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.