(R1)
(R2)
The O3 molecules produced in reaction (R2)go on to photolyze. Because the bonds in the O3 molecule are weaker than those in the O2 molecule, photolysis is achieved with lower-energy photons:
(R3)
(R4)
Simple relationships between O2, O, and O3 concentrations can be derived from a chemical steady-state analysis of the Chapman mechanism. As we saw in section 3.1.2 , chemical steady state can be assumed for a species if its production and loss rates remain roughly constant over its lifetime. We first examine if chemical steady state is applicable to the shortest-lived species in Figure 10-3 , the O atom. The lifetime tO of the O atom against conversion to O3 by (R2)is
where we have used the low-pressure limit in the rate expression for (R2), as is appropriate for atmospheric conditions. In equation (10.1), [M] is the air number density na, and [O2] = CO2na where CO2 = 0.21 mol/mol is the mixing ratio of O2. Thus:
All terms on the right-hand side of (10.2)are known. Substituting numerical values one finds that tO in the stratosphere is of the order of seconds or less ( See The Chapman mechanism and steady state ). Production and loss rates of the O atom depend on the meteorological environment (pressure, temperature, radiation) and on the O3 abundance, neither of which vary significantly over a time scale of seconds. We can therefore assume chemical steady state for O atoms between production by (R3)and loss by (R2), neglecting reactions (R1)and (R4)which are much slower:
Rearrangement of (10.3)yields
Substituting numerical values
one finds [O]/[O3] << 1 throughout the stratosphere (
See The Chapman mechanism and steady state ). Observed concentrations
( Figure 10-4 ) obey closely
this steady state.
An important result of our steady-state analysis for the O atom is that O3 is the main component of the Ox family: [Ox] = [O3} + [O] ª [O3]. This result has two implications:
where we have included a factor of 2 in the denominator because (R4)consumes two Ox (one O3 and one O). The factor of 2 can be derived formally from a mass balance equation for Ox as the sum of the mass balance equations for O3 and O:
Values of tOx computed from (10.5)range from less than a day in the upper stratosphere to several years in the lower stratosphere, reflecting the abundance of O atoms ( Figure 10-4 , See The Chapman mechanism and steady state ). In the upper stratosphere at least, the lifetime of Ox is sufficiently short that chemical steady state can be assumed to hold. This steady state is defined by
Substituting (10.4)into (10.7)yields as solution for [O3]:
The simplicity of equation (10.8)is deceiving. Calculating [O3] from this equation is actually not straightforward because the photolysis rate constants k1(z) and k3(z) at altitude z depend on the local actinic flux Il(z), which is attenuated due to absorption of radiation by the O2 and O3 columns overhead. From (9.13), the general expression for a photolysis rate constant is
The actinic flux Il(z) at altitude z is attenuated relative to its value Il,· at the top of the atmosphere by
where q is the solar zenith angle, that is the angle between the Sun and the vertical ( section 7.6 ), and d is the optical depth of the atmosphere above z computed from (7.30):
Values of Il at UV wavelengths decrease rapidly with decreasing altitude in the stratosphere because of efficient absorption by O2 and O3 ( Figure 10-2 ), and k1 and k3 decrease correspondingly ( Figure 10-5 ).
Since k1(z) and k3(z) depend on the O3 column overhead through (10.9)-(10.11), equation (10.8)is not explicit for [O3] (the right-hand-side depends on [O3]). Solution to (10.8)must be obtained numerically by starting from the top of the atmosphere with Il = Il,· and [O3] = 0, and progressing downward by small increments in the atmosphere, calculating Il(z) and the resulting values of k1(z), k3(z), and [O3](z) as one penetrates in the atmosphere.
The resulting solution (Figure 10-5, right panel) is able to explain at least qualitatively the observed maximum of O3 concentrations at 20-30 km altitude. The maximum reflects largely the vertical dependence of Ox production by (R1), 2k1[O2], which we have seen is the effective source for O3. The O2 number density decreases exponentially with altitude following the barometric law, while k1 decreases sharply with decreasing altitude due to absorption of UV radiation by O3 and O2. The product k1[O2] thus has a maximum value at 20-30 km altitude. See problem 10. 1 for an analytical derivation of this maximum.
