TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-11-1417-2017Reanalysis of a 10-year record (2004–2013) of seasonal mass balances at Langenferner/Vedretta Lunga, Ortler Alps, ItalyGalosStephan Peterstephan.galos@uibk.ac.atKlugChristophhttps://orcid.org/0000-0001-9097-1203MaussionFabienhttps://orcid.org/0000-0002-3211-506XCoviFedericoNicholsonLindseyhttps://orcid.org/0000-0003-0430-7950RiegLorenzoGurgiserWolfganghttps://orcid.org/0000-0003-1150-344XMölgThomashttps://orcid.org/0000-0001-8029-8887KaserGeorgInstitute of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, AustriaInstitute of Geography, University of Innsbruck, Innsbruck, AustriaGeophysical Institute, University of Alaska, Fairbanks, USAClimate System Research Group, Institute of Geography, Friedrich Alexander University Erlangen-Nürnberg (FAU), Erlangen-Nürnberg, GermanyStephan Peter Galos (stephan.galos@uibk.ac.at)22June20171131417143915December201610January201716May201718May2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/11/1417/2017/tc-11-1417-2017.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/11/1417/2017/tc-11-1417-2017.pdf
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 >300kgm-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 kgm-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.
Introduction
Long-term records of glacier mass balance are of particular interest to the
scientific community as they reflect the most direct link between observed
glacier changes and the underlying atmospheric drivers
e.g.,. During
the past decades, considerable effort has been made to establish programs
which provide mass balance information of individual glaciers from all over
the world e.g.,. These records are
undoubtedly valuable and, among others, form the basis for the assessment of
glacier contribution to current sea level rise . However,
their usefulness is bounded by inhomogeneities and unquantified uncertainties
in the limited number of available records e.g.,.
Recently, a number of studies have addressed the topic of inhomogeneous,
biased and erroneous glacier mass balance records
e.g.,. The
number of point measurements needed to derive glacier-wide mass balance was
discussed by and , while
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.,.
Others focused on statistical approaches to evaluate annual or seasonal
glacier mass balance and their associated confidence level
e.g.,. But despite the
relatively high number of studies dedicated to the reanalysis of glacier mass
balance records, few of them e.g., include
a rigorous uncertainty analysis. Consequently, error assessment and
reanalysis of glaciological data is of central interest to both the
glaciological and climatological community .
provided a general concept for reanalyzing glacier mass
balance series and the quantification of related uncertainties in the context
of comparisons between directly measured and geodetically derived mass
balance which are commonly undertaken to cross-check the in situ
glaciological data e.g.,.
Since many records of glacier mass balance suffer from data gaps affecting
certain time periods or areas without measurements, a series of methods has
been developed to complete the respective data sets. Such reconstructions are
often based on the assumption that glacier mass balance gradients are
transferable in space or time e.g., or on other statistical relationships of varying complexity
e.g.,. However, all those
methods rely on statistical relationships which are assumed to be stationary
in time or space. This in turn limits the performance of such approaches as
they are not able to depict the full natural variability of glacier mass
balance.
As a consequence, the use of subsidiary tools such as distributed surface
mass balance models, extensive accumulation measurements 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.,, to homogenize annual or seasonal mass balance
with respect to the fixed date method or to investigate
the impact of changing glacier area and hypsometry on values of mean specific
mass balance . Extensive accumulation measurements
e.g., provide detailed information on the intractable
problem of spatial variability of snow accumulation while additional optical
imagery gives information on the evolving snow cover
e.g.,.
In this paper we present a reanalysis of the mass balance record of a small
alpine glacier over the 10-year period of 2004 to 2013 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 associated with this record showcases a method that can be
applied to glacier data sets suffering from similar inconsistencies.
Furthermore it provides insights into the reliability of existing glacier
mass balance series for which such error analyses are not possible or
practical. The reanalysis presented here involves the following:
The creation of a complete and consistent set of point mass
balance by correcting for methodological shortcomings in the original
data and the creation of pseudo-point measurements for years and locations
without measurements applying a physical mass balance model ensuring maximum
skill by integrating available snow line observations into the reanalyzed record.
The recalculation of glacier-wide mass balance based on a variety
of extrapolation techniques and the integration of new topographic data from
orthoimages and airborne laser scanning (ALS) in order to minimize the effect of
changing glacier outlines on the glacier-wide mass balance.
A sound uncertainty assessment regarding the results of this study
including a comparison of the reanalyzed cumulative mass balance to the mass
change obtained from the geodetic method based on airborne laser-scanning data.
Overview of the study area. Langenferner is shown in red,
Weißbrunnferner in orange and other glaciers in light blue (glacier outlines of
2013 derived from ALS; ). Green dots indicate the automated weather stations referred to
in this study: Zufritt reservoir (ZR), Schöntaufspitze (SS), Sulden
Madritsch (SM), Felsköpfl (FK), Langenferner Ice (LI) and Careser Dam
Station (CR). The labels LMA and CAR refer to two other glaciers with mass
balance measurements: La Mare and Careser e.g.,.
Study site and dataLangenferner
Langenferner (Vedretta Lunga) is a small valley glacier situated at the head
of the Martell Valley (46.46∘ N, 10.61∘ E) in the
Ortler–Cevedale Group, Autonomous Province of Bozen, Italy (Fig. ). It covers an area of 1.6 km2 (2013) and the highest
point of the glacier is an ice divide at around 3370 ma.s.l. The
terminus elevation is 2711 ma.s.l. and the median altitude is 3143 ma.s.l.. The upper glacier part is mainly exposed
to the north while the lower sections face east. Only a minor fraction
(<3 %) of the glacier surface is debris covered. Ground-penetrating radar
measurements in spring 2010 gave a glacier volume of approximately 0.08 km3, with a maximum thickness of more than 100 m in the upper
glacier part. The glacier runoff feeds the river Plima, which is a tributary
to the river Etsch (Adige).
