Historical and Current Mass Balances (1951-2011)
Figure 1. Bering Glacier on August 23, 1979. Photo by Austin Post. Folds on the lower glacier are indicative of a surging glacier.
The historical net, ablation and accumulation daily and annual balances of the Bering Glacier, Alaska are determined for the 1951-2011 period with the PTAA model, using daily precipitation and temperature observations collected at the Cordova and Yakutat weather stations, together with the area-altitude distribution of the glacier. The mean annual balance for this 61-year period is -0.6 mwe, the accumulation balance is + 1.4 and the ablation balance is - 2.0 mwe. Periodic surges of this glacier transported large volumes of ice to lower elevations where the ablation rate is higher, producing more negative balances. During the 1993-95 surge the average ablation balance is -3.3 mwe, over a meter greater than the 1951-2011 average.
The Bering Glacier/Bagley Icefield in Alaska, the largest glacier/icefield complex in North America, is 180 kilometers in length, ranges from sea level to 2445 meters altitude and has a total area of 4773 square kilometers. Within the past 100-200 years, the Bering Glacier began to retreat from its maximum Neoglacial position; however, in the past 100 years this retreat has been interrupted by at least six surges of substantial amplitude and duration (Molnia and Post, 1995).
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 Yakutat and Cordova, Alaska, located approximately 125 km. NW and 200 km. SE of the glacier terminus, and at elevations of 8 and 12 meters, respectively. The mean annual balance for the Bering Glacier averaged for 61 years (1951-2011) is -0.6 mwe) (Figure 4). Total thinning averaged over the glacier surface for 61 years is 39 meters of ice or 0.6 meters of ice per year (Figure 5). The mean Accumulation Balance is +1.4 mwe and the Ablation Balance is -2.0 mwe (Figure 6).
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 Bering Glacier. The total area of the glacier is 4773 km2 and there are 93 altitude intervals spaced at 50 m, ranging from 40 to 1860 meters in elevation. Latitude 60.302 N Longitude -143.20 W
Figure 3. Annual balances of the Bering l Glacier for the 1951-2011 period. The average annual balance is -0.6 mwe. The minimum balance for the period (-3.1 mwe) occurred in 2004.
Figure 4. Cumulative balance of the Bering Glacier. Total thinning during this 61 year period is 39 meters or 0.6 m of ice per year. The vertical lines at 1972 and 2003 show the period for which the volume loss determined by the PTAA and geodetic methods are compared.
Comparison with Geodetic Balances
The elevation change and volume loss of the Bering Glacier have been estimated by different authors using remote-sensing techniques (Arendt, et al, 2002, Beedle et al, 2008, Muskett, et al, 2009, Berthier et al, 2010a, Berthier et al, 2010b). For the period 1972-2003, using the 1972 USGS map as a reference, and an area of 4400 km2, the geodetic method (ASTER DEM) volume loss for the entire Bering Glacier system is 2.6 +/- 0.5 km3 w.e. a-1. For the same 31 year period, using an area of 4773 km2, the PTAA model cumulative balance change (Figure 4) is 16.8 mwe or 0.54 mwe a-1 or 2.6 km3 w.e. a-1, or precisely the same loss determined by the geodetic method.
Figure 5. Accumulation and Ablation Balances for the 1951-2011 period. The average annual accumulation balance for this period is +1.4 and the average ablation balance is -2.0 (mwe). Maximum ablation (-4.3 mwe) occurred in 2004.
Bering Surges and Mass Balance
Surges of the Bering glacier can produce an ice displacement of as much as 13 km (Post, 1972). Transporting such a large volume of ice to a lower elevation over a short time period (several months) significantly affects the mass balance by increasing ablation rates of ice. Observed surges occurred in 1958-60, 1966-67, 1981, 1993-95 and 2008-11. Each of the four surges on Bering Glacier in the period 1950 to 2000 occurred after a running total of snow (accumulation or winter balance) on the glacier was above average for five or more years, suggesting a sustained build-up of mass as one requirement for a surge. When sufficient snow has accumulated on the glacier there is evidence that a surge is triggered by an abnormal influx of water as runoff. As high rates of snow accumulation are inversely correlated with high rates of runoff, there appears to be a tendency for the Bering Glacier to alternate between surging and non-surging states depending on the timing of snowfall and runoff periods (Tangborn, 2002, in press).
