# Von Karman curve fitting to field measured spectrum

1. Oct 18, 2012

### doutormanel

Hello everybody,

So for this wind monitoring project I'm getting data from a couple of 3d sonic anemometers, specifically 2 R.M.Young 81000. The data output is made digitally with a sampling frequency of 10Hz for periods of 10min. After all the pre-processing (coordinate rotation, trend removal...) I get 3 orthogonal time series of the turbulent data. Right now I'm using the stationary data of 2 hours of measurements with windows of 4096 points and a 50% overlapping to obtain the frequency spectrums in all three directions. After obtaining the spectrum I apply a logarithmic frequency smoothing algorithm, which averages the obtained spectrum in logarithmic spaced intervals.

I have two questions:

1. The spectrums I obtain from the measured show a clear downward trend in the highest frequencies as seen in the attached figure. I wonder if this loss of energy can have anything to do with an internal filter from the sonic anemometer? Or what else? Is there a way to compensate this loss or better just to consider the spectrum until the "break frequency"?

http://i.imgur.com/8gOHH.png

2. When applying the curve fitting algorithm to determine the integral length scales according to the von Karman equation what is the correct procedure: curve fitting the original data, which gives more weight to higher frequency data points? or using the logarithmic frequency smoothed data to approximate the von karman equation, giving an equal weight to data in the logarithmic scale? In some cases I obtain very different estimates for the integral length scales using both approaches (ex: Original -> Lu=113.16 Lv=42.68 Lw=9.23; Freq. Smoothed -> Lu=148.60 Lv=30.91 Lw=14.13).

Curve fitting with Original data:
http://i.imgur.com/U72wV.png

Curve fitting with Logarithmic frequency smoothing:
http://i.imgur.com/cnnPu.png

Let me know if something is not clear. I'm relatively new in this field, and I might me be making some mistakes in my approach, so if you could give me some advice or tips it would be amazing.