2.1 Chapman Cycle for Ozone Production

Ozone photochemistry is driven by the interaction of the Sun's radiation with various gases in the atmosphere, particularly oxygen. The understanding of the basics of ozone photochemistry began with Chapman (1930), who hypothesized that UV radiation was responsible for ozone production and proceeded to lay the foundation of stratospheric photochemistry: the Chapman reactions. He proposed that atomic oxygen is formed by the splitting (dissociation) of O2 by high energy ultraviolet photons (i.e., packets of light energy with wavelengths shorter than 242 nanometers) via

O2 + hc/lambda --> O + O

Where h is the Planck constant, c is the speed of light, and is the wavelength of the photon, given in nanometers (abbreviated nm, where 1 nm=10-9 meter). Collectively, hc/lambda represents the photon of light that breaks up the O2 molecule. The top panel of Figure 5.01 displays the absorption cross section for oxygen multiplied by 10,000. The cross-section is proportional to the probability that a photon from the Sun will be absorbed by an oxygen molecule. While this probability increases for the shorter, more energetic photons, the amount of UV radiation with wavelength shorter than 242 nm reaching into the atmosphere falls dramatically with decreasing altitude.

The bottom of Figure 5.01 shows the amount of solar energy per unit area (the flux) of different wavelengths reaching to three different altitudes: the top of the atmosphere, 30 km, and the surface. The amount of very energetic UV (< 242 nm) radiation falls off sharply. Thus, the splitting apart or photolysis of oxygen molecules by solar radiation is relatively slow in the lower and middle stratosphere because the photons of sufficient energy have already been absorbed by molecular oxygen in the upper stratosphere in the Chapman reaction given above. Few such photons are able to penetrate deeply into the atmosphere.

Oxygen atoms are highly reactive, and quickly react with oxygen molecules to form ozone via\

O2 + O + M --> O3 + M

The M represents any other molecule (most probably N2 or O2 since these two molecules comprise 99% of the atmosphere). This 3 molecule reaction is called a termolecular reaction (a reaction between only 2 molecules is a bimolecular reaction). The third neutral body (M) is needed for the energy balance of the reaction. This particular reaction proceeds at a very fast rate. Figure 5.02 shows the calculated lifetime of these oxygen atoms as a function of altitude. The lifetime is defined as the time required for the abundance of oxygen atoms (O) to decrease by about 63% (known by most scientists as the e-folding timescale). The lifetime is very short in the stratosphere, typically less than 1 second. Hence, oxygen atoms almost immediately form ozone after they are dissociated.

Ozone strongly absorbs UV radiation. The top panel of Figure 5.01 shows the ozone absorption cross section. As an example, if we looked at the top of the atmosphere and counted only the 250-nm wavelength photons striking a 1-square centimeter area every second, we would count about 6,800,000,000,000 (that's 6.8 trillion or 6.8 x 1012) photons. Yet ozone is so effective at absorbing these 250-nm photons, that we find zero 250-nm photons at Earth's surface. In fact, we could sit at the same spot for millions of years without detecting a single 250-nm photon! At these very short wavelengths, the sky is completely and utterly black.

The ozone molecule is dissociated by these UV photons into O and O2 via the reaction

O3 + hc/lambda --> O2 + O

Because the O atoms have such short lifetimes, they quickly reform ozone after dissociation, converting the energy of the photons at these wavelengths into thermal energy (note: this thermal energy is the energy which is given to the M atom in the previous equation).

The process of ozone photochemical production is summarized in Figure 5.03. Ozone is formed when an energetic ultraviolet photon splits an oxygen molecule (O2). These oxygen atoms quickly react with other oxygen molecules to form ozone. The M molecule shown as the two atom magenta colored molecule carries off the excess energy.

The production of ozone is estimated by calculating the photolysis of O2 and assuming the two resulting oxygen atoms will each form an ozone molecule. A vertical profile of this production is shown in Figure 5.04. Note that the x-axis scale increases by a factor of 10 for each tick mark. Most of the ozone production occurs in the tropical upper stratosphere and mesosphere. The total mass of ozone produced per day over the globe is about 400 million metric tons! The global mass of ozone is relatively constant at about 3 billion metric tons, meaning the Sun produces about 12% of the ozone layer each day.

2.2 Chapman Cycle for Ozone Loss

The Chapman cycle for ozone production by solar UV photolysis of oxygen would produce amounts of ozone much greater in the atmosphere than are actually observed. Hence, Chapman also hypothesized that ozone is lost by a reaction with the free oxygen atoms. This ozone loss balances production. The basic loss reaction is

O3 + O --> O2 + O2

This reaction should be relatively slow in most of our atmosphere since ozone concentrations as a total share of the atmosphere are quite small. We explore the loss reactions in the next section.

