The stratified vertical structure of the bulk properties of an atmosphere is a consequence of hydrostatic balance. For an atmosphere in a state of rest, the pressure,/», must support the weight of the fluid above it. By equating pressure forces and gravitational forces, one finds that dp = -gpdz where g is the acceleration due to gravity, p is the air density, and dp is the differential change in pressure over the small height interval dz. Combining this equation with the ideal gas law p = Mp /RT = Mn , one finds upon integration p( z) = p0(z)exp[-f dz' / H (z')] (9.1)
where M is the mean molecular weight, T the temperature, R the gas constant, and H = RT / Mg the atmospheric scale height. The ideal gas law allows us to write similar expressions for the density, p, and the concentration, n. Clearly, from a knowledge of the surface pressure p(z0) and the variation of the scale height H(z) with height z, the hydrostatic Eq. (9.1) allows us to determine the bulk gas properties at any height. Equation (9.1) applies to well-mixed gases, but not to short-lived species such as ozone, which is chemically created and destroyed.
The total number of air molecules in a 1 m2 wide vertical column extending from sea level to the top of the atmosphere is 2.15 x 1029 molecules. In comparison the total column amount of ozone is about 1.0 x 1023 molecules m-2. The height in millicentimeters (10-5 m) that the ozone gas in the atmosphere would occupy, if it
were compressed to standard pressure (1,013 [hP]; 1 hP (hectoPascal) = 1 Nm ) at standard temperature (0°C), is called the Dobson unit (DU). Thus, one Dobson unit refers to a layer of ozone that would be 10 |im thick under standard temperature and pressure. The conversion is 1 DU = 2.69 x 1020 molecules m . The 1976 US Standard Atmosphere (Anderson et al., 1987) contains about 348 DU of ozone gas.
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