### ++ Wolverine *

**Wolverine Glacier,
Alaska
** Real-Time and Historical Mass Balances

**Figure 1. ** The Wolverine Glacier is
located in the Kenai Peninsula, Alaska.

Photo by Rod March, US Geological Survey.

**Summary**

The PTAA Model (precipitation-temperature-area-altitude) is
applied to the area-altitude distribution of the Wolverine Glacier
using as meteorological input the daily temperature and
precipitation observations at Seward, Alaska, located 56 km NE and
at an elevation of 38 meters. Available weather records for this
station are for the 1951-2012 period. The area-altitude
distribution for the Wolverine Glacier is shown in Figure 2.
The mean annual balance for this 61-year period is -0.8 mwe, the
accumulation balance, 2.5 mwe and the ablation balance, -3.3
mwe. Annual balances for each year are shown in Figure 3.
Comparison of PTAA balances with USGS manual balance
measurements is made for the 1966-2004 period: the R^{2}
for a regression fit between manual and PTAA annual net balance is
0.57, for accumulation balances, 0.47 and for ablation balances,
0.18 mwe.

**Introduction**

Glaciologic, climatologic, and hydrologic research began at Wolverine Glacier in 1966 as part of the International Hydrological Decade program (Elsberg et al, 2001. The glacier is located in the maritime climate of southern Alaska (60° 23' N., 148° 55' W.) on the Kenai Peninsula.

**Mass Balance Results**

The annual mass balance for the Wolverine Glacier averaged for 61 years (1951-2011) is -0.8 mwe. Total thinning is -50 mws, or - 0.9 meters of ice per year (Figure 4). Annual Accumulation and Ablation Balances are shown in Figure 5. The average Accumulation Balance is 3.4 mwe and the Ablation Balance is -4.2 mwe. The elevation distribution of Net, Accumulation and Ablation balances averaged for the 1951- 2011 period are demonstrated in Figure 6. A previous, independent application of the PTAA model revealed similar balance results (Korn, 2010).

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. Therefore, it is both physically and mathematically incorrect, as well as confusing, to show elevation as being dependent on mass balance as is suggested in the IACS report. 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. For most Alaskan glaciers, snow accumulation at higher elevations occurs throughout the year and can be especially heavy in August and September. 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 (Yang, 2011).

**Figure 2. ** Area-altitude distribution of
the Wolverine Glacier. The total area of the glacier is 19.7
km^{2} and there are 44 altitude intervals spaced at 30.5 m
(100 ft), ranging from 400 to 1650 meters in elevation.

Latitude 60° 23' N Longitude 148° 55'W

**Figure 3. ** Annual balances of the
Wolverine Glacier 1951-2011 period. The average annual balance
is -0.8 mwe. The minimum annual balance for the period
(-3.3 mwe) occurred in 2004.

**Figure 4.** Cumulative balance of the Gulkana
Glacier. Total thinning during this 62 year period is 50 mwe
or 0.9 m of ice per year.

**Figure 5. ** Accumulation and Ablation
Balances. The average annual Accumulation balance for this
period is +2.5 mwe and the average Ablation balance is -3.3
mwe. The minimum blation Balance (-6.5 mwe) occurred in 2004.

**Figure 6. ** Net, Accumulation and Ablation
balances as a function of elevation, averaged for the 1951-2011
period. The ELA is 1235 meters.

**Model Calibration**

The PTAA model is calibrated by calculating the daily balance for each altitude interval and for each day of the 1951-2011 period, using 15 coefficients and a Simplex optimizing procedure (Nelder and Mead, 1962). The annual balance is found by integrating daily balances over one year.

The initial 15 coefficient values are random estimates, based on a reasonable range of potential values for each parameter. For example, the coefficient that converts gauge precipitation to basin precipitation is assigned 16 different values that vary from 0.107 to 0.288. The final value after 350 iterations and the calibration is completed is 0.2007. Similar estimates are made for the other 14 coefficients. The annual balances shown for each iteration in Figure 7a are based on the coefficient estimates of the 15 coefficients. The first 15 balances vary from approximately -1.0 to +1.0 mwe corresponding to the initial, pre-set coefficient values. As the calibration proceeds, coefficient values are determined automatically by the Simplex.

