TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-833-2018Geodetic reanalysis of annual glaciological mass balances (2001–2011) of Hintereisferner, AustriaKlugChristophchristoph.klug@uibk.ac.athttps://orcid.org/0000-0001-9097-1203BollmannErikGalosStephan PeterNicholsonLindseyhttps://orcid.org/0000-0003-0430-7950PrinzRainerhttps://orcid.org/0000-0003-4032-773XRiegLorenzoSailerRudolfStötterJohannKaserGeorgInstitute of Geography, University of Innsbruck, AustriaInstitute of Atmospheric and Cryospheric Sciences, University of Innsbruck, AustriaDepartment of Geography and Regional Science, University of Graz, AustriaChristoph Klug (christoph.klug@uibk.ac.at)6March20181238338494July201714August201718January20183February2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/833/2018/tc-12-833-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/833/2018/tc-12-833-2018.pdf
This study presents a reanalysis of the glaciologically obtained annual
glacier mass balances at Hintereisferner, Ötztal Alps, Austria, for the
period 2001–2011. The reanalysis is accomplished through a comparison with
geodetically derived mass changes, using annual high-resolution airborne
laser scanning (ALS). The grid-based adjustments for the method-inherent
differences are discussed along with associated uncertainties and
discrepancies of the two methods of mass balance measurements. A statistical
comparison of the two datasets shows no significant difference for seven
annual, as well as the cumulative, mass changes over the 10-year record.
Yet, the statistical view hides significant differences in the mass balance
years 2002/03 (glaciological minus geodetic records =+0.92 m w.e.), 2005/06
(+0.60 m w.e.), and 2006/07 (-0.45 m w.e.). We conclude that exceptional
meteorological conditions can render the usual glaciological observational
network inadequate. Furthermore, we consider that ALS data reliably reproduce
the annual mass balance and can be seen as validation or calibration tools
for the glaciological method.
Introduction
The mass balance of a glacier defines its
hydrological reservoir function e.g. and is a reliable
indicator of climate change e.g..
The earliest glacier mass balance measurements started around 1950, but only
about 30 reference glaciers have uninterrupted annual time series going back
to 1976 e.g.. This small number of directly
measured annual glacier mass balance series provides the basis for
reconstructing past contributions to sea level rise
e.g.;
extrapolating glacier contribution to regional water supply
e.g.; and supporting glacier
change detection, attribution e.g., and projection studies e.g..
Since uncertainties and errors in long-term mass balance records affect the results of such studies, these must be
quantified and, wherever possible, corrected e.g..
Geodetically obtained results have been used as controls for annual
glaciological mass balances at decadal scales and are commonly applied to
identify random, and to correct systematic, uncertainties in glaciological
mass balance time series . Geodetic
measurements have also been merged with glaciological mass balance series to
increase coverage and representativeness of large regions and global glacier
mass balance information e.g.. Indeed,
the interconnection of different methods is increasingly suggested in order
to advance glacier mass change estimates for large regions or even on the
global scale .
At Hintereisferner in the Austrian Ötztal Alps, glaciologically and
photogrammetrically based geodetic mass balances are available from the early
1950s e.g.. Early analyses showed good agreement between
the two data series on a decadal timescale for the periods 1952/53 to
1963/64 and 1952/53 to 1990/91 . Yet, a more
detailed examination by revealed discrepancies at
Hintereisferner for the periods 1963/64 to 1968/69 and 1978/79 to 1990/91.
Between 2001 and 2011, when high-resolution air borne laser scanning (ALS)
became available, geodetic mass balances for Hintereisferner were obtained
annually. Gross results from the first data pairs indicated considerable
differences to the glaciological mass balances . This
motivates a deeper investigation of the apparent discrepancies between the
two methods at an annual scale.
Hence, the goal of the present study is to
reanalyse the glaciological mass balance record of Hintereisferner for the
period 2001 to 2011 and to thereby detect possible shortcomings for
individual years or the whole period. We achieve this reanalysis through a
detailed uncertainty assessment using annual geodetic records from high-resolution
ALS data. The reanalysis scheme and the assessment of random
(σ) and systematic (ϵ) uncertainties presented in this paper
follows the guidelines of . Hence we refer to this paper for
detailed explanations regarding the principal work flow.
Hintereisferner
Hintereisferner (46.79∘ N, 10.74∘ E) is a
valley glacier in the Austrian part of the Ötztal Alps (Fig. ).
The glacier consists of three main tributary basins. Langtaufererjochferner
(1.11 km2) and Stationsferner (0.28 km2) disconnected from
Hintereisferner in 1969 and 2000, respectively, but are still treated as part
of the glacier in order to maintain consistency in mass balance assessments
over the whole time series of observations. Hence, ”Hintereisferner” in this
paper refers to all three glacier bodies.
The area of Hintereisferner in 2011 was 6.78 km2, about 15 % smaller
than in 2001, when the first ALS campaign was conducted. The glacier terminus
retreated by 390 m during the same period. The glacier elevation ranges from
3720 to 2456 m a.s.l., and the median altitude is 3039 m a.s.l. The
accumulation area covers aspects from northeast to southeast, while the long
and narrow tongue faces northeast. Meltwaters feed the Hintereisbach, which
joins the run-off from Kesselwandferner, Hochjochferner and a few smaller
glaciers and subsequently drains into Rofenache and finally into the
Ötztaler Ache, one of the major tributaries of the Inn River.
Hintereisferner is located in the “inner dry Alpine zone” ,
which is among the driest regions of the entire European Alps. Precipitation
in Vent (∼ 1900 m a.s.l.), about 8 km west of the glacier
terminus, reaches 677 mma-1, with air temperatures of 1.5 ∘C on average (1906–2011). Precipitation amounts double at the
totalizing rain gauge near the Hintereis Research Station (3026 m a.s.l.;
Fig. ), reflecting not only the altitudinal difference of approximately
1100 m but also the enhanced precipitation activity further up the valley. Over
the study period 2001 to 2011, the values for annual temperature and
precipitation in Vent are 2.3 ∘C and 676 mm, respectively. The mean
annual 0 ∘C isotherm is located at 2450 m a.s.l.
