8.3 Ozone
Ozone (O₃) is a trace gas with enormous atmospheric significance. Stratospheric ozone (the "ozone layer" at 15--35 km altitude) absorbs harmful ultraviolet radiation, shielding life on Earth. Tropospheric ozone is a harmful pollutant and greenhouse gas. The discovery of the Antarctic ozone hole in 1985 and the subsequent Montreal Protocol represent one of the most successful examples of international environmental policy guided by atmospheric science.
Chapman Cycle: Pure Oxygen Chemistry
Sydney Chapman (1930) proposed the first theory of stratospheric ozone based on pure oxygen photochemistry. The four reactions of the Chapman cycle are:
$$\text{R1:} \quad \text{O}_2 + h\nu \xrightarrow{J_1} 2\text{O} \qquad (\lambda < 242\;\text{nm})$$
$$\text{R2:} \quad \text{O} + \text{O}_2 + M \xrightarrow{k_2} \text{O}_3 + M$$
$$\text{R3:} \quad \text{O}_3 + h\nu \xrightarrow{J_3} \text{O}_2 + \text{O} \qquad (\lambda < 320\;\text{nm})$$
$$\text{R4:} \quad \text{O} + \text{O}_3 \xrightarrow{k_4} 2\text{O}_2$$
R1 and R3 are photolysis reactions with rates determined by photolysis rate coefficients J (units s⁻¹). The J-value depends on the absorption cross-section of the molecule, the quantum yield for dissociation, and the actinic flux at the relevant wavelengths. R2 is the three-body recombination that forms ozone -- it is extremely fast because the third body M (N₂ or O₂) carries away the excess energy. R4 is the rate-limiting ozone destruction step in pure oxygen chemistry.
Because R2 and R3 are very fast, atomic oxygen O and ozone O₃ rapidly interconvert and are grouped as the "odd oxygen" family:
$$\text{O}_x = \text{O} + \text{O}_3$$
The steady-state odd oxygen balance gives the Chapman equilibrium ozone concentration. Setting production equal to loss for Oₓ:
$$\frac{d[\text{O}_x]}{dt} = 2J_1[\text{O}_2] - 2k_4[\text{O}][\text{O}_3] = 0$$
$$[\text{O}_3]_{\text{Chapman}} = \left(\frac{J_1\,k_2\,[\text{O}_2]^2\,[M]}{J_3\,k_4}\right)^{1/2}$$
The steady-state atomic oxygen concentration is found from the rapid equilibrium between R2 and R3:
$$[\text{O}]_{ss} = \frac{J_3[\text{O}_3]}{k_2[\text{O}_2][M]}$$
The Chapman mechanism overpredicts observed ozone by approximately a factor of 2 because it neglects catalytic destruction cycles involving HOₓ, NOₓ, and halogen radicals that dominate actual ozone loss.
Photolysis Rates and J-Values
The photolysis rate coefficient J (s⁻¹) for a molecule is computed by integrating the product of the absorption cross-section, quantum yield, and actinic flux over wavelength:
$$J = \int_{\lambda_1}^{\lambda_2} \sigma(\lambda, T)\;\Phi(\lambda, T)\;F(\lambda)\;d\lambda$$
where:
- $\sigma(\lambda, T)$ = absorption cross-section (cm²/molecule), typically temperature-dependent
- $\Phi(\lambda, T)$ = quantum yield (dimensionless, 0 to 1), fraction of absorptions leading to dissociation
- $F(\lambda)$ = spectral actinic flux (photons cm⁻² s⁻¹ nm⁻¹), depends on solar zenith angle (SZA), altitude, and ozone column above
The actinic flux decreases exponentially with increasing solar zenith angle through the atmosphere (Beer-Lambert law), making photolysis rates strongly dependent on SZA:
$$F(\lambda, z) = F_0(\lambda)\,\exp\!\left(-\frac{\tau(\lambda, z)}{\cos\theta_0}\right) \qquad \text{where } \theta_0 = \text{SZA}$$
For O₂ photolysis at $\lambda < 242$ nm (the Herzberg continuum), the cross-section is very small ($\sigma \sim 10^{-23}$ cm²), so significant photolysis only occurs in the upper stratosphere and mesosphere where the actinic flux at short UV wavelengths is still appreciable. For O₃ photolysis, two channels are important:
$\text{O}_3 + h\nu \rightarrow \text{O}(^3\text{P}) + \text{O}_2 \quad (\lambda < 1180\;\text{nm})$ -- produces ground-state O
$\text{O}_3 + h\nu \rightarrow \text{O}(^1\text{D}) + \text{O}_2 \quad (\lambda < 310\;\text{nm})$ -- produces excited O(¹D), crucial for OH production
Key photolysis rates: $J(\text{O}_2) \sim 10^{-11}$ s⁻¹ in upper stratosphere; $J(\text{O}_3 \rightarrow \text{O}(^1\text{D})) \sim 3\times10^{-5}$ s⁻¹; $J(\text{NO}_2) \sim 8\times10^{-3}$ s⁻¹ at surface with overhead sun.
