The Cryosphere, 9, 25–35, 2015
www.the-cryosphere.net/9/25/2015/
doi:10.5194/tc-9-25-2015
© Author(s) 2015. CC Attribution 3.0 License.
Quantifying mass balance processes on the Southern
Patagonia Icefield
M. Schaefer1,2, H. Machguth3, M. Falvey4, G. Casassa5,6, and E. Rignot7,8
1Instituto de Ciencias Físicas y Matematicas, Facultad de Ciencias, Universidad Austral de Chile, Valdivia, Chile
2Instituto de Ciencias Marinas y Limnológicas, Facultad de Ciencias, Universidad Austral de Chile, Valdivia, Chile
3Arctic Technology Centre, Technical University of Denmark, Kgs. Lyngby, Denmark
4Department of Geophysics, Universidad de Chile, Santiago, Chile
5Geoestudios, Las Vertientes, San José de Maipo, Chile
6Universidad de Magallanes, Punta Arenas, Chile
7Jet Propulsion Laboratory, Pasadena, CA, USA
8University of California, Department of Earth System Science, Irvine, CA, USA
Correspondence to: M. Schaefer (mschaefer@uach.cl)
Received: 9 April 2014 – Published in The Cryosphere Discuss.: 11 June 2014
Revised: 15 November 2014 – Accepted: 20 November 2014 – Published: 6 January 2015
Abstract. We present surface mass balance simulations of
the Southern Patagonia Icefield (SPI) driven by downscaled
reanalysis data. The simulations were evaluated and interpreted
using geodetic mass balances, measured point balances
and a complete velocity field of the icefield for spring
2004. The high measured accumulation of snow of up to
15.4 m w.e. yr−1 (meters water equivalent per year) as well
as the high measured ablation of up to 11 m w.e. yr−1 is reproduced
by the model. The overall modeled surface mass
balance was positive and increasing during 1975–2011. Subtracting
the surface mass balance from geodetic balances,
calving fluxes were inferred. Mass losses of the SPI due to
calving were strongly increasing from 1975–2000 to 2000–
2011 and higher than losses due to surface melt. Calving
fluxes were inferred for the individual glacier catchments and
compared to fluxes estimated from velocity data. Measurements
of ice thickness and flow velocities at the glaciers’
front and spatially distributed accumulation measurements
can help to reduce the uncertainties of the different terms in
the mass balance of the Southern Patagonia Icefield.
1 Introduction
The Southern Patagonia Icefield (SPI, Fig. 1) is the largest
ice mass in the Southern Hemisphere outside of Antarctica.
The great majority of its outlet glaciers have been retreating
and thinning at high rates in recent decades (Rignot et al.,
2003; Masiokas et al., 2009; López et al., 2010; Willis et al.,
2012b; Davies and Glasser, 2012; White and Copland, 2013).
Mass balance processes for most of the glaciers of the SPI,
however, are poorly quantified, which makes it difficult to
understand the reasons for the fast ice loss from the SPI. Increase
in surface melt, decrease in accumulation or changes
in the ice dynamics are possible candidates. Another explanation
could be sub-glacial volcanic activity (Orihashi et al.,
2004) which is supported by the fact that the SPI co-locates
with four volcanoes of the Andean Austral Volcanic Zone
(Stern, 2004, 2008).
Locally varying warming trends have been observed in
southern South America in the last century with rates up to
0.028 ◦C yr−1 next to the Atlantic Ocean (Rosenblüth et al.,
1995; Ibarzabal y Donangelo et al., 1996; Rasmussen et al.,
2007; Falvey and Garreaud, 2009). Large interannual and
inter-decadal variations of precipitation have been observed
in Patagonia, although with no significant overall trends in
the last century (Rosenblüth et al., 1995; Carrasco et al.,
2002; Aravena and Luckman, 2009).
Prominent acceleration of the ice flow (and therefore ice
losses due to calving) were detected at the Jorge Montt
(Rivera et al., 2012a) and Upsala glaciers(Jaber et al., 2012;
Published by Copernicus Publications on behalf of the European Geosciences Union.
26 M. Schaefer et al.: Quantifying mass balance processes on the SPI
Figure 1. The Southern Patagonia Icefield (SPI): false color composite
of Landsat ETM+ satellite image mosaic; names of examined
glacier catchments in black; yellow triangles mark the positions
of some of the meteorological stations that were used to validate
the downscaling of the reanalysis data; red dots mark direct
surface mass balance measurements on the SPI (1–6); the four active
volcanoes that co-locate with the SPI are represented by red triangles.
The yellow crosses with numbers mark individual measurements
of fjord depth provided by the Chilean Navy Hydrographic
and Oceanographic Service (SHOA). Inset: position of the SPI in
southern South America.
Sakakibara et al., 2013). For both glaciers a fast retreat was
observed together with the acceleration.
The surface mass balance was modeled for two glaciers
of the SPI: Chico (Rivera, 2004) and Perito Moreno (Stuefer
et al., 2007), both using degree-day models. For the period
1975–2001, Rivera (2004) obtained an average negative
yearly surface mass balance of the Chico glacier, which
showed high interannual variations and a slightly negative
trend. Stuefer et al. (2007) obtained a near-zero cumulative
glacier mass balance for the Perito Moreno glacier between
1973 and 2000, with the annual specific balances varying between
+1 and −1 m w.e.