Although the Chapman mechanism is successful in reproducing the general shape of the O3 layer, it overestimates the observed O3 concentrations by a factor of 2 or more ( Figure 10-5 ). In the lower stratosphere, a steady state solution to the mechanism would not necessarily be expected because of the long lifetime of Ox; there, transport may play a dominant role in shaping the O3 distribution. In the upper stratosphere, however, where the lifetime of Ox is short, the discrepancy between theory and observations points to a flaw in the theory. Either the source of Ox in the Chapman mechanism is too large, or the sink is too small. Considering that the source from (R1)is well constrained by spectroscopic data, the logical conclusion is that there must be additional sinks for O3 not accounted for by the Chapman mechanism. This flaw was not evident until the 1950s, because the relatively poor quality of the stratospheric ozone observations and the uncertainties on the rate constants of reactions (R1)- See could accommodate the discrepancies between theory and observations. As the experimental data base improved, however, the discrepancy becameclear.
(R5)
The hydroxyl radical OH produced by See can react with O3, producing the hydroperoxy radical HO2 which in turn reacts with O3:
(R6)
(R7)
We refer to the ensemble of OH and HO2 as the HOx chemical family. The sequence of reactions (R6)and (R7)consumes O3 while conserving HOx. Therefore HOx acts as a catalyst for O3 loss; production of one HOx molecule by (R5)can result in the loss of a large number of O3 molecules by cycling of HOx through (R6)and (R7). Termination of the catalytic cycle requires loss of HOx by a reaction such as
(R8)
(R9)
(R10)
Further investigation of NOx chemistry in the stratosphere showed that a fraction of the NO2 molecules produced by (R9)reacts with oxygen atoms produced by (R3):
(R11)
Each cycle consumes two Ox molecules, which is equivalent to two O3 molecules (see section 10.1.2 ). The rate-limiting step in the cycle is (R11)because NO2 has the option of either photolyzing (null cycle) or reacting with O (O3 loss cycle). The O3 loss rate is therefore given by
Termination of the catalytic cycle involves loss of NOx radicals. In the daytime, NOx is oxidized to HNO3 by the strong radical oxidant OH ( section 10.2.1 ):
(R12)
(R13)
(R14)
(R15)
(R16)
(R17)
(R18)
A diagram of the ensemble of processes is shown in Figure 10-6 . The loss rate of O3 can be calculated from knowledge of the aircraft emission rate of NO, the chemical cycling within the NOy family, and the residence time of air (and therefore NOy) in the stratosphere. Model calculations conducted in the 1970s found that an aircraft fleet in the stratosphere would represent a serious threat to the O3 layer. This environmental concern, combined with economic considerations, led to scrapping of the supersonic aircraft plan in the United States (the Europeans still built the Concorde).
The identification of a NOx-catalyzed mechanism for O3 loss turned out to be a critical lead towards identifying the missing O3 sink in the Chapman mechanism. Beyond the source from supersonic aircraft, could there be a natural source of NOx to the stratosphere? Further work in the early 1970s showed that N2O, a low-yield product of nitrification and denitrification processes in the biosphere ( section 6.3 ), provides such a source. N2O is a very stable molecule which has no significant sinks in the troposphere. It is therefore transported to the stratosphere where it encounters high concentrations of O(1D), allowing oxidation to NO by
(R19)
On the basis of Figure 10-6 , we see that the loss rate of O3 by the NOx-catalyzed mechanism can be calculated from knowledge of the production and loss rates of NOy, and of the chemical cycling within the NOy family. We examine now our ability to quantify each of these terms:
Ice core data show that atmospheric concentrations of N2O have risen from 285 ppbv in the 18th century to 310 ppbv today, and present-day atmospheric observations indicate a growth rate of 0.3 % yr-1 ( Figure 7-1 ). There is much interest in understanding this rise because of the importance of N2O not only as a sink for stratospheric O3 but also as a greenhouse gas (chapter 7). Table 10.1 gives current estimates of the sources and sinks of atmospheric N2O. Although the estimates can provide a balanced budget within their ranges of uncertainty (atmospheric increase ª sources - sinks), the uncertainties are in fact large. Biogenic sources in the tropical continents, cultivated areas, and the oceans provide the dominant sources of N2O. The increase of N2O over the past century is thought to be due principally to increasing use of fertilizer for agriculture.
(R20)
(R21)
(R22)
The rate-limiting step for O3 loss in this cycle is (R22)(see problem 10. 5 ), so that the O3 loss rate is
The catalytic cycle is terminated by conversion of ClOx to non-radical chlorine reservoirs, HCl and ClNO3:
(R23)
(R24)
(R25)
(R26)
We thus define a chemical family Cly as the sum of ClOx and its reservoirs. A diagram of the ensemble of processes is shown in Figure 10-8 . Note the similarity to Figure 10-6 .
