reanalyzed record of annual mass balance for a significant systematic bias, we compare the results for the period 2005 to 2013 to the mass change inferred using the geodetic method. Doing so, it has to be considered that the two 15 methods are subject to generic differences since the glaciological method only captures (near) surface mass changes, while the geodetic approach also detects volume (and mass) changes due to internal and basal processes. Consequently, we avoid using the term "validation" for the methodological cross check. Especially since we omit the explicit consideration of the above mentioned processes due to the fact that respective estimates without related measurements are speculative. However, method comparisons were performed for the period 2005 to 2013, as well as for the sub-periods 2005 to 2011 and 2011 to 2013. 20 After applying the corrections described in section 3.4.1, the reduced discrepancy δ  between the two methods can be calculated as Agreement between the two methods can be assumed within the 95 % (90 %) confidence interval if |δ| < 1.96 (|δ| < 1.64).
See  for a detailed description of this test. deviation (RMSD) of 128 kg m −2 and an R 2 of 0.96 between modeled and measured values (Fig. 7). The magnitude of this error is similar to the uncertainty of glaciological point measurements reported in the literature (e.g., Thibert et al., 2008;Huss et al., 2009;Carturan et al., 2012), and since no significant systematic errors such as biases for single stakes or years are detectable, the 47 newly-created point values of annual mass balance constitute a valuable basis for the reanalysis of the glacier wide annual balance. Note that in years with persisting snow cover the model could not be applied in its current form. Hence 5 for 2010 and 2013 the mass balance of only a few stakes could be modeled. This reduced the number of validation points but did not affect the reanalysis procedure, since for these years measurements at all stake locations are available.

Mean specific annual mass balance
Mean specific annual mass balances and their altitudinal distribution were calculated based on the homogenized set of measured and modeled point values, applying five different extrapolation methods and using the set of newly created annual glacier 10 outlines and topographies. The results for the two contour-line based extrapolation methods are almost identical and differ by only 0 to 5 kg m −2 (RM SD < 2 kg m −2 ). Consequently, we chose the results obtained by the raster-based contour line method as our reference since this method has the advantage of being less labor intensive than the traditional contour method and it results in high resolution (1x1 m) grids of surface mass balance which were also used to calculate annual glacier topographies and outlines (Section 3.5).

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The results show a persistent mass loss in all observation years. For the reference method, single year numbers vary between -1556±47 kg m −2 in 2012 and -247±31 kg m −2 in 2013, with a study period average of -1138±80 kg m −2 ( Fig. 8 and Table 1). While all applied extrapolation methods display a common signal in terms of inter-annual mass balance variability (R 2 > 0.98), the three automatic extrapolations yield mass-balances which are considerably more negative than those obtained by the contour line approaches ( Table 2). The respective biases are -249 kg m −2 for the topo to raster-based automatic method,  Table 1.

Mean specific seasonal balance
In contrast to annual mass balances, no modeling was involved in the calculations of the winter mass balances. However, the 10 same extrapolation methods as used for the calculation of annual balances were applied to derive glacier wide winter balances.
Again the two contour line based approaches displayed very similar results. For winter mass balances the differences between the two methods are slightly larger than for the annual balances which can be explained by smaller spatial balance gradients and consequently a lower spatial density of contour lines. Nevertheless, the differences for single years do not exceed 12 kg m −2 .
The mean fixed date winter balance for the study period is 929±52 kg m −2 with a maximum of 1267±37 kg m −2 in the wet or the use of different glacier extents which both have little impact (< 50 kg m −2 ) on the winter balance at Langenferner due to generally small spatial (altitudinal) gradients in winter mass balance at this specific glacier.
The correlation between the original and reanalyzed records of winter mass balance is larger (R 2 = 0.90) than for annual balances which can be explained by the fact that the same set of point measurements has been used for both series and that differences in glacier wide values can mainly be attributed to the corrections applied to the original data set (section 3.1).

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The homogenization

Geodetic mass balance 2005-2013
The mean surface elevation change at Langenferner during the eight-year period 2005 to 2013 amounts to -10.35±0.21 m.
Surface elevation changes in the lower most glacier part reach the order of -40 m while in the highest regions changes in the 10 order of one to three meters are detectable (Fig. 4). Assuming a bulk glacier density of 850±60 kg m −3 , this corresponds to an uncorrected geodetic mass balance of -9397±687kg m −2 . The correction for differences in snow cover between the two acquisition dates changes the result to -9596±694 kg m −2 . Note that the values slightly differ from those presented by Galos et al. (2015) since the study in hand makes use of reanalyzed data sets. The results of the geodetic analyses (including those for the sub-periods 2005-11 and 2011-13) are summarized in Table 3. 15

Uncertainties in glaciological and geodetic balances
The largest source of uncertainties in the reanalized glaciological record is the spatial extrapolation of of point measurements.
The largest spread between individual extrapolation methods is shown in the years 2008 and 2009 in which the negative off-sets of the automatic extrapolation methods are especially large. We attribute this to very strong spatial mass balance gradients in these two years given by the fact that mass balances at stake locations were quite negative, but at the same time snow of the was not the case in that year. For both, annual and winter mass balances, the second largest uncertainty source is given by the uncertainties of point measurements. For annual balances they are in the order of 25 kg m −2 while for winter balances they range from 7 to 16 kg m −2 due to the generally higher number of measurements combined with less distinct spatial mass balance gradients.
Uncertainties in the corrected geodetic balances are mostly determined by the applied density range of 850±60 kg m −3 .

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Other error sources only account for a few percent of the total random error, except for the short period 2011 to 2013, when the remaining uncertainty of the DEMs exceeds the uncertainty related to the density assumption. 19 The Cryosphere Discuss., doi:10.5194/tc-2016-286, 2017 Manuscript under review for journal The Cryosphere Published: 10 January 2017 c Author(s) 2017. CC-BY 3.0 License.

