Wind gradient

In common usage, wind gradient, more specifically wind speed gradientor wind velocity gradient,or alternatively shear wind,is the vertical gradient of the mean horizontal wind speed in the lower atmosphere. It is the rate of increase of wind strength with unit increase in height above ground level. In metric units, it is often measured in units of meters per second of speed, per kilometer of height (m/s/km), which reduces to the standard unit of shear rate, inverse seconds (s−1). In common usage, wind gradient, more specifically wind speed gradientor wind velocity gradient,or alternatively shear wind,is the vertical gradient of the mean horizontal wind speed in the lower atmosphere. It is the rate of increase of wind strength with unit increase in height above ground level. In metric units, it is often measured in units of meters per second of speed, per kilometer of height (m/s/km), which reduces to the standard unit of shear rate, inverse seconds (s−1). Surface friction forces the surface wind to slow and turn near the surface of the Earth, blowing directly towards the low pressure, when compared to the winds in the nearly frictionless flow well above the Earth's surface. This layer, where surface friction slows the wind and changes the wind direction, is known as the planetary boundary layer. Daytime solar heating due to insolation thickens the boundary layer as winds warmed by contact with the earth's hot surface rise up and become increasingly mixed with winds aloft. Radiative cooling overnight gradually decouples the winds at the surface from the winds above the boundary layer, increasing vertical wind shear near the surface, also known as wind gradient. Typically, due to aerodynamic drag, there is a wind gradient in the wind flow, especially in the first few hundred meters above the Earth's surface—the surface layer of the planetary boundary layer. Wind speed increases with increasing height above the ground, starting from zero due to the no-slip condition. Flow near the surface encounters obstacles that reduce the wind speed, and introduce random vertical and horizontal velocity components at right angles to the main direction of flow.This turbulence causes vertical mixing between the air moving horizontally at various levels, which has an effect on the dispersion of pollutants, dust and airborne sand and soil particles. The reduction in velocity near the surface is a function of surface roughness. Wind velocity profiles are quite different for different terrain types. Rough, irregular ground, and man-made obstructions on the ground, retard movement of the air near the surface, reducing wind velocity. Because of the relatively smooth water surface, wind speeds do not decrease as much close to the sea as they do on land. Over a city or rough terrain, the wind gradient effect could cause a reduction of 40% to 50% of the geostrophic wind speed aloft; while over open water or ice, the reduction may be only 20% to 30%. For engineering purposes, the wind gradient is modeled as a simple shear exhibiting a vertical velocity profile varying according to a power law with a constant exponential coefficient based on surface type. The height above ground where surface friction has a negligible effect on wind speed is called the 'gradient height' and the wind speed above this height is assumed to be a constant called the 'gradient wind speed'. For example, typical values for the predicted gradient height are 457 m for large cities, 366 m for suburbs, 274 m for open terrain, and 213 m for open sea. Although the power law exponent approximation is convenient, it has no theoretical basis. When the temperature profile is adiabatic, the wind speed should vary logarithmically with height, Measurements over open terrain in 1961 showed good agreement with the logarithmic fit up to 100 m or so, with near constant average wind speed up through 1000 m. The shearing of the wind is usually three-dimensional, that is, there is also a change in direction between the 'free' pressure-driven geostrophic wind and the wind close to the ground. This is related to the Ekman spiral effect. The cross-isobar angle of the diverted ageostrophic flow near the surface ranges from 10° over open water, to 30° over rough hilly terrain, and can increase to 40°-50° over land at night when the wind speed is very low. After sundown the wind gradient near the surface increases, with the increasing stability.Atmospheric stability occurring at night with radiative cooling tends to contain turbulent eddies vertically, increasing the wind gradient. The magnitude of the wind gradient is largely influenced by the height of the convective boundary layer and this effect is even larger over the sea, where there is no diurnal variation of the height of the boundary layer as there is over land.In the convective boundary layer, strong mixing diminishes vertical wind gradient. The design of buildings must account for wind loads, and these are affected by wind gradient. The respective gradient levels, usually assumed in the Building Codes, are 500 meters for cities, 400 meters for suburbs, and 300 m for flat open terrain. For engineering purposes, a power law wind speed profile may be defined as follows: