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The effective area per target for absorbing incident radiation at a specified wavelength. For independent absorbers with number column $N$, the absorption optical depth is $\tau ={\sigma }_{\mathrm{abs}}N$. Absorption does not guarantee a particular chemical product; a channel's quantum yield is also needed in its photolysis rate coefficient.

Chapman ozone equilibrium balances production and destruction of atomic oxygen and ozone in a minimal oxygen-only atmospheric photochemistry model. Write square brackets for number densities. Define photolysis rate coefficients $J_1,J_3$ and collisional rate constants $K_2,K_4$ byThe collision partner $\mathrm{M}$ removes excess formation energy without being consumed. The third-body requirement reflects conservation of energy and momentum conservation during ozone formation.^[ref]

Adding the reaction rate equations for atomic oxygen and ozone cancels their rapid interconversion. A local steady state givesIf ozone loss is predominantly photolytic, $J_3\gg K_4[\mathrm{O}]$, its separate balance isCombining the two balances yieldsThe two factors of two in oxygen-atom production and destruction cancel in the first balance. This is a sunlit local steady state, with specified temperature, radiation and background number densities; transport and additional catalytic chemistry need not obey this four-reaction estimate.

For one specified channel, the photolysis rate coefficient isIt depends on spectral actinic flux, absorption cross section, and channel quantum yield. Solar zenith angle, season, overhead absorbers, clouds and aerosol scattering affect the photon field; branching and collisional quenching affect the chemical yield. Absorption alone does not guarantee the desired dissociation.

Curve A is oxygen photodissociation; curve B is ozone photodissociation. Molecular oxygen needs relatively short-wavelength ultraviolet photons, which are strongly screened at lower altitudes, so its rate increases steeply with height. Ozone can dissociate using longer wavelengths that penetrate much further, producing the much larger, less height-sensitive rate shown by B. The plotted quantity is a first-order coefficient with units ${\mathrm{s}}^{-1}$, rather than a bimolecular rate constant.

In a vertical-beam, effective-wavelength Beer-Lambert law approximation, the optical depth above altitude $z$ is $\tau (z)={\sigma }_{{\mathrm{O}}_2}{N}_{{\mathrm{O}}_2}(z)+{\sigma }_{{\mathrm{O}}_3}{N}_{{\mathrm{O}}_3}(z)$. Using centimetres consistently givesThe transmitted photon flux is proportional to $e^{-\tau }$. If the parent-gas absorption cross section and photodissociation yield are otherwise the same, they cancel in the ratio of photolysis rate coefficients:The corresponding fractions of the unattenuated beam are about $7.52\times 10^{-7}$ and $0.654$. Strong shielding by the overlying oxygen and especially ozone therefore makes destruction vastly faster higher in the stratosphere, even though the molecular absorption properties have not changed.

This numerical ratio uses the intended simplified radiation model. A real photolysis rate coefficient integrates wavelength-dependent actinic flux, absorption cross section and quantum yield. A nonvertical direct beam would use slant optical depth $\tau /\cos \theta$; diffuse scattering and the true solar spectrum would also matter. The supplied effective cross sections do not specify a unique broadband radiative-transfer calculation.