Like many glaciers in the Eastern Alps, Hintereisferner has experienced strong
shrinkage compared to its Little Ice Age maximum extent, which was reached
sometime between 1847 and 1855 (Richter, 1888). Since that time, the glacier
area in the Ötztal Alps has shrunk by more than 50 % . After
a period of rather stationary glacier lengths in the late 1970s and early
1980s e.g., glacier mass loss and area shrinkage
dominate, with particularly high rates during and after the extraordinarily
hot summer of 2003 e.g..
A map of Hintereisferner with the locations of the rain gauges and
the glaciological mass balance measurement points in 2004 as an example. Also
depicted are the glacier outlines for 2001 and 2011. Note that in 2003 no
accumulation measurements could have been carried out due to the strongly
reduced accumulation zone. Hence, only ablation stakes were available.
Coordinates are in WGS84/UTM32N.
Mass balance methods and data
There are two primary methods for determining the mass
balance of a glacier: the glaciological (or direct) and the geodetic method.
The glaciological method e.g. is the most widely used for
assessing annual and – more rarely – seasonal mass changes of individual
glaciers. It spatially extrapolates in situ point measurements of ablation
and accumulation to the glacier-wide surface mass balance, encompassing all
mass changes at (near) the glacier surface during the hydrological year
cf..
In contrast to the surface mass balance obtained with the glaciological
method, the geodetic method differences two consecutive digital elevation
models (DEMs) of a glacier and provides its volume change. This method
integrates all processes that lead to surface height changes at any
single point of a glacier, i.e. the surface, internal, and basal mass
changes, as well as those from ice flux divergence and densification
. Consequently, the mass balance values at a certain point
of the glacier may differ significantly between the glaciological and the
geodetic mass balance method. However, according to the principles of mass
conservation, the ice flux divergence becomes zero if integrated over the
entire glacier. Moreover, by assuming internal and basal mass changes on mid-latitude mountain glaciers to be of minor importance
e.g., and by applying either measured or estimated
snow or ice density to convert volume into mass changes, the two methods
should obtain fairly similar numbers for the glacier-wide mass balance. In
this way, geodetically obtained results can be used to cross-check
glaciological mass balances on various timescales and references
therein.
In the subsequent sections we introduce the glaciological
and the geodetic measurement methods as applied at Hintereisferner. We first
determine a common base for the two datasets, by the homogenization of
glacier outlines and DEMs, followed by quantifying method-inherent
uncertainties.
The glaciological method
Annual glaciological measurements at Hintereisferner
commenced in 1952 , resulting in one of the longest
continuous glacier mass balance time series worldwide. The distribution of 40
to 50 (maximum 100) ablation stakes over the main tongue of Hintereisferner
is a compromise between representative coverage and logistic feasibility
. During the study period no ablation stakes were
maintained in the upper part of the glacier, where the accumulation was
usually determined by means of snow pits and probings at the end of the mass
balance year. The location of individual snow pits has been kept more or less
constant over the whole study period. Their number changed according to the
varying extent of the accumulation area from none in, for example, 2002/03 up to 14
pits in 2003/04 (see Fig. ). The series follows the fixed-date
system as defined by the hydrological year, spanning from 1 October to
30 September of the following year, with additional measurements in
spring and during approximately fortnightly visits between June and October.
The annual mass balance at each measurement point is derived by converting
the individual change of surface height as obtained from stakes and pits. Ice
ablation obtained from repeat stake readings is converted into point-specific
mass balance by applying an assumed constant density of 900 kgm-3.
Accumulation is determined by measuring the snow depth in conjunction with
depth-averaged snow density in snow pits. The point values and additional
observational information such as the position of the snow line from an
automatic camera and from terrestrial and air photographs, topographic
conditions, and the expert knowledge about typical spatial patterns are the
basis for drawing contour lines of equal mass balance. The resulting areas of
equal mean mass balance are then intersected with 50 m altitude bands in
order to derive the vertical mass balance profile. By integrating over the
altitude bands, the total glaciological mass balance of the glacier ΔMglac is obtained. Dividing ΔMglac by the glacier area S
results in the glacier-wide mean specific mass balance Bglac. Results are submitted to the World Glacier
Monitoring Service (WGMS) annually e.g.and earlier
volumes.
In order to provide a common base for both the glaciological and geodetic
analyses, we regenerate the annual glacier outlines from the ALS data
strictly following the guidelines presented in . The
remaining annual random uncertainties due to possible errors in glacier
outlines σglac.ref are estimated as ±0.015 mw.e.a-1cf..
Before approaching the reanalysis of the annual surface mass balances of
Hintereisferner for the time period 2001 to 2011, further uncertainties in the
glaciological mass balances series must be addressed. The glaciological
method suffers mainly from uncertainties related to (i) point measurements
and (ii) their spatial extrapolation over the entire glacier
e.g.. Due to the lack of respective data on
Hintereisferner we synthesize appropriate information from the literature to
estimate both sources of uncertainty. analysed the mass
balance series of Hintereisferner for six periods between 1953 and 2006 and
attributed an uncertainty of ±0.10 mw.e.a-1 to field
measurements for the years after 1964 and doubled the value for the years
before. For the spatial interpolation of point data they assigned values
between ±0.14 and ±0.54 mw.e.a-1 with an average of
±0.33 mw.e.a-1 for the entire period.
