Characterization of oscillation and a period-doubling transition to chaos reflecting dynamic instability in a simplified model of tropospheric chemistry


  • Richard J. Field,

  • Peter G. Hess,

  • Leonid V. Kalachev,

  • Sasha Madronich


A simplified box model extracted from tropospheric photochemistry is investigated as the influx of NO (FNO) is increased. A subcritical Hopf bifurcation is encountered as FNO is increased, beyond which the steady state is unstable, and the system evolves to an oscillatory state resulting from alternate dominance of two radical chain processes. The first is an O3-consuming process of net stoichiometry, CO + O3 → {CO2} + {O2}, occurring at high [CO] and [O3] and very low [NOx], but leading to increased [NOx] via FNO as CO and O3 are depleted. As [NOx] thus grows, passes through a maximum, and then declines, the second, an O3-producing process of net stoichiometry, CO + 2{O2} + hν → {CO2} + O3, is dominant. It remains so as O3 and CO accumulate (CO via its influx, FCO) until [NOx] again reaches very low values at high [O3] and [CO] as a result of the removal of NO2 by HO photochemically generated from the increasing [O3]. This alternation occurs because each process affects [NOx] and [HOx] so as to lead to dominance of the other. A period-doubling transition to chaotic oscillation occurs as FNO is increased further. The embedding dimension of the chaos is estimated to be four, and the original six-variable model can be reduced to a four-variable (CO, O3, [NO + NO2] and [HO + HO2]) system that behaves nearly identically to the full six-variable model. While the oscillatory and chaotic periods seem too long (at least weeks) to be observed in real atmospheres, the model displays the nonlinear nature and dynamic instability of tropospheric photochemistry and offers insight into the behavior of and transitions between higher and lower [NOx] states, which may be observable. The importance of the ratios [CO]/[NO2] and [O3]/[NO] to net O3 change is illustrated. The appearance of this instability suggests that predictions based upon the temporal evolution of this or even more complex models of tropospheric chemistry sometimes may be very sensitive to the exact initial conditions of [CO]/[NO2] and [O3]/[NO] prevailing.