Homework #6 earth surface processes Humphrey 2012, a little long, but you have 2 weeks to do this!

Question 1. Write a paragraph on your term project. Say what geomorphic feature you want to look at, and include a sentence or two on the dominant processes that you think are active on your landform. (you can change your mind later, but I want you to start thinking). Be neat, legible, and grammatically correct.

We are now going to revisit the homework of last week. See last week’s homework if you need to be reminded of solution techniques. Below is a profile through a small fault (earthquake) scarp, which has broken the surface of a desert landscape.

The height of the scarp is 2 meters.

Question 2, This week we assume a whole suite of processes are operating over time; some purely diffusional, and some that depend on distance from the divide (you can think: rainslash and sheetwash). Assume; that in this desert environment, the time evolution of this feature can be approximately described by a simple addition of the difference equations we developed in class:

………. Eqn A

where Z is the elevation of “bin” i at time t, and the x length of bins is Dx. Note if D_process is zero, this is the same as the pure rainsplash equation. The time step size is Dt, and the governing rate coefficient for the distributed process is C_process (assume a value of 5x10^-12m²s^-1) and for the slope length process is D_process (assume a value of 5x10^-13ms^-1). Note; in the equation all the quantities on the right are known at time “now” (or t) and only the new elevation at t+1 appears on the left as the unknown. Calculate the time evolution of this (2D) feature for 10,000yrs into the future, and report the elevation of the node at the top of the scarp. Assume the nodes at x=0 and at x=10 remains at a constant elevation.

Question 3, We will now try to apply a different Boundary Condition at the points x=0 and x=10. The BC we will apply is that the sed flux (q_sed) is zero at these two points. To make the flux zero, all we need to do is make the slope zero. So the our question is to repeat question 2, but with zero flux entering and exiting the diagram.

The easiest way to change the BC to a zero slope condition is to add an extra node to the left of the zero node (and for the right BC, an extra node past the right end of the problem). For the constant elevation BC in question 2, you made the nodes on the boundaries, at x=0 and at x=10, constants. Now make them variable, but add an extra (dummy) node just outside the boundary (you will have 2 extra nodes compared to question 2). At each time step you need to add an extra equation that sets this dummy node equal to the node one node inside the boundary (not equal to the boundary node but one node inside the boundary node, and note this node will change with time!). This will force the slope at the boundaries to remain zero (note that this makes Z_i+1 – Z_i-1 zero [ie the slope is 0] if the boundary node is i). It also allows you to calculate a curvature at the interfluve and to calculate the erosion of the node at the interfluve (left boundary). Extend the time out to 20,000 years, and report the amount of erosion at the interfluve.

Question 4, A final hillslope modeling problem, using only diffusion creep (no sheetwash).

The above figure is a cross-section of two gulleys in the Laramie Basin, separated by a remnant pile of erodable material 5m high, with dimensions as above. Model the behavior of the interfluve, under the process of just rainsplash. Assume the erosion rate, C, is as in previous problems. Assume points A and B are the locations of small streams. Point A is eroding downward at 1m per 5000years, but B is not eroding. What happens to the interfluve and streams over time? Specifically, when will the stream at A capture the stream at B? (Hint, what you need to do is change the Boundary Condition [BC] at the location of A. The way to do this is to move the elevation of A down the appropriate amount with each time step. Other than that, the problem is again similar to the previous problem).

This weeks geomorph puzzle (only for the brave). If you get interested in this type of work, you can try the geomorphic puzzle of applying both creep and Sheetwash to the above problem. To do it correctly requires very careful thinking. Good luck if you try it, but you will learn a lot by doing it correctly.