Homework #3 Glaciology, GEOL 4888, Spring 2018 Humphrey
To do this homework you will need to
plot the results on a computer, or if you want to do it by hand, it must be
done on graph paper with correctly scaled axes.
1.
On the lee side of Medicine Bow Peak, the wind in the last storm has
deposited a 1 meter deep snow drift with a temperature of -15C. In this following week the sun will melt
about 2cm of water equivalent from the surface.
Is there enough energy in the melt water to ripen the snow pack to
0C? Assume the snow has a density of
300kg/m3. (hint, use the cold content Index we
discussed in class)
2. Let’s look
at the deformation velocity expected in the ablation region of Greenland.
Assume the ice is approximately a ‘slab glacier’, uniform in all
directions. With a coordinate system x-downglacier,
and z-down from the surface, the shear stress at any depth is due to the weight
of the overlying ice and the slope, so the shear stress is given by rice g sin(a)Z,
where alpha is the surface slope and Z is the depth below the surface. If the
ice is 800m thick, with a surface slope of 1 degree:
a. plot the
value of the shear stress versus depth?
Label the axes, and plot depth as the Y value
Now to make the discussion specific, let’s look at a region where the ice temperature is about -10C. See table below (notice how much A varies with temperature!). The equation we developed in class for velocity versus depth (the signs have been adjusted so that Z is positive downward):
Vsurface - V(depth=z) = A/2 * (rice g sin(a))3 * z4
Calculate the total expected deformation velocity over the full depth. For consistency, use 900kg/m3 for the ice density. The deformation velocity is not known at the surface, but if the ice is not sliding, the actual velocity is equal to 0 at the bed. This allows you to calculate the surface velocity as the total difference between the bed and surface velocity.
b. Plot, using graph paper or a computer, the velocity profile
Table of Values of A(T), s-1 Pa-3 |
Temperature (Celsius) |
2.4 x 10-24 |
0 |
9.3 x 10-25 |
-5 |
3.5 x 10-25 |
-10 |
1.2 x 10-25 |
-20 |