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Mass Balance: Theory and Application. Steve Wilson. South Cascade Glacier - 1928. South Cascade Glacier - 2004. Outline. Basics Methods Stratigraphic Annual Hydrologic Photogrammetric Flux Gate (Ice Sheets) South Cascade Glacier Comparative Methods Dynamics. Mass Balance Basics.

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mass balance theory and application

Mass Balance:Theory and Application

Steve Wilson

South Cascade Glacier - 1928

outline
Outline
  • Basics
  • Methods
    • Stratigraphic
      • Annual
    • Hydrologic
    • Photogrammetric
    • Flux Gate (Ice Sheets)
  • South Cascade Glacier
    • Comparative Methods
    • Dynamics
mass balance basics
Mass Balance Basics

“Wavering between the profit and the loss.”

-T.S. Eliot, Ash Wednesday

The bank account model

Bn vs. bn

Measurements made

twice a year

Net balance (~October 1)

Winter balance (~May 1)

Summer balance (calculate)

stratigraphic method
Stratigraphic Method
  • Similar to annual mass balance method
  • Direct measurement of accumulation and ablation
  • Very labor intensive
terminology
Terminology
  • Stratigraphic balance vs. annual balance
  • Mass balance is a time transgressive process using time dependent variables and methods

from Mayo et al. (1972)

measurement tools
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.
measurement points
Measurement Points

from Kaser et al. (2003)

  • Established positions
  • Stakes/pits should cover even elevation distribution
  • Account for velocity
transient snow line
Transient Snow Line

Early Season

Late Season

slide11
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
measurement tools12
Measurement Tools
  • Probes, stakes, pits, and cores
  • Material properties

from Kaser et al. (2003)

surface area
Surface Area

1992

1993

hydrologic method
Hydrologic Method
    • (square = Δ)
  • Where is the glacier?
  • Accounts for internal water storage
  • Primarily used in conjunction with other methods

from Krimmel (1995)

photogrammetric method
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
flux gate
Flux Gate
  • Primarily used on ice sheets
  • Accumulation
    • Total accumulation over grounded ice
  • Ablation
    • Annual ice flux across grounding line
south cascade glacier
South Cascade Glacier
  • Benchmark Glacier
  • Multiple mass balance methods used and compared
  • Long term glaciological and meteorological records
internal consistency
Internal Consistency
  • Meier and Tangborn (1965) use three methods on South Cascade Glacier
    • (squares = Δ)
  • Photogrammetric values and directly measured balance should be equal
  • Can be checked against hydrologic data to check for consistency or water storage
emergence velocity
Emergence Velocity
  • Describes relationship between net balance, flow, and thickness changes
  • Submergence in the accumulation area
  • Emergence in the ablation area
  • Crossover point=equilibrium ELA
slide21

The End

Be careful where you dig!!!

references
References
  • Fountain, A.G., Krimmel, R.M., Trabant, D.C., A Strategy for Monitoring Glaciers: United States Geological Survey, Circular 1132, 25 p.
  • 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.