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Auxiliary Material for
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Melt water input from the Bering Glacier Watershed into the Gulf of Alaska
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Edward G. Josberger, Robert A. Shuchman, Liza K. Jenkins, K. Arthur Endsley
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(Michigan Tech Research Institute, Michigan Technological University, Ann Arbor, MI)
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Journal of Geophysical Research, 2014
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Found in this Supplementary Section are additional details on how the discharge estimates were
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calculated and supporting data for determining melt rate. Supplementary Table 1 provides the
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input data values used to calculate discharge. Conceptually, discharge from melting ice or snow
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is calculated as the product of the ground cover area of ice or snow as measured from satellite
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remote sensing, the respective melt coefficient, and the Melt Degree Days (MDD). The melt
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coefficient relates the amount of water-equivalent melt produced for every MDD and is thus
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given in units of meters water equivalent (mweq) per MDD. It is a linear reference of the column
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of water produced from melting a column of ice or snow. The melt coefficients derived for this
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analysis, based upon the in-situ melt measurements, are presented in Table 1 of the main article
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text. The ice coefficient used is the average from sites B02, B03, B04, and B05 (3.68
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mweq/MDD x 10-3). The snow coefficient is from site B06 (2.76 mweq/MDD x 10-3). The
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formulas for annual discharge from melting ice or snow are given as:
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[𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒]𝐼𝑐𝑒 = [𝑀𝑒𝑙𝑡 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡]𝐼𝑐𝑒 × [𝑀𝐷𝐷𝑠] × [𝐴𝑟𝑒𝑎]𝐼𝑐𝑒
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[𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒]𝑆𝑛𝑜𝑤 = [𝑀𝑒𝑙𝑡 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡]𝑆𝑛𝑜𝑤 × [𝑀𝐷𝐷𝑠] × [𝐴𝑟𝑒𝑎]𝑆𝑛𝑜𝑤
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MDDs are calculated for each summer melt season as the sum of positive mean daily
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temperature when the ambient temperature rises above freezing (0° C). The observation window
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for this analysis is April 1 to October 31 of each year. This is based on the assumption of very
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little melt (discharge) during the winter months (see Supplemental Figure 1). Total discharge is
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taken to be the sum of the respective contributions of ice and snow melt and the contribution
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from liquid precipitation:
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[𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒] 𝑇𝑜𝑡𝑎𝑙 = [𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒]𝐼𝑐𝑒 + [𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒]𝑆𝑛𝑜𝑤 + ([𝐿𝑖𝑞𝑢𝑖𝑑 𝑃𝑟𝑒𝑐𝑖𝑝. ] × [𝐼𝑐𝑒 𝐴𝑟𝑒𝑎])
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For the future scenarios, the ice and snow area inputs are an average of the 2002-2012 record.
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The contributions to discharge from precipitation are similarly an average of the known record
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and therefore these estimates are based on temperature only and not future changes in cloud
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cover or precipitation.
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Supplementary Table 1. Total yearly discharge estimates for the Bering Glacier watershed
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are presented as well as the input data used to calculate discharge.
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Year
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
future (+1°C)
future (+2°C)
future (+4°C)
future (+6°C)
Liquid
Precipitation (m)
1.18
1.20
1.04
1.60
1.71
1.24
1.72
1.34
0.95
1.26
1.28
Melt Degree
Days
1829
1861
2025
2049
1844
1803
1721
1820
2077
2043
1673
1960
2174
2602
3030
Ice Area (m2)
2389750000
3122875000
2545000000
2720187500
2934250000
2507187500
2921151274
1909500000
2287375000
2432312500
1713458278
2498458823
2498458823
2498458823
2498458823
Discharge from Discharge from
Snow Area (m2)
Ice (km3)
Snow (km3)
3521437500
16.10
17.78
2835875000
21.40
14.57
3434687500
18.98
19.20
3523000000
20.53
19.92
2950250000
19.93
15.02
3471375000
16.65
17.27
3241687500
18.51
15.40
4085625000
12.80
20.52
3677312500
17.50
21.08
4034500000
18.30
22.75
5080312500
10.56
23.46
3623278409
18.03
19.60
3623278409
20.00
21.74
3623278409
23.94
26.02
3623278409
27.88
30.30
Discharge from
Precipitation
Total Yearly
(km3)
Discharge (km3)
2.83
36.70
3.73
39.70
2.66
40.83
4.34
44.79
5.03
39.97
3.11
37.03
5.03
38.94
2.56
35.88
2.18
40.76
3.06
44.11
2.19
36.20
3.34
40.97
3.34
45.08
3.34
53.30
3.34
61.52
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Direct discharge estimates for the Bering Glacier watershed are non-existent, however a field
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program in 2003 and 2004 carried out discharge measurements in the Seal River which drains
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the majority of the watershed. These Accoustic Doppler Current Profiler (ADCP) measurements,
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water level measurements in Vitus Lake and ocean tidal elevation predictions from NOAA were
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used to develop and calibrate a hydrodynamic model of the flow in Seal River [Josberger et al.
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2010]. Over a tidal cycle, for 2003 and 2004, the average daily discharge was 1550 m3/s in 2003
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and 2250 m3/s in 2004. As Supplemental Figure 1 shows, the hydrology of this region is greatly
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reduced during the winter the winter months. Using these ADCP measurements and assuming a
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four or six month melt season, discharge values range, respectively, from 16.1 to 24.1 and 23.3
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to 34.9 km3. These values compare favorably to the calculations derived in the watershed
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discharge analysis presented in this study. However, the calculations from ADCP measurements
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are smaller. This is expected as they represent only a portion of the watershed. In addition, other
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contributions include ground water transport through the porous, unconsolidated sediments that
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make up the barrier between the lake and the ocean, and discharge from peripheral streams that
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do not flow into Vitus Lake, notably the Bering River that flows out of Berg Lake.
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Supplemental Figure 1 displays a comparison between a moving monthly average of the water
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level of Vitus Lake, as measured in-situ, and ambient air temperature measured by a National
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Weather Service station in nearby Cordova, AK approximately 140 km to the west. The
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correspondence in trend, despite the moving average (which shifts the air temperature curve
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slightly forward in time), is compelling. As the water level in this proglacial lake is dominated by
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discharge from the Bering [Josberger et al. 2010], this correlation of air temperature and water
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level suggests that, in turn, ambient air temperature drives discharge from the Bering, which is
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the underlying assumption of temperature index modeling for glacier ablation [Hock, 1999;
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Ohmura, 2001].
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Supplementary Figure 1: This figure shows a representative example of Vitus Lake level: a
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moving monthly average of lake level as measured in-situ compared to a moving monthly
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average of the air temperature in Cordova, AK from June 2008 - July 2009.