Homework #1 Humphrey Geology 4880 Fall 2022
These are due next Thursday (Sept 8, no class on sept 6 Tuesday, since I will be giving a talk at a conference). Your work must be neat, legible, and organized, or you will be asked to do it again. Homework is generally marked out of 5 points, and each homework set is worth about 3% of your final grade.
Notes:
Answers only need to be (or for that matter can only be) approximate. There are 5 questions, 1 and 2 are very straightforward, although question 1 will require estimating, or finding, the area of the Platte river above Seminoe reservoir. 3 is an exercise in neat and tidy graphing (use a computer). You will need to have access to the internet for several of these questions. This homework set will take several hours at least(!), make sure you have time. You should not need to do any extensive calculations.
Try to couch your answers at the appropriate level of accuracy that is implied by the question. You are free to use data from any source or to make reasonable assumptions, but state what you assume, or show the data you use and give the source of the data. Be aware that data and ideas from the Web are of highly variable quality. To do the homework you will have to take 4 steps: figure out how to do the problem, decide on the data you need (if any), collect the necessary information, and finally produce the answer.
Often the homework will include one or more questions that are quite hard. Usually the last one(s) are virtually impossible to get correct, however I expect an attempt, since I want to see how you approach a difficult question.
1 Rivers currently carry about 1010 cubic meters of soil and eroded rock to the sea each year, throughout the world.
a) Roughly how long will it take, at the present rate and assuming we can average over the entire landscape, for all the continents to lower by an average of 1 meter in elevation (if all other processes, such as tectonics and isostacy, are ignored)
b) This implies a world averaged erosion rate of what (answer in units of mm per year)?
c) If the Platte River basin above the Seminoe reservoir (see Google Earth) is lowering at the average rate of 0.2 mm per year from erosion, what is the approximate total sediment (including dissolved load ) in kg per year, entering the reservoir? You can assume that all the material leaves the upper basin via the Platte River (a fairly good assumption), but you will need to find the drainage area of the basin above the reservoir. (You may find data at the USGS site water.usgs.gov to be useful, although it is not an easy site to navigate). Note you will have to convert from volume eroded to mass, which will require a density for the material removed by surface lowering.
d) (very Tricky) Most of the eroded material will be soil particles from the surface. The question is: should you use the density of soil, or what density(?) in part c?
2 We argued in class that big mountains are mostly held together by friction.
a)
In
class I said that that the coefficient of friction is the same as the tangent
of the Angle of Repose or the internal angle of
friction, (which is the angle at which a block of earth material will
slide on a slope of that angle). Demonstrate this
is true by showing that a block with a certain coefficient of friction will
just about slide when placed on a slope at the internal angle of friction.
[hint: the coefficient of friction is the ratio of driving stress to normal
stress, and you need to demonstrate that a block with a friction coefficient
will slide at the angle of repose]. The best approach is to resolve the
gravitational force on a block into slope parallel and slope perpendicular
forces and show, using trigonometry that all the forces
balance at the angle of repose.
b) Use Google earth to find a ‘talus’ (a talus slope). Measure the angle. What is it? There is a good talus on the north side of Boulder creek, about ½ way between Centenial and Snowy range ski area. There are also a lot of talus slopes on Medicine Bow peak, but if you measure their slopes, it will be highly variable, and a minor geomorphic mystery is: Why are the ‘talus’ slopes on Med Bow peak at too low an angle??
c) Use Google Earth to check
out the idea that mountains are held up by friction by looking at the slopes of
mountains. Volcanoes such as Rainier or Fuji have very low rock
strength. Find the slope angle of Volcanoes? Then look at the slopes of some big mountains, such as
the south face of Everest or Denali? Finally look at some really steep
smaller mountains such as the Grand Tetons or the Wind River mtns? While
you are looking, see if you can find the highest vertical face? [note that
the ‘path’ function in Google Earth will also show you the slope if you check
the ‘profile’ box] Report your findings for at least 5 mountains.
d) If the coefficient of friction for basalt is 0.6, what will the angle of repose of a basalt block on a basaltic crater wall be on the moon?