found combined uncertainties for (i) and (ii) of up to ±0.33 mw.e.a-1 by analysing the modelled variability of the mass
balance of South Cascade Glacier. and
analysed 51 years of mass balance for Glacier de Sarennes and reported a
combined annual uncertainty of ±0.20 mw.e.a-1 for (i) and
(ii). For Gries- and Silvrettagletscher, assumed overall
uncertainties related to (i) and (ii) of ±0.16 to ±0.28 mw.e.a-1. By investigating the glaciological and geodetic mass
balances of Storglaciären, determined the random
uncertainty for (i) and (ii) with ±0.10 mw.e.a-1 each, which
resembles the results of . For Findelengletscher,
roughly estimated a random uncertainty of ±0.04 mw.e.a-1 for (i), referring to , and of
±0.17 mw.e.a-1 for (ii) by evaluating contour lines drawn
independently by 18 analysers. On Nigardsbreen,
obtained a total point measurement uncertainty of ±0.25 mw.e.a-1 as the root sum square (RSS) of a false determination of
the previous year's summer surface (±0.15 mw.e.a-1),
upwelling of stakes (±0.20mw.e.a-1), and incorrect density
assumptions of snow and firn (±0.05 mw.e.a-1). Uncertainty of
spatial integration was taken as ±0.21 mw.e.a-1, made up by
point measurements insufficiently covering both the vertical range and the
total area of the glacier.
Based on the findings of combined
with expert knowledge about the study site, we assess the uncertainty related
to point measurements at Hintereisferner and find it to be in the order of
σglac.point=±0.10 mw.e.a-1, resulting in a
decadal value of about ±0.32 m w.e. For Hintereisferner we estimated the
uncertainty related to extrapolation of point data based on
leading to an annual value of ±0.15 mw.e.a-1. Additionally we
accounted for the presence of large areas not covered by point measurements.
According to , we assume that the extrapolation over
those areas inherits further uncertainties of ±0.10 mw.e.a-1.
Hence, the uncertainty due to spatial integration of the respective
measurements over the entire glacier is defined as σglac.spatial=±0.18 mw.e.a-1, and the related decadal uncertainty is
±0.57 mw.e.. Overall uncertainties for the glaciological mass
balances are calculated, following Eq. 14, leading to an
annual value of σglac.total=±0.21 mw.e., which
corresponds to a cumulative uncertainty of the glaciological method (2001 to
2011) of ±0.65 mw.e.
Key parameters for the 11 ALS data acquisition campaigns at
Hintereisferner from 2001 to 2011. Point density is averaged over the study
area, while the horizontal accuracy is calculated based on a flat reference
area in the vicinity of the study area.
Between 2001 and 2011, 11 ALS flight campaigns were
carried out near the end of each mass balance year (see Table ).
During each ALS acquisition campaign, the glacier was covered with a number
of overlapping flight strips in order to increase the point density and to
ensure high quality and complete coverage of the glacier . As there is essentially no high vegetation in the study area, ALS
points are classified into ground points and flying objects (outliers) only.
The ground points of all datasets are imported into a laser database system
which facilitates storage and further processing. DEMs of
1 m resolution were calculated for all datasets, whereby the mean value of all
ALS points located in each cell represents the elevation of the cell. The
elevation values for the few raster cells that do not contain a single point
are interpolated from the neighbouring cells using a least squares method. In
order to provide high-quality DEMs used for mass balance calculations,
horizontal misalignment of the DEMs being differenced has to be excluded.
Therefore a statistical co-registration correction procedure as suggested by
was performed for this study. Following we
applied the first two steps of the procedure to the ice-free areas for
identifying potential horizontal shifts and vertical offsets between two
ALS DEMs. The statistical co-registration reveals horizontal shifts smaller
than the DEM pixel resolution with no elevation-dependent bias; hence, the
DEMs can be subtracted from each other without performing DEM corrections.
The total volume change ΔV between two dates is then derived from the
respective elevation difference Δhk of the two grids at pixel k
with cell size r of the DEMs, summed over the number of pixels K covering
the glacier, and is expressed as follows cf.:
ΔV=r2∑k=1KΔhk.
For a comparison with the glaciological balance, ΔV is then converted into a specific mass balance in units of metre water equivalent (mw.e.):
Bgeod=ΔV1/2⋅(St0+St1)⋅ρ‾ρwater,
where St0 and St1 are the glacier areas at the first (t0) and
second (t1) acquisition date, respectively, and ρ‾/ρwater is the ratio between the average bulk density (see Eq.
in Sect. ) of ΔV and the density of water.
Original glaciological mass balances (BWGMS), the impact of
reference-area adjustment (ϵref), the homogenized glaciological
mass balance Bglac.hom with related random uncertainties
σglac, the corrected geodetic mass balances Bgeod.corr and
their uncertainties σgeod.corr, the difference between homogenized
glaciological and corrected geodetic balances ΔB, the common variance
of the two series σcommon, and the reduced discrepancies δ.
The acceptance of the null hypothesis (H095), indicating if the
glaciological balance is statistically different from the geodetic balance or
not, is evaluated at the 95 % confidence level, which corresponds to
δ values inside (outside) the ±1.96 range.
β95 depicts the probability of fulfilling H095 in spite of
differences at the 95 % confidence level. Bold entries refer to years in
which H095 is not fulfilled.
Comparison of the homogenized glaciological and corrected geodetic
annual and cumulative mass balances of Hintereisferner over the study period.
Dark grey bars and the dashed black line indicate geodetic balances, while
light grey bars and the dotted black line show the glaciological series.
Vertical black lines show the annual uncertainties (σglac and
σgeod) of the two methods.
Despite a
thorough co-registration, surface elevation differencing of two DEMs is still
subject to various uncertainties. The vertical accuracy of the raw ALS point
data was first assessed by comparing the point clouds with differential
global navigation satellite system (dGNSS)-measured points on a homogeneous
horizontal surface outside the study area (in our case a football field in
Zwieselstein 20 km down-valley of Hintereisferner). The standard deviations
(SDs) of vertical accuracies of the individual datasets are shown in Table . As the reference surface does not reflect the surface conditions in
terms of slope, aspect, and roughness, and therefore is not representative for
vertical accuracies, Bollmann et al. (2011) compared dGNSS ground control
points with laser returns (deviation to laser points: 0.07 m; standard
deviation: 0.08 m) and calculated an absolute slope-dependent vertical
accuracy for Hintereisferner ALS point data (< 0.10 m on slopes
< 40∘). analysed the uncertainties resulting
from rasterizing laser point clouds, revealing that a cell size of 1×1 m as
used for our study causes only negligible errors of less than 0.10 m. For the
geodetic balance (Bgeod), the results of DEM differencing over stable
terrain are taken to define uncertainties associated with the DEM comparison.
