### Characteristics of the atmospheric boundary layer

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The atmospheric boundary layer, also known as the Earth’s boundary layer, is the lowest part of the atmosphere whose properties are directly affected by the Earth’s surface. Here, physical quantities like speed, temperature, relative humidity can vary drastically in time and space. For example, an important parameter of wind resource characteristics is the variation of horizontal wind speed along the height above ground level. It can be expected that the horizontal wind speed is zero at the earth’s surface and increases with height in the atmospheric boundary layer. The change of wind speed with height is called the vertical wind profile of wind speed or vertical wind shear. In wind energy engineering, vertical wind shear is an important design parameter because: (1) it directly determines the output of wind turbines on a tower of a certain height; (2) It will strongly affect the life of the wind turbine blades. The fatigue life of wind turbine blades is affected by cyclic loading, which results from blade rotation through a vertically varying wind field.

In wind energy applications, there are at least two fundamental issues of interest in determining vertical wind profiles:

· Instantaneous changes in wind speed as a function of height (time scale on the order of seconds);

· Seasonal variation in mean wind speed as a function of altitude (monthly or annual average).

It should be noted that these are separate and distinct problems, and it is often mistakenly assumed that there is one approach to both. Changes in the “instantaneous” wind profile are related to the boundary layer similarity theory (Schlichting, 1968). On the other hand, changes in the long-term average as a function of height, related to the statistical incidence of various influencing factors such as atmospheric stability (discussed later), must rely on more empirical methods (Justus, 1978).

In addition to changes due to atmospheric stability, wind speed changes with altitude are also related to ground roughness and topography. These factors are discussed in the following sections.

**Atmospheric ****d****ensity and ****p****ressure**

In addition to changes due to atmospheric stability, wind speed changes with altitude are also related to ground roughness and topography. These factors are discussed in the following sections.

Atmospheric Density and Pressure

Wind power is a function of air density as shown in the wind power per unit area P/A or wind power density formula (1.1). Air density ρ is a function of temperature T and pressure p, both of which vary with altitude. The density of dry air can be determined using the ideal gas law and can be expressed as (1.2):

P/A=1/2ρAU^{3} (1.1)

ρ=p/RT=3.4837p/T (1.2)

In the formula, the density unit is kg/m³, the pressure unit is kPa (kN/m²), and the temperature unit is Kelvin. Wet air is slightly less dense than dry air, but there are few corrections for air humidity. Air density as a function of humidity can be found in many thermodynamic textbooks, such as Balmer (1990).

The International Standard Atmosphere assumes that the temperature and pressure at sea level are 288.5K and 101.325kPa, respectively, so the air density at standard sea level is 1.225kg/m³ (see Avallone and Baumeister, 1978). Air pressure decreases with altitude. The pressure of the International Standard Atmosphere below 5000m above sea level can be approximately expressed as:

p= 101. 29 -(0. 011837)z+(4. 793×10^{-7})z^{2} (1.3)

where z is the height in m and the pressure in kPa. Of course, the actual pressure may vary around the standard pressure as the weather changes. In fact, at any location, the effect of daily and seasonal temperature fluctuations on air density is much greater than the effect of daily and seasonal changes in pressure and air humidity on air density.