This assignment requires the use of Matlab. The program may be run from any computer; no additional toolboxes beyond the standard Matlab installation are required. The program itself, oa.m, may be accessed from the the OC/MR linux network, via the link below, or though the course Blackboard page.
On the OC/MR linux network, you can obtain file by typing (both upper and lower case):
cp ~paduan/OC4331/oa.m ./oa.m
Alternatively, click the link here to download the program text: oa.m
You may execute the command file from within Matlab
by typing:
oa
The command file presents a figure of a Gaussian hill constructed from the equation: f(x,y) = exp[-(x**2+y**2)/20]. We'll take this to be the "true" property value, e.g. temperature, in the experiment domain.
The command file makes a total of 4 plots in separate plot windows. You may need to move the windows around your screen to see them and the instructions in the command window.
You will select locations at which to sample the true field using the Left mouse button. To end the location selection, use the Right mouse button (or CTRL-click) to choose the final location. You will then be asked to select shape and length scale parameters of the covariance function used to objectively map the sampled points over the entire domain.
The instructions below ask you to run several trials and to comment on the impact of the mapping parameters and the data locations. The program reports the rms difference between the true and mapped fields as one relative measure of error. (Note: type the word "return" in the program to cycle through without selecting new observation points.)
Specific Instructions
Run the oa program and select 10-15 fairly evenly
distributed observation points.
Try both Exponential and Gaussian covariance functions
with length scales in the range L=0.5 to L=20; Also try L= ~200.
Run the oa program and select poorly distributed
observations points (i.e. in clumps).
Repeat 2) above.
Write up answers to the following questions:
What is the effect of the shape of the covariance function (Exp versus Gaussian)?
What is the effect of the length scale, L, for a given choice of covariance function?
What is the effect of data distributions relative to the true field (and how does this relate to L)?
What combination of covariance function and L (approximately) gives the best answer (compared with the known true field and given the RMS difference values)?
What are the estimated integral time scales (in lags or hours) for vsampe.dat and vsample2.dat (see below)?
Support your conclusions with 3 or 4 plots of your mapped fields. (You should be able to do most of your work from the computer screen. Print out only representative plots to save trees and toner!)
Copy the following two ASCII data files: ~paduan/OC4331/vsample.dat
and ~paduan/OC4331/vsample2.dat. Each of these is a one-column data file with north-south current every two hours. Vsample2.dat is a low-pass-filtered version of vsample.dat. Submit a plot of the data and a plot of the autocorrelation function computed from the data for both records (hint: use MATLAB's XCOV function). Also indicate the integral time (or space) scale apparent the results.
Sample Output
A look at the program output
Last Modified: 20 December 2005
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