Therefore, we selected five stable control areas (3×104m2)
surrounding the glacier (Fig. ), in order to quantify grid-based
uncertainties of spatially averaged elevation differences. The selection of
these sites is based on visual inspection and expert knowledge about the
terrain around Hintereisferner . According to
, we assumed that the DEM uncertainty over stable terrain
is representative for the entire glacier. However, we did not correct our
sample size for spatial autocorrelation, but due to the high sampling density
of the ALS data used, we assumed that the number of independent items is
about the number of glacier pixels cf.. Thereby, the
influence of random pixel-elevation uncertainty on the geodetic mass balance
(σDEM) was calculated based on the stable control areas:
σDEM=SDΔZK,
where SDΔZ (see Table S1 in the Supplement) denotes the vertical
standard deviation in stable control areas and K is the total number of
grid cells used for the calculation of the glacier-wide geodetic mass
balance. This procedure yields uncertainties of ±0.012<σDEM<±0.024mw.e., and σDEM=±0.087 mw.e. for
the 2001 to 2011 analysis (Table ).
Method-inherent differences and uncertainties as quantified in this
study. Differences related to DEM (ϵDEM and σDEM),
density conversion (ϵdc and σdc), survey dates
(ϵsd), internal processes (ϵint and
σint), and crevasse volume (ϵcrev). While the overall ϵgeod
accumulates from all individual differences, the overall σgeod is
calculated by propagating the individual uncertainties. The unit for
ρ‾ is kgm-3. All mass balance uncertainties are
given in metre water equivalent (mw.e.).
The differences between the glaciological and the geodetic mass
balance series vary from year to year, being particularly high in certain
years (Fig. , Table ). The potential causes of these
discrepancies are related to a number of factors: snow cover at the time of
ALS acquisition, different glacier-wide density assumptions in mass balance
calculation, survey date differences between the glaciological and geodetic
observations, the way the methods consider the existence of crevasses, and the
different processes captured by the two mass balance methods. All those
issues are thoroughly assessed below.
Differences induced by snow cover present in DEMs
Whereas the vertical accuracy of ALS DEMs is high, biases as
a result of snowfall events preceding the ALS surveys significantly influence
the calculated volume change. From the analysis of elevation differences in
the non-glaciated terrain, the mean difference between two DEMs in stable
areas (Δz‾stable) can be used to correct for DEM biases
(ϵDEM) caused by the presence of snow as follows:
ϵDEM=∑i=1nΔzi‾n,
where n is the number of DEM grid cells covering stable and non-glacierized
terrain. For the years 2001/02, 2005/06, 2006/07, and 2007/08 the
investigation of stable areas within the differential DEMs (dDEMs) revealed snow-induced absolute
vertical offsets between 0.18 and 0.58 m (see bold numbers for
Δz‾stable in Table S1 of the Supplement). In all other
dDEMs, the vertical bias was below 0.10 m. In 2004 and 2010 a snowfall event
occurred some days before the ALS measurements. However, this is not
reflected in the stable areas of the respective dDEM, because the snow in
non-glacierized areas had melted from off-glacier surface by the time of the ALS
survey. This leads to a small offset in the non-glacierized terrain in the
related mass balance periods. Yet, as snow cover increases, the ALS
elevations measured on reference surfaces have to be cross-checked with snow
depth data from the closest field survey, and subsequently they have to be
corrected. Based on the altitude distribution of stable areas and in situ
measurements, a linear regression in 50 m elevation bands yields mean snow
depths of 0.52 m in 2001, 0.23 m in 2004, 0.46 m in 2005, 0.13 m in 2006,
0.12 m in 2007, and 0.26 m in 2010. This leads to adjusted DEMs and, finally,
to a respective mass balance correction value ϵDEM (Table ). Furthermore this approach was integrated into the estimation of
differences related to unequal survey dates (see Sect. ).
Intensity of the reflected laser beam of the ALS acquisition in 2008
(a) and derived surface classes (b). The classes are perennial firn
with an average density of 700 ± 50 kgm-3 and bare glacier ice
of 900 ± 17 kgm-3. Map coordinates are in WGS84/UTM32N.
Density conversion
While glaciological mass balances are derived calculating
mass change based on well-constrained in situ measurements of density,
geodetic balances are based on volume change measurements, which require
volume-to-mass conversion using estimates of bulk density. Several studies
assume that density in the accumulation area is constant over time and,
hence, use glacier ice density for the conversion
e.g.. But as long as snow or firn is
present, doing so causes an overestimation of mass change. Hence, the use of
the density of ice is only appropriate in glacier areas without firn. If
year-to-year firn line changes are known, the volume-to-mass conversion can
be improved by using an average density of firn for changes in the
accumulation area e.g..
In the present study, ice density (ρice=900kgm-3) was only applied to
the ablation areas, where altitudinal changes are either due to ice ablation
or glacier dynamics, while the geodetic mass change in (perennial) firn areas
was calculated using a density of ρfirn=700±50kgm-3. Consequently, we
calculate the annual conversion density ρ‾ as used in Eq. () as follows:
ρ‾=ρice⋅ΔVice+ρfirn⋅ΔVfirnΔV,
where ΔVice and ΔVfirn are the volume changes in ice
and firn areas, respectively, which both add up to the glacier-wide volume
change ΔV.