A combined modeling approach was recently applied on
the Northern Patagonia Icefield (NPI) (Schaefer et al., 2013):
global meteorological data were downscaled using the regional
climate model Weather Research and Forecasting and
statistical downscaling techniques. These data were used to
drive a surface mass balance model of intermediate complexity
(Oerlemans, 2001; Machguth et al., 2009). An increase
of accumulation was detected over the NPI during 1975–
2011. The increased observed mass loss of the NPI in 2000–
2011 (Willis et al., 2012a) as compared to 1975–2000 (Rignot
et al., 2003) was explained by an increase of losses by
calving.
In this paper, a similar methodology is applied to make
first inferences of the components of the mass balance of the
SPI as a whole and for its individual glacier catchments. We
give a summary of the methods applied in Sect. 2. In Sect. 3
we present the results and discuss them; in Sect. 4 we draw
the conclusions of our study.
2 Methods
To obtain realistic meteorological input data for the surface
mass balance model in the modeling period 1975–2011, a
downscaling procedure has been realized, which includes a
number of steps (Schaefer et al., 2013). As a first step, version
3.2 of the Advanced Research Weather Research and
Forecasting model (WRF model hereafter) was run for a 7year
period from 2005 until 2011, using a nested computational
grid (five-point relaxation zone between grids), with
the inner grid having a spatial resolution of 5 km over an area
of 675 km × 425 km that includes both the NPI and SPI. The
model was forced at its boundaries by NCEP-NCAR atmospheric
reanalysis data (Kalnay et al., 1996), which consist
of three-dimensional atmospheric fields on a 2.5◦ resolution
grid at 6 h intervals. The WRF model’s output was saved at
hourly intervals, which were used to yield the daily averages
required by the surface mass balance model. To obtain
downscaled meteorological data for the entire 1975–2011 period,
statistical downscaling techniques were applied similar
to the ones used to relate local climate observations to
large-scale atmospheric parameters that are predicted by lowresolution
global circulation models (Fowler et al., 2007).
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M. Schaefer et al.: Quantifying mass balance processes on the SPI 27
Figure 2. Maps of (a) downscaled incoming solar radiation over SPI; (b) annual surface mass balance of the SPI (green line denotes zero
mass balance); (c) annual averaged glacier surface mass balance. All maps show averages of 1975–2011.
The basic assumption is that local variability (which in this
case is simulated rather than observed) is to a large extent
controlled by the overriding synoptic conditions, and that
long-term changes in these synoptic conditions are the key
drivers of long-term changes in local variables. The series
of daily fields of precipitation, temperature and incoming
shortwave radiation for the period 2005–2011 are modeled
in terms of 11 predictors taken from the NCEP-NCAR reanalysis
data at a grid point some 250 km upstream (west)
of the NPI, which include atmospheric temperature, relative
humidity, zonal moisture flux and meridional moisture flux
at different pressure levels (Schaefer et al., 2013). The correlations
between the daily averaged output of the WRF model
and the statistical downscaling technique at the different grid
points range between 0.65 and 0.80 for precipitation, 0.85
and 0.93 for temperature and 0.56 and 0.77 for solar radiation
and indicate that the statistical downscaling is applicable.
A further downscaling of the input data of the mass balance
model is realized to obtain input data with a resolution
of 180 m, the resolution used for the surface mass balance
model. Temperature and precipitation are “physically interpolated”
by applying constant lapse rates (−0.65 ◦C/100 m
and 5%/100 m, respectively) and incoming solar radiation on
the 180 m grid is computed by comparing the radiation computed
for the 5 km grid with calculations from clear-sky radiation
on the 180 m grid (Schaefer et al., 2013; Corripio,
2003).
In the surface mass balance model, ablation was calculated
according to a simplified energy balance model (Oerlemans,
2001; Machguth et al., 2009): the net short-wave radiation
was determined by the incoming solar radiation and three different
albedo values for snow (0.7), firn (0.45) and ice (0.3),
while the sum of the net long-wave radiation and the turbulent
fluxes was approximated by a linear function of the air
temperature. Since the SPI is situated in a relatively mild,
maritime climate, the ice is supposed to be temperate, so we
assume that ice which melts at the surface will not refreeze
but immediately run off from the SPI. Accumulation at every
grid cell was defined as solid precipitation, which is as
a fraction of the total precipitation that varied between zero
and one depending on the air temperature of the grid cell
(Schaefer et al., 2013).
3 Results and discussion
3.1 Climate
The result of the downscaling process are daily maps of the
surface mass balance input variables temperature, incoming
solar radiation and precipitation at the resolution of the mass
balance model. In Fig. 2a, we present the annual mean incoming
solar radiation (averaged over 1975–2011). The radiation
pattern can be divided in two main parts: the central
and western part of the icefield, where yearly average
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28 M. Schaefer et al.: Quantifying mass balance processes on the SPI
incoming solar energy is below 70 W m−2, and the eastern
part which corresponds to the lower part of the eastern outlet
glaciers, where the incoming solar radiation is much higher,
reaching values of up to 150 W m−2 on some glacier tongues.
