sectorwise frequencies in lib file

[pdoubrawa]

Hello,

I am having a hard time understanding why the sectorwise frequency distributions are different for different roughness classes in the lib file.

I have thoroughly read the documentation and the European Wind Atlas trying to understand what those lines mean and I have not succeeded. I have extensively tried to recreate the frequency distributions in the lib file but I have not succeeded because I do not understand what they represent.

My questions are:

- The sectorwise frequency distributions per roughness class are representative of which height? (is it the original anemometer height of the data, or the geostrophic level?)

- How does wasp calculate these wind direction changes from one roughness to another? The only reference for wind direction changes that I found in the European Wind Atlas was on page 567 and it refers to the angle between the surface and geostrophic winds.

Thank you very much for your help!

Paula

[YOCUI]

hi pdoubrawa ,

the height is actually a group ,which normally with default settings of 10m 25m 50m 80m 200m , this group called atlas , which is calculated base on your measured height and your other inputs , you can change the default height to match your hub height to reduce the uncertainty of interpolation.

[YOCUI]

regarding the change of direction due to roughness , would you provide more detail when you find this ? i think the direction change should be induced by terrain not roughness.

[Morten]

Hi Paula,


If you look at the geostrophic drag law in equation (8.5) on p. 567 of the European Wind Atlas, you will see that a given combination of geostrophic wind G and surface roughness z0 determines the friction velocity u*. This fixes the u*/G ratio and thereby determines the angle between surface wind and geostrophic wind. If you consider the same geostrophic wind but a new surface roughness z0, you will get a new friction velocity u* and wind-veer angle alpha.


The distributions for different conditions in the WAsP wind atlas file (*.lib) corresponds to the same distribution of Geostrophic winds, but frequency distributions for different surface roughness will differ because of the different wind-veer angles alpha, i.e. they have different rotations relative to the directional distribution of Geostrophic winds. The height-dependence of wind-speed distributions is determined by logarithmic wind profiles for the different values of the surface roughness.


Best regards,
Morten

[pdoubrawa]

Thank you very much for your answer, it was very helpful.

[pdoubrawa]

I have yet another question about this...

Equations (8.5) in page 567 of the European Wind Atlas provide the geostrophic wind in a rotated coordinate system aligned with the surface wind.

In order to rotate the geostrophic wind coordinates back to a cartesian system, do you use the original mast time series of wind direction to determine the angle of rotation (thus assuming the direction at anemometer height to be the same as the direction at the surface) ?

Thank you very much!
Paula

[Morten]

Hi Paula,


I think it would be most accurate to use time series as you suggest. However, WAsP only has access to the observed mean wind climate (*tab; *.owc; *.omwc). This file is produced by a independent program, usually the WAsP climate analyst, and it provides statistics in sectors and wind-speed bins only. The directional corrections for different surface roughness in the Wind Atlas File (*.lib) are done inside WAsP. This redistributes of the sector frequencies in the wind rose depending on the wind veer angle.


Cheers,
Morten

[pdoubrawa]

Hello, Morten


Thank you for your answer. Finally, I am still a bit confused about how WAsP calculates the Weibull parameters from the frequency distribution. I have two questions, can you please take a look at them?


Question 1:
After redistributing the frequencies across sectors based on the veer angle, WAsP uses the logarithmic wind profile to calculate wind speed values for each of the standard heights. Then, does it redistribute the frequencies in the same manner that it was done for wind direction according to the veer angles?


Question 2:
From what I understand, WAsP uses the method of moments. The A,k calculation is based on the mean of the wind speed, the mean of the cubed wind speed, and the probability of winds higher than the mean. How is this obtained from the frequency distribution for a certain height and roughness?


Again, thank you for your help!


Paula

[Morten]

Hi Paula,


The answer to your first question is no. The generalized winds are defined for flat terrain, so there is no terrain-induced wind veer. The veer related to the Ekman spiral is not included either, perhaps because we do not assumed a specific value for the boundary layer height.


Regarding the second question, then the basic fitting of Weibull distributions to histograms is actually done by a method conserving 1) the third moment and 2) the probability of winds beyond the observed mean wind. This often distorts the mean wind slightly, but it gives a better fit of wind speed probabilities in the range of turbine operation. As for the wind-veer correction, then WAsP first applies the Weibull distributions to calculates two moments for each sector, I think the first and third one. These moments are redistributed among sectors in accordance with the wind veer. Finally, the new Weibull parameters are calculated by the veer-corrected moments.


Cheers,
Morten

[pdoubrawa]

Thank you very much, Morten.


I realized that my Question 1 above was not very clear. What I was actually asking, was about the redistribution of frequencies within one sector, but across the wind speed bins. Once the log law is used to calculate the wind speed for a certain height and roughness, what before was 1m/s may now be 1.2m/s for example. Does that mean that 20% of the frequency that was previously in bin 1 should now be moved to bin 2, and so on?


