Preliminary Results of Ice Stream Shear Margin Basal Melting Calculation

1
Preliminary Results of Ice Stream Shear Margin
Basal Melting Calculation

• Lucas Beem
• Ken Jezek
• CReSIS

2
Objectives

• Continuation and expansion of work done by Van
  Der Veen, Jezek and Stearns.
• Theoretically calculate the amount of basal melt
  generated along ice stream shear margin
• Create a spatial basal melt map
• Investigate potential mechanisms of streaming
  flow, onset of streaming flow and shear margin
  migration

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Area of Interest Whillans Ice Stream (formally
ice stream B) Northern Shear Margin (Snake)
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Basics

• An ice stream is a region of faster moving ice
  (up to 700 m/yr) within a larger stagnate body of
  ice (1-10 m/yr)
• With small driving force (12 kPa) there is
  likely little or no resistance to flow in main
  trunk of ice stream

• As a result, the interstream ridges need to
  support the faster ice by supplying addition
  friction through the shear margins.

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Data

• Surfacial Velocities
• GPS velocities from repeated survey.
• InSAR velocity has a much greater spatial
  coverage.

• Ice thickness from Bedmap
• Surface slope from OSUDEM

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Uncertainties

• Sensitive
• Sliding ratio
• Geometry of the transitional zone between no and
  total basal sliding
• Balance Force
• Surface Slope
• Ice Thickness

• Less sensitive
• Geothermal Heat Flux
• Rate Factor B
• Vertical Temperature Gradient
• Parameter m (depth variation of rate factor)
• Ice Stream width
• Thermal conductivity

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Process

• Calculate basal Drag (no sliding S0)
• Calculate Driving Stress and Total Resistance
• Use these to help determine the location of basal
  sliding onset through integrated excess basal
  shear
• Calculate Melt

?d ?gH?
Ftotal ?d w
Fbed ? (?b - ?d) ?y
1
?T
M (G-k ?bu(b)(1-s))
Li?
?z
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GPS derived Velocity Profile
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Basal Drag with no Sliding?bBb (
u(y)(1-S))1/n
mn1
2H
Bb 120 kPa yr1/3, m 2, n3, S0
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Integrated Excess Basal ResistanceFbed ? (?b -
?d) ?y
y
0
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Basal Drag With Sliding
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Basal Melting
Li 333.5 kJ/kg G0.06 W/m2 k 2.1 W/(m K)
0.4 K/m
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Profile Location
4
3
1
2
14
Velocity Along Snake Margin
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Basal Melting Rates Along Snake Margin (cm/yr)
4
3
1
2
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Conclusions

• Theoretically these calculations predict melting
  along ice stream margins.
• Magnitude of melting rate is still uncertain due
  to many assumptions.