Langenferner is situated at the southern periphery of the inner alpine dry
zone, and thus the climate is shaped by relatively dry conditions due to
precipitation shadow effects from surrounding mountain ranges. The largest
part of annual precipitation is associated with air flow from southern
directions, often resulting from cyclonic activity over the Mediterranean,
while the location south of the main Alpine divide means that fronts from the
north are of only minor importance. Mean annual precipitation rates in the
region range from about 500 kgm-2 at the bottom of the Vinschgau
(Valle Venosta) to about 800 kgm-2 at Zufritt reservoir (1851 ma.s.l.), up to
approximately 1200 kgm-2 at Careser
Reservoir Station, 2605 ma.s.l.. During the
study period the mean zero degree level as inferred from the automatic weather
stations (AWS) used in
this study was at an altitude of 2500 ma.s.l. As in most regions of
the Eastern Alps, glaciers in the Ortler Alps have been far from equilibrium
during the past decade and have hence experienced drastic loss in mass, area
and volume e.g.,. A comparison of
the geodetic mass balance of Langenferner (-9.4×103kgm-2)
to those of about 90 other glaciers in the Etsch catchment (sample mean:
-6.0×103kgm-2) shows that at least during the period 2005
to 2013 Langenferner was amongst the glaciers with the most negative glacier-wide specific mass balances in the region .
Measured and modeled point balances as used for the calculation of
annual balance at Langenferner. Black glacier outlines are those used in the
original analyses while gray lines refer to the reanalyzed outlines used in
this study. Green and blue symbols indicate direct measurements which were
used in the original analyses and after homogenization also in this study.
Black dots symbolize modeled point values generated and used in the
reanalysis.
Glaciological measurements
Direct glaciological measurements at Langenferner were initiated by the
University of Innsbruck on behalf of the Hydrological Office of the
Autonomous Province of Bozen/Südtirol (HOB) in the hydrological year 2004.
The program was established as a supplement to the mass balance program at
Weißbrunnferner/Fontana Bianca, which was (i) considered as potentially
threatened by rapid glacier retreat and (ii) deemed to be not representative
for the region due to the specific setting of the glacier .
Since the start of the program, the initially provisional measurement network
has gradually evolved (Fig. ) and, hence, has changed
substantially over time, especially in terms of spatial stake distribution,
which poses a particular challenge for understanding the spatiotemporal
variability of the glacier mass balance.
In autumn 2002, a number of ablation stakes were installed in the lower part of
Langenferner and systematic readings began in October 2003, when additional
stakes were drilled, still only covering the lover half of the glacier. In
August 2005, the stake network was extended to the upper glacier sections by
adding seven more stakes, the position of which was initially not accurately
recorded. Systematic readings of the stakes in the upper glacier part at the
end of the hydrological year were not performed regularly until the year
2009, when the measurement network was further refined by adding five
additional stakes to the upper glacier sections. In the course of the study
period four stakes in the lower most glacier part were removed after the
respective locations became free of ice. The position of stake 13 in the
middle part of the glacier had to be changed in 2011 due to outcropping rock
at the original location.
Reanalyzed and original annual and seasonal mass balances and
corresponding glaciological key numbers for Langenferner. Srea
stands for the glacier area used in the reanalysis, Ntot is the
total number of point mass balances used for glacier-wide reanalysis
calculations, Nmod is the number of modeled point balances,
Bref is the resulting glacier-wide specific balance,
σglac.tot is the total random error and ELAref and
AARref are the reanalyzed ELA and AAR. Sorig is the
glacier area used in the original series, Borig is the original
glacier-wide specific balance, ELAorig and AARorig
are the original ELA and AAR and orig-ref refers to the
difference between original and reanalyzed record. Bold entries refer to
results which are influenced by mass balance modeling.
The stake network at the end of the study period (2013) was made up of 30
ablation stakes which consist of elastic white PVC tubes of roughly 2 m length, connected by a piece of rubber hose. Drilling depths vary
between 4 m in the uppermost glacier part and 12 m in the lower
sections. During the study period stake readings were performed once to six
times a year, depending on the local conditions at the individual stake.
Extensive measurements of annual net accumulation at the end of summer were
only necessary in the years 2010 and 2013 when the accumulation area ratio
(AAR) made up for about 37 and 50 % of the total glacier area, respectively.
In the other observation years accumulation areas were restricted to only a
few percent of the total glacier area (see Table ). Up to the
year 2007 no measurements of annual net accumulation were performed. From
2008 to 2013, annual net accumulation was measured at the end of the
hydrological year by means of one to four snow pits at more or less
arbitrarily chosen locations and, if necessary, by a varying number of snow
depth probings.
Winter balance measurements have been carried out annually in the first half
of May performing numerous snow depth 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 were 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. Locations of point measurements used for annual mass balance
are shown in Fig. , measurement locations for winter balance
and all measurement dates are shown in the Supplement of this
paper.
Since the year 2013, the observational setup includes two AWS on and near the glacier and in spring 2014 a runoff gauge was
installed 3 km down stream of the glacier terminus. Seasonal and annual mass
balances are regularly submitted to the World Glacier Monitoring Service
(WGMS) since the beginning of measurements in the year 2004.
Meteorological data
The mass balance model used in this study requires meteorological data as
input. These data originate from AWS (1851 to 3325 ma.s.l.) in the
vicinity of the glacier (Fig. ) and were provided by the HOB.
Hourly values of air temperature, relative humidity and global radiation
were taken from the station Sulden Madritsch, 2825 ma.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 were taken from the
station at Schöntaufspitze, 3325 ma.s.l., 5 km north of
Langenferner. Air pressure was downscaled from ERA-Interim reanalysis data
of the nearest surface grid point (46.5∘ N, 10.5∘ E). Daily precipitation sums
originate from the station at the dam of Zufritt reservoir, 1851 ma.s.l.
in the Martell Valley, approximately 11 km northeast
of the glacier (Fig. ).
Since 2013 the Institute of Atmospheric and Cryospheric Sciences, University
of Innsbruck (ACINN), operates two AWS at Langenferner. One station is drilled
into the ice of the upper glacier part at an altitude of 3238 ma.s.l.
and is designed to measure all meteorological parameters
needed to calculate the glacier 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.
Digital terrain models (DTMs) from airborne laser scanning
Data from three ALS campaigns were used for this study. Respective surveys
were conducted around 14 September 2005, on 4 October 2011
and on 22 September 2013. For the area on and around Langenferner the
point density of the 2005 and 2013 data sets is 1.06 and 2.65 points per
m2, respectively, and the density of the 2011 data set is 2.84 points
per m2. High-resolution (1 m) 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 cells without measurements
were interpolated from surrounding grid cells. For more details on the ALS
data and resulting DTM the reader is referred to .
Glacier outlines from orthoimages, ALS and Global Navigation Satellite System (GNSS)
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, 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
following the approach of . This method also enabled 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.
However, debris cover is a minor issue at Langenferner since only a few
percent of the lower glacier part are covered by debris. The glacier outline
of 2010 was assessed from extensive differential GNSS measurements in early October 2010.