Thank you again!
Paula

[Morten]

Hi Paula,

There will be a shift of wind-speed probability and it could be calculated by shifting probabilities in wind-speed bins, just like you suggest. However, the WAsP method is to first calculate sector-wise Weibull distributions for the height of interest, and then calculate the frequency of occurrence in wind speed bins by the Weibull distributions.


Cheers,
Morten

[pdoubrawa]

Thank you, Morten! I am starting to understand it a bit better. I am sorry to be asking so many questions, I am just trying to understand what assumptions are being made behind the calculations.


Since the third moment and probability of winds higher than the mean are conserved, the only thing that changes with height is the first moment (mean) of the distribution.


In order to calculate this new mean for the desired height, does WAsP use the new wind speed bin limits obtained through the logarithmic profile, along with the original sector-wise probabilities from the tab file?

Paula

[Morten]

Hi Paula,

WAsP calculates the mean wind speed for new heights by the new Weibull distribution. There is a formula stating that a moment of order n can be calculated by Mn=A^n*Gamma[1+n/k]. When WAsP needs new wind-speed frequencies for AEP calculations, these also calculated by the Weibull distribution using p(u1
Cheers,
Morten

[pdoubrawa]

Hi, Morten


My numbers for A and k are still off when compared to WAsP's. Can you please answer a couple more questions?


At which point in the process of going from tab to lib does WAsP calculate the weibull parameters for the first time? From that point on, does it ever go back to probability distributions again, or are all calculations performed on A and k values?


It seems that the first thing WAsP does is calculate the first and third moments per sector given the frequencies in the tab file. Then it redistributes those according to the veer angle going up to the geostrophic wind, and then again according to the backing angle coming down to the surface for a given roughness class (is this correct?). However, moments are statistical measures of the sector, while the veer angle is a function of G and u* and therefore also a function of u. There is no one veer angle value per sector. Does WAsP use an average veer angle or the veer angle for a specific speed to do this redistribution?


Finally, when you say that the third moment and the probability of winds greater than the mean are conserved, are they conserved for a given roughness class no matter what height we are considering, or are they conserved for any roughness class and height? If the latter is the case, then the third moment calculated straight out of the tab file and redistributed across sectors according to the veer angle, will be the only third moment ever used in the entire calculation of the wind atlas?


Thank you so much for helping me move along with my research!

Paula

[Morten]

Hi Puala,


There is something I got wrong, something I did not explain well, and something I haven’t mentioned yet.


Let us start with my misunderstanding. I told you that WAsP starts by converting histograms to Weibull distributions and then work entirely with these. I now talked to Ib Troen who designed the algorithms (and wrote much of the European Wind Atlas). He explained that histograms of observed data actually are converted to histograms for the wind atlas roughness classes before fitting Weibull distributions. The geostrophic drag law is applied using individual wind speeds with different surface roughness in different directions, as I think you suspected. The fitting is done by the method matching the 3rd statistical moment and the probability of exceeding the observed mean wind. Later on WAsP will interpolate in the standard cases and then use the two-moment method.


The thing I did not explain well was the conversion of 3rd statistical moment and the probability of exceeding the observed mean wind. What I meant was that these statistics of the fitted Weibull distribution matches similar statistics of the observations. All wind-speed statistics will, however, change with height.


Finally I should say that there are things regarding the conversion of TAB files to LIB files, which we have not yet discussed. WAsP will correct the observed wind climate for orographic speed-up and veer (with the IBZ flow model), roughness changes (IBL model for internal boundary layers), obstacle shelter (Perera model) and the surface roughness in the geostrophic drag law will differ for each sector. You can see a table of these parameters if you right click a site in WAsP and select ‘show| site corrections’. Furthermore, the stability correction of the unperturbed wind profile will depend on heat-flux statistics specified in the project options, and by default these will differ for land and offshore surfaces. It is a little bit complicated and I must admit that I once gave up implementing these corrections in an independent program.


Cheers,
Morten

[pdoubrawa]

Hello, Morten


Thanks for clarifying that.


Still about the first point, which of the following two is correct:


1) WAsP obtains histograms for each roughness class and then calculates Weibull parameters per sector. Then for the different standard heights the shape parameter is kept constant and the scale parameter is calculated for the different heights according to the log law.


2) WAsP obtains a histogram for each combination of roughness class and standard height (redistributing frequencies across sectors and across wind speed bins) and only then does it fit the Weibull distribution.


I am using constant roughness, no terrain, and no heat flux in WAsP so I am just trying to "recreate" the most simple possible case scenario. My results should be close to WAsP's but there is still a significant offset in the scale parameter.


Thanks again
Paula

[Morten]

Hi Paula,


Method 2 is used,i.e. WAsP obtains a histogram for each combination of roughness class and standard height. The shape parameter will normally change with height for non-neutral atmospheric stability, but if you set all heat fluxes to zero it should be the same at all heights when the surface roughness is constant. There is some pages in the EWA (which I dont have at hand at the moment) explaining the stability corrections. However, I have been told that the exact method has been revised, so you will not be able to reconstruct this just by looking in the EWA.


Best regards,
Morten