ATMS 552 Objective Analysis

Homework on Spectral analysis using MatLab (or whatever you like)

1.) Data: I have made two time series named x552csp.mat and y552csp.mat,

which you can get from anonymous ftp to eos.atmos.washington.edu

ftp/pub/dennis/552_Class/ .

These time series of daily observations are each 4096 days long.

x552csp and y552csp are different physical variables measured at the same time

and place, or possibly the same variable measured at different spatial locations,

but at the same set of times. You have no a priori idea of what periods might

be present, but you can think of the data as being meteorological and

on daily time steps.

2.) The primary tool I would like you to use is the spectral analysis package within Matlab.

I have written a program to do the calculations called mspec.m, which is also on the ftp page,

but which you can also pick up from the Matlab Software web page.

You can modify it as needed, or use as is. It has a number of different options

that you can select from, or you can modify the code. I hope it is self-explanatory.

It uses Hamming window and 50% overlap WOSA. It also computes MTM spectra

with the same chunk length as the WOSA analysis.

3.) Seek the Peaks: OK, first look for the periodicities in x and y.

You may want to experiment with different chunk lengths, look at parts

of the data, etc.

First decide what confidence level you require, then decide at which frequencies

you might have significant variance. The program also does multi-taper spectra.

Experiment with this a bit to see if it helps your decision process.

4.) Cross-Spectral Analysis: Now we want to search for relationships between

the two time series x and y. The program computes, coherency, phase,

cross-spectrum amplitude, co-spectrum amplitude and quadrature spectrum amplitude.

The sign of the co- and quad- spectra are lost here, but they are reflected

in the phase. You can learn a bit by comparing the cross-spectral amplitude

with its two components.

5) Summarize: Where do you have significant peaks in power in x and y? In

which of these frequency bands are x and y coherent? What is the phase

relationship between x and y where they are coherent?

Do you have peaks that are not coherent?