Catalytic Ozone Destruction Cycles
The general catalytic cycle involves a radical species X that destroys odd oxygen without itself being consumed:
$$\text{X} + \text{O}_3 \rightarrow \text{XO} + \text{O}_2$$
$$\text{XO} + \text{O} \rightarrow \text{X} + \text{O}_2$$
$$\text{Net:} \quad \text{O}_3 + \text{O} \rightarrow 2\text{O}_2$$
The efficiency of a catalytic cycle is determined by its rate constant and the abundance of the catalyst. The ozone loss rate from catalyst X is:
$$L_X = 2\,k_{X+O_3}\,[\text{X}]\,[\text{O}_3]$$
Four major catalytic families dominate stratospheric ozone loss at different altitudes:
HOₓ Cycle (X = OH)
OH + O₃ → HO₂ + O₂
HO₂ + O → OH + O₂
Dominant in the mesosphere and lower stratosphere. Source: H₂O oxidation by O(¹D). Rate constant $k_{\text{OH+O}_3} = 1.7 \times 10^{-12}\,e^{-940/T}$ cm³ s⁻¹. Each HOₓ radical destroys ~10² O₃ before removal.
NOₓ Cycle (X = NO)
NO + O₃ → NO₂ + O₂
NO₂ + O → NO + O₂
Dominant ozone loss in the middle stratosphere (25--40 km). Source: N₂O from surface. Rate constant $k_{\text{NO+O}_3} = 3.0 \times 10^{-12}\,e^{-1500/T}$ cm³ s⁻¹. Each NOₓ molecule destroys ~10⁴ O₃.
ClOₓ Cycle (X = Cl)
Cl + O₃ → ClO + O₂
ClO + O → Cl + O₂
Dominant in the lower stratosphere, especially at high latitudes. Source: CFCs. Rate constant $k_{\text{Cl+O}_3} = 2.3 \times 10^{-11}\,e^{-200/T}$ cm³ s⁻¹. Each Cl atom destroys ~10⁵ O₃ before sequestration into HCl or ClONO₂.
BrOₓ Cycle (X = Br)
Br + O₃ → BrO + O₂
BrO + ClO → Br + Cl + O₂
Bromine is 40--60 times more efficient per atom than chlorine for ozone destruction because BrONO₂ and HBr reservoirs are less stable. Sources: CH₃Br, halons. The coupled BrO-ClO cycle is important in polar ozone loss.
Ozone Depletion Potential (ODP)
ODP measures the relative ozone-destroying ability of a substance compared to CFC-11 (ODP = 1.0). It accounts for atmospheric lifetime, number of halogen atoms released, and their catalytic efficiency. Examples: CFC-12 = 0.82, HCFC-22 = 0.034, CH₃Br = 0.51. The ODP framework is central to Montreal Protocol regulation of ozone-depleting substances.
Antarctic Ozone Hole
The Antarctic ozone hole, discovered by Farman, Gardiner, and Shanklin (1985), is the most dramatic manifestation of anthropogenic ozone depletion. It results from a unique combination of meteorology and heterogeneous chemistry.
1. Polar Vortex Formation (Winter)
The strong winter polar vortex isolates Antarctic stratospheric air from midlatitude mixing. Temperatures drop below -78°C (195 K), the threshold for formation of polar stratospheric clouds (PSCs).
2. Polar Stratospheric Clouds (PSCs)
Two types of PSCs play critical roles in ozone depletion:
Type I PSCs (T < 195 K)
Composed of nitric acid trihydrate (NAT: HNO₃ · 3H₂O). Form at temperatures 3--8 K above the frost point. Provide surfaces for heterogeneous reactions and cause denitrification by sedimenting HNO₃ out of the gas phase.
Type II PSCs (T < 188 K)
Composed of water ice. Form only at the coldest temperatures in the Antarctic. Larger particles cause dehydration in addition to denitrification. More reactive surfaces for chlorine activation.
3. Heterogeneous Chemistry on PSC Surfaces
PSC surfaces catalyze reactions that convert stable chlorine reservoirs into reactive forms:
$$\text{ClONO}_2 + \text{HCl} \xrightarrow{\text{PSC}} \text{Cl}_2 + \text{HNO}_3$$
$$\text{ClONO}_2 + \text{H}_2\text{O} \xrightarrow{\text{PSC}} \text{HOCl} + \text{HNO}_3$$
$$\text{HOCl} + \text{HCl} \xrightarrow{\text{PSC}} \text{Cl}_2 + \text{H}_2\text{O}$$
HNO₃ is sequestered in PSC particles (denitrification), suppressing the formation of the ClONO₂ reservoir and prolonging chlorine activation.
4. Chlorine Activation and the ClO Dimer Cycle (Spring)
When sunlight returns in spring, Cl₂ and HOCl are rapidly photolyzed to release active Cl and ClO radicals. Because atomic O is scarce in the lower stratosphere, the standard ClOₓ cycle is slow. Instead, the ClO dimer cycle dominates:
$$2(\text{Cl} + \text{O}_3 \rightarrow \text{ClO} + \text{O}_2)$$
$$\text{ClO} + \text{ClO} + M \rightarrow \text{Cl}_2\text{O}_2 + M$$
$$\text{Cl}_2\text{O}_2 + h\nu \rightarrow 2\text{Cl} + \text{O}_2$$
$$\text{Net:} \quad 2\text{O}_3 \rightarrow 3\text{O}_2$$
At peak depletion (typically late September/early October), total column ozone drops from ~300 DU to below 100 DU over an area exceeding 20 million km². The ozone hole persists until the vortex breaks down in late spring.
Dobson Units, Brewer-Dobson Circulation, and Age of Air
Dobson Units (DU)
Total column ozone is measured in Dobson Units: 1 DU = 0.01 mm of pure O₃ at STP = 2.687 × 10¹⁶ molecules/cm². Global mean total ozone is approximately 300 DU (3 mm at STP). Measured by ground-based Dobson/Brewer spectrophotometers and satellite instruments (TOMS, OMI, TROPOMI).
Brewer-Dobson Circulation
The large-scale stratospheric overturning circulation transports ozone from its photochemical production region (tropical upper stratosphere) poleward and downward. This explains why total column ozone is highest at high latitudes in spring despite ozone being produced mainly in the tropics. The circulation is driven by planetary wave breaking in the extratropical stratosphere.
Age of Air and Stratospheric Transport
The "age of air" is the mean transit time since an air parcel entered the stratosphere from the tropical tropopause. It is measured using long-lived tracers such as SF₆ and CO₂. Typical mean ages are 1--2 years in the tropical lower stratosphere and 4--7 years in the extratropical upper stratosphere. The age spectrum is broad due to mixing, meaning a given parcel contains air with a distribution of transit times:
$$G(\mathbf{r}, t | \mathbf{r}_0, t_0) = \text{Green's function (age spectrum)}$$
$$\Gamma(\mathbf{r}) = \int_0^{\infty} \tau \, G(\mathbf{r}, \tau) \, d\tau \quad \text{(mean age)}$$
QBO and Ozone Variability
The quasi-biennial oscillation (QBO) -- alternating easterly and westerly zonal wind regimes in the tropical stratosphere with a period of ~28 months -- modulates the Brewer-Dobson circulation and thus extratropical ozone. During the westerly QBO phase, enhanced poleward transport increases high-latitude ozone by 10--20 DU.
