Roughness length

Roughness length is an important parameter in the evaluation of vertical wind profile.

(1)\[\begin{equation} u(z) = \frac{u_{*}}{\kappa} \left[ \ln\left(\frac{z-d}{z_0}\right) + \psi \left(\frac{z-d-z_0}{L}\right) \right] \end{equation}\]

where :

• \(u_{*}\) is friction velocity.

• \(\kappa\) is Von Kármán constant (~0.4).

• \(z_0\) is roughness length.

• \(L\) is the Monin-Obukhov length.

On standard condition (1) becomes :

(2)\[\begin{equation} u(z) = \frac{u_{*}}{\kappa} \ln \left(\frac{z}{z_0}\right) \end{equation}\]

Deriving (2) we obtain the log wind profile to derive mean wind speed knowing the roughness length & wind speed at \(z_1\).

\[u(z_2) = u(z_1)\frac{\ln (z_2 - d) / z_0}{\ln (z_1 -d) / z_0}\]

Roughness length evaluation

The surface roughness length over land depends on the surface cover and land use and is often difficult to estimate.

Class index	Short terrain description	z0 (m)
1	Open sea, fetch at least 5 km	0.0002
2	Mud flats, snow; no vegetation, no obstacles	0.005
3	Open flat terrain; grass, few isolated obstacles	0.03
4	Low crops; occasional large obstacles, x/H > 20	0.10
5	High crops; scattered obstacles, 15 < x/H < 20	0.25
6	Parkland, bushes; numerous obstacles, x/H ≈ 10	0.5
7	Regular large obstacle coverage (suburb, forest)	1.0
8	City centre with high- and low-rise buildings	≥ 2

Todo

Roughness length user guide under construction.

User Guide Wind Distribution