### ++ Hintereisferner

**HINTEREISFERNER,
AUSTRIA**

Historical Mass Balances (1942-2011)

**Figure 1.** Hintereisferner, Austrian
Alps. Photo taken by Astrid Lambrecht in 2006

**Summary**

The historical Net, Ablation and Accumulation daily and
annual balances of the Hintereisferner, Austria are determined for
the 1942-2011 period with the PTAA model. Input to the model are
daily precipitation and temperature observations collected at the
Innsbruck weather station, located 100 km NE of the glacier,
together with the area-altitude distribution of the glacier.
The mean annual (Net) balance for this 70-year period is
-0.4 mwe, the Accumulation balance is +0.7 and the Ablation
balance is -1.1 mwe. The glacier thinned 29 meters , or 0.4
meters of ice per year during this 70-year period. The average
Equilibrium Line Altitude is 3040 meters. Comparison of measured
versus PTAA annual balances for the 1953-2011 period produced an
r^{2} of 0.47.

**Mass Balance Results**

The PTAA Mass Balance Model (precipitation-temperature-area-altitude) is applied to the area-altitude distribution shown in Figure 2 to produce daily and annual balances, using as input the daily temperature and precipitation observations at Innsbruck, Austria, located approximately 100 km northeast of Hintereisferner. Available weather records for this station are for the 1942-2012 period.

The annual mass balance for Hintereisferner averaged for 70 years (1942-2011) is -0.4 mwe (Figure 3). Total thinning is 26 mwe, or 29 meters of ice loss (Figure 4). The average Accumulation Balance is 0.7 mwe and the Ablation Balance is -1.1 mwe (Figure 5).

Mass balance terminology used in this report deviates slightly from that proposed by the IACS Working Group of Mass Balance Terminology and Methods (Cogley et al, 2011). The main variables that determine mass balance, such as precipitation, temperature, lapse rates and snowfall, are directly dependent on elevation. Glacier balance models are constructed by applying relationships between these variables (for example precipitation and temperature) to calculate mass balance as a function of elevation. The IACS study suggests that elevation should be shown on the Y axis. In this report, balance and other variables are all shown to be dependent on elevation.

In addition, the terms Accumulation Balance and Ablation Balance are preferred over Winter Balance and Summer Balance, that are used in the IACS report. Snow accumulation continues at higher elevations for this and other Alpine glaciers throughout most of the year. For many Himalayan Range glaciers, snow accumulation is greatest during the Monsoon season, from June through September, and at lower elevations ablation often occurs during the winter months.

**Figure 2.** Area-altitude distribution of
Hintereisferner. The total area of the glacier is 8.39
km^{2} and there are 124 altitude intervals spaced at 10 m,
ranging from 2475 to 3700 meters in
elevation.

Latitude 46.58 N Longitude 10.82 W

**Figure 3.** Annual balances of the
Hintereisferner, 1942-2011 period. The average annual balance is
-0.36 mwe. The minimum annual balance for the period (-2.6
mwe) occurred in 2003. The extremely negative balance this
year is due to unprecedented ablation caused by much above normal
temperatures, and an unusually low winter snowfall.

**Figure 4.** Cumulative balance of
Hintereisferner. Total thinning during this 70 year
period is 29 mwe or 0.4 m of ice per year. From 1980 to 2011,
thinning is 0.8 m of ice per year.

**Figure 5.** Accumulation and Ablation
Balances. The average annual Accumulation balance for this
period is +0.7 mwe and the average Ablation balance is -1.1
mwe. The minimum Ablation Balance for this period (-3.2 mwe)
occurred in 2003.

**Balance versus Elevation, b(z)**

The net, accumulation and ablation balances as a function of elevation are shown in Figure 6, averaged for the 1942-2011 period, Average ablation at the terminus is 2 mwe and accumulation ranges from approximately 0.3 mwe at the terminus to a maximum of 1.0 mwe above 3600 meters. The ELA is 3040 meters.

**Figure 6a.** Net, Accumulation and Ablation
balances as a function of elevation, averaged for the
1942-2011 period. The ELA is 3040 meters.

**Figure 6b.** Net, Accumulation and Ablation
balances as a function of elevation, averaged for 2003. The
ELA is 3570 meters.