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 snow line 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 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
snowmelt could be determined with an estimated accuracy of ±5 days,
and in many cases probably even better.
Homogenization of data and methodsPoint measurements
Besides a sparse and unevenly distributed measurement setup
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.,.
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
1 October) in order to obtain values corresponding to the fixed date
period. As part of the reanalysis process we accounted for this problem
(which was not considered in the original analyses up to the year 2008) by
subtracting the respective snow water equivalent, which for all years was
measured at the stake locations at the end of the previous hydrological year.
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 30 September) only affects the seasonal mass balances. In most years of the
study period ice ablation during late autumn at 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 for late autumn ice
melt during the reanalysis process.
Fixed date versus floating date
Measurements for annual mass balance were in all years carried out very close
to end of the hydrological year and, if necessary, stratigraphic corrections
for snow cover were applied. Hence original annual balances were reported as
fixed date balances and thus no additional correction was applied during the
reanalysis. 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 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 (30 April). 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:
bfix=bfld⋅∑Pfix∑Pfld,
where bfix and bfld are the fixed date and floating date point
values of winter balance and ∑Pfix and ∑Pfld are the
precipitation sums recorded at Zufritt reservoir during the fixed date and
the floating date period, respectively. Note that this approach is based on
the assumption that no meltwater drains from the glacier during the
hydrological winter period, which is a reasonable assumption for Langenferner
(see Supplement for a more detailed discussion).
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 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, a central aim of this study was to create a spatially and
temporally consistent set of point annual mass balance. To achieve this we
generated artificial measurement points in the poorly represented upper
glacier section by applying a physically based energy and mass balance model
. We have chosen a physical approach since reconstructions
based on the spatial or temporal transfer of known mass balance gradients or
altitudinal profiles e.g., often show
limited performance. More comprehensive statistical approaches such as
presented by , or
were not applicable due to the short series of available data (at some
locations 5 years or less). However, the performance of modern model
approaches is generally expected to be superior to statistical approaches.
This is due to the integration of additional information such as the
influence of local topography and related implications on governing
micro-climatological parameters like temperature and radiation, snow line,
snow depth and density, etc., which enables a more accurate calculation of the
local mass balance. In contrast, statistical methods damp the spatiotemporal
variability of mass balance as they imply (linear) correlation between
measurement points or glacier parts. Nevertheless, the use of models driven
with meteorological data in glacier mass balance series can be problematic
(see Sect. ). For this reason we clearly flag all results
related to modeling and provide full methodical transparency in order to
enable possible data users to decide whether the data suit their purpose or
not.
The applied 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
but is rather 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 setup 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.,
and the choice of the optimal parameter setting
e.g.,. The application of a
relatively complex physical model is justified by the dominant influence of
local topographic factors on micro-meteorological variability and the
resultant large spatial variability of the surface mass balance, which can
only be resolved in a sufficient way by a process-based model. Furthermore,
we aim to create a set of homogenized point mass balances in addition to
glacier-wide balances, since point balances have proven to be valuable
information sources for investigations on glacier–climate interactions
e.g.,.
Transfer of meteorological variables
Although our study does not aim to explicitly resolve individual energy
fluxes, we extrapolated meteorological variables using techniques which have
also been applied in process-oriented studies since insufficient
extrapolation of meteorological input data is often a dominant error source
in the application of physical glacier mass balance models
e.g.,. The extrapolation
techniques used here were optimized using data from the on-glacier weather
station in the upper part of the glacier for the period July 2013 to August 2015,
a period when measurements at all AWS were available. Air temperature
from Sulden Madritsch was extrapolated to the glacier applying an altitudinal
lapse rate of 6.5×10-3Km-1 and an offset of
-0.56 K,
reflecting the different micro-climates 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 were not further modified since no
clear spatial pattern was detectable in the analyzed data sets. Global
radiation was used to calculate a cloud factor e.g., 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 observed wind speeds at the glacier station using a
scaling factor of 0.67. ERA-Interim atmospheric air pressure from the nearest
surface grid point (46.5∘ N, 10.5∘ E; 8.5 km from
the glacier) was reduced to the altitude of the stake locations by the
barometric equation; since the mass balance model is relatively
insensitive to small changes in air pressure, the temporal resolution of 1 h was achieved by linear interpolation of the 6-hourly reanalysis data.
Daily precipitation sums measured at Zufritt reservoir (1851 ma.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
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 kgm-2 on the annual scale
compared to a model driven with daily precipitation sums equally distributed
over 24 h.
Monte Carlo optimization of model parameters
The mass balance model approach was set up as follows (Fig. ): first the model was precalibrated 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 P0model was generated applying a precipitation
scaling factor Γ0 to the measured and temporally redistributed
record of Zufritt Pobs.red. in order to fit the model to the observed
values of winter mass balance (Eq. ).
P0model=Pobs.red⋅Γ0
This precalibration was done for the location of stake 22 (Fig. ),
a stake situated in the upper glacier part, in the center of
the area where the point modeling was carried out. This stake was chosen as
the relatively homogeneous surrounding 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., performing 1000 model runs
with different parameter 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 part. An individual Monte Carlo
optimization for each stake was not possible due to the low number of
available readings at some stakes.
Schematic flow-chart illustrating the applied model approach.
ALS-derived surface elevation change at Langenferner for the period
September 2005 to September 2013. Also shown are the stakes used for the
automatic extrapolation schemes, where black dots refer to locations to which
the mass balance model was applied. The blue line indicates the equilibrium
line at the end of the hydrological years averaged over the study period.
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 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.,. In order to minimize respective uncertainties in the mass
balance model, we made recourse of a calibration procedure which integrates
available snow information. For this purpose, the mass balance model with the
optimized parameter setting was tuned by replacing Γ0 in Eq. () by the individual (for stake i and year a) scaling factor
Γi,a, which accounts for all site-specific properties related to
accumulation. Γi,a should hence not be seen as a precipitation
scaling factor but rather as a way to correct for the unresolved accumulation
processes listed above. These processes are highly variable in space and
time, and therefore Γi,a is allowed to vary freely, ensuring a high
model skill as it enables the model to account for the full spectrum of
natural mass balance variability (see Sect. ). This stake
and year individual tuning procedure was performed 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 1 day from the observed
date.
