++ Mendenhall

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

Figure 1.  The Mendenhall Glacier is located in the Alaska Coastal Range.  The glacier thinned nearly 50 meters between 1958 and 2011 when these photos were taken.

Photo Credits: Millett, Marion T. 1958 Mendenhall Glacier: From the Glacier Photograph Collection. Boulder, Colorado USA: National Snow and Ice Data Center/World Data Center for Glaciology. Digital media.
The 2011 image used with permission from Matthew J. Beedle and GlacierChange.org

Summary

The historical net, ablation and accumulation daily and annual balances of the Mendenhall Glacier, Alaska is determined for the 1951-2011 period with the PTAA model, using daily precipitation and temperature observations collected at the Juneau weather station, together with the area-altitude distribution of the glacier. The annual balance for this 61-year period is  -1.0 mwe, the accumulation balance is +1.5 and the ablation balance is -2.5 mwe. The glacier thinned 50 meters, or 0.8 meters of ice per year during this period. The average Equilibrium Line Elevation  is 1210 meters and 1420 meters in 2004 when the balance was a record minimum. Total ablation in 2004 for the entire glacier is 230 10 6 m3, about 10 times the calving loss. Thus, iceberg calving into Mendenhall Lake has a minor effect on the glacier's annual balance.

Mass Balance Results

The PTAA mass balance (precipitation-temperature-area-altitude) model is applied to the glacier's area-altitude distribution shown in Figure 2, using as input the daily temperature and precipitation observations at Juneau, Alaska, located approximately 9 km south of the Mendenhall glacier. The annual mass balance for the Mendenhall Glacier averaged for 61 years (1951-2011) is -1.0 mwe (-.09 km3) (Figure 4). Total thinning averaged over the glacier surface was 50 meters of ice (Figure 5). The Accumulation Balance is +1.5 mwe (+0.14 km3) and the Ablation Balance is -2.5 mwe (0.23 km3) (Figure 6).  Comparison of  PTAA annual balances with balances produced manually by the Glaciological Method for five years by the University of Alaska shows agreement in sign only (Table 1, Boyce, 2008 ). The large difference between the two methods can be partly attributed to the difficulty of manually measuring both ablation and  snow accumulation over a glacier that is nearly 100 km2 in area.

Figure 2.  Area-altitude distribution of the Mendenhall Glacier. The total area of the glacier is 94 km2 and there are 183 altitude intervals spaced at 10 m, ranging from 40 to 1860 meters in elevation.  Distributions were calculated and provided by Matthew Beedle.

Latitude  58.50 N  Longitude 134.53 W

Figure 3.  Annual balances of the Mendenhall Glacier for the  1951-2011 period. The average annual balance is -1.0 mwe.  The minimum balance for the period (-2.4 mwe) occurred in 2004.

Figure 4.  Cumulative balance of the Mendenhall Glacier. Total thinning during this 62 year period is 50 meters or 0.8m of ice per year.

Figure 5.  Accumulation and Ablation Balances for the 1951-2011 period. The average annual accumulation balance for this period  is +1.5 and the average ablation balance is -2.5 (mwe).  Maximum ablation (-4.2 mwe) occurred in 2004.

 ** 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). 

Effect of Iceberg Calving on Mass Balance

Iceberg calving into Mendenhall Lake has a minor effect on the glacier's annual balance.  The largest recorded calving loss, observed during the summer of 2004, was approximately 17 million cubic meters of ice (Boyce, 2008).  Ablation at the terminus, from 40 to 50 meters elevation, during the same period was -13 mwe, or 18 106 m3 translated to ice volume, nearly equal the observed calving loss. Total ablation in 2004 for the entire glacier is 230 10 6 m3, about 10 times the calving loss. It is noteworthy that annual mass balance in 2004 was -2.4 mwe, the most negative balance determined during the 1951-2011 period.  It is likely the cause of the large calving event and terminus collapse 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, and in Figure 6a for the 2004 balance year.  The widespread forest files in Alaska in 2004 emitted ash and particulates that decreased the albedo of glacier surfaces and strongly affected mass balances (Figures 3 and 5).  The contrast between b(z) curves in Figures 6a and 6b demonstrate how ablation and the ELA of Mendenhall Glacier were affected by these wildfires.  Ablation at the terminus increased from 9 to 13 mwe and the ELA moved up 210 m, from 1210 m average elevation to 1420 m in 2004. The annual balance in 2004 (-2.4 mwe) is the most negative for the 1951-2011 period of record.

Figure 6a.  Net, Accumulation and Ablation balances as a function of elevation averaged for the 1951-2011 period. The ELA is 1210  meters.

Figure 6b.  Net, Accumulation and Ablation balances as a function of elevation for the 2004 balance year. The  ELA is 1420 meters, 220 m above the 1951-2011 average. Ablation at the terminus is -13 mwe, 4 mwe  greater than the average.


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 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. Figure 7 shows the progression of errors throughout the calibration process.  

Figure 7.  Calibration error versus iteration number of the optimizing Simplex.  Coefficients 1-15 are preset.  Coefficients 16-350 are determined by the Simplex optimizing process.   When the calibration error reached the minimum of  about  30%,  the average annual balance is -1.0 mwe, the Simplex closed and the final coefficients saved.


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 future years.    

Figure 8.   Daily balances: Net (b),  Accumulation (c) and Ablation (a), (b = c + a) throughout the 2011 balance year.  The Net Balance is nearly equal to the Accumulation Balance from October 1, 2010 to approximately May 1, 2011 because negligible ablation occurred during the winter season.  On September 30, 2011, the annual balance is - 0.3 mwe, the Accumulation balance +1.52 mwe and the Ablation balance -1.82 mwe

Conclusions

The daily and annual mass balances of the Mendenhall Glacier are calculated with the PTAA model for the 1951-2011 period using daily observations of temperature and precipitation at the Juneau weather station 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 University of Alaska for five years.  The agreement between modeled and measured balances is poor.  Ablation at the terminus in 2004 determined by the model was -13 mwe, or 18 106 m3 translated to ice volume, nearly equal the observed calving loss.

Wendell Tangborn

HyMet

May 12,  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

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

Boyce, E. 2006. Instability and retreat of a lake-calving terminus, Mendenhall Glacier,
Southeast Alaska. (MS thesis, Univ. AK, Fairbanks.)

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.

Motyka, R., O'Neel, S., Connor, C., and Echelmeyer, K. 2002. Twentieth century thinning of Mendenhall Glacier, Alaska, and its relationship to climate, lake calving,
and glacier run-off. Global Planet. Change, 35, 93-112.

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. nwis.waterdata.usgs.gov. Accessed December 2003 - February 2006.

Van der Veen, C. J. 1996. Tidewater calving. J. Glaciol., 42(141), 375-385.

Van der Veen, C. J. 2002. Calving glaciers. Proc. in Phys. Geogr., 26(1), 96-122.
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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.