 # Wind Profile Log Law

Wind energy density estimates are presented as a wind class from 1 to 7. Speeds are average wind speeds over the course of a year, although the frequency distribution of wind speed can provide different power densities for the same average wind speed.  To estimate wind speed at a given altitude z, the relationship with the wind profile of the atmospheric boundary layer (surface up to about 2000 meters) is usually logarithmic and is best approximated using the logarithmic wind profile equation, which takes into account surface roughness and atmospheric stability. Relationships between surface performance and wind are often used as an alternative to logarithmic wind characteristics when information on roughness or surface stability is not available. Power law is often used in wind energy evaluations where wind speeds at wind turbine height (≥ {displaystyle geq } 50 meters) must be estimated from shallow wind observations (~10 meters) or when wind speed data at different heights need to be set to a standard height before use. Wind profiles are created and used in a number of air pollution dispersion models.  The logarithmic wind profile is a semi-empirical relationship used to describe the vertical distribution of horizontal wind velocities above the ground in the atmospheric surface layer. The relationship is well described in the planetary boundary layer literature . The logarithmic wind profile is generally considered a more reliable estimator than the wind profile performance law, which is often used when neutral conditions are assumed and roughness information is not available. If there is some stability, there will be a Monin–Obukhov correction, but it will usually be small and the above equation should be more suitable than a simple linear interpolation. This is the night when the boundary layer should be the most stable, although I would still expect the above equation to fit better than simple linear interpolation. In almost all circumstances, wind speed increases faster at the surface and this is better represented by a logarithmic equation than by linear interpolation. The neutral atmospheric stability assumption discussed above is reasonable when the hourly average wind speed at an altitude of 10 m exceeds 10 m/s, when turbulent mixing overwhelms atmospheric instability.

 The value of 1/7 for α is generally assumed to be constant in wind resource assessments, as the differences between the two levels are usually not so large that significant errors are introduced into the estimates (usually < 50 m). However, if a constant exponent is used, it does not take into account surface roughness, the displacement of calm surface winds due to the presence of obstacles (i.e. zero plane shift) or the stability of the atmosphere.   In places where trees or structures obstruct the wind near the surface, the use of a constant exponent of 1/7 may result in completely incorrect estimates, and the logarithmic wind profile is preferred. Even under neutral stability conditions, an exponent of 0.11 over open water (e.g. for offshore wind farms) is more appropriate than 0.143,, which is more applicable on open land areas. where u {displaystyle u} is the wind speed (in meters per second) at z {displaystyle z} (in meters) and u {displaystyle u_{r}} is the known wind speed at a reference height z r {displaystyle z_{r}}. The exponent ( α {displaystyle alpha } ) is an empirically derived coefficient that varies with the stability of the atmosphere. Under neutral stability conditions, α {displaystyle alpha} is about 1/7 or 0.143. The logarithmic profile of wind speed is generally confined to the lowest 100 m of the atmosphere (i.e. the surface layer of the atmospheric boundary layer). The rest of the atmosphere consists of the remaining part of the planetary boundary layer (up to about 1000 m) and the troposphere or free atmosphere.

In the free atmosphere, the geostrophic relationships of the wind must be used. The logarithmic profile of wind speed is generally confined to the lowest 100 metres (325`) of the atmosphere (i.e. the surface layer of the atmospheric boundary layer). In the free atmosphere, the geostrophic relationships of the wind must be used. The equation for estimating wind speed (u) at altitude z (meters) above the ground is as follows: At the Reading site (-0.9685° East, 51.445° North), there were 13 profiles where no logarithmic equation was found when all the data we had was used (at 6:30 a.m. on the 21st). May 1983, 10:30 a.m. on May 31, 1983, 4:30 p.m. on August 23, 1983, 11:30 a.m. on August 27, 1983, 11:30 a.m.

on August 27, 1984, 7:30 a.m. on September 10, 1988, 3:30 p.m. on February 12, 2004, 7:30 a.m. on October 14, 2004, 3:30 p.m. on March 28, 2005, 11:30 p.m. on June 2, 2008, 10:30 a.m. on August 31, 2008, 8:30 p.m. on August 8, 2009 and 6:30 p.m.

on June 21, 2010). The equation for estimating the average wind speed (u z {displaystyle u_{z}} ) at the height z {displaystyle z} (meters) above the ground is: The above equation has three unknowns, A, h and z0, which can be solved because we have three wind speeds at 2m, 10m and 50m, which we call speed2m, speed10m and speed50m. It can be shown that the wind profile law is a relationship between wind speeds at one altitude and those at another altitude. The roughness length (z0) is a corrective measure to take into account the influence of the roughness of a surface on the flow of the wind and is between 1/10 and 1/30 of the average height of the roughness elements on the ground. On smooth, open waters, a value of about 0.0002 m can be expected, while on shallow open grasslands z0 ≈ 0.03 m, arable land ≈ 0.1-0.25 m and bushes or forests ≈ 0.5-1.0 m (values above 1 m are rare and indicate too rough terrain). The zero plane offset (d) is the height in meters above the ground at which no wind speed is reached by flow obstacles such as trees or buildings. It is generally estimated to represent 2/3 of the average height of obstacles. For example, if winds are estimated over a forest canopy of height h = 30 m, the displacement of the plane zero d = 20 m. The roughness length ( z 0 {displaystyle z_{0}} ) is a corrective measure to take into account the influence of the roughness of a surface on the flow of the wind. That is, the value of the roughness length depends on the terrain. The exact value is subjective and the references indicate a range of values, making it difficult to give final values. In most cases, references represent a tabular format with a value of z 0 {displaystyle z_{0}} for some terrain descriptions.

For example, for very flat terrain (snow, desert), the approximate length can be between 0.001 and 0.005 m.  Similar to open ground (grasslands), the typical range is 0.01 to 0.05 m. For arable land and scrubland/forests, beaches are 0.1 to 0.25 m and 0.5 to 1.0 m, respectively. When estimating wind loads on structures, areas can be described as suburban or densely urban, with ranges typically 0.1 to 0.5 m and 1 to 5 m, respectively.  Logarithmic www.chemeurope.com/en/encyclopedia/Wind_profile_power_law.html of wind profiles are generated and used in many air pollution dispersion models. . Atmospheric shift books such as “The atmospheric boundary layer” by J.R. Garratt will show that the speed should vary during the day and near the surface according to a logarithmic equation. where u * is the friction rate (or shear rate) (m s-1), κ is the Karman constant (~0.41), d is the zero plane shift, z0 is the surface roughness (in meters) and is a stability term, where L is the Monin–Obukhov stability parameter. Under neutral stability conditions, z/L = 0 and surrenders. where u ∗ {displaystyle u_{*}} is the friction velocity (m s−1), κ {displaystyle kappa } is the Von Kármán constant (~0.41), d {displaystyle d} is the offset of the plane zero (in meters), z 0 {displaystyle z_{0}} is the surface roughness (in meters) and ψ {displaystyle psi } is a term of stability, where L {displaystyle L} is the Obukhov length of the Monin–Obukhov similarity theory. Under neutral stability conditions, z/L=0 {displaystyle z/L=0} and ψ {displaystyle psi } and the equation is simplified as follows: This equation is derived because a convective boundary layer is expected during the day, which implies a constant voltage leading to the above equation. There is a height of displacement, h, because there can be elements of roughness such as waves or bushes, which means that the variation of stress with height is only deposited somewhere above the surface at a constant.