Montreal Protocol and UV Radiation Effects
Montreal Protocol and Ozone Recovery
Signed in 1987, the Montreal Protocol phased out production of CFCs, halons, and other ODS. Stratospheric chlorine loading peaked at ~3.7 ppb around 1997 and is now declining at ~0.5%/yr. Full ozone recovery is projected for ~2066 over Antarctica, ~2045 for the Arctic, and ~2040 globally. The Protocol is regarded as the most successful environmental treaty in history, having also averted significant additional global warming since many ODSs are potent greenhouse gases.
UV Radiation and Biological Effects
The UV Index measures erythemal (sunburn-causing) UV radiation weighted by the CIE action spectrum. Every 1% decrease in total ozone increases surface UV-B by approximately 1.5--2%. The erythemal dose rate is:
$$E_{\text{ery}} = \int_{280}^{400} E(\lambda)\,S_{\text{ery}}(\lambda)\,d\lambda$$
where $S_{\text{ery}}(\lambda)$ is the erythemal action spectrum (CIE, 1987). Biological effects include skin cancer (melanoma, SCC, BCC), cataracts, immune suppression, and damage to marine phytoplankton and terrestrial crops.
The Radiation Amplification Factor (RAF) quantifies the sensitivity of a biological effect to ozone changes: $\Delta B / B = -\text{RAF} \times \Delta \Omega / \Omega$, where $\Omega$ is total ozone column. Typical RAF values: erythema = 1.1, DNA damage = 2.0, plant damage = 1.6.
Fortran: Photochemical Box Model with Diurnal Ox-HOx-NOx Cycle
This Fortran program implements a stratospheric photochemical box model that integrates the coupled Ox-HOx-NOx system through a full diurnal cycle, including time-varying photolysis rates that depend on solar zenith angle.
program strat_box_model
! Stratospheric photochemical box model: Ox-HOx-NOx
! with diurnal cycle of photolysis rates
! Compile: gfortran -O2 -o strat_box strat_box_model.f90
implicit none
integer, parameter :: dp = selected_real_kind(15, 307)
real(dp), parameter :: pi = 3.141592653589793_dp
! Time parameters
integer, parameter :: nsteps = 86400 ! 1-second timesteps
real(dp), parameter :: dt = 1.0_dp ! seconds
real(dp) :: time_s, hour, sza_rad, cos_sza
! Species (number densities, molecules/cm^3)
real(dp) :: O3, O, NO, NO2, OH, HO2, M_air, O2_nd
real(dp) :: O3_init
! Rate constants (cm^3/s or cm^6/s for three-body)
real(dp) :: k_NO_O3, k_NO2_O, k_OH_O3, k_HO2_O, k_O_O3
real(dp) :: k_O_O2_M, k_HO2_NO
! Photolysis rates (s^-1)
real(dp) :: J_O2, J_O3, J_NO2, J_O3_O1D
real(dp) :: sza_factor
! Output
integer :: i, iout
real(dp) :: lat_rad, decl, hour_angle
real(dp) :: T_strat
! --- Initialization at 30 km altitude ---
T_strat = 230.0_dp ! K
M_air = 3.0d17 ! total air (cm^-3) at ~30 km
O2_nd = 0.21_dp * M_air