Note that the present approach is not applicable in years with a persisting
snow cover at the stake location. But during the first observation years
(2004 to 2008) when measurements were partly missing, annual mass balances at
Langenferner were very negative and accumulation at the end of the year was
restricted to a few percent of the glacier area. For the few years and stakes
with missing measurements and snow cover persisting throughout the ablation
season, Γi,a was derived based on linear regression with
Γi series of neighboring stakes. Values for Γi,a vary in
the range of 1.1 to 4.7 (Fig. ), and curvature of the terrain
and other wind related factors are clearly reflected in the spatial
Γi,a patterns, while interannual variability seems to be
determined by meteorological phenomena, such as number and strength of storm
events, dominant flow direction during the accumulation period or the
absolute amount of accumulation since years with lower accumulation amounts
tend towards larger Γi,a values.
Precipitation scaling factors Γ for different locations (i) and years (a).
Spatial integration of point data
Five different methods were applied to spatially integrate the reanalyzed
values of annual and winter point mass balance in order to obtain mean
specific glacier-wide balances. We applied the traditional contour line
method in two different ways and additionally made recourse of three
automatic methods in order to assess and investigate possible differences and
uncertainties due to the applied analysis method. After the individual
extrapolation of point measurements, all applied methods calculate the total
mass change ΔM by spatial integration of the specific mass change b
over the area S based on the following equation:
ΔM=∫Sb⋅dS.
The mean specific mass balance B is then calculated as follows:
B=ΔMS.
Equations () and () can be applied to the entire glacier area
to obtain the glacier-wide specific glacier mass balance or to each single
50 m altitude band to calculate the altitudinal mass balance profile and
subsequently the equilibrium line altitude (ELA). The latter is calculated as
the lower most intersection of the altitudinal mass balance profile with the
b=0 axis . While annual (Ba) and winter
(Bw) mass balances are based on measurements, summer mass balances are
calculated as a residual:
Bs=Ba-Bw.
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 (ΔMa) from the
beginning (t0) to the end (t1) of the period of record (PoR) and
dividing the result by the average glacier area S during that period (Eq. ).
Bglac.PoR=∑t0t1ΔMa12⋅St0+St1
Contour-line-based extrapolations
The contour line method e.g., 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 snow line, date of ice
emergence at individual locations, meteorological conditions on the glacier
and other expert knowledge such as typical spatial patterns. 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: once in its purely traditional form creating areas of
equal mass balance between the manually drawn contour lines of 250 kgm-2 equidistance, and once applying the Esri ArcGIS
interpolation tool topo to raster, which is based on the ANUDEM
algorithm e.g.,, 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 1 × 1 m resolution
which were subsequently spatially integrated to obtain the mean specific mass
balance (Eqs. and ).
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: (i) the profile method based on a linear regression
of point measurements with altitude and the area–altitude distribution of the
glacier e.g.,, (ii) the automatic extrapolation
applying the topo to raster function and (iii) an inverse distance
weighting procedure. While the contour-based methods were applied making
recourse of all available information for the respective year, the three
automatic methods were based on a reduced but temporally consistent set of
reanalyzed point measurements which in this context means that the number and
position of the measurement points used in the calculations was kept (almost)
constant. This was done in order to avoid noise related to changes in the
measurement setup affecting the temporal mass balance signal. For winter
balances the creation of a consistent set of point values was not possible
due to large year-to-year differences in amount and spatial distribution of
measurements.
Geodetic mass balance calculations
The geodetic mass balance of Langenferner for the period 2005 to 2013 and the
subperiods 2005 to 2011 and 2011 to 2013 was calculated based on
differencing high-resolution (1 m) DEMs from ALS data
of the respective years. The total volume change ΔV was calculated by integrating the elevation change Δh at the
individual pixel k of length r of the co-registered DEMs following
:
ΔV=r2⋅∑k=1K⋅Δhk.
Subsequently the derived volume change was converted to a geodetic mass
balance over the period of record following Eq. ():
Bgeod.PoR=ΔMgeodS‾=ΔV⋅ρ‾12⋅St0+St1,
where ρ‾ denotes a mean glacier density of 850 ± 60 kgm-3 as
proposed by and S‾
is the mean glacier area between the two acquisition dates calculated as the
mean of the extents at the beginning and the end (St0 and St1) of
the PoR.
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:
ΔMgeod.corr=ΔMgeod+h‾st0⋅ρ‾-h‾st0⋅ρ‾st0-h‾st1⋅ρ‾-h‾st1⋅ρ‾st1,
where ΔMgeod.corr denotes the geodetically derived mass change
corrected for snow cover differences between the two acquisition dates t0
and t1, ΔMgeod is the uncorrected mass change,
h‾s denotes the mean snow depth (at dates t0 and
t1,
respectively), ρ‾ the bulk glacier density and
ρ‾s the mean snow density at the acquisition dates t0
and t1.
In 2005, no field measurements were performed close to the ALS survey date.
But field data from 4 September 2005 in combination with
meteorological records of nearby AWS, as well as photographs from nearby
glaciers, indicate that there was basically no snow cover at the date of the
2005 ALS campaign. Seasonal snow was hence regarded as negligible for glacier-wide analyses in 2005. In 2011, in situ measurements were performed on
30 September, 4 days prior to the ALS campaign. Despite the short
time difference between direct and geodetic measurements, we applied a
correction of the measured snow depths due to relatively warm weather
conditions in this period. For this purpose, 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 30 September as initial condition. In 2013,
extensive direct measurements were carried out
simultaneously to the ALS campaign on 23 September 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 measurements in the years 2005 and 2011, while
in 2013 the correction was based on direct measurements performed on
23 and 30 September.
Point values of snow and mass change were extrapolated using
topo to raster to calculate glacier-wide mean values for the individual
properties. Mean specific mass changes (representing corrections for snow cover
and survey date, respectively) were finally added (subtracted) to (from) the
geodetically derived mass change over the survey period.
Annual glacier topographies and outlines
Changes in glacier area and topography may have significant impacts on the
mass balance of mountain glaciers through various feedbacks
e.g., and since respective data are 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.,.
