Lifetimes and eigenstates in atmospheric chemistry

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 CH 4 ‐CO‐OH system are analyzed. The longest time constant (smallest eigenvalue) always exceeds the lifetime defined by the steady‐state loss frequency for CH 4 , the longest lived gas. Thus, the extent of a CH 4 perturbation—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 CH 4 , CO, and other hydrocarbons and species.