Homework #0 Humphrey Geology 4880 Fall 2015

This is due next Tuesday (Sept 8).

· Part 1 How much rock is in Medicine Bow Peak? To make it more precise: what is the mass in kilograms of Medicine Bow peak, above the elevation of Gap Lake (the lake between Medicine Bow Peak and Browns Peak)? You will need a topo map. TopoQuest on the web is a good place to look. For other views Google Earth is a fantastic tool. [You will have to decide how accurately you want to make this estimate. A general rule of thumb: there is no point in making any measurement that is significantly more accurate than any other variable in the problem. Part 2 asks you to think about this a bit more]

· Part 2 Now include an educated comment on the likely size of the error in your estimate. Again, to be precise, answer these questions:

i. What are the 3 largest potential sources of error in your estimate, in order of importance. (Note this is a straightforward question, but introduces the difficulty of answering real world problems. Include your working so I can follow your method)

ii. Based on your answer to the previous, put a % value on the potential size of the error. And look at your answer to part 1, and decide how many significant digits should be in your answer.

2 Afternoon thunderstorms are common at this time of year in Laramie. How many raindrops hit the Geology building (both wings) during a typical Laramie thunderstorm? List the assumptions you had to make. (This is an exercise in reasonable assumptions)

3 Close to ½ the surface of the earth has been transformed by human activity. One of the spatially largest activities is deforestation. Removing a forest tends to raise the albedo of the land and thus more sunlight is reflected from the earth, which in turn should cool the global climate. So could we reverse our current global warming trend by cutting down trees?

Write a comment on this idea: is it true (Note, please don’t talk about the ethics of this, I am asking for a science answer)? Part of the reason for asking this question is that you will probably find several well written but opposite viewpoints in the literature and especially on the web. I want to illustrate that many simple questions do not have a single ‘correct’ answer. Note that there really is an answer; if we did cut down all the trees, the temperature will either go up or down. (But can we really know the answer now, without cutting down trees?)

4 An interesting little factoid is that tire dust is a notable source of air pollution (mainly because it is chemically reactive). It is mainly a problem in urban environments. But a lot of vehicles drive on I-80. How many metric tons (1000kg) of tire dust is produced in the Wyoming segment of I-80 in a year, just by the 18 wheel trucks?

5 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. 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, and as it turns out another peak in abundance in the silt/clay sizes?). Hint, note I said that sand is common where physical erosion processes dominate.

Notes on the questions and on the answers:

1

1. We will discuss this in class, but here are some notes. The peaks volume could be estimated at several levels of accuracy. The best would be to look at a contour map and find the area of each contour above the lake, and then multiply the areas by the contour interval to get volume. Areas on a map can be measured by several methods; the traditional method is a planimeter. That level of accuracy is probably not needed here. Overlaying a grid and counting squares is probably good enough. A quick and dirty approach would be to assume the peak is some simple geometry (such as a pyramid) and estimate the base area and height. The accuracy of the density is irrelevant, since the volume measure will contain huge errors. The sort of number you should get would be around 10¹³ Kg (note that more accuracy than this is probably not justified).

2.

2. There are numerous ways to attack this problem, and all lead to similar but different answers. Here are two examples: (the first is somewhat observational, the 2^nd is based on typical data)

a) I noticed that during a rainstorm that lasted ½ hour, there was about 200 rain drops per minute hitting a foot square puddle (actually the puddle was about 1/20^th of a square foot, and I counted about 10 per minute). So multiplying by 30 minutes I got 6000 drops per square foot per storm. There are 10.8 square feet per square meter, so I get about 6x10⁴ drops per square meter in a Laramie thunderstorm. Then you just need the area of the Geology building from Google earth.

b) Another approach would be to estimate the total rainfall in a storm and divide by the volume of a raindrop. Raindrops are variable in size but lets assume a medium sized drop (from a report on raindrop sizes in cloud studies) of 2.5mm. This has a volume of pi*d³/6 or about 8 mm³. The amount of rain in a big thunderstorm storm is about 0.1inch, which is .00254m. Thus about 0.00254 cubic meters of rain falls per square meter. Divide this by the volume of a rain drop, (there are 10⁹ mm³ in a cubic meter), our final result is about 3x10⁵ drops.

The point of this question is twofold: first to force you make reasonable assumptions, and secondly to get you to push some big and small numbers around and not get lost! Note that the answers differ by a factor of 5, does that mean that either answer is wrong?

3. There are discussions of this on the web and it is a great example of why you have to be careful when finding “answers” on the Web. I generally assume anything on the web is incorrect until checked by an independent means. In this case the problem is complex enough, and the various agencies and societies are knowledgeable enough that it is hard for us to figure out the merits or the politics of the arguments (which are really outside the scope of this course). If you answered from first principles, the Albedo effect is so strong that it is hard to argue that cutting down forests would not cool the world, at least in the short term!

4. You need several pieces of info, some are easy, such as the length of I80 in Wyoming (405miles) and the density of rubber (1100). Some not so easy, the number of trucks per year. And finally the tire wear. A typical truck tire has about 1.5 cm of useable tread (Michelin truck tire web page), and truckers typically get about 150,000 miles out of a truck tire (from a site on tire retreading). Outer diameter is about 1.09m, with a width of .28m. And don’t forget there are 18 tires per truck. The only real difficult number to get is the number of trucks. WyDot gives an estimate of 7000 trucks per day, so I will go with that, although my own estimate from driving I80, is that there is about 15secs between trucks on average, which gives a similar number of 6000 trucks per day. With this data, it is just plug and chug. Each tire has about pi*1.09*.28*.015 wearable rubber (0.014m^3) in 150,000miles, and it loses 405/150000 of that traveling across Wyoming (4x10^-5 m^3/tire), multiply by 18, and by 7000*365, and we get the total volume of truck tires worn out in Wyoming (1,750m^3). Finally multiply by the density, and we get a lot of tire dust! 2,000 tons, with an error that is mainly due to the errors in the truck traffic figures and probably the wear rate.

5. This is a question that could take a thesis to answer, however there are some points to note. The first point is that the grains of minerals in most igneous rocks are not uniformly sand sized. For example granitic grus is not typically sand sized so there must be processes that produce sand. We then look at processes. Turns out both water transport and wind transport of mineral grains tend to break the grains apart by impact processes. The energy in impacts goes as the cube of the particle size. So smaller particles have MUCH less impact energy. Particles smaller than sand size, in both water and wind transport, do not have enough energy to exceed their strength on impacts (they can however get squished between bigger rocks). As a result mechanical size reduction slows rapidly as particles approach the sand sizes. An additional important aspect, especially in wind transport, is that there is a strong reduction in transport as the size increases, so that wind winnows sand grains from a source area and concentrates them downwind in deposits (think Sand Hills of Nebraska).

Some processes do not produce sand: chemical weathering tends to produce clay sizes, while glaciers tend to produce silt. In chemically dominated regions, sand is less common, however in glaciated regions sand is often quite common, because the melt waters from the glaciers may dominate the production of sand.