Wind Regimes - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 19

Fig. 2.2 Near-surface air density as function of air temperature and surface pressure

2.7 Air Density

Apart from wind speed, the kinetic energy content of the atmosphere also depends
linearly on air density (see Eq. ( 1.1 )). Near-surface air density, q is a direct
function of atmospheric surface pressure, p and an inverse function of air tem-
perature, T. We have from the state equation for ideal gases:

q ¼ p
RT

ð 2 : 13 Þ

where R = 287 J kg -1 K -1 is the universal gas constant. Equation ( 2.13 )is
equivalent to the hydrostatic equation ( 2.1 ) above. Figure 2.2 shows air density for
commonly occurring values of surface temperature and surface pressure. The
Figure illustrates that air density can be quite variable. A cold wintertime high
pressure situation could easily come with a density around 1.4 kg/m 3 , while a
warm low pressure situation exhibits an air density of about 1.15 kg/m 3 . This is a
difference in the order of 20 %.
Figure 2.2 is valid for a dry atmosphere. Usually the atmosphere is not com-
pletely dry and the modifying effect of atmospheric humidity has to be considered.
Humid air is less dense than completely dry air. Meteorologists have invented the
definition of an artificial temperature which is called virtual temperature. The
virtual temperature, T v is the temperature which a completely dry air mass must
have in order to have the same density as the humid air at the actual temperature,
T. The virtual temperature is defined as:

T v ¼ T ð 1 þ 0 : 609q Þ ð 2 : 14 Þ

where q is the specific humidity of the air mass given in kg of water vapour per kg
of moist air. The temperatures in Eq. ( 2.14 ) must be given in K. The difference
between the actual and the virtual temperature is small for cold air masses and low
specific humidity, but can be several degrees for warm and very humid air masses.
Figure 2.2 can be used to estimate air density of humid air masses, if the