On the tongues of some northwestern outlet glaciers, the incoming
solar radiation is also higher than in the central part
of the icefield (up to 100 W m−2). These results of incoming
solar radiation reflect well the climatic situation on the
SPI, where nearly all year long clouds are blocked by the
high peaks of the icefields, which reduces the incoming solar
radiation. East of the high peaks, cloudiness decreases and
incoming solar radiation increases. Several glacier tongues
in the northwest of the icefield reach out of this permanent
sea of clouds and receive more solar radiation than the center
part of the icefield. The downscaled average precipitation
map shows a strong increase with elevation due to the generation
of orographic precipitation in the regional climate
model. East from the Andes main ridge, the modeled precipitation
decreases rapidly. The temperature decreases with
elevation as expected. The results of the downscaling of the
meteorological data was compared in detail to meteorological
data (Schaefer et al., 2013). Subsequently a calibration
of the surface mass balance model has been realized using
mass balance measurements in the NPI. Since the climatological
situation on the SPI is very similar to the NPI we
use the same calibration for the SPI and present surface mass
balance simulations for the set of model parameters that performed
best on the NPI (Schaefer et al., 2013).
3.2 Distributed surface mass balance
In Fig. 2b we present the distributed annual surface mass balance
averaged over 1975–2011. A very positive surface mass
balance of up to 20 m w.e. is obtained for the very high peaks
of the icefield. On the flat plateau, the surface mass balance
is between 0 and 5 m w.e. and on the outlet glacier tongues
it reaches down to −15 m w.e. The direct (point) observations
of the surface mass balance on the SPI are restricted
to a network of ablation stakes with changing configuration
on the Perito Moreno glacier during 1995 and 2003 (Stuefer
et al., 2007), a tower installed near the equilibrium line
of the Chico glacier where yearly surface mass balance values
at one point were obtained from 1994 to 2002 (Rivera,
2004) and four firn cores in the accumulation areas of the
Moreno (Aristarain and Delmas, 1993), Tyndall (Shiraiwa
et al., 2002), Chico (Schwikowski et al., 2006) and PioXI
glaciers (Schwikowski et al., 2013). In Fig. 3 we compare
the results of our simulations to these direct point measurements
of the surface mass balance. Satisfactory agreement
can be observed between the modeled and the measured data
for the ablation data. In the accumulation area, however, in
two cases the modeled accumulation is much higher than
the observed one. These two points correspond to firn cores
taken on high peaks in the accumulation areas of the Perito
Moreno and PioXI glaciers. The probably large amounts
−10 −5 0 5 10 15
−10
−5
0
5
10
15
measured surface mass balance in m w.e
modeledsurfacemassbalanceinmw.e.
1
2
4
5
3 6
Figure 3. Comparison between measured and simulated surface
mass balance: numbers correspond to places marked in Fig. 1. The
values in the accumulation area are yearly accumulation values,
while the ablation data are summer, winter or yearly values depending
on the availability of data. The uncertainties of the measurements
are indicated as error bars in the x direction if available.
of snow falling at this locations do not persist on the windexposed
peaks (Schwikowski et al., 2013). Indeed, some ice
core drilling sites were specifically chosen to minimize accumulation
compared to the surroundings, to obtain longer time
series in the shallow ice cores (Schwikowski et al., 2006).
The process of wind drift, however, is not incorporated in
the model, which likely explains the difference between observed
and modeled values. These local effects are important
when comparing point measurements with modeled surface
mass balance, but should have a less important role when
estimating the surface mass balance of larger areas such as
glacier basins or even the entire SPI, since the drifted snow
will most probably contribute to the accumulation in another
part of the icefield. Since the wind direction is predominantly
west, the snow drift could, however, diminish the accumulation
on western windward glacier basins and increase the
accumulation on the eastern leeward glacier basins.
3.3 Evolution of net mass balance values of the SPI
The evolution of the annual accumulation, surface ablation
and surface mass balance from 1975 to 2010 for the
SPI as a whole are presented in Fig. 4. A high interannual
variability and an increasing overall trend (0.054 ± 0.012 m
w.e. yr−2) of the surface mass balance can be observed. Both
the variability and the increasing trend is determined by the
accumulation. Furthermore, maxima in accumulation (e.g.,
1990, 1998, 2009) are accompanied by minima in ablation,
since the higher amounts of snow present in these years reduces
the albedo of SPI surface. The variation of measured
yearly precipitation at the selected stations in Fig. 4 is similar
to the variation of the modeled accumulation. This is a
good confirmation of the model’s results, considering that
measured precipitation data are not direct input data of the
model. The average specific melt on the SPI in 1975–2011
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M. Schaefer et al.: Quantifying mass balance processes on the SPI 29
1980 1990 2000 2010
−2
0
2
4
6
Year
Annualspecificbalancesinmw.e.
smb
ablation x (−1)
accumulation
Bahia Felix
Puerto Chacabuco
Caleta Tortel
Figure 4. Annual specific accumulation, ablation and surface mass
balance (smb) averaged over the SPI from 1975–2010 and yearly
measured precipitation sums for selected weather stations in the
region: Bahía Felix (52◦58 S, 74◦08 W) south of the SPI, Puerto
Chacabuco (45◦26 S, 72◦49 W) north of the NPI and Caleta Tortel
(47◦47 S, 73◦32 W) between NPI and SPI.
is 2.63 m w.e. yr−1, and the average specific accumulation
4.87 m w.e. yr−1. The percentage of solid precipitation of the
overall precipitation was 59 %, which leads to an average of
8.36 m of yearly precipitation over the SPI for 1975–2011.
