Like the oxygen molecule, ozone is broken apart through absorption of ultraviolet (UV) photons. A photon is a packet of energy that has a particular wavelength. An example is blue light, which has a wavelength of about 430 nm, and an energy of about 4.6x10-19 Joules. Red light, on the other hand, has a wavelength of about 630 nm and an energy of about 3.5x10-19 Joules. These values are based on the photon energy formula E = hc/lambda, which we used in section 2.1. We see that energy is inversely related to wavelength (), with the shorter wavelength photon having the greater energy. Ultraviolet light has wavelengths of 1 nm to 400 nm. If we imagine molecules as collections of tennis balls joined together by some adhesive material, then the photon energy needed to break the adhesive bond depends on the strength of the adhesive material. In the case of oxygen molecules, the bond is quite strong (e.g., the tennis balls are joined with Krazy glue). Hence, the photon required to break this bond must be very energetic. The chemical bonds between the oxygen atoms in ozone, however, are much weaker than those found in molecular oxygen (e.g., the tennis balls are joined with Scotch tape). As a result, less energetic photons, meaning those with longer wavelengths, can break apart ozone molecules. In order to understand how photons interact with oxygen and ozone molecules, we must understand the concept of absorption cross-section.

3.1 The Concept of Absorption Cross-Section

Absorption cross-section refers to the ability of a particular molecule to absorb a photon of a particular wavelength. It does not refer to an actual area size, even though it has units of area. Returning to Figure 5.01, it shows the absorption cross-sections for molecular oxygen and ozone (in units of cm2) as a function of photon wavelength. In this case, the absorption cross-section conveys the probability of interaction between light photons of a given energy and the oxygen or ozone molecules. While absorption cross-sections are the result of a quantum mechanical calculation, a "Newtonian" analogy to discrete dots can convey the idea.

Figure 5.06 illustrates the UV flux in terms of a steady rain of photons from the Sun. These are denoted by red lines. If the size of the target (cross-section) is small (represented by the diameter of the blue dots on the plot), then the probability of a photon reaching the surface (i.e. the bottom of the plot) is high. This is shown in the top panel. If we keep the dots in the same positions, but increase their diameters, then we see that the number of UV photons getting through to the surface decreases. This is shown in the bottom panel. The larger dots represent a larger cross-section. Similarly, if we increase the number of dots (i.e. increase the density of ozone), then we will also intercept more UV photons, and fewer will reach the surface.

Let's now revisit the plot of the absorption cross-sections of molecular oxygen and ozone in Figure 5.01. We see that molecular oxygen cross-sections are very small for wavelengths greater than 240 nm (so small they don't even appear on this plot). At wavelengths less than 240 nm, the cross-sections increase monotonically, all the way to 200 nm. Notice that molecular oxygen cross-sections have been multiplied by a factor of ten thousand (104) to even appear on this plot. Even though O2 cross-sections are very small, recall that 1 in every 5 molecules in the atmosphere is molecular oxygen, so there are many oxygen molecules with which photons may interact. The higher energy (shorter wavelength) photons are more likely to interact with molecular oxygen.

The plot of the ozone cross-section in Figure 5.01 looks somewhat different. The ozone cross-section is small for wavelengths above 325 nm. As we move to higher energies (shorter wavelengths), the cross-section increases, with a peak value near 10-17 cm2 at a wavelength of 255 nm. The cross-section decreases as we move to still higher energies (even shorter wavelengths). Here our classical analogy with dots fails us: we expect that higher energies are more likely to be intercepted by the dots. To explain what is actually observed, however, we require quantum mechanics. Quantum mechanics tells us that atoms and molecules absorb energy in discrete bundles (or quanta). The sizes of the quanta are dependent upon the type of atom or molecule and its energy state.

The energy of a photon is related to its wavelength, with longer wavelengths having less energy. Photons with too little or too much energy cannot be absorbed by the atom or molecule. Thus, cross-sections tend to have peak values at particular wavelengths dictated by the type of atom or molecule.

When ozone absorbs photons with wavelengths below 325 nm, an oxygen atom breaks away from the molecule. We write the reaction as

O2 + hc/lambda --> O2 + O

This is the ozone photolysis reaction we already saw in Section 2.1. The heat released by this reaction explains why the stratosphere is warmer than the upper troposphere. Indeed, the existence of the stratosphere is due to this heating. The absorption of UV photons by ozone both shields the surface from UV and heats the local atmosphere.