**Model Calibration**

The model is calibrated by calculating the daily balance using 15 coefficients that convert precipitation and temperature observations to snow accumulation and snow and ice ablation for each elevation interval. One iteration performs this operation for each day of the full period of record and for each elevation interval, from the terminus to the head of the glacier. Both the annual balance and calibration error are calculated for each iteration.. In Figure 7a, the first 16 iterations use pre-set coefficients; the remaining are determined automatically by the simplex optimizing procedure. In Figure 7b, the annual balance and calibration error is shown for each iteration.

Optimum coefficient values are found by minimizing the error that occurs when one balance variable is regressed against another in a linear, least squares fitting process. Nine different, but not independent regressions are made for each day throughout the summer ablation season. From June 1 to- September 30, approximately 120 regressions are made for each set of variables. Thus, over 1000 regressions are run for each iteration of the Simplex. The calibration error determined for each iteration is the average root-mean-square-error (in percent of the mean) for all regressions that are run. The calibration error is minimized by simultaneously and minutely adjusting the 15 coefficients for the next iteration. Minimizing the calibration error produces an internal consistency in the processes within the PTAA model that cause snow and ice ablation and snow accumulation.

**Figure 7a.** Calibration error versus
iteration number of the optimizing simplex. Annual balances
1-15 are calculated with preset coefficients. Balances from 16
to 300 are calculated with coefficients determined by the
Simplex optimizing process. The final mean (1942-2011) balance
after about 200 iterations equals -0.4 mwe.

**Figure 7b.** Mean annual balance versus
calibration error. The mean annual balance equals -0.40 when the
calibration error is a minimum at 56 %. Each point represents
one iteration.

**Figure 8.** Daily Accumulation,
Ablation and Net Balance for the 2003 balance year. The
Accumulation Balance on September 30 = 0.5 mwe, the
Ablation Balance = -3.1 mwe, and the Net Balance = -2.6
mwe. The low snowfall and high summer temperatures caused this
year's balance to be the most negative since 1942.

**Figure 9a.** Annual balances produced by
field measurments and the PTAA model from 1953-2011.

**Figure 9b.** Measured versus PTAA annual
balances for the 1953-2011 period. The r2 for a regression
fit is 0.47.

**Wendell Tangborn**

**HyMet**

**March 14, 2013**

****

**References**

Elsberg, D., Harrison, W., Echelmeyer, K., and Krimmel, R. 2001. Quantifying the effects of climate and surface change on glacier mass balance.J. Glaciol.,47(159), 649-658.

Nelder,, J.A. and Mead, R., 1965, A simplex method for function minimization. Computer Journal, 7: 308-312.

Bhatt U.S., J. Zhang, W.V. Tangborn, and C.S. Lingle, L. Phillips, 2007: Examining Glacier Mass Balances with a Hierarchical Modeling Approach, Computing in Science and Engineering, 9 (2), 61-67. Abstract here.

Tangborn, W.V., 1997 Using low-altitude meteorological observations to calculate the mass balance of Alaska's Columbia Glacier and relate it to calving and speed. Report of a Workshop, February 28 - March 2, 1997, Byrd Polar Research Center, Report No. 15 PDF of paper here.

Tangborn, W.V., 1999 A Mass Balance Model that Uses Low-altitude Meteorological Observations and the Area-Altitude Distribution of a Glacier, Geografiska Annaler: Series A, Physical Geography Volume 81, Issue 4, December 1999, Pages: 753-765. PDF of paper here.

Zhang J. , U.S. Bhatt, W. V. Tangborn, and C.S. Lingle, 2007: Response of Glaciers in Northwestern North America to Future Climate Change: an Atmosphere/Glacier Hierarchical Modeling Approach, Annals of Glaciology, Vol. 46, 283 - 290. PDF of paper here.

Zhang, J., U. S. Bhatt, W. V. Tangborn, and C. S. Lingle, 2007: Climate downscaling for estimating glacier mass balances in northwestern North America: Validation with a USGS benchmark glacier, Geophysical Research Letters, 34, L21505, doi:10.1029/2007GL031139. PDF of paper here.