In order to classify the glacier surface into ice and firn zones, we designed
a pixel-based surface classification workflow based on ALS-intensity data
following and (Fig. ). This approach was applied to all years with suitable
intensity data, while for years when no such data are available, the most
contemporary ortho-images (2010) and/or Landsat TM images (2001 and 2004) were
used for surface classification (see Fig. S1 in the Supplement). The
resultant grids for each survey year were then used for a pixel-based
conversion of volumetric changes to changes in mass. Respective values for
the conversion density ρ‾ lie in the range of 820 to 930 kgm-3 and are shown in Table . Although neither firn
processes like compaction or meltwater refreezing nor the impact of glacier
dynamics are explicitly resolved, our approach is considered to notably
improve the quality of our annual results compared to calculations based on a
fixed glacier-wide conversion density.
Uncertainties related to density
conversion were estimated as follows: σdc was assessed based on the
estimated uncertainty ranges of ρice and ρfirn (±17 and
±50 kgm-3), while ϵdc was calculated as the
difference between our geodetic mass balance values and those based on a
ρ‾ of 850 kgm-3 as suggested by .
Survey date differences
Apart from 2011 with in situ measurements conducted on the
same day as the ALS flight (Table S2 in the Supplement), the mass changes
during the period between the survey dates of the two mass balance methods
have to be considered. To align the geodetic dates with the end of the
hydrological year used for the glaciological balances and for a corresponding
adjustment of the geodetic results, we incorporated data from in situ
measurements and fieldwork minutes as well as dDEM-based snow cover analysis
(Sect. ). Thereby ablation was assessed based on available stake
readings during the late summer. Observed ablation trends between the
observation dates were used to calculate mass change. If necessary, ablation
was reconstructed by linearly extrapolating observed trends beyond the stake
reading dates. Such cases were cross-checked and adjusted based on
meteorological data from Vent. The linear regression of point ablation versus
altitude was finally used to calculate spatially extrapolated ablation. Note
that the same altitudinal ablation gradient was used for the whole glacier
since considerable ablation is restricted to the lower glacier part at this
time of the year.
Accumulation between the ALS survey and the fixed date was assessed based on
recorded precipitation at Vent which was extrapolated to the glacier, applying
observed long-term precipitation gradients between Vent and five rain gauges in
the Hintereisferner basin (Fig. ). The snow–rain threshold of
0 ∘C is obtained from the Vent temperatures along a lapse rate of
0.0065 Cm-1.
The survey date adjustment is performed individually for each annual geodetic
mass balance, dependent on the presence/absence of snow during the field
survey and the ALS data acquisition as well as on the difference between the
survey dates and the end of the hydrological mass balance year. Accordingly,
we proceeded as follows:
If there was no snow cover during both surveys, and the ALS campaign took place before
the field survey, an elevation-dependent mean ablation gradient as described
above is applied. This is the case in 2003 and 2008.
If there was no snow cover present during the field survey but was snow cover before a later ALS
campaign, the mass balance was adjusted to the survey date by
subtracting the amount of snow from the corresponding DEM, as described in
Sect. . This is the case for the years 2006 and 2007. The amount
of snow determined for these years agrees well with extrapolated
precipitation data from Vent.
If snow was present during the field survey, but the ALS campaign had been conducted
before the snowfall event, the mass of the snow cover measured during the
field survey was added to the geodetic mass balance using the measured
densities and the linear regression of snow probings for the elevation
distribution. This is the case in 2002 and 2008.
If snow was present during the field survey and the ALS data acquisition, the ALS DEM
was adjusted regarding the snow cover conditions. When the ALS campaign was
conducted after the field survey, the geodetically determined snow height was
subtracted (Sect. ), and the mass of snow determined by field
survey was added to the geodetic mass balance. This is the case for the years
2001, 2004, 2005, and 2010.
Note that two corrections have been applied for the year 2008, when the ALS
data acquisition took place 21 days before the field survey, and ablation as
well as accumulation occurred in this period. For 2009 and 2011 no survey
date corrections were necessary due to ALS measurements very close to
30 September.
Representation of crevasses
While crevasses are neglected in the glaciological method, they
are partially resolved in the geodetic method. Although some crevasses might
have been covered by snow during data acquisition, a number of big crevasses
are visible in all DEMs. Depending on snow/melt conditions and their impact
on ice movement, the recognition of crevasses in the single dDEMs and, hence,
their impact on mass balance calculations vary widely. However, in this
study we detected crevasses by assuming that they are deviations from a
regular homogenous surface. By using the variance of elevation as a measure
of terrain smoothness and by applying a closing filter, we derived a surface
without crevasses . Consequently, we calculated
the volume change of a “crevasse-free” glacier, to quantify possible
uncertainties due to open crevasses ϵcrev in the geodetic mass
balance (Table ).
Internal and basal mass changes
Internal and basal mass balances are not captured by the
glaciological method but are implicitly included in the geodetic mass
balances. Thus, when comparing glaciological with geodetic balances, internal
and basal mass changes need to be assessed separately. Particularly for
mountain glaciers, studies on this topic are rare, and published values
represent estimates rather than verified measurements. On Storglaciären,
for example, estimated the contribution of basal melt
due to geothermal heat as about -0.001 mw.e.a-1, and
suggested -0.01 mw.e.a-1 of internal melt
caused by the release of potential energy from run-off.
considered internal ablation due to ice motion being small on Storglaciären
and, thus, negligible. For South Cascade Glacier, estimated
the combined effect of frictional/geothermal basal melt, melt by the release
of potential energy of water, and melt by the loss of potential energy through
ice flow as -0.09 mw.e.a-1. estimated
-0.009 mw.e.a-1 of basal ablation due to geothermal heat and
-0.008 mw.e.a-1 of internal melt due to water flow on Glacier de
Sarennes over a period of 51 years. estimated the
contribution to ablation of geothermal heat, internal deformation, and basal
friction as -0.01 mw.e.a-1 for glaciers in the Alps.
calculated internal and basal ablation based on
for 10 glaciers in Norway, yielding a range of -0.01 to
-0.08 mw.e.a-1. assessed a value of
-0.014 mw.e.a-1 for internal and basal processes at Findelengletscher
following different previous studies e.g..