Langenferner was subject to remarkable hypsometry changes during the study
period (Figs. and ). While glacier outlines for
the current study could be directly derived from orthophotos or ALS data for
all years except for 2004, 2007 and 2009, data on glacier topography are 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. Doing so we consider the change in
surface elevation Δh at one location (pixel) k of the glacier over
the time period t as the result of the following terms:
Δhk,t=Δhsurfk,t+Δhdynk,t+Δhbasalk,t,
where Δhsurfk,t denotes the surface elevation change related to
surface mass balance, Δhdynk,t represents the surface change
due to glacier dynamics and Δhbasalk,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.,, it is
neglected. The rasters of spatially extrapolated surface mass balance for
each year (Sect. ) and those referring to snow and date
corrections (Sect. ) can be summed up for the time period
between the two geodetic surveys in order to calculate the term Δhsurfk,t. Consequently, Δhdynk,t for the respective
period can be calculated as follows:
Δhdynk,t=Δhk,t-∑t0t1Δhsurfk,t=hk,t1-hk,t0-∑t0t1Δhsurfk,t,
where hk,t0 and hk,t1 are the surface elevations at the pixel k
given by the DEMs taken at date t0 and t1, respectively, and
∑t0t1Δhsurfk,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
Δhdynk to be temporally constant during the observation period.
This simplifies the calculation of the annual Δhdynk,a to
Δhdynk,a=ΔhdynkdPoR,
where dPoR is the duration of the observation period in years. The
result is a raster of Δhdynk,a which can be applied to all the
observation years. The surface elevation of a certain year hk,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 of the previous year hk,a-1
(Eq. ).
hk,a=hk,a-1+Δhsurfk,a+Δhdynk,a
Altitudinal distribution of reanalyzed annual mass balances as well
as of the glacier surface area at the beginning (2003) and the end of the
study period (2012).
The DEM taken at the end of the observation period served as a boundary
condition for surface elevation at areas which became 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 pixels as having undergone no change in surface elevation.
Note that the term Δhdynk,a represents all the differences
between the direct surface measurements and geodetically detected surface
changes. These are not only differences which can be associated with 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 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) and systematic (ϵ) 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 by the geodetic method. The individual error
sources and the respective numbers used in the uncertainty model are listed
in the Supplement of this paper.
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
(σglac.total.a) can consequently be formulated as follows:
σglac.total.a=σglac.point.a2+σglac.spatial.a2+σglac.ref.a2,
where σglac.point.a is the error due to uncertainties on the point
scale, σglac.spatial.a represents errors related to spatial
extrapolations and σglac.ref.a accounts for uncertainties due to
inaccurate glacier outlines. In this formulation σglac.point.a is
often misinterpreted since it does not represent the typical value of point
scale errors but the uncertainty of glacier-wide mass balances related to the
propagation of point uncertainties after the extrapolation of measurements.
This term depends not only on the magnitude of point uncertainties but
also on the number and spatial distribution of point measurements. Hence, it
requires thorough evaluation (Sect. ).
Uncertainties related to point measurements
Random errors on the point scale mainly originate from inaccurate readings.
This involves ablation and accumulation measurements equally. For ablation
stakes the respective error is on the order of 2 or 3 cm.
Limited representativeness of an ablation stake due to surface roughness is
not really an error on the point scale but can introduce errors to the
analysis when the data are extrapolated to larger areas. At Langenferner such
surface features are typically ≤20cm in height, although after
long periods of exceptionally strong melt, surface structures were observed
to reach the order of 30 to 50 cm in the lowest sections of the
glacier.
For accumulation measurements the error potential is generally higher. Snow
pits with measurements of snow depth and density offer the highest accuracy
(≈50kgm-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” 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 number of point measurements and their spatial
distribution. To quantify this problem, we applied a bootstrap approach
e.g., in which random errors according to a defined
normal distribution were applied to all available individual point
measurements before calculating the glacier-wide balance 5000 times for each
case using the inverse distance weighting method for extrapolation. The
respective annual uncertainties are then given by the standard deviation of
the 5000 runs and range from 11 to 26 kgm-2 for annual balances
and from 7 to 16 kgm-2 for winter balances.
Uncertainties in the extrapolation of point measurements
Similar to the propagation of point scale uncertainties, uncertainties
related to the applied extrapolation method are also dependent on the number
and distribution of point measurements, as well as on spatial balance
patterns of the individual year or season. We assessed those uncertainties
based on the analysis of the glacier-wide reanalyzed mass balances obtained
from the five extrapolation methods used. The annual extrapolation
uncertainty in our study is finally represented by the absolute range of the
bias corrected results ranging from 23 kgm-2 (2006) to 134 kgm-2 (2008). Respective values for winter vary between 31 kgm-2
(2013) and 95 kgm-2 (2004). Note that for winter
balances we used the range without bias correction (rBrea) since the
biases between the individual extrapolation methods were small and their
origin could not be unequivocally explained.
Uncertainties due to inaccurate glacier outlines
Since for this study we make use of annual glacier outlines derived from
orthophotos or ALS or calculated as described in Sect. , our
analyses are not systematically affected by this issue. Hence the remaining
uncertainties related to this problem are given by the random uncertainties
of the annual glacier areas. We estimated the related standard error to be 15 kgm-2.
For the year 2005 we applied a more conservative estimate
of 25 kgm-2, since the reference area for this year suffers from
larger uncertainties as it was derived by manually updating the 2003 glacier
extent with a few GNSS points taken in 2004.
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
overall random error of the corrected geodetic mass balances can be
expressed as
σgeod.corr=σgeod.total2+σdc2+σsc2+σsd2,
where σgeod.total refers to the remaining uncertainties related to
geodetic measurements after all applied corrections such as co-registration
etc., σdc is the error related to density conversion, σsc
refers to the error due to snow cover and σsd is the remaining
error due to different survey dates compared to the glaciological method.
Note that Eq. () differs from Eq. (18) in in two
points: firstly we split the uncertainties related to bulk glacier density
and those 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 be quantified in a
sufficient matter in the frame of the current study. Nevertheless we discuss
those effects in Sect. .
Uncertainties in ALS measurements
To minimize systematic errors in the geodetic analysis, the co-registration
of the three ALS data sets was tested using the pitched roofs of six
buildings belonging to three mountain huts in the vicinity of Langenferner
(Zufallhütte, Rifugio Casati and Marteller Hütte). Following
, the inclined roof surfaces enabled us to check the data for a
possible horizontal shift. However, no significant aspect-dependence of DEM
differences could be detected in the data sets used for this study. The
vertical error due to uncertainties in the DEMs and spatial auto-correlation
σgeod.total for the individual survey periods was tested by
calculating the surface differences in stable reference areas outside the
glacier. The surface difference in those areas is below ±0.1 m
for terrain with a slope angle below 40∘. Since there are hardly
any areas with slope angles of 40∘ or more at Langenferner, we used
0.15 m as an upper threshold of possible vertical errors over the
glacier area.
