Glacial geomorphology• Glacier: “a natural accumulation of ice that
is in motion due to its own weight and slope of its surface”
• Ice cores– Paleoclimate archive: high-resolution records
of climate change– Compared to deep sea core
Ice Ages Ice Ages Throughout Throughout
Geologic TimeGeologic Time
12°22° 17°Average Global Temperature (0C)
Ice Age
Ice Age
Ice Age
Ice Age
Figure modified after C.R. Scotese
PALEOMAP Project (www.scotese.com)
Quaternary
Karoo
Saharan
Sturtian: 750-700MyaMarinoan/Varangian: ended 635MyaGowganda: 2.3Gya
Pleistocene: 3Mya
C.R. Scotese, PALEOMAP Project, (www.scotese.com)
Last Glacial Maximum 18,000 years agoLast Glacial Maximum 18,000 years ago
Present vs. Past Glaciation
• Now – One major (Antarctica) and one minor (Greenland) ice sheets
• Then - At least three major (Antarctica, Laurentide, Fennoscandian) and numerous minor (Greenland, Cordilleran, Patagonian…) ice sheets
Milankovitch Cycles
Eccentricity90,000 to 100,000 years
Precession19,000 to 23,000 years
Obliquity (Axial Tilt) 41,000 years
Figures modified after Matt Beedle, Montana Sate University.
~5~5%%
~0%~0%
http://www.homepage.montana.edu/~geol445/hyperglac/time1/milankov.htm
How does snow become ice?• Deposition
– Reworked by wind• Destructive metamorphism
(orig. crystal becomes a rounded ball)
• Sintering (rounded grains fuse by freezing into larger crystals)
• Compaction/Cementation
How long does it take?
• It depends!– Antarctica – hundreds
of years– Greenland – 100 years– Temperate glaciers –
decades– Maritime glaciers -
years
As snow turns to ice, porosity decreases
Faster in wet snow
Ice density with no pore space = 917 kg/m3
Ice is derived from snow
Partially compressed/compacted snow is firn (snow/ice)
When a wedge of firn is thick enough to deform under its own weight and move downhill, it’s now a glacier
Mass Balance: Net Loss or Gain of Ice
x
Q
zWzb
t
H
1
H = ice thicknessW= glacier widthQ=ice discharge/unit widthb = local mass balance, m. of water/yrmass lost or gained over an annual cycle
Q represents losses due to ablation and sublimationacross the width of the glacierMore loss due to solar radiation than Earth’s heat
Ice in Motion
• If not in motion, not a glacier but a snowfield
• Motion by– Basal sliding– Internal deformation
• Q = U x H– Discharge per unit width– U, mean velocity– H, thickness
At steady state,
x
Q
zWzb
t
H
1
Ice Deformation: Internal Deformation (Force Balance for a Column of Ice)
W/A
Step 1: Resolve weight force into two components:
a normal force and a shear force
sinA
W
Body force of gravity acts upon the ice column
Step 2: Substitute for W, A, and sin
SzHg
gdxdy
dxdyzHA
gVolA
mgA
W
)(
sin)(
sin
sin
sin
Fluid Deformation
• Fluid deforms under its own weight
• As shear is applied, the ice is strained
• Strain rate is
0L
L
" viscosityeffective"dz
dUZ
U
xz
1
Strain rate
horiz vel
Ice Deformation
• How the ice responds to the stresses is determined by its rheology (rate and style of deformation under stress)
• Ice is non-Newtonian• As shear increases,
effective viscosity decreases such that ice is less “stiff” near the bed than near the surface
viscosity: resistance of fluid to deformation
Much more like “plug” flow
Ice Deformation: Highly Nonlinear
5
sin
sin
53
33
HgAQ
zHgAdz
dU
Ice discharge = f(slope and ice thickness)
S
Ice thickness
For a given slope, if the ice thickness increases by 15%, the ice discharge will DOUBLE
“flow law parameter”in Glen’s flow law
• Assumptions– basal shear stress = 0.8 bars = 8x104 Pa– glacier is wide enough that walls do not support ice– contours on the map show that the ice slope is 10m/km at
this location– density of ice = 918 kg/m3 and g = 9.8 m/s2
– 1Pa = 1
• Estimate the ice thickness H at this location• The basal shear stress is given by:
where i is the ice density, g is the acceleration due to gravity, H is the thickness of the ice, and S is the ice surface slope angle
• Rearrange:
H =8x104Pa
918 kg
m3( ) 9.8 ms2( )(0.01)
kgm
m2s2
gSH
gHS
i
i
=890 m.
Ice Deformation: Sliding
• Sliding occurs because high pressure promotes melting (in water)
• Down valley component of weight promotes motion– Resistance to motion due to pressure
variations from bumps in the bed
Pressure Melting
• For ice at PMP:– Movement increases pressure, thus melting,
on the up-ice side of an obstruction– Movement away from the obstruction causes
freezing on the down-ice side – “regelation”
meltmelt
Effects of Pressure Melting• High pressure is
experienced on the upice side of an obstruction.
• Pressure melt results
• Water migrates around/through obstacle
• Regelation occurs in low pressure zone
MELT REFREEZE
Regelation
Higher pressure on up-valley side of bumps than down-valley side of bumps
Ice melts on the stoss (high pressure) side, consuming energyMoves around bump as water filmRefreezes in the low pressure shadow (lee)Heat released by refreezing is conducted back to bump
Coupling of thermal and fluid mechanics