Quantities such as pressure, density and mean free path vary dramatically with height in the atmosphere. The variation can be over many orders of magnitude and is very much larger than horizontal or temporal variations. Meteorologists therefore commonly make use of a "standard atmosphere" in which geophysical quantities have been averaged horizontally and in time, and which vary as a function of height only. This is known as the International Civil Aviation Organisation (ICAO) Standard Atmosphere as illustrated in Figure 3.
Figure 3: Vertical variation of pressure in hPa, and density in g/m^3, for the US extension to the ICAO standard atmosphere. Adapted from Wallace and Hobbs (1977), p12.
Generally, observed values of atmospheric pressure and density are fairly close to the "standard atmosphere" values for the same level. The ICAO standard atmosphere is specified by
- sea level pressure (p) 1013.2 hPa
- sea level temperature (T) 15 deg C
- fixed lapse rates for p and T.
In the lower part of the "standard" or "average" atmosphere, which is assumed to be dry, the temperature lapse rate is 6.5 deg C per km, up to 11km altitude. From there up to 20km altitude the temperature lapse rate is 0 deg C per km, but from about 20km to 32km the lapse rate is -1.0 deg C per km, in which case the atmospheric temperature increases with altitude.
The vertical variation of pressure (p) with height (z) may be derived as approximately (see Wallace and Hobbs, 1977 pp 12-13):
p(z) = p(0) exp (-z/H)
where p(z) is the pressure at height z above sea level, p(0) is the sea level pressure, and H is a constant called the scale height. Pressure decreases by a factor of e in passing upward through a layer of depth H. For the earth's atmosphere, H is about 8.4 km.
A similar approximate expression may be derived for density p as follows:
p (z) = p (0) exp (-z/H)
Note that density also decreases rapidly with height. It can be shown that half of the mass of the earth's atmosphere is below the 500 hPa level or an altitude at about 5.5 km.
At an altitude of 50 km the pressure (ie mass of particles above unit area at that level) is about 1hPa so that only about 0.1 per cent of the mass of the atmosphere lies above that level. (Recall that 1 millibar = 100 hectoPascals and that 1 Pascal = 1 Newton/m^2). Similarly because the pressure at 90 km is about 0.001 hPa, only about one millionth of the mass of the atmosphere lies above that level.
Dr D C Griersmith
