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In this assignment you will be coding up and employing a random search strategy to find the best minimum chi-squared solution to deconvoling a time series into sine waves of different amplitude, period and phase. Use the fit_data.f90 code from before as a template to modify. You can use the make file if you want as well and modify it. Remember, these files are located in ~dkmatter/sciprog/craig. For mpirun don't forget:
module load mpi-tor/openmpi-1.7_gcc-4.8

The data set here is the El Nino Southern Oscillation Index, as best as it can be resconstructed and calibrated into a single time series that goes from 1856 to 2013. The data file consists of monthly values in units of standard devation above or below the baseline for each year.

download the data



In this exercise you are turn in the following 5 elements:

a) Before any smoothing is done, write a quick routine that determines the local peaks (on a monthly basis) and make a histogram of those peaks (in units of months for the time line). Is there evidence for periodicity in those monthly peaks?

b) The usual procedure would be to calculate the annual ENSO index and plot a smooth vesion of that. Example plots for raw and smoothed data are shown below:







But there is no reason that you have to sum the data annually to do this exercise. You may sum and smooth in anyway that you like. Just document your procedure. When you have the final data file to operate on, upload the graph of that.

c) Produce a plot of the best solution you obtain against the data by using 8 processors and as many iterations as you want to find the minimum chi squared value. Keep track of the minimum chi square value as a function of both iteration number and number of sine waves. Include a table that shows the combinations and the resulting law of diminished returns.

d) Within a small range of chi squared about your best solution, find the number of function combinations that are allowed within that small range. This is a measure of the degeneracy in this problem (which could be large).

e) There is some reason to believe that this data set is not correctly calibrated throughout all time steps. See if you can improve your fit by what you judge to be "poor data".

As usual we will discuss this assignment in class on Friday.

For Craig: Yeah, go ahead and try to fourier transform this data!!