Glaciological versus Geodetic Method
Applying equation 16 to the results of our glaciological reference method yields δ-values between 0.54 and 1 (Table 3) indicating that there is agreement between the glaciological and the geodetic results well within the 90 % confidence interval Sold et al., 2016). Hence, a further calibration of the reanalyzed glaciological record is not necessary.
The results of the profile method also fulfill the above criteria for all three (sub-) periods and could hence also be regarded as 5 acceptable. The point to raster and inverse distance weighting methods fulfill the 90 % confidence criteria only for the period 2011 to 2013 but results are within the 95 % confidence bounds for the other periods (Table 4). However, the three automatic extrapolation methods yield results which are persistently more negative than the geodetic method (Fig. 10), while from a physical perspective, the geodetic method, especially during periods of strong glacier mass loss, can generally be expected to display results more negative than the glaciological method due to the effect of internal and basal melt processes. Several studies have shown, that basal and internal melt can be important contributors to total glacier ablation, depending on the specific glacier and the climatic setting (e.g., Alexander et al., 2011;Oerlemans, 2013;Andreassen et al., 2016). Generally, the most important sources of energy for subsurface melt on temperate glaciers are related to the conversion of potential energy by water run-off inside and at the base of the glacier. The water may originate from precipitation and other accumulation processes 15 or may enter the glacier from outside. In the latter case the water may be warmer than 0°C and hence can offer an additional source of thermal energy. Other contributors to basal and internal melt are the geothermal heat flux and the conversion of potential energy related to glacier dynamics (deformation and basal friction).
In order to provide a rough estimate of subsurface melt processes at Langenferner, we calculated the melt-contribution of water run-off. We applied a similar approach than used by Andreassen et al. (2016), but instead of precipitation, we considered 20 water released by melt (Thibert et al., 2008), which was approximated by the summer mass balance. Liquid precipitation instantly running off the glacier and water from outside the glacier were neglected since both play a minor role at Langenferner. Uncertainties due to missing updates of rapidly changing glacier geometries represent another important source of uncertainty for annual balances. In our case this problem causes errors in the order of 20 kg m −2 after only one year growing almost linearly within the study period. To tackle this problem we presented a method which enables the calculation of annual glacier outlines by combining geodetic information on glacier topography and measured surface mass balance.
For winter balances the correlation between original and reanalyzed record is higher (R 2 = 0.90) than for annual balances 25 which can be explained by the generally sufficient amount and spatial distribution of winter mass balance measurements.
Winter balances at Langenferner are also less sensitive to changes in the spatial distribution of measurements and to missing updates of glacier geometry since in most years there is no significant altitudinal gradient in winter mass balance. Differences between the original and reanalyzed series of winter mass balance mainly originate from the fixed date correction which was applied in the course of the reanalysis. Corrections for snow from the previous hydrological year are also of considerable the two methods and a calibration of the glaciological results is hence not required.
While the bias correction of glaciological series based on geodetic measurements has become a common procedure in the reanalysis of glacier mass balance records, the current study also addresses the inter-annual mass balance variability, as well as related uncertainties, a problem which has yet rarely been considered. In order to increase the value of mass balance series and to better understand underlying processes, future studies should address this matter by the integration of multi-source data 10 combined with sound uncertainty analyses.
Author contributions. SG designed the study, conducted the gross part of the analyses and wrote the manuscript, CK processed ALS data sets and performed a series of GIS calculations, FM contributed to the study design and performed the boot-strap calculations, LN contributed to the paper design and writing, FC created most of the figures, LR provided the 2011 ALS data and information on ALS uncertainties, WG performed the Monte-Carlo model optimization, TM provided the mass balance model and related information. GK helped to refine the 15 manuscript and is the leader of the scientific project under which the study was carried out. All authors helped to improve the manuscript.
Acknowledgements. We thank all persons involved in the field work at Langenferner, with special thanks to Rainer Prinz. We are grateful to Roberto Dinale and Michaela Munari from the HOB for the constructive collaboration in coordinating the monitoring activities at Langenferner. Christoph Oberschmied provided his rich archive of photographs which was a great help in constraining the snow line evolution at the glacier. The work of this study was financed by: Autonome Provinz Bozen -Südtirol, Abteilung Bildungsförderung, Universität und 20 Forschung.

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The Cryosphere Discuss.    original record contour traditional point to raster reference profile method inverse distance Figure 10. Comparison between geodetic and glaciological mass balances for three periods (upper three sub plots) and cumulative series of annual mass balance calculated using the five methods described in the paper.

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The Cryosphere Discuss., doi:10.5194/tc-2016-286, 2017 Manuscript under review for journal The Cryosphere Published: 10 January 2017 c Author(s) 2017. CC-BY 3.0 License.  38 The Cryosphere Discuss., doi:10.5194/tc-2016-286, 2017 Manuscript under review for journal The Cryosphere Published: 10 January 2017 c Author(s) 2017. CC-BY 3.0 License. Table 3. Results of the geodetic analyses and the cross check between glaciological and geodetic method. Where P oR stands for the observation period, ∆Z is the mean surface elevation change, ∆V the volume change, B geod is the uncorrected geodetic balance assuming a bulk density of 850 kg m −3 , corrsc and corr sd refer to the corrections for snow cover and survey dates, B geod.corr refers to the corrected geodetic balance, σ geod.total.P oR is the total random error of B geod.corr , B glac.P oR is the cumulated glaciological mass balance, σ glac.total.P oR is the corresponding random uncertainty, ∆ rel is the relative difference between glaciological and geodetic results and δ is the reduced discrepancy .