Full Energy Distribution Units

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Full Energy Distribution Units

Posted by Ed Atkin at January 08. 2014

Hello all,

First post up here.

I have used adopps for current and the wave stats for years but I am only just getting in to the spectra side of things. 

I have read a lot on the processing of spectra data output from quickwave in this forum.

I see the common method of calculating the full Energy Distribution (E):

E(f,theta) = S(f) * d(f,theta)     ,   with S= Energy spectra (*.was)    and d=full directional spectra (*.wds)

Now the units of the wave energy spectra (.was) is m2/Hz, and the units of the full directional spectra (*.wds) is m2/Hz/deg. Surely multiplying these to units gives m4/Hz2/deg?????

That doesn't make much sense to me though, and not an energy unit I'm familiar with.

Looking on Storm(demo), the spectrum plot in the bottom right has units of m2/Hz  (right click> scaling). I read in another post that this plot is the full energy distribution

Can anybody tell me how this is?

 

Regards,

 

Ed

Re: Full Energy Distribution Units

Posted by Elin Bondevik at January 08. 2014

Hi Ed

Welcome as a first time forum poster!

In order to improve clarity on the names of the different spectra, let us refer to "D" as the Normalized Directional Spectra (*.wds). The problem you are having is the units for this. D is a distribution of Normalized energy over direction, for which there is a unique distribution for each frequency in the wave spectra. The units are therefore 1/deg. Another way to look at this is to consider the attached equation (too difficult to write in forum direct); there are not units when you integrate over the full direction - it is simply unity, What makes it confusing is that D is shown as a function of frequency but this is just to indicate that there is a unique directional distribution for each frequency in the complete spectrum. 

So in the end you will have units of the following m^2/Hz/deg.

Best regards
Elin

Re: Full Energy Distribution Units

Posted by Elin Bondevik at January 08. 2014

By the way, attached is the previously referred equation.

Attachments

Re: Full Energy Distribution Units

Posted by Ed Atkin at January 09. 2014

Hi Elin,

Thanks for your reply.

That has helped me understand the principals behind the units for D (or d, full directional spectra).

But I still don't know what the units for the calculated full Energy Distribution (E) are????

thanks 

 

Re: Full Energy Distribution Units

Posted by Elin Bondevik at January 10. 2014

Hi Ed

The units for the calculated full Energy Distribution is m^2/Hz/deg. The units for the Directional spectra is 1/deg, due to the normalization. 

Best regards
Elin

Re: Full Energy Distribution Units

Posted by Ed Atkin at January 13. 2014

Elin,

Any reason then that the header file (whr) states the Full Directional Spectrum (wds) units as m2/Hz/deg instead of 1/deg???? 

Ed

Re: Full Energy Distribution Units

Posted by Elin Bondevik at January 14. 2014

Hi Ed

What version of the software are you using? Perhaps it is time to update it, the units are not wrong in the newest Storm version.

Best regards
Elin

Re: Full Energy Distribution Units

Posted by Ed Atkin at January 16. 2014

Hi Elin,

I'm not using storm for processing. This is quickwave output. I just had a look on the Storm Demo software to check it out. 

I have done the processing as multiple threads on here suggest. I want to check that Iam using the right files etc and that the process is correct: so I want to integrate each frequency of the directional spectrum from 0 to 360 (to make unity). I have tried a number of things in Matlab, but just don't seem to get it right. Probably missing a step! Any suggestions would be most welcome.

Thanks again.

Re: Full Energy Distribution Units

Posted by Elin Bondevik at January 23. 2014

Hi Ed

We have seen on occation that if the directional spectra is very narrow, then the resolution in direction (4 degrees) is not quite sufficient to characterize the energy distribution around the peak direction. 

There are a couple of alternatives. The first is to increase the resolution, but this would make the WDS files even larger, so we try to avoid this. The second alternative is to use the Fourier coefficients (*.WCF) to reproduce the directional distribution, where you can specify your own resolution.

If you are not familiar with this approach, then it may be a bit laborious. Perhaps you can share with us what your objective is for reconstructing the directional distribution? This will not only help us understand your needs, but we may also have a ore tractable solution.

Best regards
Elin 

Re: Full Energy Distribution Units

Posted by Rose Barker at October 15. 2019

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