Similarly to the NOx-catalyzed
mechanism, the rate of O3 loss by the ClOx-catalyzed mechanism can be calculated
from knowledge of the concentrations of CFCs and other halocarbons in the
stratosphere, the residence time of air in the stratosphere, and the ClOx/Cly
chemical partitioning. Molina and Rowland warned that ClOx-catalyzed O3
loss would become a significant threat to the O3 layer as CFC concentrations
continued to increase. Their warning, backed up over the next two decades
by increasing experimental evidence and compounded by the discovery of
the antarctic ozone hole, led to a series of international agreements (beginning
with the Montreal protocol in 1987) which
eventually resulted in a total ban on CFC production as of 1996. For this
work they shared the 1995 Nobel Prize in Chemistry with Paul
Crutzen.
Discovery of this " antarctic ozone hole" (as it was named in the popular press) was a shock to atmospheric chemists, who thought by then that the factors controlling stratospheric O3 were relatively well understood. The established mechanisms presented in sections See CHAPMAN MECHANISM and See CATALYTIC LOSS CYCLES could not explain the O3 depletion observed over Antarctica. Under the low light conditions in that region, concentrations of O atoms are very low, so that reactions (R11)and (R22)cannot operate at a significant rate. This severe failure of theory sent atmospheric chemists scrambling to understand what processes were missing from their understanding of stratospheric chemistry, and whether the appearance of the antarctic O3 hole could be a bellwether of future catastrophic changes in stratospheric O3 levels over other regions of the world.
(R27)
(R28)
(R29)
The key behind discovery of this catalytic cycle was the laboratory observation that photolysis of the ClO dimer (ClOOCl) takes place at the O-Cl bond rather than at the weaker O-O bond. It was previously expected that photolysis would take place at the O-O bond, regenerating ClO and leading to a null cycle. The rate of O3 loss in the catalytic cycle is found to be limited by (R27)and is therefore quadratic in [ClO]; it does not depend on the abundance of O atoms, in contrast to the ClOx-catalyzed mechanism described in the previous section.
Another catalytic cycle found to be important in the depletion of O3 during antarctic spring involves Br radicals produced in the stratosphere by photolysis and oxidation of anthropogenic Br-containing gases such as CH3Br (see problem 6. 4 ):
(R30)
(R31)
Why are ClO concentrations over Antarctica so high? Further research in the 1990s demonstrated the critical role of reactions taking place in stratospheric aerosols at low temperature. Temperatures in the wintertime antarctic stratosphere are sufficiently cold to cause formation of persistent ice-like clouds called polar stratospheric clouds (PSCs) in the lower part of the stratosphere. The PSC particles provide surfaces for conversion of the ClOx reservoirs HCl and ClNO3 to Cl2, which then rapidly photolyzes to produce ClOx:
(R32)
(R33)
Discovery of the antarctic ozone hole spurred intense research into the thermodynamics of PSC formation. It was soon established that the stratosphere contains sufficiently high concentrations of HNO3 that solid HNO3-H2O phases may form at temperatures higher than the frost point of water. These solid phases are:
where c is the number of components of the system (here two: HNO3 and H2O), and p is the number of phases present at equilibrium. Equilibrium of a PSC phase with the gas phase (p = 2) is defined by two independent variables (n = 2). If we are given the HNO3 and H2O vapor pressures (representing two independent variables), then we can define unambiguously the composition of the thermodynamically stable PSC and the temperature at which it forms. That is the information given in Figure 10-12 .
The shaded region in Figure 10-12 indicates the typical ranges of PHNO3 and PH2O in the lower stratosphere. We see that condensation of NAT is possible at temperatures as high as 197 K, consistent with the PSC observations. It appears from Figure 10-12 that NAT represents the principal form of PSCs; pure water ice PSCs can also form under particularly cold conditions ( problem 10. 10 ). Recent investigations show that additional PSC phases form in the ternary HNO3-H2SO4-H2O system.
The chronology of the antarctic ozone hole is illustrated in Figure 10-13 . It begins with the formation of the antarctic vortex in austral fall (May). As we saw in chapter 4, there is a strong westerly circulation at southern midlatitudes resulting from the contrast in heating between the tropics and polar regions. Because of the lack of topography or land-ocean contrast to disturb the westerly flow at southern midlatitudes, little meridional transport takes place and the antarctic atmosphere is effectively isolated from lower latitudes. This isolation is most pronounced during winter, when the latitudinal heating gradient is strongest. The isolated antarctic air mass in winter is called the antarctic vortex because of the strong circumpolar circulation.
By June, temperatures in the antarctic vortex have dropped to values sufficiently low for PSC formation. Reaction (R32)then converts HCl and ClNO3 to Cl2, which photolyzes to yield Cl atoms. In the winter, however, loss of O3 is limited by the lack of solar radiation to photolyze the ClOOCl dimer produced in (R27). Significant depletion of O3 begins only in September when sufficient light is available for ClOOCl photolysis to take place rapidly.
