Wind profile power law

The wind profile power law is a relationship between the wind speeds at one height, and those at another.

The power law is often used in wind power assessments where wind speeds at the height of a turbine (>~ 50 metres) must be estimated from near surface wind observations (~10 metres), or where wind speed data at various heights must be adjusted to a standard height prior to use. Wind profiles are generated and used in a number of atmospheric pollution dispersion models.

The wind profile of the atmospheric boundary layer (surface to around 2000 metres) is generally logarithmic in nature and is best approximated using the log wind profile equation that accounts for surface roughness and atmospheric stability. The wind profile power law relationship is often used as a substitute for the log wind profile when surface roughness or stability information is not available.

The wind profile power law relationship is :

where ${\displaystyle u}$ is the wind speed (in metres per second) at height ${\displaystyle z}$ (in metres), and ${\displaystyle u_{r}}$ is the known wind speed at a reference height ${\displaystyle z_{r}}$. The exponent (${\displaystyle \alpha }$) is an empirically derived coefficient that varies dependent upon the stability of the atmosphere. For neutral stability conditions, ${\displaystyle \alpha }$ is approximately 1/7, or 0.143.

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