Altitudinal profiles of annual homogenized glaciological (a) and
geodetic (b) mass balances over the study period. Note that vertical
profiles of the two methods cannot be directly compared due to the effect of
glacier dynamics not captured in the glaciological results.
In this study, we assess internal and basal
ablation related to the dissipation of potential energy following
and . The resultant values are in
the order of -0.04 mw.e.a-1, which corresponds well to data for
glaciers similar to Hintereisferner in terms of size and climate setting
published by . Melt from basal friction and geothermal
heat flux was estimated according to as about -0.01 mw.e.a-1. Hence, we estimate the total contribution of basal and
internal processes to the mass balance to be -0.05 mw.e.a-1.
ResultsGlaciological mass balance
Within this study existing glaciological mass balance records
were homogenized in terms of reference area (see Sect. ) in
order to make them comparable to the geodetic analyses. This showed only
minor impact since glacier outlines have been frequently updated in the
original record. However, the use of methodologically homogenized glacier
outlines based on changed the annual glaciological
balances between -0.015 and +0.039 mw.e.a-1 (see ϵref
in Table ), while the overall impact over the 2001–2011 period is
+0.12 mw.e.. Numbers for annual glacier-wide specific mass balances
range from -0.624±0.21mw.e. in 2001/02 to
-1.813 ± 0.21 mw.e. in 2006/07. Results for individual years
are shown in Fig. and in Table , while the altitudinal profiles of
glaciological mass balance are depicted in Fig. . Note that the
uncertainty range σglac=±0.21mw.e. represents the
random uncertainty as assessed in Sect. and does not reflect
any possible deficiencies in the glaciological series which shall be detected
in the subsequent reanalysis.
Geodetic mass balance
The corrected geodetic mass balance of Hintereisferner over
the ten years period 2001 to 2011 is -13.41±0.29mw.e. which is
1.22 mw.e. more negative than the cumulative glaciological series
(Table ). Annual results range from -0.654±0.06mw.e. in
2003/04 to -2.713 ± 0.18 mw.e. in the year 2002/03 (Table ).
The geodetic mass balance of Hintereisferner over the entire study period was
mainly affected by snow being present in the year 2001, resulting in
ϵDEM=+0.29mw.e. Taking into account the effect of
fresh snow on the DEMs of individual years (Sect. ) leads to
-0.41<ϵDEM<+0.32mw.e. The value of
-0.41mw.e. occurs in 2004/05, when snow was present at both ALS flight
campaigns (Table ), making up 37% of the uncorrected mass change
in this year.
Applying the workflow for the spatially distributed density conversion
(Sect. ) leads to -0.04<ϵdc<+0.31mw.e.,
with maxima in 2002/03 and 2005/06 (Table ). These maxima are due to
the total lack of snow and firn at the end of these mass balance years. The
uncertainty related to our density assumption (Sect. ) lies
in the range ±0.02<σdc<±0.18mw.e., with
±0.27 mw.e. over the entire period of record.
Values for adjustments related to survey date correction are in the order of
-0.08<ϵsd<+0.06mw.e. (Sect.
and Table ). Significant melt amounts between ALS flight and field survey dates
occur on small parts of the glacier tongue only. Ice ablation of almost 1 m at the lowest stakes of Hintereisferner measured between 30 September
(field survey) and 8 October (ALS campaign) 2006 corresponds to a
glacier-wide specific mass loss of only 0.03 mw.e. during the same
time. Uncertainties related to the consideration of crevasses
(ϵcrev) in the geodetic method are small and vary between -0.04
and +0.06 mw.e. with +0.05 mw.e. for the 2001–2011 period
(Sect. and Table ). While the glacier-wide effect of
internal mass changes on an annual basis is ϵint=0.05mw.e.a-1, it is 0.50 mw.e. on the decadal timescale
(Sect. and Table ).
Annual totals for
(ϵgeod) are in the range of -0.38 to +0.57 mw.e., while
the random uncertainties for individual years are ±0.029<σgeod<±0.183mw.e. (Table ). The geodetic balance calculated from
the 2001 and 2011 DEMs yields ϵgeod=+1.03mw.e. and
σgeod=±0.29mw.e. All numbers for the applied
corrections and the single uncertainty sources (ϵ and σ) are
summarized in Table , while the altitudinal profiles of the
glaciological and geodetic mass balances for each year (2001/02 to 2010/11)
are shown in Fig. .
Methodological intercomparison
The comparison of annual glaciological-to-geodetic balances shows that all
but three annual data pairs match satisfyingly within the assessed
uncertainty ranges (Fig. ). The largest differences (ΔB=Bglac.hom-Bgeod.corr) between the two methods occur in the balance
years 2002/03 and 2005/06, with ΔB=+0.92mw.e. and ΔB=+0.60mw.e., respectively. In 2006/07 the difference between
glaciological and geodetic method is -0.45 mw.e., which means the
geodetic result is less negative than the glaciological one. The difference
for the whole study period is 1.31 mw.e. In order to detect
significant biases between the two methods, we calculated the reduced
discrepancies (δ) as described by as
δ=ΔBσcommon,
where the common variance σcommon (Table ) is defined as the
RSS of the method-inherent uncertainties
(σglac2+σgeod2). The more consistent the two
methods, the closer δ is to zero, and the null hypothesis at the 95%
confidence level (H095) can be accepted. As δ falls within the
95% confidence interval (δ<1.96) for seven annual (all but
2002/03, 2005/06, and 2006/07) and the cumulative mass balance values, the two
applied methods can be considered as statistically similar (Table ).
Note that this approach is mainly designed for comparisons on longer (typical
10 years) timescales since biases on the annual scale might be missed.
Nevertheless, in our case it allows the identification of significant
deviations in three years.