This value is 19 % higher than the 7 m inferred by Escobar
et al. (1992), analyzing water discharge data from the
1960s to the 1980s. The higher average precipitation over the
SPI obtained by our model can be explained by the increase
of accumulation (caused by an increase of precipitation) in
the 2000s (Fig. 4). The average modeled precipitation over
SPI is slightly higher than the value of 8.03 m modeled for
the NPI (Schaefer et al., 2013). It is expected that the total
amount of precipitation over the SPI is higher than on the
NPI, since wind speeds, which correlate strongly with precipitation
in this region, increase to the south (Garreaud et al.,
2012; Lenaerts et al., 2014).
When analyzing another important component of the mass
balance of the SPI, namely mass losses due to calving, we
will transform the modeled mass losses to losses in volume
of ice. We can convert the modeled specific mass changes
due into surface processes to changes of volume in ice Vsurf
by multiplying them with the surface area of the SPI and dividing
by the density of ice (900 kg m−3). Knowing the total
volume change Vtotal of the SPI from geodetic mass balance
surveys (Rignot et al., 2003; Willis et al., 2012b), we
can calculate the calving losses from the SPI according to
Qc = Vsurf − Vtotal. (1)
For 1975–2000 we obtain an increase of ice volume
due to surface processes of 27.7 km3 yr−1. Together with
the observed volume loss of 16.7 ± 0.9 km3 yr−1 observed
for this period by Rignot et al. (2003), we obtain calving
losses of Qc =44.4 km3 yr−1. For 2000–2011 we obtain
from the observed volume loss of 21.2 ± 0.4 km3 yr−1
(Willis et al., 2012b) and the modeled increase in volume
due to surface processes of 40.1 km3 yr−1 calving losses of
Qc =61.3 km3 yr−1. The uncertainties associated with these
inferred calving fluxes from the SPI are high. It is difficult
to a priori constrain the uncertainties associated with
the modeled ice volume change due to surface mass balance
(see Sect. 3.5), and we therefore try to learn about these uncertainties
by comparing inferred calving fluxes to calving
fluxes estimated from velocity measurements at the different
glacier catchments (Sect. 3.6, Table 1). Also, the uncertainties
associated with the geodetic balances might be higher
than stated by their authors: both authors of the geodetic
balances assume that all volume change is due to ice loss
and therefore convert volume loss to mass loss assuming a
density of 900 kg m−3. Willis et al. (2012b) details volume
loss for ablation area and accumulation separately. If we assume
that the volume loss in the accumulation area is due
melt of firn with a density of 550 kg m−3, the corresponding
ice loss would be lower and the calving fluxes would
lower to Qc = 56.8 km3 yr−1. Although assuming large uncertainties
on the inferred overall calving losses of SPI, we
can still state that a strong increase in calving losses took
place, which is supported by an acceleration of the glaciers
of SPI (Jaber et al., 2012; Rivera et al., 2012a; Sakakibara
et al., 2013). For comparison, the modeled yearly accumulation
over the SPI for 1975–2000 corresponds to 66.7 km3 of
ice per year and 73.1 km3 of ice per year for 2000–2011, and
the modeled melt from SPI is 39.0 km3 yr−1 for 1975–2000
and 33.0 km3 yr−1 for 2000–2011. This means that the inferred
losses due to calving are higher than losses by melt in
both periods. In all these conversions, we used the SPI reference
area of 13 000 km2 from Rignot et al. (2003) to convert
the specific values to overall change for 1975–2000 and the
area of 12 100 km2 (Willis et al., 2012b) for 2000–2011.
3.4 Surface mass balance of the individual glacier
catchments
Apart from the overall trend in the mass balance components
of the SPI, it is interesting to analyze the individual
glacier catchments as closed systems, to be able to quantify
the different contributions of the terms of the mass balance
for the different glaciers. However, due to the large flat areas
on the SPI, the definition of the catchments (especially
in the northern part of the SPI) is not unique and probably
also changes with time (Rivera et al., 2012a). In Fig. 2c,
we present the 1975–2011 average specific annual surface
mass balance of the individual glaciers using the catchments
defined in the Randolph Glacier Inventory (RGI) (Arendt,
2012). In the northern part of the SPI (north of 49.5◦ S)
the main glaciers have annual glacier surface mass balances
ranging from slightly negative (Chico glacier −1.58 m w.e.)
to clearly positive (PioXI glacier 3.45 m w.e.). The only
exception is the Occidental glacier, having a clearly negative
annual surface mass balance (−4.85 m w.e.). Since this
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30 M. Schaefer et al.: Quantifying mass balance processes on the SPI
Table 1. 1975–2011 average altitude of zero surface mass balance (ELA) computed by the model and the average altitude of the snow line at
the end of summers 2002 and 2004 computed by De Angelis (2014) (column 1 and 2). Inferred calving fluxes according to Eq. (1) using the
geodetic mass balance measurements of Rignot et al. (2003) for the period 1975–2000 and of Willis et al. (2012a) for 2000–2011 (column 3
and 4). Calving fluxes based on a velocity map from spring 2004 (column 5) and explicit data used to compute these fluxes (columns 6–8).
