Planetary Boundary Layer - Cause of Surface Wind Gradient

Cause of Surface Wind Gradient

Typically, due to aerodynamic drag, there is a wind gradient in the wind flow just a 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 one level and the air at those levels immediately above and below it, which is important in dispersion of pollutants and in soil erosion.

The reduction in velocity near the surface is a function of surface roughness, so wind velocity profiles are quite different for different terrain types. Rough, irregular ground, and man-made obstructions on the ground can reduce the geostrophic wind speed by 40% to 50%. Over open water or ice, the reduction may be only 20% to 30%. These effects are taken into account when siting wind turbines.

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 (within the surface layer), 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.