From the common variance it is also possible to
calculate the smallest bias that could theoretically be detected in the
glaciological record . The bias calculated at the 5% risk
limit lies between 0.75 and 0.99 mw.e. and is far larger than the
calculated uncertainty of annual glaciological balances of 0.21 mw.e.
In contrast, the detectable bias decreases with the length of the analysed
period, which can be explained by error propagation.
Discussion
In search for possible causes of these large discrepancies
between the methods in three of the sampled years, we explore the potential
contribution of individual components of ϵgeod in the years of
concern: the influence of temporary snow cover (ϵDEM) on the
geodetic mass balances is high, but a thorough consideration in our study
ensures that the results are within the 95% confidence interval. In
contrast, the survey date differences show little effect. Concerning the
conversion of glacier volume to mass changes, we used a new classification
approach to derive a more accurate value of annual conversion density
(ρ‾). Calculated values for ρ‾ are in the range
of 820–930 kgm-3. This is in line with the glacier-wide value of
850±60kgm-3 recommended by .
Nevertheless, in 2010 ρ‾ reaches 930 kgm-3, a value
which at a first glance appears unrealistic. In this year opposite signs of
elevation changes in the accumulation and ablation area compensate for each
other, which results in a conversion factor which is higher than the density
of ice. Such is possible in cases of (i) short observation periods (1–3 years), (ii) small volume changes, (iii) strong year-to-year changes in the
vertical mass balance profiles, or combinations of these factors. Our
approach accounts for year-to-year changes in the spatial extent and
distribution of the snow/firn zones. Highest uncertainties arise in the years
2002/03 and 2005/06, when all snow from the previous winter melted entirely.
As the uncertainty associated with density is of particular importance
, we conducted a sensitivity test for the
periods of good agreement by holding all other parameters fixed. Densities
calculated within our ρ‾ range (Table ) still lead to
results within the 95% confidence interval.
As crevasses may influence geodetically calculated volume changes, we assessed
their impact on the geodetic method. The largest impact (0.06 mw.e.,
or 3% of glaciological mass balance) was detected for 2002/03, when
numerous crevasses opened due to the extremely hot summer causing
extraordinary high glacier velocities . Hence, crevasses
contribute negligibly to the differences between geodetic and glaciological
mass balances.
Internal and basal processes are also of rather minor importance (-0.05 mw.e.a-1; Sect. ) and do not change the differences
between the two data series substantially. Yet, we note that in years with
extreme melt rates as in 2003 and 2006 additional meltwater from outside the
glacier may enter the glacier bed in the tongue area during the ablation
season, which leads to basal melt rates possibly exceeding the above estimate.
However, even a doubling of our estimate to -0.10 mw.e.a-1 does
not explain the large discrepancies between the glaciological and geodetic
method in the years 2002/03, 2005/06, and 2006/07.
Other uncertainties possibly contributing to the high mass balance
discrepancies in 2002/03, 2005/06, and 2006/07 may be method-inherent
uncertainties related to the field measurements, such as the false
determination of the previous year's summer surface. This might be an issue for
the high discrepancies in the individual survey years but cannot be
quantified due to the lack of corresponding information. However, none of the
discussed issues can explain the high deviations between glaciological and
geodetic analyses in the mass balance years 2002/03, 2005/06, and 2006/07.
The extraordinary mass balance year 2002/03. (a) Comparison of
vertical mass balance profiles (Bglac; Bgeod) including the
distribution of direct measurement points over the elevation span of the
glacier. (b) Spatially distributed difference of the methodical results with
main deviations between the methods at elevations higher than 3000 m a.s.l.
where in situ observations are missing. Note that vertical profiles of the
two methods cannot be directly compared due to the effect of glacier
dynamics, which leads to more negative geodetic results (than the glaciological ones)
in the higher-elevation areas and vice versa in the lower glacier regions.
Comparison of mass balances (Bglac.hom and Bgeod.corr) and
their differences (ΔB) with number of ablation and accumulation
measurements. Note that in areas higher than 3000 m a.s.l. only accumulation
measurements were performed.
Nevertheless, a potential reason is indicated by the altitudinal distribution
of point measurements as shown in Fig. for the exemplary year
2002/03. In all three of the poorly matched years, glaciological point data
from elevations above 3000 m a.s.l. are missing on Hintereisferner (Fig. ). Given the glacier median elevation of about
3039 m a.s.l., this means that the upper half of the glacier was not covered by measurements
in these years. At the same time the three years of concern are those with
the most negative mass balances within the Hintereisferner record (Fig. and Table ). The reason for missing measurements in
higher-elevation areas in those years is the fact that no snow from the
previous winter survived the warm summers at snow pit locations, and hence
traditional accumulation measurements were not possible. To address the
problem of a mass balance network which had not been adapted in time,
ablation rates measured at the highest stakes on the flat tongue (at about
3000 m a.s.l. and lower) were multiplied with the observed ice exposure
time of the higher slopes (Gerhard Markl, personal communication, 2017). This disregards
the impact of higher solar radiation intensity on the slopes than on the
flat tongue, and the application of formerly observed “typical” spatial
patterns of mass balance in the spatial extrapolations are considered to be
possible reasons for the differences between the two methods in these years.
After several years of gradual degradation of the firn body, ice and older
dark firn had suddenly become exposed over all altitude bands by August 2003,
with consequent effects on albedo and the surface energy budget. The east- and
south-facing high slopes of Hintereisferner exposed a low-albedo surface to
high solar radiation for several weeks in the exceptionally warm and dry
summer 2003 . As a consequence, the mass loss in the former
accumulation area of Hintereisferner became unexpectedly large in areas
without ablation stakes (>50% of the glacier area). As a consequence,
well known spatial patterns of surface melt of former years used in the mass
balance analyses were no longer valid – an effect which had also been observed
on a smaller glacier in the Eastern Alps some years earlier
.
