# Roughness length

Roughness length (${\displaystyle z_{0}}$) is a parameter of some vertical wind profile equations that model the horizontal mean wind speed near the ground; in the log wind profile, it is equivalent to the height at which the wind speed theoretically becomes zero. In reality the wind at this height no longer follows a mathematical logarithm. It is so named because it is typically related to the height of terrain roughness elements. Whilst it is not a physical length, it can be considered as a length-scale representation of the roughness of the surface.

## Application

As an approximation, the roughness length is approximately one-tenth of the height of the surface roughness elements. For example, short grass of height 0.01m has a roughness length of approximately 0.001m. Surfaces are rougher if they have more protrusions. Forests have much larger roughness lengths than tundra, for example. Roughness length is an important concept in urban meteorology as the building of tall structures, such as skyscrapers, has an effect on roughness length and wind patterns.

 Terrain description ${\displaystyle z_{0}}$ (m) Open sea, Fetch at least 5 km 0.0002 Mud flats, snow; no vegetation, no obstacles 0.005 Open flat terrain; grass, few isolated obstacles 0.03 Low crops; occasional large obstacles, x/H > 20 0.10 High crops; scattered obstacles, 15 < x/H < 20 0.25 parkland, bushes; numerous obstacles, x/H ≈ 10 0.5 Regular large obstacle coverage (suburb, forest) 1.0 City centre with high- and low-rise buildings ≥ 2

## References

1. ^ WMO Guide to Meteorological Instruments and Methods of Observation WMO-No. 8 page I.5-13