Column 9 indicates if the calving fluxes computed from the velocity field agree within one standard deviation with the inferred fluxes for
1975–2000 (R) or 2000–2011 (W) or both (RW).
Qc
Qc Inferred Qc Inferred from velocities Agreement
Glacier ELA (m) SLA (m) 1975–2000 2000–2011 spring 2004 Wtot V H within
1975–2011 De Angelis 2014 (km3 yr−1) (km3 yr−1) (km3 yr−1) (km) (km yr−1) (m) 1σ
Amalia 861 930±40 0.78±0.05 (0.92–0.96)±0.07 0.42±0.35 2.45 0.57 300±250 R
Asia 918 800±20 0.32±0.03 (0.48–0.50)±0.05 0.26±0.21 0.85 1.00 300±250 RW
BGOT 1068 945±30 1.54±0.18 (1.72–2.12)±0.18 1.80±1.03 12.51 0.48 300±250 RW
CV 1438 1264±24 −1.00±0.24 (1.86–2.25)±0.09 0.36±0.30 1.97 0.41 230±180 –
Europa 995 940±30 no data (2.75–2.81)±0.08 0.41±0.34 0.92 1.48∗ 300±250 –
Grey 1021 980±50 1.33±0.05 (1.51–1.55)±0.10 0.39±0.32 2.17 0.47 300±250 –
HPS12 983 1150±30 no data (1.38–1.43)±0.05 0.55±0.46 0.80 2.29∗ 300±250 –
HPS13 967 1140±60 no data (1.37–1.38)±0.04 1.07±0.89 0.94 3.80∗ 300±250 W
HPS15 928 950±50 no data (0.85–0.88)±0.04 0.55±0.46 0.92 2.00∗ 300±250 W
HPS19 981 1070±60 no data (1.37–1.42)±0.06 0.43±0.36 0.75 1.93∗ 300±250 –
HPS29 951 1170±70 0.47±0.02 (0.57–0.60)±0.05 0.52±0.43 1.22 1.41 300±250 RW
HPS31 951 990 ±51 1.07±0.03 (1.04–1.08)±0.06 0.41±0.34 0.75 1.80∗ 300±250 –
HPS34 869 1240±100 1.32±0.03 (1.66–1.72)±0.06 0.85±0.71 1.89 1.50∗ 300±250 RW
Jorge Montt 1112 930±40 1.96±0.10 (1.43–1.58)±0.06 1.20±0.54 2.10 2.59 220±50 W
O’Higgins 1282 1200±20 2.15±0.15 (2.97–3.27)±0.13 1.78±0.52 2.33 2.25 340±100 R
Penguin 955 1070±70 no data (4.61–4.72)±0.08 0.83±0.69 1.20 2.30∗ 300±250 –
Perito Moreno 1150 1230±40 0.99±0.04 (1.44–1.57)±0.08 0.44±0.16 4.90 0.65 140±50 –
Pío XI 1055 930±50 3.69±0.32 (5.99–6.35)±0.14 2.69±1.71 9.82 1.74∗ 200±100 R
Tyndall 899 940±10 0.83±0.06 (1.58–1.69)±0.11 0.14±0.08 2.28 0.35 181±100 –
Upsala 1249 1170±30 1.75±0.17 (4.67–5.05)±0.08 2.41±0.40 2.64 1.52 540±100 R
∗ Velocity data that were taken from a point farther than 1 km upstream of the glacier front.
glacier does not show an exceptional retreat or thinning behavior
(López et al., 2010; Willis et al., 2012b), we think
that the exceptionally negative glacier surface mass balance
is caused by an erroneous delineation of glacier catchments
where parts of the glacier’s accumulation area were considered
as belonging to neighboring glaciers. The PioXI glacier
has the most positive annual surface mass balance in the area,
which agrees with the advance of the glacier observed until
recently (Rivera et al., 1997). In the middle–southern part
of the SPI (between 49.5 and 50.5◦ S), the annual surface
mass balance of the western glaciers are very positive (up to
10.0 m w.e. for glacier HPS13) and moderately positive for
the eastern glaciers. The very positive modeled surface mass
balance of the western glaciers agrees with the accumulation
area ratios of > 0.8 observed at these glaciers (Aniya
et al., 1996; Casassa et al., 2013). At the periphery of the
SPI, several small glaciers can be spotted in Fig. 2c which
often exhibit negative surface mass balance, which is in good
agreement with the high relative area loss observed at these
glaciers (Davies and Glasser, 2012).
A characteristic parameter of a glacier is the altitude at
which accumulation and ablation are of same magnitude, the
equilibrium line altitude (ELA). We present 1975–2011 averaged
ELAs computed by the model in Table 1. For comparison
we also present the average snow line altitude (SLA)
at the end of the summers 2002 and 2004 computed recently
by De Angelis (2014). For several glaciers (Amalia, Europa,
Grey, HPS15, HPS19, HPS31, Penguin, Perito Moreno) the
model ELAs agree with the average SLA at the end of the
summers 2002 and 2004 within twoσ. At the glaciers Asia,
BGOT, CV, O’Higgins, Pío XI, Upsala and Jorge Montt the
average model ELA is higher than the average SLA at the
end of the summers 2002 and 2004. This discrepancy can
be explained by the possibility of snowfalls before the acquisition
of the examined satellite images and by the high
interannual variability of the surface mass balance (Fig. 4).
