Nonlinear Dynamics in Atmospheric Chemistry Rate Equations

Nonlinear terms in the gas-phase rate equations of atmospheric trace constituents give rise to unexpected oscillations in the concentrations. For a simplified chemical scheme of the troposphere that contains only the generic reaction paths, the underlying dynamical structure is investigated. It is shown that the source strengths of CO and NO are the controlling parameters of the system. A linear stability analysis reveals that the steady state solutions lose stability due to the occurrence of two Hopf bifurcations. Furthermore, it appears that the dynamical behaviour of the oscillatory solutions is dominated by O₃ and CO. Based on the two-variable system (CO–O₃) it is shown that the oscillatory solution involves an autocatalytic ozone production phase which is followed by a phase in which CO is oxidised quickly. A simple expression is presented from which the period of the oscillation can be obtained. The implications for the present troposphere are unclear, since other hydrocarbons are present and transport is taking place. Nevertheless, the system nicely shows the general nonlinear mechanisms that operate in the tropospheric chemistry equations.