GEOL1100, Spring 2013

Global Physical/Descriptive Oceanography, or Notions for the Motions of the Oceans

Assignment 2: Weeks 2-3

This assignment revisits some data analysis and dimensions and scaling ideas.

  1. Descriptive Physical Oceanography, 7th ed. Chapters 1-2, 6

Homework Assignment (Due 2/7/13)

  1. Matlab Proof of Central Limit theorem
    1. Use function rand to generate a variable A that contains a list of 10,000 uniformly distributed numbers.
    2. Use function hist to produce a histogram of the values of A (note, a histogram is like an estimate of the PDF, but its y-axis is labeled with number of occurences per bin rather than probability density). Experiment with different bin sizes.
    3. Use the following related loop
      clear B Bavg
      for i=1:1000
      B=rand(1,10);
      Bavg(i)=mean(B(:));
      end
      Now use the following to estimate the shape of the PDF of Bavg.
      y=hist(Bavg,0:.001:1);
      Bpdf=y/sum(y);
      plot(0:.001:1,Bpdf);
      axis([0.45 0.55 0 0.15]);

      What distribution shape is it? Why? What happens if there are 1000 "observations" of B instead of 10? Make a second variable C, with statistics Cavg and Cpdf the same way, but use C=rand(1,1000);. How wide is the pdf of C vs. that of B? Try plot(0:.001:1,Bpdf,0:.001:1,Cpdf) and std(B),std(C),std(Cavg),std(Bavg)?
  2. Over a flat bottom, the 1-d shallow water equation momentum equation can be written as: 
    1. Write out the two Eulerian frame terms inside of the material derivative.
    2. u is velocity, h is depth, t is time, x is distance along the direction of u, g is gravitational acceleration (9.81 m/s2)
    3. Use the scales U, T, H, L to estimate the size of each of the three terms. In class, we plugged in real numbers for these scales. Now, you will just use abstract capital letters to symbolize that you have made an estimate (lower case are the real variables that you might measure).
    4. The Froude Number (here: Fr2=U2/(gH)) determines the relative sizes of two of the terms. Estimate the time scale T in this equation if U and H are such that Fr is very small and if Fr is very large.

    Optional additional reading may be useful for the paper #1 plans:

    1. "3 Kinds of Lies" from 2010's class. username: atoc5051_10 password: Oshuns?Noshuns!
    2. "3 Kinds of Lies" from 2008's class. username: atoc5051_08 password: 2OshunNoshun?
    3. "Ready to Roll" and "What Do You Mean Mean?" from 2007's class. username: atoc5051_07 password: 4OshunNoshun! (Note: these were not revised papers, so they are first drafts.)