Page 599 - Geosystems An Introduction to Physical Geography 4th Canadian Edition

aQuantitativeSOLUTiOn Glacier Mass Balance
Mass balance calculation is a method used to monitor the behav- iour of glaciers and can give an indication, if a long enough time series exists, of the regional warming or cooling of climate. Net mass balance is total accumulation (gains of mass) minus total ablation (losses of mass) over a given time which is normally one year. A positive net balance implies that the glacier accumulation is greater than the ablation in a given time period; a negative
net balance implies that there is greater ablation than accumula- tion. Across the surface of the glacier, there is an elevation where accumulation and ablation annually are equal—this is marked by the equilbrium line.
Table AQS 17.1 shows a sample mass balance data set for a 15-year period. Values in the table are expressed with units metres of water equivalent (m w.e.). Total mass gained or lost by the glacier has been converted into the equivalent depth of liquid water (density of 1 g·cm−3) averaged over the entire glacier surface area. Mass balance values are provided for the “winter season” (when accumulation exceeds ablation; thus mass balance is positive) and the “summer season” (when ablation exceeds accumulation; mass balance is negative). Annual net balance can be calculated as the sum of winter and summer values.
To discern whether there is a trend in a glacier’s mass balance, cumulative net mass balance is calculated. To cumulate values in a series, each value is added to the sum
of the previous values. For year 1, there is no previous value, so the cumulative net balance is the net balance of year 1 (−0.05 m w.e.). For year 2, the annual net balance of year 2 (+0.12 m w.e.) is added to the value for year 1, giving a cumulative value of +0.07 m w.e. For year 3, the annual net balance of year 3 (−0.04 m w.e.) is added to the previous sum (+0.06 m w.e.), giving +0.03 m w.e. This procedure is contin- ued down to the end of the series.
Inspection of the mass balance graph in Figure AQS 17.1 reveals that the amount of accumulation in a given year is not a direct indication of the amount of ablation. Note that for the first 8 years in this sample data set, accumulation, ablation, and net glacer mass values fluctuate annually but there is little cumulative change (+0.19 m w.e.). For the last 7 years, however, all of the net mass balance values are negative, the cumulative mass balance
is −2.94 m w.e., and there is a clear trend—the glacier is losing mass and shrinking. Such a trend is indicative of climate change (higher air and ocean temperatures)—and accelerating anthro- pogenic warming.
TABLE AQS 17.1 Sample Glacier Mass Balance Data1 (all values in metres of water equivalent, m w.e.)
Year in Series
Winter Season
Summer Season
Net Mass Balance
Cumulative Balance
1 0.95 3 1.57 5 0.71 7 1.08 9 0.55
11 0.96 13 0.98 15 1.13
−1.00 −0.05 −1.61 −0.04 −0.25 0.46 −1.39 −0.31 −1.64 −1.09 −1.88 −0.92 −1.17 −0.19 −1.20 −0.07
−0.05 0.03 −0.42 −0.39 −0.90 −2.05 −2.45 −2.94
2
1.12
−1.00
0.12
0.07
4
0.69
−1.60
−0.91
−0.88
6
1.29
−0.95
0.34
−0.08
8
1.44
−0.86
0.58
0.19
10
1.12
−1.35
−0.23
−1.13
12
1.39
−1.60
−0.21
−2.26
14
1.35
−1.77
−0.42
−2.87
1Winter and summer mass balance data for gulkana glacier, alaska, 1966–1980, acquired from USgS alaska Science Center, Water resources Office at ak.water.usgs.gov/glaciology/gulkana/balance/index.html.
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