By September, however, temperatures have risen sufficiently that all PSCs have evaporated. One would then expect HNO3 in the vortex to scavenge ClOx by
There is indeed much concern at present over the possibility of an O3 hole developing in the arctic. Temperatures in arctic winter occasionally fall to values sufficiently low for PSCs to form and for HCl and ClNO3 to be converted to ClOx ( Figure 10-11 ), but these conditions are generally not persistent enough to allow removal of HNO3 by PSC sedimentation. As a result, O3 depletion in arctic spring is suppressed by (R16)+(R24). If extensive PSC sedimentation were to take place in arctic winter, one would expect the subsequent development of a springtime arctic O3 hole. Observations indicate that the arctic stratosphere has cooled in recent years, and a strong correlation is found between this cooling and increased O3 depletion. One proposed explanation for the cooling is increase in the concentrations of greenhouse gases. Greenhouse gases in the stratosphere have a net cooling effect (in contrast to the troposphere) because they radiate away the heat generated from the absorption of UV by O3. Continued cooling of the arctic stratosphere over the next decades could possibly cause the development of an "arctic ozone hole" even as chlorine levels decrease due to the ban on CFCs. This situation is being closely watched by atmospheric chemists.
This large decline of O3 was again a surprise. It was not forecast by the standard gas-phase chemistry models based on the mechanisms in section 10.2 , which predicted only a ~0.1% yr-1 decrease in the O3 column for the 1979-1995 period. The models also predicted that most of the O3 loss would take place in the upper part of the stratosphere, where CFCs photolyze, but observations show that most of the decrease in the O3 column actually has taken place in the lowermost stratosphere below 20-km altitude ( Figure 10-15 ). This severe failure of the models cannot be explained by the polar chemistry discussed in section 10.3 because temperatures at midlatitudes are too high. Dilution of the antarctic ozone hole when the polar vortex breaks up in summer is not a viable explanation either because it would induce a seasonality and hemispheric asymmetry in the trend that is not seen in the observations.
Recent research indicates that aerosol chemistry in the lower stratosphere could provide at least a partial explanation for the observed long-term trends of O3 at midlatitudes. Laboratory experiments have shown that the aqueous H2SO4 aerosol ubiquitously present in the lower stratosphere ( section 8.1 ) provides a medium for the rapid hydrolysis of N2O5 to HNO3:
(R34)
When all these processes are considered, one finds in model calculations that (R34)has little net effect on the overall rate of O3 loss in the lower stratosphere, because the slow-down of the NOx-catalyzed loss is balanced by the speed-up of the HOx- and ClOx-catalyzed losses; in this manner, the gas-phase models of the 1980s were lulled into a false sense of comfort by their ability to balance Ox production and loss ( Figure 10-7 ). The occurrence of (R34)implies a much larger sensitivity of O3 to chlorine levels, which have increased rapidly over the past two decades. Figure 10-16 illustrates this point with model calculations of the relative contributions of different catalytic cycles for O3 loss, considering gas-phase reactions only (left panel) and including (R34)(right panel). Whether or not the enhanced sensitivity to chlorine arising from (R34)can explain the observed long-term trends of O3 ( Figure 10-14 ) is still unclear.
Field observations over the past five years have provided ample evidence that N2O5 hydrolysis in aerosols does indeed take place rapidly in the stratosphere. The observed NOx/NOy ratio in the lower stratosphere at midlatitudes is lower than expected from purely gas-phase chemistry mechanisms, and more consistent with a mechanism including (R34). In addition, the observed ClO/Cly ratio is higher than expected from the gas-phase models, because of the slower ClNO3 formation resulting from the lower NOx levels. Aircraft observations following the Mt. Pinatubo eruption in 1991 indicated large decreases of the NOx/NOy ratio and increases of the ClO/Cly ratio, as would be expected from (R34)taking place on the volcanic aerosols. The resulting enhancement of ClO is thought to be responsible in part for the large decrease in the O3 column in 1992, the year following the eruption ( Figure 10-14 ).
McElroy, M.B., R.J. Salawitch, and K.R. Minschwaner, The changing stratosphere, Planet. Space Sci., 40, 373-401, 1992. Catalytic loss cycles.
Warneck, P., Chemistry of the Natural Atmosphere, Academic Press, New York, 1988. Historical survey, photochemistry of O2 and O3.
World Meteorological Organization, Scientific assessment of ozone depletion: 1998, WMO, Geneva, 1999. Polar ozone loss, ozone trends.