(HW 8) Stratospheric Ozone Depletion Mechanisms and Calculations

Main limitation of the Chapman Mechanism for stratospheric ozone

It overestimates ozone concentration by a factor of 2-3.

Reservoir species for NOₓ in the stratosphere

HNO₃ (Nitric acid)

Catalytic cycle that mainly destroys stratospheric ozone

ClOₓ (Chlorine radical) cycle

Reason for ozone hole formation in Antarctic spring

PSCs release active chlorine from reservoir species.

Rate-limiting step in NOₓ-catalyzed ozone destruction

Reaction of NO with O₃ to form NO₂.

Cause of high ClO levels in Antarctic spring

Conversion of chlorine reservoir species on PSCs.

Limitation of standard ClOₓ mechanism in explaining Antarctic spring depletion

Low O atom concentrations slow the reaction.

Driver of mid-latitude ozone depletion

Stratospheric aerosols interacting with nitrogen and chlorine.

Effect of volcanic eruptions on ozone

SO₂ forms aerosols that enhance heterogeneous chemistry.

Persistence of the ozone hole despite CFC bans

CFCs have long atmospheric lifetimes, keeping chlorine levels high.

Reactions in the Chapman Mechanism

1) O₂ + hν → 2O 2) O + O₂ + M → O₃ + M 3) O₃ + hν → O₂ + O 4) O + O₃ → 2O₂

Derivation of the lifetime of Ox from the Chapman Mechanism

Use steady-state approximation based on production and loss of O and O₃.

Reaction rate calculation for O + O₂ + M → O + O at 25 km

k₀(T) = k₀₍₃₀₀₎ × (T/300)⁻ⁿ

Steady-state [O]/[O₃] derivation

From balance of O₃ photolysis and O recombination using j, k, [O₂], [M]

Calculation of air number density at 25 km

Use ideal gas law: n = P / (k_B × T)

Steady-state [O]/[O₃] computation at 25 km

Plug values into steady-state expression with jO₃, k, [O₂], [M]

Finding steady-state [O] at 25 km

Multiply [O]/[O₃] ratio by [O₃]

Estimation of Ox lifetime at 25 km

Use reaction rate and concentrations of O and O₃.

Calculation of NO yield from N₂O loss

Fraction = k₁[O(¹D)] / (k₁[O(¹D)] + k₂[O(¹D)] + jN₂O)