The time scales and mode of the atmosphere's response to chemical perturbations are defined by the eigenvalues and eigenvectors of the system. The eigenstates of a simplified one-box CH₄-CO-OH system are analyzed. The longest time constant (smallest eigenvalue) always exceeds the lifetime defined by the steady-state loss frequency for CH₄, the longest lived gas. Thus, the extent of a CH₄perturbation—the methane response time—is always longer than predicted by the steady-state lifetime and is independent of size of the perturbation in the linear limit. This lengthening of the atmospheric recovery time can be diagnosed by how close we are to a chemically unstable troposphere, i.e., how much OH production exceeds that minimum needed to oxidize just the global emissions of CH₄, CO, and other hydrocarbons and species.

A detailed photochemical model of the upper stratosphere and mesosphere is compared with three extensive sets of ozone observations: Atmospheric Explorer-E backscattered ultraviolet experiment (BUV), Nimbus-4 BUV, and rocket flights from Wallops Flight Center (ROCOZ). The Nimbus-4 and rocket observations are most sensitive to ozone between 30 and 50 km, whereas observations from AE-E measure the abundance of ozone up to 70 km. The photochemical model accurately reproduces the observed relationship between BUV intensity and local solar zenith angle, although the absolute calibration on AE-E appears to be in error. The AE-E observations and the model both exhibit a morning-afternoon asymmetry, with more ozone in the morning owing to the build up of HO_x species in the afternoon. Seasonal changes in atmospheric temperature produce an annual maximum in tropical mesospheric ozone during June-July-August. The amplitude of the observed effect is somewhat larger than calculated by the model. Some problems appear to remain with the presently accepted kinetic rates for HO_x species in the atmosphere.

Atmospheric CH₄ perturbations, caused directly by CH₄ emissions or indirectly by those of CO are enhanced by chemical feedbacks. They can be diagnosed in terms of the natural modes of atmospheric chemistry that are general solutions of the continuity equations. Each mode is a pattern in the global distribution of all chemical species, and each has a single time-constant that accurately describes its exponential decay about a given atmospheric state. This mathematical theory extends earlier work and is general for 2-D and 3-D chemistry-transport models. A formal proof relates the steady-state distribution and its lifetime to the integral of the true time-dependent response (properly included in the recent IPCC assessment). Changes in CO are also known to perturb CH₄; however, the impact of CO emissions on climate has not been formally assessed in part because the short lifetime of CO (months) relative to that of CH₄ (decade) was believed to limit the integrated impact. Using the IPCC model studies, this theory predicts that adding 5 CO molecules to today's atmosphere is equivalent to adding 1 CH₄ molecule with the same decadal duration as direct CH₄ addition. Extrapolating these results, CH₄ sources would have to triple before runaway growth, wherein CH₄ emissions exceed the oxidizing capacity of the troposphere.

Methyl bromide (CH₃Br) supplies about half of the chemically active bromine (Br_y) in the stratosphere. Efforts to control Br_y-catalyzed ozone depletion by phasing out, for example, agricultural use of CH₃Br may be thwarted by a lack of understanding of how the varied biogeochemical processes interact as a coupled system: in addition to the chemical industry, large natural sources come from the ocean; and losses occur in the atmosphere, ocean, and soils. A simplified one-dimensional stratosphere-troposphere-ocean model for {CH³Br, Br_y} that fits current understanding of sources and sinks is analyzed in terms of natural modes. Surface and ocean sources have effectively different steady state lifetimes (1.0 and 0.5 years, respectively), but the natural-mode decay times of the system (1.8 years for CH₃Br and 4.5 years for stratospheric Br_y) do not depend on the location of sources. The cumulative ozone depletion resulting from a single atmospheric release of CH₃Br integrates over the consequent slow rise and fall of Br_y in the lower stratosphere. Thus, in spite of the 1-year lifetime of CH₃Br, only half of the anticipated ozone recovery occurs in the first 7 years.