This idea is supported by the observation of an SLA at the
end of the summer 1986 of 1300 m at the O’Higgins glacier
(Aniya et al., 1996), which is even higher than the model average
ELA. The model ELAs are considerably lower than the
average SLA at the end of the summers 2002 and 2004 for
the glaciers HPS12, HPS13, HPS29 and HPS34. This could
also be due to the interannual variability of the surface mass
balance; however, since the SLA at the end of the summer
tends to underestimate the ELA rather than to overestimate it
(due to possible snowfalls on the SPI during the whole year),
this could also indicate a local overestimation of the surface
mass balance by the model at these glaciers. At HPS34 the
SLA at the end of the summer 1986 of 900 m (Aniya et al.,
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M. Schaefer et al.: Quantifying mass balance processes on the SPI 31
1996), agrees much better with the average model ELA than
the SLA computed by De Angelis (2014).
3.5 Sources of uncertainties for the modeled surface
mass balance
We want to point out that our surface mass balance modeling
approach is subject to different uncertainties, which are
difficult to quantify in a systematic way. Several reanalysis
data sets were suspected to have spurious increases in precipitation
at high southern latitudes due to the inclusions of
new data sets (Nicolas and Bromwich, 2011). Regional climate
models still have problems with correctly quantifying
orographic precipitation, which was the reason why we had
to apply a global correction factor to the precipitation data
(Schaefer et al., 2013). This factor could vary spatially and
temporally. Also, no direct air temperature data from the icefield
itself were available to validate the modeled temperatures.
The acquisition of climate data on the icefield itself
would be very valuable to be able to better constrain the uncertainties
of the model results.
3.6 Calving losses of the individual glaciers
In addition to mass losses due to surface melt, nearly all major
outlet glaciers of the SPI have additional mass losses due
to calving (Warren and Aniya, 1999), which makes the total
mass balance of the glaciers negative. Calving fluxes Qc
can be inferred for the individual catchments using Eq. (1)
again. In Table 1 we present the inferred calving fluxes in
1975–2000 and 2000–2011 for the most important outlet
glaciers of the SPI. Since the ice divides in the flat parts
of the SPI are difficult to determine, in Table 1 we present
the Bernardo, Greve, Occidental and Tempano glaciers in the
north of the SPI as one glacier (BGOT). We did the same for
the Chico and Viedma (CV) glaciers which share the glacier
plain around the Paso de los Cuatro glaciers. The errors indicated
for the inferred calving fluxes presented in Table 1
are the inherited (quantifiable) uncertainties of the geodetic
measurements. They should not be interpreted as the total
uncertainty of the inferred fluxes, since the (unknown) uncertainties
of the model results are not included. For calving
fluxes inferred for 2000–2011, we present a range, which is
obtained by converting the volume loss in the accumulation
area detected by Willis et al. (2012b) to mass loss, using the
density of firn (550 kg m−3) as the lower limit and the density
of ice (900 kg m−3) as the upper limit.
To validate the inferred calving fluxes, we computed calving
fluxes from a complete velocity field of the SPI obtained
from a speckle-tracking analysis of RADARSAT-1 images
from September to November 2004. For every glacier we
computed the average velocity at the front V and derived
calving flux from the width at the front W, V and the average
ice thickness at the front H. The latter, however, was
mostly unknown. Bathymetric measurements of the water
bodies in which the glaciers are calving were available for
the glaciers Jorge Montt (Rivera et al., 2012b), O’Higgins
(unpublished data), Perito Moreno (Rott et al., 1998), Upsala
(Skvarca et al., 2003), PioXI (Warren and Rivera, 1994) and
Tyndall (Raymond et al., 2005), which provided a good constraint
to the ice thickness at the front. There are bathymetric
measurements from the Chilean Navy Hydrographic and
Oceanographic Service (SHOA) in many Patagonian fjords
as well, but mostly they do not extend towards the glacier
fronts. In Fig. 1 we present some point measurements from
SHOA. Therefore, for most of the other glaciers, an ice thickness
of 300 ± 250 m was assumed, which means that we assign
a 68 % probability to the event that at an arbitrary calving
glacier tongue of the SPI has an ice thickness between 50
and 550 m. This is supported by our experience that calving
glaciers of similar size normally have ice cliffs of 50 m and
larger and are normally not able to persist in water bodies of
depth greater than 500 m. For the Chico glacier we estimated
H = 100±50 m. Calving fluxes were computed according to
Qc = V · H · W, where the products were obtained for every
tongue and summed up in the case of several tongues (BGOT
for example). The obtained calving fluxes, together with the
explicit data for mean velocity, tongue width and estimated
ice thickness are presented in Table 1 as well. The uncertainties
of the calving fluxes estimated from the velocity field are
dominated by the uncertainties of the ice thickness.
