Homework #0 Humphrey Geology 4880 Fall 2012

Notes on the questions and on the answers:

1. We discussed 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 gap lakes, 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 10¹² Kg.

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.

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!

4. 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.