### ++ Vernagt Ferner *

**Vernagt Ferner,
Austria**

Historical Mass Balances (1942-2011)

**Figure 1**. Vernagtferener on Sept 13, 2011
(composite photos by M. Kuhn, combined by M. Weber). Commission for
Geodesy and Glaciology, Academy of Sciences, Munich, Germany

**Summary**

The historical Net, Ablation and Accumulation daily and annual balances of the Vernagtferner, 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 100km NE of the glacier, together with the area-altitude distribution of the glacier. The mean annual (Net) balance for this 70-year period is -0.03 mwe, the Accumulation balance is +0.8 and the Ablation balance is -0.8 mwe. The glacier gained mass from 1952 to 1989, then thinned from 1990 to 2011. The annual balance in 2003 was -1.7 mwe, the most negative for the period of record (70 years), caused by a combination of one of the lowest Accumulation balances on record and much above normal temperatures during the ablation season. The average Equilibrium Line Altitude is 3040 meters.

**Mass Balance Results**

The PTAA Mass Balance Model 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 Vernagtferner. Available weather records for this station are for the 1942-2012 period.

The annual mass balance for Vernagtferner averaged for 70 years (1942-2011) is -0.03 mwe (Figure 3). oss (Figure 4). The average Accumulation Balance is 0.8 mwe and the Ablation Balance is -0.8 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
Vernagtferner. The total area of the glacier is 7.92
km^{2} and there are 19 altitude intervals spaced at 50 m,
ranging from 2750 to 3650 meters in elevation. Latitude
46.866 N Longitude 10.833 W

**Figure 3**. Annual balances of the
Vernagtferner, 1942-2011 period. The average annual balance
is -0.03 mwe. The minimum annual balance for the period (-1.6
mwe) occurred in 2003. The extremely negative balance this
year is due to unprecedented ablation produced by much above normal
summer temperatures, and an unusually low winter snowfall.

**Figure 4**. Cumulative balance of
Vernagtferner. The glacier gained mass from 1952-1989
and thinned 9 meters of ice from 1990 to 2011.

**Figure 5**. Accumulation and Ablation
Balances. The average annual Accumulation balance for this
period is +0.8 mwe and the average Ablation balance is -0.8
mwe. The minimum Ablation Balance for this period (-2.2 mwe)
occurred in 2003, and is partly due to the below normal
Accumulation balance of 0.55 mwe.

**Balance versus Elevation**

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. Accumulation ranges from 0.5 mwe at the
terminus to 1.0 mwe at 3600 meters. The ELA is 3040 meters compared
to 3120 meters that is observed for the 1965-2011 period.

**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 for Vernagtferner 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
300 iterations equals -0.02 mwe.

**Figure 7b**. Mean annual balance versus
calibration error. The mean annual balance equals -0.02 when the
calibration error is a minimum at 52%. Each point represents one
iteration. At the end of each iteration a retrospective is applied
to seek ways to improve the process for the next
iteration.

**Real-time Glacier Balances**

One goal of the PTAAGMB project is to continuously monitor all 200 glaciers in the set and display the current mass balance of each one, in real-time if up-to-date weather observations are available, or near real-time if weather observations are delayed. The daily balances for the 2003 balance year shown in Figure 7 demonstrate how real-time mass balances will be displayed in the future years

**Figure 8**. Daily Accumulation,
Ablation and Net Balance for the 2003 balance year. On
September 30, 3003 the Accumulation Balance = 0.5
mwe, Ablation Balance = -2.2 mwe, and Net
Balance = -1.7 mwe. The low snowfall and high summer temperatures
made this year's balance the most negative for the period of
record.

**Comparison of Manual With PTAA Balances**

Annual balances have been measured for Vernagtferner using the
glaciological method since 1965 (reference). Retrospective balances
are calculated independently with the PTAA model for the 1942-2011
period. Comparison of annual balances for the 1965-2011 period
produced by the two methods are shown in Figure 9a. It is
emphasized that the PTAA balances are
produced without beforehand knowledge of the
manually measured balances. Calibration of the model is
accomplished by minimizing the error of regressing balance
variables that are calculated internally. The vaiance that is shown
in Figure 9b is caused by balance errors in both methods.

**Figure 9a ** Annual balances of the
manually measured and the PTAA balances for the 1965-2011
period.

**Figure 9b** Manually measured annual
balances versus PTAA balances. The R^{2} for a
regression fit is 0.67 and the average PTAA balance tends to be
0.15 mwe lower than manually measured balances. Both methods
contribute to the scatter shown for this regression.

**Figure 9c** Ablation balances of the
manually measured and the PTAA for the 1965-2011
period.. Both methods contribute to the scatter shown for
this regression.

**Figure 9d** Annual balances of the
manually measured and the PTAA Accumulation balances for the
1965-2011 period. . Both methods contribute to the
scatter shown for this regression.

**Conclusions**

The mass balance of Vernagtferner is generated daily and
annually using the daily

precipitation and temperature observations collected at the
weather station in Innsbruck, Austria, and the area-altitude
distribution of this glacier. The accuracy of the annual
balances and the distribution of balance with altitude appears to
be approximately equal to accuracy produced by manually
measured balances using the glaciological method.

**Wendell Tangborn**

**HyMet**

**November 4,2012**

****

**Links**

Beedle, Matthew ,www.GlacierChange.org

A new website that chronicles the rapid changes in the world's
glaciers.

Korn, D., "Modeling the mass balance of the Wolverine Glacier Alaska USA using the PTAA model", American Geophysical Union, Fall Meeting 2010 (Abstract here)

Korn, D., MA Thesis: "Glacier and climate fluctuations in South-Central Alaska as observed through the PTAA model" ( David Korn MA Thesis, PDF)

Medley, B., MS Thesis: "A Method for Remotely Monitoring Glaciers with Regional Application to the Pacific Northwest" ( Brooke Medley MS Thesis, PDF)

Tangborn, W., "Mass Balance of Glaciers in the Wrangell Range, Alaska Determined by the PTAA Model" ( Draft paper here)

Tangborn, W., "Mass Balance, Runoff and Internal Water Storage of the Bering Glacier, Alaska (1950-96), A Preliminary Report" (Draft paper here)

Tangborn, W., "Connecting Winter Balance and Runoff to Surges of the Bering Glacier, Alaska" (Draft paper here)

Tangborn, W. and Rana, B., "Mass Balance and Runoff of the Partially Debris-Covered Langtang Glacier, Nepal" (Draft paper here)

Wood, J., MS Thesis: "Using the Precipitation Temperature Area Altitude Model to Simulate Glacier Mass Balance in the North Cascades" ( Joseph Wood MS Thesis, PDF)

**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, oi:10.1029/2007GL031139. PDF of paper here.