Wind Shear Exponent

From Wind wiki

Wind moving across the Earth’s surface is slowed by trees, buildings, grass, rocks, and other obstructions in its path. The result is a wind velocity that varies with height above the Earth’s surface – a phenomena known as wind shear. For most situations, wind shear is positive (wind speed increases with height), but situations in which the wind shear is negative or inverse are not unusual. The increase in wind speed with height only holds true for the height above the effective ground level. The wind rushing over a field of corn sees the top of the corn, not the soil on which it grows, as the effective ground level.

The wind shear exponent, α, is a parameter used to factor in wind shear when determining how wind speed varies with height. One way of calculating this is from the following equation:

α=1/ln(z/z0 )

,where z_0 is the surface roughness length in meters and z is the reference height. Where this exponent is factored in is called the power law equation. The power law equation is given as:

v/v₀ =(h/h₀ )^α

v=v₀ (h/h₀ )^α

,where h_0 is the original height, h is the new height, v_0 is the velocity of the wind at the original height, and v is the velocity of the wind at the new height.

If you have the actual data for the wind speeds at various heights you can derive the wind shear exponent from the power law method. Simply taking the natural logarithm of both sides of the power law equation and with a few algebra steps, we get the following equation for the wind shear exponent:

α=ln(v/v₀ )/ln(h/h₀ )

,where v and h are the wind speed at the upper anemometer and the height of the upper anemometer, respectively, and h_0 and v_0 are the wind speed at the lower anemometer and the height of the lower anemometer, respectively.