Matlab psd and csd analysis of N/S Flow Mow currents

SRV 5/30/02

Previous effort: (Cross) Correlation functions

This page presents the analysis of the N and S current meter records using the Matlab psd and csd commands, which basically:

  1. separate the time series into (potentially overlapping) sections of length nfft
  2. detrend the sections and taper each with a Hanning window of specified width
  3. Discrete Fourier transform each
  4. Calculate the magnitude of each DFT to get individual (cross) power spectral estimates
  5. Average the DFTs of the subseries to get a mean spectral estimate

The script cohphase.m does the work:

  1. Calculates along/across axis components of velocity (called v and u)
  2. Gets maximum temporal overlap between the 2 series
  3. Calls psd and csd with specific values and plots results
  4. Calculates coh and phase and plots the results

In the subsequent plots, the 2 original series have length N=1775. I varied the values of nfft and the Hanning window width and decided that nfft=512 and a window width of 512 yielded the best combination of frequency resolution and confidence in spectral peaks. These values result in an effective degree of freedom EDOF~5.

This procedure should be tested with synthetic data to gain confidence. Further experimentation with the field data and more advice is certainly warranted. Also, a good next exercise might be to do all the psd/csd steps manually to gain more intuition about the DFTs (or FFTs) and the windowing process. Try raw FFTs and band or block averaging, as an alternative to windowing the time series prior to transformation.

The first 3 plots show the (auto) spectra GNN, GSS, and the cross spectrum GSN. Each plot has three curves: the central blue spectrum and the bounding 95% confidence intervals (red upper, green lower) at each frequency.




The next 2 plots show the coherence and phase lag between the southern and northern meter. The latter plot has a zoomed x-axis that focuses on tidal and subtidal frequencies.


I don't understand how the coherence can be significant for frequencies near the sampling frequency of 1/hr.


This plot suggests there are peaks at the following frequencies and periods: 

f     T (hr)
.082  12.2 
.070  14.3
.058  17.2
.032  31.25
<.013 >76

Only the nearly semidiurnal peak makes sense to me (near 12hrs) and it would be helpful if the associated phase lag was near zero (+45). The 17.2 could be inertial, but previous work suggest that there isn't much power at inertial frequencies down in the valley.

One thing that is frustrating is that the spectral resolution is so low in the tidal to subtidal frequency range (0-0.1 cphr). This is why it might be worth next trying to calculate raw FFTs and proceed toward coherence after some minimal band averaging...