Wind Regimes - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 11

not suited for windpower generation. Rather turbines have to be constructed in a
way that they can stand these destructive forces while being shut off. See also
Sects. 2.6 and 6.5 for wind hazards.

2.2 Driving Forces

The equations in the following Subchapters describe the origin and the magnitude
of horizontal winds in the atmosphere. We will start with the full set of basic
equations in Sects. 2.2.1 and 2.2.2 and will then introduce the usual simplifications
which lead to the description of geostrophic and gradient winds in Sect. 2.3 .
Geostrophic and gradient winds, which blow in the free atmosphere above the
atmospheric boundary layer, have to be considered as the relevant external driving
force in any wind potential assessment and any load assessment. Vertical varia-
tions in the geostrophic and gradient winds are described by the thermal winds
introduced in Sect. 2.4 .

2.2.1 Hydrostatic Equation

The most basic explanation of the wind involves horizontal heat gradients. The sun
heats the Earth's surface differently according to latitude, season and surface
properties. This heat is transported upward from the surface into the atmosphere
mainly by turbulent sensible and latent heat fluxes. This leads to horizontal tem-
perature gradients in the atmosphere. The density of air, and with this density the
vertical distance between two given levels of constant pressure, depends on air
temperature. A warmer air mass is less dense and has a larger vertical distance
between two given pressure surfaces than a colder air mass. Air pressure is closely
related to air density. Air pressure is a measure for the air mass above a given
location. Air pressure decreases with height. In the absence of strong vertical
accelerations, the following hydrostatic equation describes this decrease:

o p

oz ¼ gq ¼ gp

ð 2 : 1 Þ

RT

where p is air pressure, z is the vertical coordinate, g is the Earth's gravity, q is air
density, R is the specific gas constant of air, and T is absolute air temperature. With
typical near-surface conditions (T = 293 K, R = 287 J kg -1 K -1 , p = 1,000 hPa
and g = 9.81 ms -2 ) air pressure decreases vertically by 1 hPa each 8.6 m. In
wintry conditions, when T = 263 K, pressure decreases 1 hPa each 7.7 m near the
surface. At greater heights, this decrease is smaller because air density is