Homework #0 Humphrey Geology 4880 Fall 2022

This is due next Tuesday (Aug 30).

Notes on all homework:

This course deviates from most courses in that it recognizes that the world around us is complex, and that therefore questions and answers must only be approximations.  Learning to answer approximate questions in a reasonable way is fundamental in learning how to ask questions about how our world works.  It is both more advanced and more difficult than “plug and chug” homework, since you will have to think more.

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, so if you use web ideas, you must include the URLs.  You can get data from the web, but it is up to you to decide the data’s accuracy. 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 an answer, or a discussion of a possible answer.  Note for these questions I expect an answer based on your thinking.  If by chance you actually find an answer to a question elsewhere, I will expect you to explain that answer.

Your work must be neat, legible, and organized. I am not willing to wade through a mess and I will just give it back to you to re-do.  You can work with others, but be aware that you will have to do similar questions on exams and quizzes, by yourself. To emphasize: you can hand write your work, but it must be of a quality that you could hand to a colleague or boss in a professional situation!

Often the homework will include one or more questions that are quite hard. Warning, usually the last one(s) are virtually impossible; however I expect an attempt, since I want to see how you approach a difficult question. (Homework #0 does not have an impossible last question, but question 2 is really just a couple of brain teasers).  Note that these questions are mostly just to get you thinking in the wide ranging style that is needed to solve a lot of geomorphic type questions. Actual answers only need to be (or for that matter can only be) approximate.  Since it is early in the course, these questions do not require deep geomorphic knowledge, but do introduce concepts in geomorphology and environmental Geology.

If you stumped by a question, I am totally willing to discuss the problem.

Now the actual homework

1

· Part a Global climate is warming our planet and causing the permanent ice of glaciers and ice sheets to melt faster than in the past.  To get an idea of the scale of this effect, assume that the increased melt averages about a centimeter of water equivalent each year over the area of the ice and that this water runs off into oceans.  How much will sea-level rise each year? (this is a question about ‘mass balance’, or if you prefer ‘volume balance’)

· Part b There is a direct effect of the warming climate on the oceans, in that the water is getting warmer.  How much will the ocean surface rise if its temperature on average rises by 1 degree C? (this is a question about thermal expansion)

2 Our 2 main tools for approaching geomorphic problems will be to use a mass balance or force balance approach. Here are two brain teasers that illustrate these two approaches. These are largely for fun, you won’t lose points for not answering.

A You have two glasses the same size, one is filled with water, one with wine. You take one spoonful of wine and put it in the water, stir it, and then take one spoonful of the diluted mixture and put it back into the wine. Is there more wine in the water glass than water in the wine glass, or which? Explain the result (hint, mass balance).

B You are driving in your SUV to your kid’s birthday party, and she is holding a helium filled balloon that is floating on a string above her. You have to brake hard to avoid another car and it is good your daughter is in a seat belt as she is thrown forward. Where does the balloon go? Explain (hint, force balance).

3 How much does Medicine Bow Peak mass in Kilograms? Consider only the mass above the elevation of the gap lakes between Medicine Bow Peak and Browns Peak. This question is mainly to make sure you know about tools like Google Earth. Note that you can get an area in Google earth (although not a volume, as far as I know).

4 Now think on the likely size of the error, or the uncertainty, in your estimates in questions 1 and 3.  (‘error’ is presented in many ways, such as by a +/- value, or a percentage, or most simply by only using the correct number of significant digits; we will talk on this subject later).  For the current problem you can use the following ‘rules of thumb’ when doing calculations involving values with errors or uncertainty, especially when one of the variables has much larger error than the other variables in the problem.

i. Rule of thumb for addition operations: the error of the result is approximately the same as the error of the input variable with the largest error.

ii. Rule of thumb for multiplication operations: the error of the result is approximately the percentage or fractional error of the variable with the largest error.

To proceed beyond this rule of thumb approach, we will need to consider more precise definitions of error, such as the ‘standard deviation’ and other statistical measures.

For this question, what I want is an answer with your estimate of the correct number of significant digits in your answers to questions 1a, 1b and 3. (If you wrote down more significant figures in your answers to the above, then what I want to see is the 3 answers re-written with the (approximately) correct number of digits)