Temperature (K)

Figure 1.1 Typical temperature and pressure profiles. Based on the 1976 US Standard Atmosphere.

Temperature (K)

Figure 1.1 Typical temperature and pressure profiles. Based on the 1976 US Standard Atmosphere.

radiation would reach the ground. The role O, plays in absorbing these photons is crucial because a photon of 250 nm wavelength has an energy of ~5 eV, enough to break chemical bonds in DNA or interfere in other ways with biological processes [2^4],

Luckily for the Earth's various life forms, O, has a prodigious ability to absorb radiation with wavelengths between 200 and 300 nm. At its maximum at 250 nm, the absorption cross-section of O, is 1.15 x 10" cm2, dropping to 3.4 x 10 19 cm2 at 300 nm (see DeMore et al. [5], Table 7). To get an idea of how effective Os is as an absorber, we can estimate the transmission of radiation through a typical atmospheric column using the Lambert-Beer exponential absorption law:

where Tr is the fraction of the incident beam that is transmitted, a is the cross-section of 0( at that wavelength (cm2), and C is the total column abundance of 03, which is typically around l()w molecules cm'2. At 250 nm, the transmission is -10 50. This is a phenomenally small number, and indicates that essentially none of the 250 nm radiation incident on the top of the atmosphere makes it through the O, to the surface. At 300 nm, where the O, cross-scction is considerably smaller. about 3% of the incident beam makes it to the surface.

The study of O, has become a subject of public interest since it was noted that the effluents of our society might lead to a gradual lowering of the amount of O, in the atmosphere. This reduction, in turn, would lead to enhanced ultraviolet radiation at the surface of the Earth, which would be detrimental to various life forms at the surface. Much of the research detailed in this book was performed with the goal of better understanding the processes by which mankind affects the abundance of O,. For a history of the early research into (),, see Dobson [6| and Nicolet [71.

O, is also an important component of the atmosphere for other, less politically charged reasons. One of these is the role O, plays in the energy balance of the stratosphere. As discussed above, O, is a prodigious absorber of ultraviolet photons. In addition, O, also absorbs strongly in the infrared, especially near 9.6 pm [8]. This absorption of solar and infrared radiation heals the stratosphere, and is one of the main reasons the temperature of the stratosphere increases with height.

On an annual and global mean, the stratosphere is approximately in radiative equilibrium. The absorption of solar and infrared radiation by O, exceeds the emission of infrared radiation by O, by about 15 W m 2. Thus, O, is a net heat source for the stratosphere. This net heating of the stratosphere is balanced by the net infrared cooling of CO, and H .O [9].

Stratospheric O, also causes a net heating of the troposphere-surface system. Solar absorption by stratospheric 0; reduces the input of solar energy to the troposphere-surface system by 7 W m \ Downward infrared emission by stratospheric O,, on the other hand, warms the troposphere-surface system by 2 W m Enhanced infrared emission from stratospheric CO, and H,0 owing to the higher stratospheric temperatures warms the troposphere -surface system by 7 W m The net effect is a warming of the troposphere-surface system by about 2 Wm2 [9]. Depletion of stratospheric O, will therefore tend to cool the surface [10], although the exact magnitude and sign of the effect is dependent on the altitude of O, changes [11].

O, is indeed an important molecule in the stratosphere. Because it plays a role in so many aspects of the stratosphere, an understanding of O, requires the development of an integrated view of the dynamical, chemical, and radiative processes of the stratosphere. Such a view bridges traditional disciplines of chemistry and physics, and is emblematic of the necessity of thinking broadly in order to understand the problems confronting Earth.

1.1 The Ideal Gas Law

Before talking about 0„ lei us first discuss the ideal gas law, which relates pressure, density, and temperature:

In stratospheric research, pressure is usually expressed in hectopascals (hPa) or millibars (mb), which are equivalent units, e.g. 1 hPa = 1 mb. Pressure is also occasionally expressed in torr (1 torr = 1.3332 hPa). When using the ideal gas law, however, pressure must generally be converted to the MKS unit pascal (Pa; 1 Pa = 0.01 hPa = 1 kg m ' s 2). Temperature is always expressed in degrees kelvin (K). The constant used determines the form of density. If the constant is the universal gas constant (R = 8.31 J mol1 K ') then the density is in moles per cubic meter (mol ' m '). If the constant is the gas constant for dry air (R = 287 J kg 1 K ') then the density is in kilograms per cubic meter (kg m '). Finally, if the constant is Boltzmann's constant (k = 1.38 x 10'23 J molecule 1 K '), then the density is in molecules per cubic meter—also known as the number density. It should be obvious that it is crucial to make sure that the units in the equation are consistent. Failure to do so can result in errors of several orders of magnitude and cause you to look foolish in front of your colleagues. Trust me.

The most common form of density used in stratospheric research is number density, almost always with units of molecules per cubic centimeter. If the pressure used in the ideal gas law is the partial pressure of a gas, then the density determined will be the density of that particular gas. The number density of constituent X (X = 02, N>, Of, 11,0, etc.) is generally denoted [X). If the total pressure is used in the ideal gas law, then the total number density, denoted [M], is determined. We will also use the symbol M in chemical equations to refer to "any molecule", without regard to its elemental make-up. In practice, this means that M refers to N2 and 02. A useful shortcut to calculating number density is where pressure P is the partial pressure of X in hectopascals and temperature T is in Kelvin. If P is the total pressure, then the total number density [M] is calculated. Note that the sum of the number densities of the individual components of the atmosphere must sum to the total number density—just as the sum of the partial pressures must sum to the total pressure.

Another useful way of expressing the abundance of a constituent is the volume mixing ratio (VMR). Conceptually, the VMR of constituent X is the fraction of molecules in a given volume that are X. Mathematically, the VMR is the ratio of the number density of X to the total number density: [Xj/IMJ. VMRs are dimensionless pressure = constant x density x temperature

and never exceed I. Because the VMR is typically small, it is usually multiplied by 10h, 10", or 1()12 to obtain parts per million by volume (ppmv), parts per billion by volume (ppbv), or parts per trillion by volume (pptv), respectively. For example, a VMR of 5 x 10 6 or 5 ppmv of O, means that 5 out of every 1x10" (or 1 out of every 200,000) molecules in a sample is an O, molecule. Finally, the sum of the VMRs of all of the constituents in an air mass must equal 1.

Why is the VMR useful? Assume that the number density of X in an air parcel at pressure P0 and temperature T„ is [X]„. Now assume that the air parcel moves to a new location in the atmosphere and the temperature and pressure change to and T1KV. According to Boyle's law and Charles' law, the number density of X changes to

Now consider the VMR. The initial mixing ratio of X is [XJu/lM],,, where [MJ„ is the initial total number density. The VMR at the new temperature and pressure is [X|mrw/|Ml„ew, where [X|,ll lv is given in Equation 1.4 and

Combining Equations (1.4) and (1.5), the VMR at the new location is

Thus, while the number density of a constituent changes when temperature or pressure in an air mass change, the VMR does not. In other words, the VMR is conserved for changes in the pressure or temperature of a parcel. This property makes VMR useful. It should be noted that one can also define a mass mixing ratio (see problem 4 at the end of the chapter), but this is rarely used in stratospheric research.

Figure 1.2 shows contours of both the number density and VMR of O, in the 1 at i -tude—height plane. O, reaches maximum values of both number density (4.6 x 1012 molecules cm ' at -25 km) and VMR (10 ppmv at -32 km) over the equator. As one moves away from the equator, the number density peak moves to lower altitudes, but

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