Q. Can you set the wind shear exponent in the WAsP wind profile model?
A. No, you can't. And the reason is that WAsP is based on a logarithmic wind profile governed by the terrain surface roughness length z0:
U(z) = (u*/κ) ln(z/z0)
The wind shear exponent is used in connection with the assumption of a power-law wind profile:
U(z) = Ur (z/zr)α
In limited height ranges you may find the best wind shear exponent fit to a certain surface roughness length, and vice versa; but the fit is only approximate since logarithmic and power-law profiles are functionally different. Thus for a small height range around a height zr such a fitted relation is:
α = 1 / ln(zr /z0)
Furthermore, one should keep in mind that WAsP does not use a strict logarithmic profile; when WAsP takes terrain inhomogeneities and stability effects into account, the resulting wind profile will in general differ from a simple logarithmic profile.