Homework #3               Glaciology, GEOL 4888,  Spring 2017                        Humphrey

This is similar to what we did in class (poorly..my fault). Here I give you correct values for ‘A’.

1.    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 r_ice g sin(a)Z, where alpha is the surface slope and Z is the depth below the surface. What is the symbol for this deviatoric stress? If the ice is 800m thick, with a surface slope of 1 degree, plot the value of the shear stress versus depth?

2.    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:

V_surface - V_(depth=z) = A/2 * (r_ice g sin(a))³ * z⁴

a.    Calculate the total expected deformation velocity over the full depth.

b.    Plot, using graph paper or a computer, the velocity profile (warning, the deformation velocity is not known at the surface, but if the ice is not sliding, the actual velocity is 0 at the bed, which is how you should plot the profile.)