Thelog wind profile is a semi-empirical relationship commonly used to describe thevertical distribution of horizontalmeanwind speed within the lowest portion of theplanetary boundary layer (PBL).^[1]Thelogarithmic profile of wind speeds is generally limited to the lowest 100 m of the atmosphere (i.e., thesurface layer of theatmospheric boundary layer). The rest of the atmosphere is composed of the remaining part of the PBL (up to around 1 km) and thetroposphere or free atmosphere. In the free atmosphere,geostrophic wind relationships should be used, instead.

The equation to estimate the mean wind speed (${\displaystyle u_z}$) at height${\displaystyle z}$ (meters) above the ground is:

${\displaystyle u_z=\frac{u_{\ast }}{\kappa }\left[\ln \left(\frac{z-d}{z_0}\right)+\psi (z,z_0,L)\right]}$

where${\displaystyle u_{\ast }}$ is thefriction velocity (m s⁻¹),${\displaystyle \kappa }$ is theVon Kármán constant (~0.41),${\displaystyle d}$ is the zero plane displacement (in metres),${\displaystyle z_0}$ is thesurface roughness (in meters), and${\displaystyle \psi }$ is astability term where${\displaystyle L}$ is theObukhov length fromMonin-Obukhov similarity theory. Underneutral stability conditions,${\displaystyle z/L=0}$ and${\displaystyle \psi }$ drops out and the equation is simplified to,

${\displaystyle u_z=\frac{u_{\ast }}{\kappa }\left[\ln \left(\frac{z-d}{z_0}\right)\right]}$.

Zero-plane displacement (${\displaystyle d}$) is the height in meters above the ground at which zero mean wind speed is achieved as a result of flow obstacles such as trees or buildings. This displacement can be approximated as²/₃ to³/₄ of the average height of the obstacles.^[2] For example, if estimating winds over a forest canopy of height 30 m, the zero-plane displacement could be estimated as d = 20 m.

Roughness length (${\displaystyle z_0}$) is a corrective measure to account for the effect of the roughness of a surface on wind flow. That is, the value of the roughness length depends on the terrain. The exact value is subjective and references indicate a range of values, making it difficult to give definitive values. In most cases, references present a tabular format with the value of${\displaystyle z_0}$ given for certain terrain descriptions. For example, for very flat terrain (snow, desert) the roughness length may be in the range 0.001 to 0.005 m.^[2] Similarly, for open terrain (grassland) the typical range is 0.01-0.05 m.^[2] For cropland, and brush/forest the ranges are 0.1-0.25 m and 0.5-1.0 m respectively. When estimating wind loads on structures the terrains may be described as suburban or dense urban, for which the ranges are typically 0.1-0.5 m and 1-5 m respectively.^[2]

In order to estimate the mean wind speed at one height (${\displaystyle z_2}$) based on that at another (${\displaystyle z_1}$), the formula would be rearranged,^[2]

${\displaystyle u(z_2)=u(z_1)\frac{\ln \left((z_2-d)/z_0\right)}{\ln \left((z_1-d)/z_0\right)}}$,

where${\displaystyle u(z_1)}$ is the mean wind speed at height${\displaystyle z_1}$.

The log wind profile is generally considered to be a more reliable estimator of mean wind speed than thewind profile power law in the lowest 10–20 m of the planetary boundary layer. Between 20 m and 100 m both methods can produce reasonable predictions of mean wind speed in neutral atmospheric conditions. From 100 m to near the top of the atmospheric boundary layer the power law produces more accurate predictions of mean wind speed (assuming neutral atmospheric conditions).^[3]

The neutral atmospheric stability assumption discussed above is reasonable when the hourly mean wind speed at a height of 10 m exceeds 10 m/s where turbulent mixing overpowers atmospheric instability.^[3]

Log wind profiles are generated and used in manyatmospheric pollution dispersion models.^[4]

• Wind profile power law
• List of atmospheric dispersion models

• Atmospheric dispersion modeling
• Boundary layer meteorology
• Wind power
• Vertical distributions

• Articles with short description
• Short description matches Wikidata