and depends on the effective broadening pressure, pe (atm), given by
m where pm is the partial pressure of atmospheric constituent molecule, m, and Z is the broadening coefficient. For CO2, Z takes values 1.3, 1.0, 0.81, and 0.78, for collisions between CO2 molecules and CO2 (self broadening), N2, O2, and argon, respectively. For ozone, we can take pe = 1 and Z = 1, for ozone-air collisions, as it is a minor constituent of the atmosphere. Care must be taken with the units when the effective broadening pressure is involved in the definition of the dimensionless line-structure parameter, [. If pe is in atm, then the band mean line half-width, bc, must be in cm"1 atm"1 according to eqn (4.5).
220.127.116.11 Limiting forms Let us first examine the variation of the band absorp-tance with absorber amount. First, we note that the line structure parameter, 3, is a measure of the overlapping of the rotational lines in the band. When 3 ^ 1, the lines are non-overlapping, as the effective band mean line half-width, bcpe, for collisionally broadened lines, is much smaller then the mean line spacing. When 3 ^ 1 the overlapping of the rotational lines is so large that the line structure of the band is smeared out. In Fig. 4.15 is shown the band absorptance for the 9.6 ¡m bands of ozone as a function of effective broadening pressure for ozone amounts ranging from a typical present atmospheric amount (0.001 g cm"2) to a very low amount (0.00001 g cm"2). We can observe three important limits. As the absorber amount becomes very small the band absorptance goes to the pressure-independent linear limit. As the pressure becomes very small the band absorptance is that of Doppler-broadened non-overlapping lines, and hence the band absorptance is independent of pressure. At sufficiently high pressures, line overlapping due to collisional broadening smears out the line structure and so the band absorptance becomes independent of pressure.
In Fig. 4.16 is shown the variation of the band absorptance for the CO2 15 Im bands as a function of absorber amount, for a relatively high pressure of 1 atm and a low pressure of 0.001 atm. First, we note the linear limit, A = Aou, as the absorber amount becomes small, u ^ 1, independently of pressure. For very high absorber amounts, u ^ 1, the band absorptance varies as the logarithm of the absorber amount, A = Ao ln u for 3 ^ 1 and A = Ao ln 3u for ¡3 <C 1, independently of pressure. The square-root limit, A = A0^f]3u, is attained depending on three conditions. First, the lines must be non-overlapping (3 ^ 1). Secondly, the line strengths are large, u/3 ^ 1, and thirdly the path length, or absorber amount, is not too large, 3u ^ 1. We see that the square
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