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 kgm-3. 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 kgm-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 (Sect. ). 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 1
order of magnitude smaller than the uncertainties related to the used bulk
glacier density and are hence of minor importance. However, the respective
errors for both problems were estimated as 100 kgm-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 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 abovementioned 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 subperiods 2005 to 2011 and 2011 to 2013.
After applying the corrections described in Sect. , the reduced
discrepancy δ between the two methods can be
calculated as
δ=ΔPoRσcommon.PoR=Bglac.PoR-Bgeod.PoRσglac.PoR2+σgeod.PoR2.
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.
Results and discussionModeled annual point mass balance
Overall, 80 values of annual point mass balances were calculated using the
presented model approach. For 33 of those cases field measurements are
available which allows for independent validation of the applied approach,
yielding a root mean square deviation (RMSD) of 128 kgm-2 and a
R2 of 0.96 between modeled and measured values (Fig. ).
The magnitude of this error is similar to the uncertainty of glaciological
point measurements reported in the literature e.g., and is lower than reported uncertainties of
statistical approaches e.g.,. Since no
significant systematic errors such as biases for single stakes or years are
detectable, the 47 newly created point values constitute a valuable basis for
the reanalysis of the glacier-wide annual balance. Despite the convincing
performance, the transferability of the approach is restricted by several
factors. First the method is based on data from nearby AWS which are not
available for every glacier. Second, the model in its current form cannot be
applied to years/locations with persisting snow cover since it is based on
observations of the emergence of last year's reference surface. However, snow
line observations could for instance be replaced by snow measurements taken
at some time in summer. As such observations at Langenferner are missing in
2010 and 2013, the mass balance at only a few stake locations could be
modeled in these years. This reduced the number of validation points but did
not affect the reanalysis procedure, since measurements for these years are
available at most stake locations.
Scatter plot of modeled annual point mass balances against observations.
Glacier-wide specific annual mass balance
Mean specific annual mass balances and their altitudinal distribution
(Fig. ) 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
outlines and topographies. The results for the two contour-line-based
extrapolation methods are almost identical and differ by only 0 to 5 kgm-2
(RMSD <3kgm-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 (1 × 1 m)
grids of surface mass balance which were also used to calculate annual
glacier topographies and outlines (Sect. ).
Statistical evaluation of mass balance series based on different
extrapolation methods compared to the reference method: bias, R2 and root
mean square deviation before (RMSD) and after (RMSDbc) a bias
correction of the results.
Original and reanalyzed seasonal mass balances at Langenferner
during the study period. Error bars account for random uncertainties of the
reference method as calculated in this study.
The results show a persistent mass loss in all observation years. For the
reference method, single year numbers vary between -1556 ± 47 kgm-2 in 2012 and
-246 ± 31 kgm-2 in 2013, with a
study period average of -1137 ± 79 kgm-2 (Fig.
and Table ). While all applied extrapolation methods display
a common signal in terms of interannual mass balance variability
(R2>0.98), the three automatic extrapolations yield mass balances which
are considerably more negative than those obtained by the contour line
approaches (see Tables 2 and S5 in the Supplement). The respective biases
are -249 kgm-2 for the automatic
method based on topo to raster, -189 kgm-2 for the profile method and -247 kgm-2
for inverse distance weighting (Fig. ). Those
negative biases can be well explained by the underrepresentation of
accumulation areas in the consistent set of point balances (Sect. )
on which the three automatic methods are based. This problem is
not reflected in the contour-line-based calculations since those benefit from
snow line observations, sporadic accumulation measurements and at least a
rough knowledge about the amount of accumulation and its spatial
distribution. The availability of a few continuous accumulation measurements
at fixed locations would strongly reduce the biases of automatic
extrapolations and would enable the calculation of the glacier-wide mass
balance based on a reduced number of point observations and simplified
extrapolations. However, this would lead to a loss of information on the
spatial pattern of surface mass balance, which constitutes an important
component of modern and high-level glacier mass balance monitoring as it is
an important source of information for studies on energy balance and other
glacier surface processes.
A comparison of the reanalyzed mass balance series to the original record
shows that the two records strongly differ in their interannual variability
(R2=0.84), though the bias of the original series (-58 kgm-2)
is relatively small (Fig. , Table ).
Differences for single years are highest for the years 2004 and 2008 when
they reach 384 and 319 kgm-2, respectively. For
5 of the 10 observation years, differences between the original record
and the reanalyzed series exceed the uncertainty range of the reanalyzed
reference values. These large differences can mainly be attributed to two
causes: (i) the lack of measurements in the upper glacier part during the
first half of the study period and the hence insufficient representation of
spatial mass balance patterns in the extrapolation of point measurements;
(ii) the usage of outdated glacier extents, which in our case biases the
calculated glacier-wide annual balances towards more negative values. The
latter problem at Langenferner leads to a negative bias of typically about 20 kgm-2
after only 1 year. After only a few years without
updating the glacier outlines this effect can reach the order of 100 kgm-2.
This matter is particularly affecting the original mass
balance of 2004. For this first observation year, the original analyses were
based on glacier outlines of 1996 (Fig. ) since newer
topographic data at this time were not available.
Annual mass balances as obtained from the different extrapolation
methods plotted against the results of the reference method. Basic statistics
related to this plot are shown in Table .
Finally, the diligent consideration of snow line information in the
reanalyzed series enabled a more accurate determination of important
glaciological key parameters such as ELA and AAR in the individual
observation years. All relevant results of the reanalysis, as well as the
original numbers for mass balance, ELA and AAR, are listed in Table .
For annual and seasonal results of all extrapolation
methods the reader is referred to the Supplement.
Glacier-wide specific seasonal balance
In contrast to annual mass balances, no modeling was involved in the
calculations of the winter mass balances. However, the 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 kgm-2. The mean fixed date winter
balance for the study period is 929 ± 52 kgm-2 with a maximum
of 1267 ± 34 kgm-2 in the wet accumulation period of 2009. The
exceptionally dry and warm winter 2007 resulted in the lowest value of 558 ± 44 kgm-2.
Note that in this winter period, the lowermost
parts of the glacier displayed negative mass balance due to considerable ice
melt in late autumn 2006. Except for the year 2011, all reanalyzed winter
mass balances are less positive than the original values (bias of original
record = 71 kgm-2). This can be explained by the fact that all
applied corrections in our case generally lower the mass balance value and
more positive values can only be the result of differences in the spatial
extrapolation of point values or the use of different glacier extents, both of which
have little impact (<50kgm-2) on the winter balance at
Langenferner due to generally small spatial winter balance gradients at this
specific glacier.