O3_init = 4.0d12 ! ~4 ppmv at 30 km
O3 = O3_init
O = 1.0d7
NO = 2.0d9 ! ~7 ppbv
NO2 = 1.0d9
OH = 1.0d6
HO2 = 5.0d7
lat_rad = 30.0_dp * pi / 180.0_dp ! 30 deg N
decl = 23.45_dp * pi / 180.0_dp ! Summer solstice
! Rate constants at 230 K
k_NO_O3 = 3.0d-12 * exp(-1500.0_dp / T_strat)
k_NO2_O = 5.1d-12 * exp(210.0_dp / T_strat)
k_OH_O3 = 1.7d-12 * exp(-940.0_dp / T_strat)
k_HO2_O = 3.0d-11 * exp(200.0_dp / T_strat)
k_O_O3 = 8.0d-12 * exp(-2060.0_dp / T_strat)
k_O_O2_M = 6.0d-34 * (300.0_dp / T_strat)**2.4_dp
k_HO2_NO = 3.5d-12 * exp(250.0_dp / T_strat)
write(*,'(A)') 'Hour O3(cm-3) O(cm-3) NO(cm-3) OH(cm-3) SZA(deg)'
write(*,'(A)') '----------------------------------------------------------------------'
do i = 1, nsteps
time_s = real(i, dp) * dt
hour = mod(time_s / 3600.0_dp, 24.0_dp)
! Solar zenith angle
hour_angle = (hour - 12.0_dp) * 15.0_dp * pi / 180.0_dp
cos_sza = sin(lat_rad)*sin(decl) + cos(lat_rad)*cos(decl)*cos(hour_angle)
cos_sza = max(cos_sza, 0.0_dp)
! Photolysis rates (scale with cos(SZA))
sza_factor = cos_sza ! Simple scaling
J_O2 = 1.0d-11 * sza_factor
J_O3 = 5.0d-4 * sza_factor
J_NO2 = 8.0d-3 * sza_factor
J_O3_O1D = 3.0d-5 * sza_factor
! --- Forward Euler integration ---
! dO/dt = J_O3*O3 + J_O2*O2 - k_O_O2_M*O*O2*M - k_O_O3*O*O3
O = O + dt * (J_O3*O3 + 2.0_dp*J_O2*O2_nd &
- k_O_O2_M*O*O2_nd*M_air - k_O_O3*O*O3 &
- k_NO2_O*NO2*O - k_HO2_O*HO2*O)
O = max(O, 0.0_dp)
! dO3/dt = k_O_O2_M*O*O2*M - J_O3*O3 - k_O_O3*O*O3
! - k_NO_O3*NO*O3 - k_OH_O3*OH*O3
O3 = O3 + dt * (k_O_O2_M*O*O2_nd*M_air - J_O3*O3 &
- k_O_O3*O*O3 - k_NO_O3*NO*O3 - k_OH_O3*OH*O3)
O3 = max(O3, 0.0_dp)
! NOx partitioning
NO = NO + dt * (J_NO2*NO2 - k_NO_O3*NO*O3 + k_HO2_NO*HO2*NO)
NO2 = NO2 + dt * (k_NO_O3*NO*O3 - J_NO2*NO2 - k_NO2_O*NO2*O)
NO = max(NO, 0.0_dp); NO2 = max(NO2, 0.0_dp)
! HOx (simplified)
OH = OH + dt * (2.0_dp*J_O3_O1D*O3*1.0d-5 - k_OH_O3*OH*O3 &
+ k_HO2_NO*HO2*NO)
HO2 = HO2 + dt * (k_OH_O3*OH*O3 - k_HO2_O*HO2*O - k_HO2_NO*HO2*NO)
OH = max(OH, 0.0_dp); HO2 = max(HO2, 0.0_dp)
! Output every hour
if (mod(i, 3600) == 0) then
sza_rad = acos(min(max(cos_sza, -1.0_dp), 1.0_dp))
write(*,'(F5.1, 5ES13.4)') hour, O3, O, NO, OH, &
sza_rad * 180.0_dp / pi
end if
end do
write(*,'(/,A,F8.2,A)') 'O3 change over 24h: ', &
(O3 - O3_init) / O3_init * 100.0_dp, '%'
end program strat_box_modelInteractive Simulation: Chapman Cycle Ozone Chemistry
PythonModel the Chapman cycle to compute steady-state ozone concentration vs altitude. Compares the pure oxygen chemistry result with the effect of catalytic destruction cycles (NOx, HOx, ClOx), showing the ozone layer peak near 25 km and how catalysts reduce ozone by approximately 50%.
Click Run to execute the Python code
Code will be executed with Python 3 on the server