Should we rescale TurbSim data?
This is a copy of an e-mail I sent to Neil Kelley today. I thought it might be useful to allow everyone to comment on it.
The Europeans rescale their wind data so they get better agreement between the statistics of their wind files and the targets from the standard. There are four things that cause the statistics of a subset of the TurbSim-generated time series to differ from the standard’s targets. One is the loss of frequency due to the fact that we don’t use an infinitely long time series, which would produce infinitesimal delta frequencies. The second is due to the fact that this is a stochastic process and there will be variations in the statistics for different seeds, the third is that we use only a subset of the data generated, and the fourth is interpolation smoothing.
The way the folks at Risoe do it is to take the average values of the four center points of an even grid. They do this for each time step that will be used in the aeroelastic simulation. For instance, if they intend to throw away the first 30 seconds of a 630 second time series and use 600 seconds, they compute the statistics of the 30-630 seconds.
Using that series, they compute the mean and standard deviation (Mean_act, SD_act). Then they rescale all points for all grids from 0 to 630 seconds with the following formula:
U_new = ((U_old-Mean_act)/(SD_act))*SD_target + Mean_target
They do something similar for V and W.
V_new = ((V_old-Mean_act)/(SD_act))*SD_target W_new = ((W_old-Mean_act)/(SD_act))*SD_target
We have the addition wrinkle in that we cannot depend on people choosing an even number of grid points. If we choose to use the average of four points near, but not at, the center of the y-z planes, we won’t be at hub height, so we’ll have a problem with wind shear.
Obviously, we don’t want to choose the center (or any other point) because we won’t rescale to eliminate the interpolation smoothing. We should also not use the average of the eight points of any grid cube because that is the worst case. We need to choose some point at a certain distance from a grid point so that it will experience an “average” amount of interpolation smoothing. I imaging that someone who has taken calculus more recently than me could figure out what the distance is. My first guess is that the surface of equal smoothing describes a sphere that is centered at the middle of each cube. The method of using the center of a face would be ideal only if the sphere had a diameter equal to the grid spacing. Adding the additional wrinkle that the grid spacing is not the same in every direction, it may be difficult or impossible to determine the surface of average smoothing.
To come up with something that may work for odd-sized grids, I propose that we use the center of one face that lies in the x-y plane at hub height.
I think it is important that this new feature be added to TurbSim. I’d like to see it available for all models, but if not, please do it for the Kaimal model.