3. Many processes in geomorphology are non-linear in the sense that the results are not linearly related to some of the controlling variables. I want you to get more familiar with some of the typical geomorphic non-linearities, which are often logarithmic, exponential or power-law relationships in time or space.
a)
Plot the following 4 functions of X and Y, with X going from about 0 to 10 (use
more than 10 steps, 100 would be good):
linear Y = X, logarithmic Y = 10* log10 X, exponential Y = e(X/4.4), power law Y = X2 /10
(linear, logarithmic, exponential, power law (square))
Plot 3 different graphs, but with the 4 functions on each graph, as follows:
1- a graph with linear x-y axes that go from 0 to 10,
2- a graph with horizontal linear scale (0-10) and a vertical logarithmic scale (0-1, equivalent to 0-10 in non-log space),
3- a log-log plot with a scale from 0-1 on both axes
(in all cases x will go from about 0 to near 10 (in non-log units), however all values of y will not plot on some graphs).
Use different colors or symbols for each curve, and label them, either by hand or have the computer do it. The purpose of this question is to get you to think about non-linear relations, but also to get you to figure out how to plot with various axes. I recommend either EXCEL or some other computer or spreadsheet program that you already know. Please be aware that EXCEL plotting defaults are not setup to plot non-linear plots, and often produce very strange results.
4 A major jargon phrase in Geomorphology is “Magnitude and Frequency.” It refers to the idea that huge, infrequent events may dominate the evolution of a landscape, or conversely that small very frequent events may dominate. To get you thinking concretely, think of the Snowy Range. Currently there are a lot of interesting slow repetitious processes modifying the landscape, however the whole range is totally dominated by the fact that 20,000 years ago it was over-run by glaciers. The glaciers represent an unusual high magnitude event, while the current processes are high frequency, but in this case, swamped by the high magnitude event. The Happy Jack area to the east of town is an example of the opposite; dominated by high frequency events. Let’s look at a couple of high magnitude, low frequency events.
The Cretaceous probably ended with a major asteroid impact on earth. Large (10km. diameter or more) impacts appear to occur randomly in time, but with a mean time spacing of order 75 million years. Most of the larger life forms all over the globe suffer near complete mortality rates as a result of such an impact. Meteor impacts are an extreme example of a process dominated by high magnitude, not high frequency events. Remember the impacts are Random events.
a) What are the odds, or more precisely, the probability, of a catastrophic impact somewhere on earth in your life time? (it would probably end your lifetime)
b) Since we are now talking about Landslides, which is more likely: that you will die from a landslide, or that you will die (with the rest of us) by an asteroid impact? (Data on landslide deaths in the US can be found on the Web, or I found one number in ‘Environmental Geology” by Keller, in the library.) If you want to get depressed about living in the Rocky mtns, you can calculate your odds of dying from a Yellowstone super eruption, which occurs on a ¾ Myr time scale, but kills all life in Wyoming (and most of the US.)
5 (hard) Sand sized particles are common in the weathered surface material of our planet. Sand is common everywhere that physical (as opposed to chemical) weathering occurs, such as in rivers, beaches and deserts. Indeed, virtually all surficial deposits, that are not marine, have a strong peak in the sand size of the distribution. Laramie overlies a large indurated pile of sand, the Casper sandstone. The preponderance of sand has economic ramifications since gravel costs about twice as much as sand. About $7Billion of sand and gravel are used in construction, compared to about $25Billion of all other minerals mined in the US, thus making sand and gravel the most valuable single mineral resource in the US.
Question: Why is sand so common? Or, why isn’t there a continuum or smooth distribution of sizes from big to tiny, instead of this preponderance of sand? (as it turns out there is another peak in abundance in the silt/clay sizes). Hint, note I said that sand is common where physical erosion processes dominate.