A chemical reaction occurs when two or more molecules combine to form new products. In the ozone loss reaction given above, the reactants are O3 and O, while the products (reagents) are the two O2 molecules. Mathematically,

the decrease of ozone molecules = k[O3][O]

The concentration of ozone is [O3], and the concentration of the oxygen atoms is [O], while k is the reaction rate constant. The reaction rate is the rate at which one of the reactants (in this case O3 or O) decreases with time or one of the reagents (in this case O2) increases with time.

Reactants not only have kinetic energy and potential energy, but also internal energy associated with the strength of the bonds holding the molecules together.

Reactions that absorb heat or energy are known as endothermic reactions, while those that give off energy are exothermic reactions. An example of an endothermic reaction is the photolysis of oxygen molecules to form ozone, since this reaction requires the energy of UV photons. The reactions of O3+O to form the two oxygen molecules is exothermic since it gives off energy.

The loss rate is proportional to the concentrations of O3, O, and the reaction rate constant. The O3+O reaction rate constant is about 3 times slower than the O2+O reaction rate constant, and there are typically more than 100,000 oxygen molecules for each ozone molecule. Hence, the rate at which an oxygen atom will react with ozone is quite small.

In Chapman's model, this loss process balanced the photochemical production from the photolysis of oxygen molecules. (As we shall see in Section 2.2.1, this explanation turned out to be inadequate for explaining observed ozone amounts.) Figure 5.05 illustrates the Chapman life cycle of ozone. We can conceptualize a balance of production and loss, such that the production is a fixed number that depends on the solar output and overhead screening of UV (top pathway in Figure 5.05), while the loss process is due to the oxygen atoms and ozone reacting with one another (bottom pathway in Figure 5.05).

Because oxygen and ozone molecules are rapidly interconverted, atmospheric chemists regard the sum of ozone and oxygen atoms as a "family" known as odd oxygen (see the dashed box on the right hand side of Figure 5.05). The source of odd oxygen (denoted by Ox) is the photolysis of oxygen molecules (a relatively slow process with a time scale of many weeks at 30-km over the equator), and the loss of odd oxygen is the reaction of ozone and oxygen atoms (also a slow process with a comparable time scale). The time between creation and destruction (referred to as the lifetime, see section 3.4) of Ox is much longer than the lifetime of either O3 or O individually because of this rapid interconversion. All the ozone in a given air parcel is destroyed many times over during the course of a single day when the parcel is in sunlight. Indeed, at an altitude of 30 km above the equator, the lifetime of an ozone molecule due only to UV photolysis is less than 1 hour. However, ozone is reformed in the parcel at almost exactly the same rate through the reaction between O and O2. Hence, ozone concentrations in the middle stratosphere change only very slowly over the long time scales (weeks to months) of production and loss.

2.2.1 Beyond the Chapman Cycle: Additional Chemical and Transport Processes -- In spite of the conceptual breakthrough by Chapman, this simple balance of ozone doesn't work well. First, the Sun is overhead in the tropics, yet column ozone amounts are quite low. The Chapman chemical reactions lead to predicted ozone amounts that are twice as high as actual tropical observations. In addition to this tropical problem of too little ozone, middle to high latitude predictions of ozone by the Chapman cycle are too low.

The problems with Chapman chemistry result from two processes. First, there are other ozone loss reactions with gases containing chlorine, bromine, nitrogen, and hydrogen that contribute to the overall ozone loss process. In Figure 5.05, these reactions create additional pathways from Ox back to O2. Second, there exists an equator-to-pole stratospheric circulation known as the Brewer-Dobson Circulation that transports ozone from the photochemical production region in the tropics to the middle and high latitudes. Discussed at length in Lecture 6, the Brewer-Dobson Circulation decreases tropical ozone amounts, while increasing extratropical amounts.

In summary, Ox is formed by the photolysis of O2 (Figure 5.05, left side). These odd oxygen compounds are destroyed by the reaction of O3 and O (bottom pathway) on time scales of months in the lower stratosphere and days in the upper stratosphere. On time scales of minutes to hours (i.e., time scales that are short compared to Ox lifetimes), the sum of O3 and O is nearly constant. However, while their sum is constant, these species are rapidly cycling back and forth, photochemically interconverting: all of the O3 is destroyed by UV photolysis every few minutes, leading to the formation of free O atoms, and all of the O atoms are immediately consumed in reactions with O2 to reform O3 in a fraction of a second. Since ozone lasts for minutes to hours in the tropical middle to lower stratosphere, and oxygen atoms last for less than a second, most of the odd oxygen exists in the form of ozone.