Von Karman curve fitting to field measured spectrum

[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.

Thanks in advance for your help

Nuno

 

[Achy47]

Dear Nuno,

Thank you for sharing your data and questions with us. As a fellow scientist, I am happy to offer some insights and suggestions for your wind monitoring project.

1. The downward trend in the highest frequencies observed in your spectrum could be due to various factors such as instrument limitations, environmental conditions, or data processing errors. It is important to carefully analyze and understand the potential sources of this trend before attempting to compensate for it. One possibility is that the sonic anemometers have an internal filter that is limiting the high frequency data. You can try to investigate this further by comparing the spectra obtained from different instruments or by checking the specifications of the anemometers for any mention of a high frequency filter. Another approach could be to use a different data processing method that may be less susceptible to this trend. Ultimately, it is important to consider the spectrum until the break frequency, as you mentioned, and to carefully interpret the results within this range.

2. When determining the integral length scales, it is important to use a consistent approach and to carefully consider the limitations and assumptions of each method. Curve fitting with the original data may give more weight to higher frequency data points, but it also takes into account the full spectrum and can potentially capture more variability. On the other hand, using the logarithmic frequency smoothed data may provide a more accurate approximation of the von Karman equation, but it may also smooth out some of the variability in the original data. It is important to carefully evaluate the results obtained from both approaches and to choose the method that best fits your research goals and objectives.

In addition, I would recommend consulting with other experts in the field and considering different data processing methods to ensure the accuracy and reliability of your results. Good luck with your project and please feel free to reach out if you have any further questions or concerns.