3.2 Ozone Shielding of UV Radiation From the Surface

In the bottom panel of Figure 5.01 we can see just how well ozone protects life at the surface from energetic photons. The figure depicts the amount of solar energy incident on Earth per unit area as a function of wavelength. The line labeled, "Top of the atmosphere," provides the level of solar radiation incident on Earth's atmosphere. The curve labeled "30 km" provides the amount of radiation received at 30 km above the surface, while the curve labeled "Surface" shows the amount of radiation incident at the surface. At 30 km (above the peak in the ozone layer) we observe substantial reductions in the amount of radiation received between 225 and 275 nm. The difference between the incident radiation at the top of the atmosphere and that received at 30 km is due to the absorption by ozone and oxygen. The closer we get to the surface, the more oxygen and ozone molecules to shield us from the radiation incident at the top of the atmosphere, with more and more absorption. By the time we get to the surface, virtually all photons with wavelengths less than 290 nm have been absorbed.

Also shown in Figure 5.01 are the locations of the parts of the spectrum that correspond to UV-a and UV-b radiation. The UV-a radiation is less energetic and extends from 320 to 400 nm. UV-b radiation is defined to be radiation with wavelengths between 280 and 320 nm. Exposure to significant amounts of UV-a and UV-b radiation increases the likelihood of skin cancer in susceptible individuals. UV-a radiation at the surface is reduced by about a factor of 2, while, in the UV-b band, ozone absorption has a significant impact, reducing the amount of radiation at 300 nm by a factor of over 1000. The decrease is even greater for UV-c, the most energetic of all ultraviolet radiation, with wavelengths between 1 and 280 nm. No UV radiation of this intensity reaches the surface, and it is a good thing, as it is highly destructive of genetic material and would do serious damage to biological organisms, including people.

3.3 Ozone Photolysis

The dissociation of molecules such as ozone by UV photons is known as photolysis (e.g., O3+hc/lambda --> O2+O). The photolysis rate is proportional to the density of the gas (e.g., O3 or O2) and the photolysis rate coefficient. Mathematically, ozone photolysis is represented as

Photolysis = J [O3]

Here, J is the photolysis rate coefficient, and [O3] is the ozone density. The photolysis rate generally depends upon the absorption cross-section of ozone and the number of incident photons at the necessary wavelengths. The number of photons in turn depends upon a number of other parameters: altitude, latitude, season, and time of day. All four of these parameters implicitly depend on the solar zenith angle (the angle between the rays of sunlight reaching Earth's surface and the overhead direction, known as the zenith).

In the following sections, we will look at the dependence of photolysis rates on each of our parameters, altitude, latitude, season, and time of day.

3.3.1 Ozone photolysis: dependence on altitude -- Since the photolysis rate depends upon the number of photons reaching the ozone molecule, we expect there to be an altitude dependence on UV photolysis. Figure 5.07 illustrates this dependence on altitude. At the top of the atmosphere, there is a steady solar flux of UV photons. As they travel down through the atmosphere, these photons are intercepted by ozone and other molecules. In the low density region at the top of the atmosphere, there are very few molecules to absorb photons, hence little absorption occurs at the highest altitudes. At lower altitudes, the density of molecules increases, hence the absorption becomes quite strong, reaching a maximum in the middle layers of the atmosphere.

In the figure, note that only 3 photons are intercepted in the first (topmost) layer, while 6 photons are intercepted in the second layer and 7 photons are absorbed in the third layer. Despite the large number of molecules present in them, the lowest layers again absorb few photons, but this time it is because there are not many photons left to absorb: only 1 photon penetrates all of the way to the lowest level. The absorption process is thus density limited in the upper atmosphere and photon limited in the lower atmosphere.

3.3.2 Ozone photolysis: dependence on latitude -- The dependence of photolysis rates on latitude is really just an extension of the altitude argument above. Figure 5.08 illustrates the dependence of photolysis on latitude for two observers: one near the equator and one much further poleward. Consider the position of the Sun in the sky at noontime over both locations. The Sun appears much higher in the sky to our tropical observer than to our observer at middle latitudes. Now consider the path that a ray of sunlight must travel to reach these two observers. The path through Earth's atmosphere is much longer in the middle latitudes than in the tropics. Recall that the important quantity in the altitude dependence was the number of ozone molecules overhead which had the chance to interact with the incident radiation. The longer the path that light must travel through the atmosphere, the more molecules the light will encounter, the more photons that get absorbed. So at a given altitude, we expect the photolysis rate to decrease as you move poleward away from the tropics.