Balance versus Elevation, b(z)
The net, accumulation and ablation balances as a function of elevation are shown in Figure 6a, averaged for the 1951-2011 period, and in Figure 6b for the 2004 balance year. The widespread forest files in Alaska in 2004 emitted ash and particulates that decreased the albedo of the glacier surface 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 Bering Glacier were affected by these wildfires. Ablation at the terminus increased from 5 to 14 mwe and the ELA moved up 550 m, from 1300 m average elevation to 1850 m in 2004. The annual balance in 2004 (-3.1 mwe) is the most negative for the 1951-2011 period of record.
Figure 6a. Net, Accumulation and Ablation balances of the Bering Glacier as a function of elevation, averaged for the 1951-2011 period. The ELA is 1300 meters.
Figure 6b. Net, Accumulation and Ablation balances of the Bering Glacier as a function of elevation, averaged for the 2004 period. The ELA is 1850 meters, 550 meters above average.
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 45 %), and the mean annual balance is an optimum value (about -0.6 mwe).
Figure 7a. Mean annual balance versus iteration number of the optimizing Simplex. Coefficients 1-15 are preset. Coefficients16-350 are automatically determined by the Simplex optimizing process. When the calibration error reached the minimum of about 45%, the average annual balance is -0.6 mwe.
The scatter plot in Figure 7b shows the mean annual balance versus the corresponding error for each iteration. When the error is a minimum at 45 %, the mean annual balance is -0.60 mwe. For most glaciers the balance- error distribution shows a more distinct balance value (Figure 8b in the Gulkana Glacier report shows a definite mean annual balance at the minimum calibration error). The immense size of the Bering Glacier may tend to reduce the balance-error distinction and make the determined mean annual balance less definite.
Figure 7b. Mean annual balance versus calibration error. When the calibration error reached the minimum of about 45%, the average annual balance is -.60 mwe. Each point represents the mean annual balance based on 61 years daily balance determinations.
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 demonstrates how real-time mass balances for the Bering Glacier will be displayed in future years. On September 30, 2011, the Net Balance is - 1.7 mwe, the Accumlation Balance, 1.0 mwe, and the Ablation Balance, -2.7 mwe. Analysis of the daily balances of a large number of glaciers simultaneously is expected to produce an improved understanding of glacier/climate relationships.
Figure 8. Daily balances of the Bering Glacier during the 2011 balance year.
The daily and annual mass balances of the Bering Glacier, calculated with the PTAA model for the 1951-2011 period using daily observations of temperature and precipitation at the Cordova and Yakutat weather stations and the area-altitude distribution of the glacier, show that this glacier has lost 190 km3 of mass during this 61 year period. In 2004, ash and smoke particulates from wild fires in Alaska and above normal temperatures produced a record annual balance of -3.1 mwe.
September 19, 2012
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", 2002 (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)
Arendt, A. A., Echelmeyer, K. A., Harrison, W. D., Lingle, C.
and Valentine, V. B.: Rapid wastage of Alaska glaciers and their
contribution to rising sea level, Science, 297, 382-386, 2002.
Beedle, M.J. and 7 others. 2008. Improving estimation of glacier volume change: a GLIMS case study of Bering Glacier System, Alaska. Cryosphere, 2(1), 33-51.
Berthier, E., E. Schiefer, G.K.C. Clarke, B. Menounos and F. Re´my. 2010. Contribution of Alaskan glaciers to sea-level rise derived from satellite imagery. Nature Geosci., 3(2), 92-95.
Berthier E. Volume loss from Bering Glacier (Alaska), 1972 - 2003: comment on Muskett and others (2009). Journal of Glaciology, 56(197), 555-557, 2010
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.
Cogley, J.G., R. Hock, L.A. Rasmussen, A.A. Arendt, A. Bauder, R.J. Braithwaite, P. Jansson, G. Kaser, M. Möller, L. Nicholson and M. Zemp, 2011, Glossary of Glacier Mass Balance and Related Terms, IHP-VII Technical Documents in Hydrology No. 86, IACS Contribution No. 2, UNESCO-IHP, Paris.
Molnia, B. F. and Post, A.: Holocene history of Bering
Alaska: A prelude to the 1993-1994 surge, Phys. Geogr., 16(2),
Muskett, R. R., Lingle, C. S., Tangborn, W. V., and Rabus,
T.: Multi-decadal elevation changes on Bagley Ice Valley and
Malaspina Glacier, Alaska, Geophys. Res. Lett., 30(16), 1857,
Nelder,, J.A. and Mead, R., 1965, A simplex method for function minimization. Computer Journal, 7: 308-312.
Post, Austin, 1972. Periodic surge origin of folded moraines on Bering Peidmont Glacier, Journal of Glaciology, 11, 219-226.
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.