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
• The bank account model
• Bn vs. bn
• Measurements made
twice a year
• Net balance (~October 1)
• Winter balance (~May 1)
• Summer balance (calculate)
Bn   bn dS   bn dS
Sc
Sa
Bn  Bw  Bs
“Wavering between the profit and the loss.”
-T.S. Eliot, Ash Wednesday
Stratigraphic Method
• Similar to annual mass
balance method
• Direct measurement of
accumulation and
ablation
• Very labor intensive
Terminology
• Stratigraphic balance vs.
annual balance
• Mass balance is a time
transgressive process
using time dependent
variables and methods
from Mayo et al. (1972)
from Mayo et al. (1972)
Measurement Tools
• Selecting representative • R. Hock (2008)
points
• Calculated mass
• Mapping transient snow
balance can depend on
line
glacier outlines, number
of measurements,
• Measurement tools
human error, and other
• Surface area
factors.
estimations
Measurement Points
from Kaser et al. (2003)
• Established positions
• Stakes/pits should cover even
elevation distribution
•Account for velocity
Transient Snow Line
Early Season
Late Season
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 Tools
• Probes, stakes, pits, and
cores
• Material properties
from Kaser et al. (2003)
Surface Area
1992
1993
Hydrologic Method
Bn  P  Q  E  S
– (square = Δ)
• Where is the glacier?
• Accounts for internal
water storage
• Primarily used in
conjunction with
other methods
from Krimmel (1995)
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
• Primarily used on ice
sheets
• Accumulation
– Total accumulation over
grounded ice
• Ablation
– Annual ice flux across
grounding line
South Cascade Glacier
• Benchmark Glacier
• Multiple mass balance
methods used and
compared
• Long term glaciological
and meteorological
records
South Cascade Glacier:
Mass Balance
Internal Consistency
• Meier and Tangborn
(1965) use three
methods on South
Cascade Glacier
– (squares = Δ)
M   h dS 
S
1
b dS


S
• Photogrammetric
values and directly
measured balance
should be equal
• Can be checked against
hydrologic data to check
for consistency or water
storage
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
The End
Be careful where
you dig!!!
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.