3.3.3 Ozone photolysis: seasonal dependence -- Since the photolysis rate depends on the angle of the Sun, it's not surprising that photolysis rates also depend upon the seasons. The Sun is much higher in the sky overhead during the summer than during the winter, as demonstrated by Figure 5.09. The path length of light from the Sun through Earth's atmosphere will therefore be shorter in summer than winter. The shorter the path length at a given location, the less absorption of UV photons occurs, and the greater the photolysis rate. So at a given altitude, we expect photolysis rates to have maximum values during summer when the path length is shorter and minimum values during winter when the path length is longer. A seasonal cycle is therefore observed in photolysis rates.

3.3.4 Ozone photolysis: diurnal dependence -- Finally, a diurnal cycle must also exist, as illustrated in Figure 5.10. At night when there is no sunlight, photolysis rates drop to zero. In the morning and late afternoon, the Sun is lower in the sky than near noontime. The path lengths are therefore relatively long at sunrise and sunset and short at noontime. Not surprisingly, photolysis rates for a given altitude and latitude are faster at noontime than at sunrise and sunset.

3.4 Lifetimes of Odd Oxygen Molecules

We've already defined the lifetime of an odd oxygen molecule as the amount of time between its creation and destruction. We will now explore the concept of the lifetime of a molecule in more detail.

Another way of thinking about the lifetime of a molecule is to view it as the average amount of time the molecule spends in the atmosphere before it either chemically reacts with another molecule or is broken down by sunlight (photolysis). Since we've already seen that photolysis is dependent upon a number of variables (altitude, latitude, season, and time of day) and that chemical reactions are dependent upon temperature and the amount of available reactants, the lifetimes of molecules are also going to vary with changes in any of these quantities. Using typical values for the daytime, middle latitude, lower stratosphere, we find a lifetime for O atoms of about 0.002 second and for O3 molecules of about 1000 seconds. These short lifetimes are telling us that ozone molecules don't survive very long (less than 20 minutes) and that O atoms are snapped up nearly the moment they are formed!

The above discussion may prompt us to ask: if ozone molecules have such short lifetimes, why isn't the atmosphere completely depleted of ozone? When sunlight is present and energetic photons are reaching the upper atmosphere, oxygen molecules are constantly torn apart, freeing O atoms. These O atoms react with O2 on very short timescales to form O3. So despite rapid photolysis of ozone, the creation of ozone is also rapid. The result is that, on average, the local amount of stratospheric ozone does not change very much.

Similarly, O atoms have even shorter lifetimes than ozone. Although they are around for only a fraction of a second, they are constantly being formed by photolysis of O2 (slow) and O3 (fast). In our simple Chapman atmosphere, the destruction of O3 results in the creation of an O atom, while the loss of the O atom involves the creation of O3. Hence, the combined number of O and O3 (i.e., odd oxygen) molecules changes very slowly, since they are constantly being swapped. Recalling our definition of odd oxygen, Ox, we have in terms of amounts,

[Ox] = [O] + [O3]

While Ox is useful conceptually, at most stratospheric altitudes the O+O2 reaction is so fast that the [O] concentrations are very small (less than 1 percent of the total odd oxygen), and we can approximate [OX] with [O3].

The overall lifetime of Ox (either as ozone or free oxygen atom) can be computed from our Chapman chemistry. OX has a lifetime of 2 months at about 32 km in the northern middle latitudes during spring. The lifetime of free oxygen at the same altitude is about 4/100ths of a second, while O3 has a lifetime of about 3100 seconds (nearly an hour). At 20 km, the lifetime of O3 is about 4200 seconds, while the lifetime of O is about 1/1000 of a second. This is schematically illustrated in Figure 5.05, which shows the slow steady production of ozone on the left of the figure, and the rapid exchange between O and O3 or the right hand side of the figure.

3.4.1 OX partitioning -- The amount of Ox that is made up by O3 relative to the amount of OX made up of O atoms is known as the partitioning of odd oxygen. The partitioning depends upon the photolysis rate of ozone, the O+O2 reaction rate, and the air density. For our middle latitude, spring conditions, the [O]/[O3] varies from 1/1,000,000 in the lower stratosphere to 1/100 in the upper stratosphere near 50 km. Chapman chemistry predicts, therefore, that 99% or more of Ox is made of O3 throughout the stratosphere, which is indeed what is observed.