Mass Balance: Theory and Application

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Mass BalanceTheory and Application

• Steve Wilson

South Cascade Glacier - 1928
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South Cascade Glacier - 2004
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Outline

• Basics
• Methods
• Stratigraphic
• Annual
• Hydrologic
• Photogrammetric
• Flux Gate (Ice Sheets)
• South Cascade Glacier
• Comparative Methods
• Dynamics

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Mass Balance Basics

• The bank account model
• Bn vs. bn
• Measurements made
• twice a year
• Net balance (October 1)
• Winter balance (May 1)
• Summer balance (calculate)

• Wavering between the profit and the loss.
• -T.S. Eliot, Ash Wednesday

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Stratigraphic Method

• Similar to annual mass balance method
• Direct measurement of accumulation and ablation
• Very labor intensive

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Terminology

• Stratigraphic balance vs. annual balance
• Mass balance is a time transgressive process
  using time dependent variables and methods

from Mayo et al. (1972)
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from Mayo et al. (1972)
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Measurement Tools

• Selecting representative points
• Mapping transient snow line
• Measurement tools
• Surface area estimations

• R. Hock (2008)
• Calculated mass balance can depend on glacier
  outlines, number of measurements, human error,
  and other factors.

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Measurement Points
from Kaser et al. (2003)

• Established positions
• Stakes/pits should cover even elevation
  distribution
• Account for velocity

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Transient Snow Line

• Early Season

• Late Season

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ELA

• Low ELA/sharply defined
• High ELA/sharply defined
• ELA separated from ice by old firn

• Bn
• Increased accumulation following years of Bn
• Bn more negative than in preceding years

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Measurement Tools

• Probes, stakes, pits, and cores
• Material properties

from Kaser et al. (2003)
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Surface Area

• 1992

• 1993

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Hydrologic Method

• (square ?)
• Where is the glacier?
• Accounts for internal water storage
• Primarily used in conjunction with other methods

from Krimmel (1995)
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Photogrammetric Method

• Requires high accuracy
• Works on ice, difficult on snow
• Elevation change at a specific point due to
  multiple processes
• Timing is critical
• Still requires snow/firn densities

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Flux Gate

• Primarily used on ice sheets
• Accumulation
• Total accumulation over grounded ice
• Ablation
• Annual ice flux across grounding line

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South Cascade Glacier

• Benchmark Glacier
• Multiple mass balance methods used and compared
• Long term glaciological and meteorological records

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South Cascade GlacierMass Balance
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Internal Consistency

• Meier and Tangborn (1965) use three methods on
  South Cascade Glacier
• (squares ?)

• Photogrammetric values and directly measured
  balance should be equal
• Can be checked against hydrologic data to check
  for consistency or water storage

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Emergence Velocity

• Describes relationship between net balance, flow,
  and thickness changes
• Submergence in the accumulation area
• Emergence in the ablation area
• Crossover pointequilibrium ELA

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The End
Be careful where you dig!!!
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References

• Fountain, A.G., Krimmel, R.M., Trabant, D.C., A
  Strategy for Monitoring Glaciers United States
  Geological Survey, Circular 1132, 25 p.
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• Hock, R., Hulth, J., Pettersson, R., 2008, Mass
  Balance of Storglacieren American Geophysical
  Union, Fall Meeting 2008, abstract C11D-0527
• Kaser, G., Fountain, A.G., Jansson, P., 2003, A
  Manual for Monitoring the Mass Balance of
  Mountain Glaciers Technical Documents in
  Hydrology, UNESCO, no. 59, 137 p.
• Krimmel, R.M., 1995, Water, ice, and
  meteorological measurements at South Cascade
  Glacier, Washington, 1994 balance year U.S.
  Geological Survey Water-Resources Investigations
  Report 95-4162, 41 p.
• Krimmel, R.M., 1994, Runoff, precipitation, mass
  balance, and ice velocity measurements at South
  Cascade Glacier, Washington, 1993 balance year
  U.S. Geological Survey Water-Resources
  Investigations Report 94-4139, 34 p.
• Krimmel, R.M., 1993, Mass balance,
  meteorological, and runoff measurements at South
  Cascade Glacier, Washington, 1992 balance year
  U.S. Geological Survey Open-File Report 93-640,
  38 p.
• Mayo, L.R., Meier, M.F., and Tangborn, W.V.,
  1972, A System to Combine Stratigraphic and
  Annual Mass Balance Systems A Contribution to
  the International Hydrological Decade Journal of
  Glaciology, v. 11, no. 61, p. 3-14.
• Meier, M.F., and Tangborn, W.V., 1965, Net budget
  and flow of South Cascade Glacier, Washington
  Journal of Glaciology, v. 5, no. 41, p. 547-566.
• Paterson, W.S.B., 1994, the Physics of Glaciers,
  Third Edition Butterworth-Heinemann, Oxford, pp.
  26-52.