Homework #4 Glaciology, GEOL 4888, Spring 2014 Humphrey
Here are some calculations to back
up some of our thoughts from the lectures.
They are due on Thursday. I suggest
you look over them to be able to ask me questions in class on Tuesday.
1.
If
the longitudinal strain rate (exx with a dot over it) in a glacier is
0.1 per year, what is the approximate longitudinal stress (txx)? Assume the ice
is temperate. You can also assume that
the longitudinal stress is the only significant deviatoric
stress.
2.
Since
most of you missed this question last time, I will ask it again (just hand your
answer back in if it was correct before).
Let’s look at a region where the ice is 800m thick, with a surface slope
of 1 degree. The ice temperature is
about -10C. See table below (notice how
much A varies with temperature!)
a.
Plot,
using graph paper or a computer, the downglacier velocity profile of the
glacier, from the base up to the surface.
3.
We
are going to compare the amount of heat that can be conducted into a snow pack,
with the heat from water advection.
a)
Calculate
how much heat can flow from the surface of snow of density 500kg/m3
to a depth of 5m, per square meter of snow surface. Assume a constant vertical temperature
gradient of -2C per meter, lasting over a 3 month summer period. The heat conductivity of the snow can be
assumed to be ½ that of ice.
b)
Now
calculate how much water is required to be refrozen to produce that much heat
per square meter.
4.
Calculate
how much ice you can melt with a cubic meter of water in a conduit flowing down
a pressure gradient of 100KPa per 100m, if the flow path is 1kilometer
long. In other words calculate the
energy gained by the water over the kilometer, and convert that into ice
melt. You can assume the conduit is
horizontal, so that there is no change in gravitational potential energy.
5.
Here
is a puzzle for you (bonus point if you get the answer, no worries if you don’t). At the Olympics they have been known to spray
antifreeze on the ski runs, when the weather gets so warm that the snow starts
to melt and get slushy. Why do they put
antifreeze on slushy snow, what does it do?
If you figure this out, then you should be able to say whether it is
better to use concentrated or dilute antifreeze?
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 |