The comparison of the inferred calving fluxes with the
calving fluxes computed from the velocity field in spring
2004 shows that the inferred calving fluxes are systematically
higher. One immediate explanation for this is the fact
that at the glacier fronts the method of speckle-tracking analysis
of RADARSAT-1 images does not work very well due to
the loss of coherence induced by fast ice deformation which
changes the characteristic patterns of the glacier over the 24day
cycles of the satellite. Therefore the data presented in Table
1 do not always correspond to the glacier’s velocity right
at the glacier front. Since calving glaciers normally show
high shear rates at the glacier fronts, for example the San
Rafael glacier (Willis et al. (2012a)), this leads to an underestimation
of the calving flux. This might explain the discrepancy
between inferred calving fluxes and the calving fluxes
estimated from the velocity measurements for the glaciers
Europa, HPS12, HPS19 and Penguin, where clearly higher
velocity has been registered for the period 2005–2011 using
cross-correlation techniques with satellite images (M. Willis,
personal communication, September 2014).
Not very coherent data on calving fluxes could be inferred
for the CV glacier complex. In 1975–2000, Rignot et al.
(2003) detected very low thinning (0.01±0.25 m w.e.), while
the model is producing a negative glacier surface balance,
which produces the negative calving fluxes. We think that in
this case, Rignot et al. (2003) underestimated the thinning
of the glacier, since it contradicts the considerable area loss
and retreat of the glacier detected during 1986–2001 (Davies
and Glasser, 2012; White and Copland, 2013). Here it has
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32 M. Schaefer et al.: Quantifying mass balance processes on the SPI
to be noted that the annual balances for Argentinean glaciers
in Rignot et al. (2003) are in reality averages over the period
1968–2000 and that the digital elevation model generated
for the Argentinean glaciers in 1968 has a much lower
precision than the digital elevation model of Chilean glaciers
from 1975. On the other hand, the high thinning observed in
2000–2011 seems to disagree with the moderate calving estimated
from the velocity data. However newer velocity data
from the Viedma glacier (Riveros et al., 2013) indicate front
velocities 3 times higher than our data, which would bring
the calving flux estimation into better agreement with the inferred
fluxes for 2000–2011.
For the glaciers Moreno, Grey and Tyndall the velocity
data from the speckle-tracking analysis of RADARSAT-1
images are available at the front of the glaciers. And for the
Perito Moreno glacier, similar velocity data were obtained
before and after 2004 (Rott et al., 1998; Ciappa et al., 2010).
Still, the inferred calving fluxes are much higher than the
ones estimated from the velocity data. According to Eq. (1),
this disagreement could be due to a local overestimation
of the modeled surface mass balance or an overestimation
of the volume losses by the geodetic mass balances. Since
the thinning observed in the geodetic mass balances (Rignot
et al., 2003; Willis et al., 2012b) at the Perito Moreno glacier
contradicts its stable behavior with even some advances observed
during the end of the 20th century and the beginning
of the 21st century, we computed calving fluxes assuming
a total glacier mass balance of zero at the Perito Moreno
glacier. In this case we would obtain Qc = 0.78 km3 yr−1 for
1975–2000 and Qc = 1.10 km3 yr−1 for 2000–2011. These
inferred calving fluxes are still clearly higher than the ones
estimated from velocity data, and we therefore examine the
modeled surface mass balance at the Perito Moreno glacier
in more detail.
3.7 Mass balance of the Perito Moreno glacier
In Fig. 5 we present the modeled 1975–2011 average specific
surface mass balance as it varies with altitude. In the
same graph, we present the specific surface mass balance
profile obtained by Stuefer et al. (2007) for the balance year
1999/2000 using a degree-day model calibrated with stake
measurements in the ablation zone between 1995 and 2003
and precipitation data from a precipitation climatology which
was extrapolated to the glacier assuming a linear precipitation
increase below the ELA and a precipitation increase determined
by a curve which asymptotically approached a maximum
precipitation value at an elevation of 2500 m above
the ELA. This maximum precipitation value was adjusted to
obtain an overall mass balance of zero of the glacier. Furthermore,
we show the specific surface mass balance profile
obtained by De Angelis (2014) using a degree-day model
for ablation as well and stochastically modeled precipitation,
which was also constrained by an inferred total accumulation
value. Furthermore we show a bilinear profile obtained by
-20 -10 0 10 20
0
500
1000
1500
2000
2500
3000
Specific surface mass balance in m w.e.
Elevationinm
this study
Stuefer2007
De Angelis2014
Bilinear
Figure 5. Specific surface mass balance profiles for Perito Moreno
glacier obtained from this study (blue), Stuefer et al. (2007) (reddashed)
and De Angelis (2014) (green dotted). Theoretical bilinear
profile for comparison.
assuming a constant specific surface mass balance gradient
of 0.0135 m w.e. m−1 in the ablation zone and of 0.0075 m
w.e. m−1 in the accumulation zone. The profiles agree relatively
well in the ablation zone. The profiles of De Angelis
(2014) and Stuefer et al. (2007) have a slightly lower specific
surface mass balance at lower elevations. In the accumulation
zone, the profiles show strong differences. Stuefer et al.