While higher winter snow cover buried the dark ice surface far enough into
the autumns of 2004 and 2005, protecting higher glacier portions and allowing
for snow pits at the end of summer, the 2002/03 problem became evident again
in summer 2006 when dark glacier surfaces were again exposed after an
early-summer heat wave.
In 2006/07, when the glaciological mass balance obtains more negative values
than the geodetic one, we face a different situation. During summer 2007 a
number of snowfall events increased the surface albedo in the upper part of
Hintereisferner, while stake measurements in the lower part of the glacier
indicated relatively high ablation rates. We suspect that those high ablation
rates were mistakenly extrapolated to higher elevations, but the lack of
metadata for this particular year disables any further discussion and
interpretation.
However, based on our findings we argue for the geodetic data being closer to
reality than the glaciological ones in the years 2002/03, 2005/06, and 2006/07
cf.. For all other years when
differences between the methods are statistically insignificant and where
error bars overlap, the glaciological analyses yield plausible results. This
interpretation is corroborated by comparison of the mass balance of
Hintereisferner with those of other glaciers in the region (see Fig. S3 in
the Supplement).
Conclusions
Over the past decades it has become a standard
procedure to review annual glaciological data alongside decadal geodetic
mass balances from a variety of sources e.g.. However, none of the
mentioned studies uses annually obtained high-resolution ALS data over 1
decade. were the first authors to compare glaciological and
ALS-based geodetic results on an annual timescale at Hintereisferner for the
period 2001 to 2005. Their findings revealed considerable differences between
the methods, especially in the year 2002/03. Yet, the study focuses on
methodical issues only and includes neither a thorough data homogenization
nor a robust uncertainty assessment and discussion.
In our review of the 2001–2011 Hintereisferner mass balance record we show
that the explicit consideration of uncertainty sources – such as the presence
of snow cover, survey dates, and density assumptions – is mandatory for
accurately calculating annual geodetic mass balances. Conversely, crevasses
and internal processes seem not to play a key role. The largest potential
source for differences between the geodetic and glaciological method on the
annual scale is the presence of snow cover during geodetic data
acquisition. Although its reliance on a variety of raw data and meta
information might limit its applicability to other sites or cases, our method
allows correction for method-inherent differences and provides an appropriate
basis for detecting discrepancies in the direct glaciological method. Joint
analysis of glaciological and geodetic data series shows that the
glaciological method in our case successfully captures the mass change in
7 out of 10 mass balance years, and both methods generally agree on the
annual as well as on the decadal timescale.
Our analysis further shows that, in years with very negative mass balances and
a low extent of the accumulation area, the glaciological measurement network
has to be adapted accordingly. In the case of Hintereisferner, this means
that additional ablation stakes in higher parts of the glacier are needed to
properly assess the mass changes in regions where snow measurements could be
performed in former times. If appropriate changes to the measurement network
are not made in time, attempting to overcome the resultant lack of data with
mass balance extrapolation approaches based on spatial patterns observed
during preceding years might be inappropriate. In the 2001–2011
Hintereisferner series the application of such approaches led to considerable
deviations from the geodetic results in three years, and the careful revision
of both series identifies three cases where the applied glaciological
measurement set-up proves deficient. Hence, we conclude that, in times of
increasing availability of high-resolution topographic data, geodetic mass
balances can represent a valuable possibility to unravel shortcomings in the
glaciological measurements even on an annual scale if these data are
thoroughly analysed.
Although major discrepancies between the glaciological and geodetic methods
on Hintereisferner could be explained by our workflow, further
investigations should address a better quantification of error sources, such
as internal and basal processes, in both the glaciological and
geodetic mass balances. Moreover, in times of vanishing firn areas and
disconnecting glacier tributaries, existing mass balance measurement networks
might have to be reassessed.
With the high-quality ALS DEMs reliably
reproducing the annual mass balance, the workflow presented here is
recommended (i) for a reanalysis of annual glaciological with annual
geodetic data and (ii) as a grid-based tool for deriving a glacier-wide
geodetic mass balance of high spatial resolution suitable for a better
understanding of the nature and origin of the differences between the two
methods.
Mass balance data related to this study are submitted to
the WGMS and will hence be publicly available through their website (http://wgms.ch/products_ref_glaciers/hintereisferner-alps/).
Additional information on study site and data are available on request at the
Institute of Geography (ALS and geodetic data) and the Institute of
Atmospheric and Cryospheric Science (glaciological and meteorological data),
University of Innsbruck. Coarser (10 m) versions of all the ALS DEMs are
available at Pangea.de (10.1594/PANGAEA.875889; Sailer et al., 2017).
The Supplement related to this article is available online at https://doi.org/10.5194/tc-12-833-2018-supplement.
CK performed the gross part of analyses and designed and wrote the paper; EB designed
an early version of the study and carried out preliminary analyses; SG
contributed to methodical development and writing and led the
revision process of the paper; LN refined the paper by native-speaker editing
and comments on the manuscript; RP added expert knowledge on study site and
data and performed related analyses; LR was involved in handling and
analysing ALS data; and RS, JS, and GK are the leaders of scientific projects
related to this study and contributed to study-related discussions, paper
design, and writing. All authors contributed to the refinement of the
manuscript.
The authors declare that they have no conflict of interest.
Acknowledgements
The ALS data are hosted at the Institute of Geography of the University of
Innsbruck and were acquired during different scientific projects: the
EU project OMEGA – Operational Monitoring of European Glacial Areas
(project no.: EVK2-CT-200-00069); ASAP – Austrian Space Applications
Programme – ALS-X (project no.: 815527); and ACRP – Austrian Climate Research
Programmes – C4AUSTRIA (project no.: A963633). Mass balance data, field survey
minutes, and meteorological data are provided from the Institute of
Atmospheric and Cryospheric Sciences of the University of Innsbruck.
Glaciological mass balance acquisition is funded by the Tyrolean Hydrological
Survey (Hydrographischer Dienst Tirol).
Edited by: Valentina Radic
Reviewed by: Michael Zemp and one anonymous referee
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