++ Gulkana *

Gulkana Glacier, Alaska
Historical  Mass Balances (1951-2011)

Figure 1.  The Gulkana Glacier is located in the Alaska Range.   Gulkana Glacier is thinning rapidly,  now losing approximately 0.8 meters of ice each year. 

Photo by Rod March, 2003, US Geological Survey.


The historical net, ablation and accumulation daily and annual balances of the Gulkana Glacier, Alaska is determined for the 1951-2011 period with the PTAA model, using daily precipitation and temperature observations collected at the Big Delta and McKinley Park weather stations, together with the area-altitude distribution of the glacier.  The annual balance for this 61-year period is  -0.7 mwe, the accumulation balance is +0.6 and the ablation balance is -1.3 mwe. The glacier thinned 47 meters , or 0.8 meters of ice per year during this period.  Regression of PTAA  balances with USGS manually measured balances for this period produced an R2 of 0.51 for annual, 0.01 for accumulation and 0.58 for ablation balances. The average Equilibrium Line Altitude for this period is 1970 meters.

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 McKinley Park and Big Delta, Alaska, located approximately 182 km and 87 km, respectively,  north of Gulkana Glacier.  Available weather records for these stations are for the 1951-2012 period.

The annual mass balance for the Gulkana Glacier averaged for 61 years (1951-2011) is -0.7  mwe  (Figure 3). Total thinning was 42 mwe, or 47 meters of ice loss (Figure 4). The average Accumulation Balance is  0.6 mwe  and  the Ablation Balance is -1.3  mwe  (Figure 5) **.

** The terms Accumulation Balance and Ablation Balance are preferred over Winter and Summer balance.  In many parts of the world (including Alaska) snow accumulation at higher elevations occurs throughout the summer season (June - September).  In some regions ablation frequently occurs at lower elevations during the winter season.  

Figure 2. Area-altitude distribution of the Gulkana Glacier.  The total area of the glacier is 19.7 km2 and there are 44 altitude intervals spaced at 30.5 m (100 ft), ranging from 1130 to 2440 meters in elevation.  
Latitude 63.27 N   Longitude 145.42 W

Figure 3.  Annual balances of the Gulkana Glacier 1950-2011 period. The average annual balance is -0.68 mwe.  The minimum annual balance for the period (-3.5 mwe) occurred in 2004.  The extremely negative annual balance this year is due to unprecedented ablation caused partly by widespread forest fires that greatly reduced  the albedo of the Gulkana and many other glaciers in the Alaska Range.

Figure 4. Cumulative balance of the Gulkana Glacier.  Total thinning during this 61 year period is 42 mwe or 0.7m of ice per year

Figure 5.  Accumulation and Ablation Balances.  The average annual Accumulation balance for this period is +0.6 mwe and the average Ablation balance  is -1.3 mwe.  The minimum Ablation Balance for this period (-4.0 mwe) occurred in 2004.

Balance versus Elevation , b(z)

The net, accumulation and ablation balances as a function of elevation are shown in Figure 6, averaged for the 1951-2011 period,  Ablation at the terminus is 3 mwe and  accumulation ranges from approximately 0.3 mwe at the terminus to a maximum  of 0.8 mwe above 2000 meters.  The ELA is1970 meters.

Figure 6.  Net, Accumulation and Ablation balances as a function of elevation,  averaged for the 1951-2011 period. The ELA is 1970 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. One iteration of the Simplex determines 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 calibration  error automatically determines the slight adjustment that is made to each coefficient for the next iteration. Figure 7a shows the progression of annual balances throughout the calibration process.  Figure 7b shows the relationship between the mean annual balance and the calibration error.  See Tangborn, 1999 for a detailed description of the PTAA Model.

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

Figure 7a. Calibration error versus iteration of the optimizing Simplex. Coefficients 1-15 are preset. Coefficients16-300 are determined by the Simplex optimizing process.

Figure 7b. Mean annual balance versus calibration error. The mean annual balance equals -0.70 when the calibration error is 38 %

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 7 demonstrate how real-time mass balances will be displayed in the future years.  

Figure 8.  Daily Accumulation, Ablation and  Net Balance for the 2011 balance year. The  Accumulation Balance on September 30  = 0.5 mwe,  the Ablation Balance  =  -0.8 mwe, and the Net Balance = -0.3 mwe.

Comparison with USGS Manually Measured Balances

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

It is noteworthy that the Ablation balance comparison for the two methods shows  a much higher R2  than the Accumulation balances (0.58 and 0.0, respectively), which signifies greater accuracy in simulating and measuring ablation than measuring accumulation on this glacier.  The generally low R2 shown for these balance comparisons reflects high measurement errors for both the USGS and the PTAA methods of determining mass balance.

Figure 9a.    PTAA Annual balances  and  USGS Annual balances. The R2    from a linear regression of these annual balances is 0.51.

Figure 9b.    PTAA Annual balance versus USGS Annual balances

Figure 9c.    PTAA Ablation balance versus USGS Ablation balances

Figure 9d.     PTAA Accumulation balance versus USGS Accumulation balances


The daily and annual mass balances of the Gulkana Glacier are calculated with the PTAA model for the 1951-2011 period using daily observations of temperature and precipitation at two low-elevation weather stations and the area-altitude distribution of the glacier.  Comparison of annual balances determined with the model are made with manual field balances measured by the USGS.  Regression of modeled versus measured balances produced R2 of  0.51 for Annual, 0.58 for Ablation and 0.01 for Accumulation Balances.

Wendell Tangborn


May 11, 2012



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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

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