## 09 May 2006

### Statistical Analysis of Wind Data

Before I take a look at the Woods Hole data a commentor providing in my Proclivity of Wind post I wanted to take a last look at the structure of the sample wind data that I used from HOMER.

The Fourier transform is a technique used in signal processing, statistics, and a host of other applications to determine the periodicity of a signal. It essentially tries to fit a very large number of sinusoidal waveforms to a provided signal (like wind velocity data) to see if there are any periodic elements. I did exactly that to the wind data I used previously.
Figure 1: Periodogram of sample wind data provided for Block Island, RI
by HOMER software package.

A large portion of the data isn't periodic so there's a big spike at 'zero' frequency that can't be seen on this scale. Essentially this corresponds to the direct-current component of the signal. Interestingly, the strongest components appear at relatively low frequencies (and hence long periods of time). Hence we can see seasonal variations present but there's not much help here for the concept of predicting wind speed variations on an hour to hour timescale. There is a strong peak at the frequency of 0.041718 hr-1, which corresponds to a period of 24 hours. The graph extends out to a frequency of 0.5 hr-1 but it shows nothing so I shortened the scale.

This shows part of the problem associated with trying to simulate wind data. If I tried to use 'white' noise to simulate wind I would get a wrong result. White noise is evenly composed of all frequencies and hence the Fourier transform should provide a straight line. Wind appears to be more likely 'red' or 'brownian' type noise. See Wikipedia for definitions of types of noise.

The other thing I should look at is the autocorrelation of the data. Unfortunately I can't do that (easily) from school.