One iteration of the Simplex determines for each elevation level the daily and annual balances for the period of record, and calculates the average error that occurs when multiple balance parameters are regressed against each other. The average root-mean-square-error resulting from these regressions is minimized to obtain the optimum coefficients. The size of the error automatically determines the minute adjustment that is made to each coefficient for the next iteration. After approximately 350 iterations, the calibration error reaches a minimum (in this case about 55 %), and the mean annual dalance is an optimum value (about -0 .8 mwe). See Tangborn, 1999 for a detailed description of the PTAA Model.

**Figure 7a.** Mean annual balance versus iteration
of the optimizing Simplex. Annual balances 1-15 are derived from
preset coefficients. Balances 16-350 are calculated automatically
by the Simplex optimizing process. The final mean balance is -0.81
after 350 iterations.

**Figure 7b. ** Mean annual balance versus
calibration error. The mean balance is - 0.8 when the
calibration error is a minimum (55 %).

**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 2011 balance year shown in Figure 8 demonstrate how real-time mass balances will be displayed in the future years.

**Figure 8. ** Daily balances of the
Wolverine Glacier throughout the 2011 balance year. The
Net balance on September 30 is zero but the minimum balance (-0.3
mwe) occurred in mid-August, demonstrating the importance of snow
accumulation during the summer season in this region of Alaska.

**Comparison with USGS Manual Measured
Balances**

Annual, Accumulation (winter) and Ablation (summer) balances have been measured manually for the Wolverine Glacier by the US Geological Survey since 1966. Comparison of measured annual balances with the PTAA balances for each year is shown in Figure 9a, scatter plot comparisons of Net annual balances in Figure 9b, Ablation (summer) balances in Figure 9c, and comparison of Accumulation (winter) balances in Figure 9d.

It is noteworthy that the Ablation balance comparison for the
two methods shows a

much lower R^{2 } than the Accumulation balances
(0.18 and 0.57, respectively), which indicates greater
accuracy in simulating and measuring accumulation than measuring
ablation on this glacier (The opposite was found for the Gulkana
Glacier). The generally low R^{2} shown for these
balance comparisons reflects high measurement errors for both the
USGS and the PTAA methods of determining mass balance.

**Figure 9a. ** PTAA and
USGS annual balances of the Wolverine Glacier. The
R^{2 } from a regression of these annual balances is
0.57 (see Figure 9b).

**Figure 9b ** PTAA Annual balance
versus USGS measured balances.

**Figure 9c. ** PTAA Ablation balance
versus USGS Ablation balances.

**Figure 9d. ** PTAA Accumulation
balance versus USGS Accumulation balances.

It is emphasized that annual balances determined by this calibration process are based only on minimizing the regression errors. The regressions of PTAA versus manually measured balances, shown in Figures 9a to 9d, are made independently of the calibration.

**Conclusions**

The Wolverine glacier is steadily losing mass at a rate approximately equal to other glaciers in Alaska.

A summary of mean annual balances for glaciers studied so far:

(1951-2011 period)

MWE

Mendenhall -1.0

Gulkana -0.7

Wrangell

North-facing -0.4

South-facing -0.7

Bering -2.0

Wolverine -0.8

**Wendell Tangborn**

**HyMet**

August 31, 2012

**Links**

**Beedle, Matthew , www.GlacierChange.org**

A new website that chronicles the rapid changes in the world's
glaciers and the impact these changes are having on the lives of
all living creatures.

http://adsabs.harvard.edu/abs/2010AGUFM.C21C0560K

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.

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

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

U.S. Geological Survey Water Resources of Alaska
(2003-2006). USGS 15052500

Mendenhall R NR Auke Bay AK. (click here) accessed December 2003 -
February 2006.

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., 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., 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)