(2007) assumed an upper limit 7.6 m of precipitation which
constrains the accumulation above 2500 m elevation. De Angelis
(2014) obtained a very pronounced kink in the specific
surface mass balance profile at an elevation of 1700 m. The
bilinear profile, by definition, has a kink at the ELA, while
in our modeled profile the specific surface mass balance continues
to increase with altitude in the accumulation area at a
similar rate as in the ablation area. The consequence of this
strong increase is a very high specific surface mass balance of
around 17.5 m w.e. at an elevation of 2800 m. This high gradient
of the surface mass balance in the accumulation area
is producing an elevated surface mass balance for the entire
glacier which causes the overestimation of the calving fluxes
when applying Eq. (1). Since the accumulation which determines
the specific surface mass balance profile above the
ELA was tuned by the other two studies (De Angelis (2014)
and Stuefer et al. (2007)) to match the overall observed zero
mass balance of the glacier, their profiles probably quantify
better the surface mass balance at higher altitudes. However,
without having spatially distributed accumulation measurements
at our disposal, we can not judge which of the specific
surface mass balance profiles quantifies best the accumulation
on the Perito Moreno glacier.
Another explanation for a local overestimation of the calving
fluxes computed by Eq. (1) could be the existence of an
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M. Schaefer et al.: Quantifying mass balance processes on the SPI 33
additional process of mass loss which is not accounted for in
the equation. Since there are four active volcanoes that coincide
with the southern part of the SPI (see Fig. 1), volcanic
activity could induce sub-glacial melt which would lower the
mass balance of the glaciers and possibly explain the discrepancy
between inferred calving fluxes and measured ones.
However, assuming a high constant geothermal heat flow of
1000 mW m−2 (mean heat flow over the continental crust is
65 mW m−2) would only lower the specific mass balance by
0.09 m w.e. On a glacier like Perito Moreno, for example, this
would only cause an additional mass loss of 0.03 km3, a very
low value compared to the high mass turnover of the glacier
and the large uncertainties concerning the calving fluxes.
4 Conclusions
In this contribution we present a first quantification of mass
balance processes for the Southern Patagonia Icefield. We
conclude that the surface mass balance of the SPI is positive
and that it was increasing during 1975–2011. The increase
and the variability of the modeled surface mass balance was
determined by the accumulation which was 67.7 km3 of ice
per year on average in 1975–2011. The modeled average surface
melt was 36.5 km3 of ice per year and showed good
agreement with sparse data from stakes. Using overall balances
from geodetic mass balance surveys, calving fluxes
could be inferred from the modeled surface mass balance.
The inferred losses due to calving showed a strong increase
from 44.4 km3 (1975–2000) to 61.3 km3 ice per year (2000–
2011). In both cases they were higher than losses due to melt
of snow and ice (39 km3 of ice per year for 1975–2000 and
33 km3 for 2000–2011). Since due to scarcity of validation
data the uncertainties of the modeled surface mass balance
are difficult to constrain, the uncertainties of these numbers
are relatively high. Additionally, geodetic mass balance surveys
are subject to important uncertainties, because of the often
unknown density in the accumulation area of the glaciers.
Assigning a density of 550 kg m−3 (instead of 900 kg m−3)
to the mass loss in the accumulation area of SPI, for example,
would lower the inferred calving fluxes in 2000–2011 to
56.8 km3 yr−1.
Comparison of the inferred calving fluxes of the most important
outlet glaciers with calving fluxes estimated from a
velocity field obtained in spring 2004 showed satisfactory
agreement for several glaciers. However, the uncertainties of
the calving fluxes estimated from the velocity data are large,
due to the mostly unknown ice thickness at the glaciers’
fronts. On some glaciers the inferred calving fluxes overestimate
the losses due to calving. Therefore, the inferred overall
calving fluxes should be better interpreted as an upperboundary
estimate.
Long-term velocity measurements and ice-thickness measurements
at the calving front of the glaciers are necessary
to better constrain the calving losses from the SPI, which
would help significantly to reduce the uncertainties of surface
mass balance reconstructions as well. Ablation measurements
at more glaciers (especially at the western side of the
SPI) could help to better judge the performance of surface
mass balance models on the SPI. Since precipitation is one of
the most uncertain outputs of regional climate models, spatially
distributed accumulation measurements could help to
better judge the performance of these models. Appropriate
sites for accumulation measurements are smooth and rather
flat areas in the central plateau of the accumulation area of
the glaciers at elevations of about 1500 m a.s.l. and not wind
exposed peaks and ridges where snow drift dominates the accumulation
patterns.
Author contributions. M. Schaefer, H. Machguth and G. Casassa
designed the overall research, M. Falvey ran the regional climate
model and did the statistical downscaling, M. Schaefer ran
the surface mass balance code and wrote the manuscript, E. Rignot
provided the velocity data and all authors commented on the
manuscript.
Acknowledgements. The authors would like to thank the Chilean
Weather Service (DMC) and the Chilean Water Directory (DGA)
for providing meteorological data, Andres Rivera for sharing
the data of his PhD thesis, Mike Willis for sharing the glacier
outlines used in his work and anticipating his unpublished velocity
data, Hernán De Angelis and Martin Stuefer for sharing their
mass balance profile data electronically and the Chilean Navy
Hydrographic and Oceanographic Service (SHOA) for providing
bathymetric data for the Patagonian fjords. We would like to
thank Mauricio Pelto, Helmut Rott and an anonymous reviewer,
whose comments helped to significantly improve the manuscript.
M. Schaefer is FONDECYT Postdoc Fellow (project no. 3140135).
This work was partly supported by funding from the ice2sea
programme from the European Union 7th Framework Programme,
grant no. 226375. Ice2sea contribution no. 168.
Edited by: J. L. Bamber
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