# Wind profile in a stable atmosphere

Hi,

I have a question regarding the wind profile computed by TurbSim based on z0 and RICH_NO in a stable atmosphere. It seems to me that TurbSim uses a constant psi in the wind profile calculation, based on a constant z/L calculated from the RICH_NO input. Did I understand correctly? If so, can you explain to me why the psi should be a constant?

I don’t understand why psi should not be a function of height, (z/L from RICH_NO → L from z=HH → psi from Ht/L and z_ref/L):
U=U_Ref*( LOG( Ht / Z0 ) - psiM(Ht) )/( LOG( z_Ref / Z0 ) - psiM(z_ref) )

Example of the difference:
When I calculate the profile with a constant psi of -1.516 (Ri=0.1205 z/L=0.303), I obtain the same profile as TurbSim, ranging from 15.7 m/s at 8.75 m to 18.3 m/s at 229.25 m. When I calculate a varying psi of 0.112 (8.75 m) to 2.921 (229.25 m) (Ri=0.1205 & HH=119m → L=393), I rather obtain a profile ranging from 14.9 m/s (8.75 m) to 19.8 m/s (229.25m). The profiles are obtained with a reference height of 80 m and a reference wind speed of 17.4 m/s.

Regards,
Astrid

Hi, Astrid.

There is a single stability parameter, RICH_NO, for each TurbSim simulation. Stability could, of course, vary with height, but that was not what was implemented in the code.

You’d have to ask Neil Kelley, who originally pulled together the theory for TurbSim (and its predecessor codes), but I believe that he wanted to use a single z/L because he had data relating Richardson Number with z/L. Since RICH_NO is constant in the code, z/L is, too. It became just an alternate way of expressing stability.

You could certainly change it if you wanted to.