The correlation between the original and reanalyzed records of winter mass
balance is larger (R2= 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 (Sect. ).
Nevertheless, differences between the original and the
reference record exceed the corresponding random uncertainties for 6 out of
10 winter periods.
The homogenization of original winter balance point measurements revealed that the
recalculation of point winter balances according to the fixed date system generally
showed the largest impact of the applied corrections. For the year 2010, the effect of
this correction reached 140 kgm-2 on the glacier-wide scale (17 % of the
winter net accumulation). Corrections for snow of the previous hydrological year were showing
a smaller effect but are still on the order of up to 100 kgm-2 on the glacier-wide
scale. For 2011, when the corresponding corrections were already applied in the original series,
skipping this correction would change the mean specific winter balance by more
than 200 kgm-2. The impact of ice ablation during the hydrological winter
period was greatest in the years 2004 and 2006 when it reached the order of 30 and
55 kgm-2, respectively. On the point scale respective values reach the order of
300 kgm-2 in the lower most glacier part, which, in this very dry and warm winter,
resulted in a negative fixed date winter balance at the lower part of the glacier tongue.
For glaciers with large tongues reaching low elevations or with large sun-exposed area
fractions, this issue may be of even higher relevance than at Langenferner.
Values of summer mass balance range from -2488 ± 71 kgm-2 in
2012 to -1336 ± 99 kgm-2 in 2010. Differences between original
and reanalyzed summer mass balances exceed the uncertainties of the
reanalyzed series in 8 out of 10 observation years reaching up to 446 kgm-2 in 2004.
A comparison of the two series yields R2 of 0.70 while between the individual reanalysis series R2 is ≥0.97. Summer
balances suffer from the largest uncertainties as they are calculated as a
residual from annual and winter mass balances and are hence affected by the
uncertainties in both series.
Integration of meteorological data in mass balance observations
The aim of the present study was, amongst others, the creation of a best
possible estimate of Langenferner's mass balance during the study period
serving as a reference for further investigations on the glacier. But, as
already stated in Sect. , the integration of meteorological data in
observational records of glacier mass balance may be problematic because
there is a risk of circular reasoning: observational series of glacier mass
balance are often used in investigations of glacier response to climate
forcing. We argue that this risk is limited since a large part of the
systematic influence that meteorological data could have on our time series
is canceled out by the calibration of Γi,a and the constraint of
matching snow observations. However, this paper and the Supplement provide
full insight into the applied reanalysis process and all data partly or fully
resulting from the integration of meteorological data are clearly flagged in
the tables or in data published through the WGMS or elsewhere. This enables a
individual-case user decision on whether these data are suitable for a
specific purpose or not.
Results of the geodetic analyses and the cross-check between
glaciological and geodetic method. PoR stands for the observation period,
ΔZ is the mean surface elevation change, ΔV the volume
change, Bgeod is the uncorrected geodetic balance assuming a bulk
density of 850 kgm-3, corrsc and corrsd
refer to the corrections for snow cover and survey dates,
Bgeod.corr refers to the corrected geodetic balance,
σgeod.total.PoR is the total random error of
Bgeod.corr, Bglac.PoR is the cumulated glaciological
mass balance, σglac.total.PoR is the corresponding random
uncertainty, Δrel is the relative difference between
glaciological and geodetic results and δ is the reduced discrepancy
.
PoRΔZΔVBgeodcorrsccorrsdBgeod.corrσgeod.total.PoRBglac.PoRσglac.total.PoRΔrelδm106m3kgm-2kgm-2kgm-2kgm-2kgm-2kgm-2kgm-2%-2005–13-10.35-18.98-9397-198-49-9644709-89642417.10.912005–11-8.34-15.28-7439-3841-7436560-71052344.50.552011–13-2.20-3.66-1908-169-8-2084248-18295612.21.00Geodetic mass balance
The mean surface elevation change at Langenferner during the 8-year
period of 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 on the order of 1 to 3 m are
detectable (Fig. ). Assuming a bulk glacier density of 850 ± 60 kgm-3,
this corresponds to an uncorrected geodetic mass balance
of -9397 ± 691kgm-2. The correction for differences in snow
cover between the two acquisition dates changes the result to -9596 ± 694 kgm-2.
Note that the values slightly differ from those (-9381 and
-9702 kgm-2) presented by since the study in
hand makes use of reanalyzed data sets. For the two subperiods 2005 to 2011
and 2011 to 2013 the uncorrected geodetic balances are -7439 ± 558 and
-1908 ± 228 kgm-2, respectively. The corrected values change to
-7436 ± 560 and -2084 ± 248 kgm-2, showing that especially
the snow cover correction for the short period 2011 to 2013 leads to a large
relative change (-9 %) in the result. The results of the geodetic analyses
are summarized in Table including raw and corrected values,
as well as numbers for the individual corrections applied.
Uncertainties in glaciological and geodetic balances
The largest source of uncertainties in the reanalyzed glaciological record is
the spatial extrapolation of point measurements. The largest spread between
individual extrapolation methods is shown in the years 2008 and 2009 in which
the negative offsets of the automatic extrapolation methods are especially
large. We attribute this to very strong spatial mass balance gradients in
these 2 years given by the fact that mass balances at stake locations were
quite negative, but at the same time snow of the previous winter could
sustain throughout the summer in concavely shaped areas of the upper glacier
part. While these patterns are reflected in the contour-line-based
extrapolations, automatic methods did not capture this due to missing
measurements in the respective areas. This shows the importance of the
integration of accurate snow line observations in calculations of glacier mass
balance e.g.,. For winter balances the
largest extrapolation uncertainties occur in 2004 when only 22 point
measurements are available. However, this number would most probably be
sufficient if the measurements were well distributed over the glacier area
(), which was not the case in that year. For both annual and
winter mass balances, the second largest uncertainty source is given by the
uncertainties related to point measurements. For annual balances they are on the order of 22 kgm-2 while for winter balances they range from 7 to
16 kgm-2 due to the generally higher number of measurements
combined with less distinct spatial mass balance gradients. Uncertainty terms
for all years and seasons are presented in the Supplement.
Uncertainties in the corrected geodetic balances are mostly determined by the
applied density range of 850 ± 60 kgm-3. 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 DEM exceeds
the uncertainty related to the density assumption.
