Download Surficial Processes Take Home Problems

Take Home Problems
Due 10/20
A. Learning Objective: Understand physiographic controls on annual catchment water
balance. Recognize the relative roles of the atmosphere and hydrologic processes in
regulating the partitioning of precipitation into ET, Runoff, and Storage within the
context of the Budyko curve.
Problem 1: The theoretical boundaries of the Budyko Curve produce 2 linear
segments. Explain why real watersheds plot below the theoretical boundaries.
B. Learning Objective: Understand the concept of pattern similarity in watersheds, and
be able to pose hypotheses about why they occur.
Problem 2: Name and explain 2 patterns of similarity that tend to occur across
watersheds, and briefly explain the prevailing geomorphologic thought on why
such patterns occur.
C. Learning Objective: Understand the concepts of driving and resisting forces, and
constitutive equations in geomorphologic processes.
Problem 3. Consider a soil particle on a moderately steep hillslope in the Boise
foothills. Summarize 4 different processes by which that particle can move
downslope. Include qualitative descriptions of the driving forces and resisting
forces for each process.
Problem 4. List 4 physical variables (landscape properties or forces) that promote
or inhibit slope failure and explain where they fit in a simple slope stability
equation.
Problem 5. I used the channel head as an example of a geomorphic threshold.
Explain the term geomorphic threshold and come up with another example.
Problem 6. A debris flw of thickness h moves down a slope α with a maximum
velocity of U. The bulk density ρ is 2200 kg m-3, the shear strength k is 300 Pa,
and the viscosity when moving is 1000 Pa s. Assume that the debris flow deforms
as a Binham plastic. If the debris flow thickness is 5 m and the slope is 0.01,
a. What is the thickness of the rigid plug?
b. What is the maximum velocity, measured at the base of the rigid plug?
c. If the debris flow continues to travel over a diminishing slope, at what
slope will the flow freeze?
Problem7. A continuous evolution of hillslopes in the absence of landslides can
be modeled as diffusive (hillslope erosion is dominated by chronic processes such
as erosion by overland flow, as opposed to discrete sources such as landslides).
Diffusion models are based on the conservation of mass, or sediment continuity.
Mathematically, sediment continuity can be expressed as:
Q
y
 b
(1)
x
t
where Q is the discharge of sediment per unit width of hillslope, b is the bulk
density of the soil x is the horizontal distance coordinate, y the elevation, and t is
time.
a. Write a sentence or two that explains what equation 1 says.
b. Now assume that the discharge of sediment is proportional the local
topographic slope. Write an equation (transport law) that expresses this
assumption mathematically.
c. Now combine the two equations to derive the diffusion model for sediment
transport.
Problem 8: Suppose the equation in 7c models the hillslope in the figure below. The
geometry of the hillslope at any time depends on the diffusion coefficient, as well as the
rate of incision of the stream. So, that rate, E, is a boundary condition used to obtain the
analytical solution to the equation in 3c.
Y
E
x
L
If the horizontal length of the hillslope is L, the erosion rate of the bounding stream is E,
and the x coordinate is set to 0 at the hillcrest, the steady-state solution to the equation in
3c is
y
E 2
(L  x 2 )
2k
where k is a diffusion coefficient.
a. Suppose a stream and a ridge top are 50 m apart, and the incision rate of the
stream is 0.5 mm/yr. Calculate the profile of the hillslope assuming the
denudation to be diffusional with a diffusion coefficient of 50x10-3 m2/y.
b. Calculate the maximum height between the ridge and the stream.
c. What is the maximum gradient (dy/dx) of the hillslope? (this one involves some
calculus).
d. The geology of this problem is all encompassed in the diffusion coefficient.
Explain what the diffusion coefficient does mathematically, and what it means
physically.
Learning Objective: Be familiar with basic DEM analysis techniques, and how to
extract basic geomorphologic and hydrologic information.
Problem 9: Explain the concepts behind the D8 and Dinf flow direction methods.
Comment on the pros and cons of each approach for hydrologic and
geomorphologic analysis.