Log wind profile
Encyclopedia
The Log wind profile is a semi-empirical relationship used to describe the vertical distribution of horizontal wind speeds above the ground within the atmospheric surface layer. The relationship is well described in the planetary boundary layer
literature .
The logarithmic
profile of wind speeds is generally limited to the lowest 100 meters (325') of the atmosphere (i.e., the surface layer
of the atmospheric boundary layer). The rest of the atmosphere is composed of the remaining part of the planetary boundary layer (up to around 1000m) and the troposphere or free atmosphere. In the free atmosphere, geostrophic wind relationships should be used.
The equation to estimate the wind speed (
) at height 
(meters) above the ground is:
where
is the friction
(or shear
) velocity
(m s-1),
is von Karman's
constant
(~0.41),
is the zero plane displacement, 
is the surface roughness
(in meters), and
is a stability
term where
is the Monin-Obukhov
stability parameter. Under neutral stability
conditions,
and 
drops out.
Zero-plane displacement (
) is the height in meters above the ground at which zero wind speed is achieved as a result of flow obstacles such as trees or buildings. It is generally approximated as 2/3 of the average height of the obstacles. For example, if estimating winds over a forest canopy of height h = 30 m, the zero-plane displacement would be d = 20 m.
Roughness length (
) is a corrective measure to account for the effect of the roughness of a surface on wind flow, and is between 1/10 and 1/30 of the average height of the roughness elements on the ground. Over smooth, open water, expect a value around 0.0002 m, while over flat, open grassland 
≈ 0.03 m, cropland ≈ 0.1-0.25 m, and brush or forest ≈ 0.5-1.0 m (values above 1 m are rare and indicate excessively rough terrain).
The log wind profile is generally considered to be a more reliable estimator than the Wind profile power law
, which is commonly used when neutral conditions are assumed and roughness information is not available.
.
Planetary boundary layer
The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...
literature .
The logarithmic
Logarithmic
Logarithmic can refer to:* Logarithm, a transcendental function in mathematics* Logarithmic scale, the use of the logarithmic function to describe measurements* Logarithmic growth* Logarithmic distribution, a discrete probability distribution...
profile of wind speeds is generally limited to the lowest 100 meters (325') of the atmosphere (i.e., the surface layer
Surface layer
The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface...
of the atmospheric boundary layer). The rest of the atmosphere is composed of the remaining part of the planetary boundary layer (up to around 1000m) and the troposphere or free atmosphere. In the free atmosphere, geostrophic wind relationships should be used.
The equation to estimate the wind speed (
) at height (meters) above the ground is:where
is the frictionFriction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
(or shear
Simple shear
In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value:\ V_x=f\ V_y=V_z=0And the gradient of velocity is constant and perpendicular to the velocity itself:...
) velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
(m s-1),
is von Karman'sTheodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
constant
Von Kármán constant
In fluid dynamics, the Von Kármán constant , named for Theodore von Kármán, is a dimensionless constant describing the logarithmic velocity profile of a turbulent fluid flow near a boundary with a no-slip condition...
(~0.41),
is the zero plane displacement, is the surface roughnessRoughness Length
Roughness length 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 is zero. It is so named because it is typically related to the height of terrain...
(in meters), and
is a stabilityAir pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...
term where
is the Monin-ObukhovMonin-Obukhov Length
The is used to describe the effects of buoyancy on turbulent flows, particularly in the lower tenth of the atmospheric boundary layer. It was first defined by Alexander Obukhov in 1946,...
stability parameter. Under neutral stability
Air pollution dispersion terminology
Air pollution dispersion terminology includes the words and technical terms that have a special meaning to those who work in the field of air pollution dispersion modeling...
conditions,
and drops out.Zero-plane displacement (
) is the height in meters above the ground at which zero wind speed is achieved as a result of flow obstacles such as trees or buildings. It is generally approximated as 2/3 of the average height of the obstacles. For example, if estimating winds over a forest canopy of height h = 30 m, the zero-plane displacement would be d = 20 m.Roughness length (
) is a corrective measure to account for the effect of the roughness of a surface on wind flow, and is between 1/10 and 1/30 of the average height of the roughness elements on the ground. Over smooth, open water, expect a value around 0.0002 m, while over flat, open grassland ≈ 0.03 m, cropland ≈ 0.1-0.25 m, and brush or forest ≈ 0.5-1.0 m (values above 1 m are rare and indicate excessively rough terrain).The log wind profile is generally considered to be a more reliable estimator than the Wind profile power law
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 must be estimated from near surface wind observations , or where wind speed data at various...
, which is commonly used when neutral conditions are assumed and roughness information is not available.
Applications
Log wind profiles are generated and used in many atmospheric pollution dispersion modelsAtmospheric dispersion modeling
Atmospheric dispersion modeling is the mathematical simulation of how air pollutants disperse in the ambient atmosphere. It is performed with computer programs that solve the mathematical equations and algorithms which simulate the pollutant dispersion...
.