Glaciological versus geodetic method
Applying Eq. () to the results of our glaciological reference method
yields δ values between 0.55 and 1 (Table )
indicating that there is agreement between the glaciological and the geodetic
results well within the 90 % confidence interval .
Hence, a calibration of the reanalyzed glaciological record is not necessary
although we did not yet account for internal or basal melt.
Comparison between geodetic and glaciological mass balances for
three periods (upper three subplots) and cumulative series of annual mass
balance calculated using the set of extrapolation methods described in the
paper.
The results of the profile method also fulfill the above criteria for all
three (sub) periods and could hence also be regarded as 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 ).
However, the three automatic extrapolation methods yield results which are
persistently more negative than the geodetic method (Fig. ),
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.
Reduced discrepancies δ for all extrapolation methods used in
this reanalysis and for the original mass balance record. The upper panel
shows results without the consideration of basal and internal melt, while the
lower panel (∗) refers to δ calculated accounting for
subsurface melt. Bold values refer to agreement on the 90 % confidence
interval.
1 Agreement on the 95 %
confidence interval. 2 Not acceptable on the 95 % confidence
interval.
The role of basal and internal melt
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.,. Generally, the most important sources of energy for
subsurface melt on temperate glaciers are related to the conversion of
potential energy by water runoff inside and at the base of the glacier. The
water may originate from precipitation and other accumulation processes 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 runoff. We
applied a similar approach as used by , but, instead of
precipitation, we considered water released by melt ,
which was approximated by the reanalyzed 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. For the
period 2005 to 2013 our calculation gives a total value of 178 kgm-2. Melt caused by geothermal heat and glacier dynamics is
estimated based on values in the literature e.g., as 10 and 1 kgm-2a-1, respectively.
However, combining the estimates for
all the mentioned individual contributors during the 8-year period of 2005
to 2013 results in a total subsurface melt of 266 kgm-2, which
explains about 37 % of the difference between the glaciological and the
geodetic method during the same period.
After recalculating the reduced discrepancy δ (Eq. ),
taking the estimate for subsurface melt into account, the contour-line-based
extrapolation methods show the best agreement with the geodetic
results (Table ). While the results of the profile method are still
acceptable on the 90 % confidence interval for the periods 2005 to 2013 and
2011 to 2013 and on the 95 % confidence interval for the period 2005 to
2011, the results of the other two automatic methods (point-to-raster and
inverse distance weighting) fulfill neither the 90 % nor the 95 % criteria
for 2005 to 2013 and 2005 to 2011, respectively.
Conclusions
In this paper we have presented a detailed workflow for reanalyzing series
of annual and seasonal glacier mass balances. The approach was applied to the
10-year record of Langenferner, a small glacier in the Italian Eastern Alps.
Existing sets of annual and seasonal point mass balance data were homogenized
based on methodological corrections and were completed by pseudo-observations
of point mass balance obtained by a physical model. Based on the homogenized
point data, glacier-wide mass balances were reexamined using a variety of
extrapolation methods. Finally a detailed uncertainty assessment was
performed including a cross-check of glaciological results to those obtained
by the geodetic method.
The reanalysis revealed that common problems often neglected in mass balance
analyses can significantly disturb the derived interannual mass balance
signal. Comparing the reanalyzed results to those of the original record
yielded differences in annual mean specific mass balances of up to 384 kgm-2. This by far exceeds the uncertainties of the reanalyzed
values, which are in the range of 31 to 136 kgm-2. Considering
that two mass balance series for the same glacier and time period are
compared, the correlation of the two records is rather low (R2=0.84).
This misfit for annual balances could mainly be attributed to missing point
measurements for the upper glacier part in the original data series.
In the reanalysis, this drawback was overcome by applying a process-based
mass balance model. After a Monte Carlo-based parameter optimization, the
performance of the model was enhanced through individual precipitation tuning
for every stake and year using the observed date of ice emergence as a
constraint. The validation of modeled annual point balances against
independent observations showed a RMSD of 128 kgm-2, which is
comparable to the uncertainties of glaciological point measurements reported
in the literature. The applied model approach can consequently be regarded as
a useful tool to generate additional accurate point mass balances given that
meteorological data and snow line information such as time lapse photos or
satellite images are available.
Uncertainties due to missing updates of rapidly changing glacier geometries
represent another important source of uncertainty, especially for annual
balances. In our case this problem causes errors on the order of 20 kgm-2
after only 1 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 (R2=0.90) than for annual balances, 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 over the course of the reanalysis. Corrections for
snow from the previous hydrological year are also of considerable importance
while ice melt at the beginning of the hydrological year only plays a role in
2 years.
We also presented a thorough uncertainty analysis which is transferable to
other sites independently of the physical model applied in this study. The
analysis revealed that the typical random uncertainty of the reanalyzed mass
balances is on the order of 79 kgm-2 for annual and about 52 kgm-2
for winter mass balances. Numbers for single years/seasons
range from 31 to 136 kgm-2. The largest part of
the uncertainties can be attributed to the extrapolation of point values to
the glacier scale, which apparently depend not only on the number and
distribution of measurement points but also on annual characteristics such
as spatial balance gradients. The propagation of point scale uncertainties to
the glacier scale constitutes the second largest error source in our study
with typical values of 22 kgm-2 for annual and 10 kgm-2
for winter balances. Finally, the comparison of the cumulative reanalyzed
glaciological mass balance over the period 2005 to 2013 to the geodetic mass
balance over the same period yields agreement between the two methods,
indicating that there is no significant bias between the two methods and a
calibration of the glaciological results is hence not required.
While the calibration (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
interannual mass balance variability, as well as related uncertainties. 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 combined with sound uncertainty analyses.
All mass balance data resulting from this study were
submitted to the world glacier monitoring service. Reanalyzed point values
for annual and winter mass balance are listed in the Supplement
of this paper. Any further data or information are available on request at the
ACINN.
The Supplement related to this article is available online at https://doi.org/10.5194/tc-11-1417-2017-supplement.
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 bootstrap 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 manuscript and is the leader of the scientific
project under which the study was carried out. All authors helped to improve the
manuscript.
The authors declare that they have no conflict of interest.
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. We thank the two referees Liss M. Andreassen
and Emmanuel Thibert whose comments helped to improve the manuscript. The
work on this study was financed by Autonome Provinz Bozen – Südtirol,
Abteilung Bildungsförderung, Universität und Forschung, and the Austrian
Science Fund (FWF) grant V309-N26.
Edited by: Jon Ove Hagen
Reviewed by: Emmanuel Thibert and Liss M. Andreassen
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