Toward an understanding of the nonlinear nature of atmospheric photochemistry: Origin of the complicated dynamic behaviour of the mesospheric photochemical system

Abstract

Abstract. The methods of nonlinear dynamics are used to reveal the origin of complicated dynamic behaviour (CDB) of a dynamic model of the mesospheric photochemical system (PCS) perturbed by diurnal variations in photolysis rates. We found that CDB appearance during the multi-day evolution is unambiguously determined by two peculiarities in the model behaviour during its 24-hours evolution. These peculiarities are the presence of a stage of abrupt changes in reagent concentrations and the "humped" dependence of the end-night atomic hydrogen concentrations on those at the beginning of the night. Using a successive analysis we found that these two peculiarities are, in turn, conditioned by the specific features of the chemical processes involved in the model, namely, by the catalytic cycle whose net rate is independent of the concentration of the destroyed species (here, it is atomic oxygen). We believe that similar peculiarities inherent in other atmospheric PCSs indicate that under appropriate conditions they may also demonstrate CDB. We identified the mechanism of the CDB appearance and described it in two ways. The first one reveals a sequence of the processes causing the exponential (on the average) growth of a perturbation of the solution with time. In particular, we found that the behaviour of small perturbations of an arbitrary solution of model equations is identical to the behaviour of a linear oscillator excited parametrically. The second way shows the mechanism of CDB appearance by means of 1-dimensional mapping, which is, basically, the same as the well-known Feigenbaum mappings.

The mechanism of non-linear photochemical oscillations in the mesopause region

“…The principal feature of this cycle in the conditions of the upper mesosphere is that its rate does not depend on the concentration of the destroyed substance and is determined only by a catalytic agent (atomic hydrogen concentration). As was demonstrated by Konovalov and Feigin (2000), this feature ensures MPCS instability that manifests itself as a sequence of period doubling bifurcations and the transition to chaotic behavior as the control parameters are varied (the variation of height in Fig. 1a).…”

“…The nonlinear dynamic mechanism of MPCS response to diurnal variations of solar radiation was described in the work by Konovalov and Feigin (2000). It was shown that this mechanism is closely connected with the system dynamics in the nighttime, when nonlinear relaxation of the great majority of MPCS variables occurs in the absence of a light source.…”

“…The research performed by Fichtelmann and Sonnemann (1992), Sonnemann andFichtelmann (1997), Feigin et al (1998), and Konovalov and Feigin (2000) points to a possible nonlinear response of the MPCS to diurnal variations of solar radiation. Analysis within the framework of the zero-dimensional MPCS model revealed a wide spectrum of periodic (subharmonic) and chaotic modes of behavior of minor gas constituents of the mesosphere that are realized depending on the values of control parameters, such as H 2 O, is single-valued, correspond to the oscillations with a period of one day.…”

“…It is also clear from this figure that allowance for diffusion leads to pronounced expansion (primarily upwards) of the regions of heights of nontrivial MPCS behavior. We will omit detailed analysis of the causes of this expansion and will only note that that, with the diffusion coupling taken into consideration, the nonlinear dynamic mechanism described by Konovalov and Feigin (2000) is triggered at higher altitudes.…”

“…Sonnemann andFichtelmann (1987, 1997), Fichtelmann and Sonnemann (1992), Feigin et al (1998), and Konovalov and Feigin (2000) used zerodimensional models (without spatial transport) to show that a wide spectrum of periodic (subharmonic, with periods of 2, 3, 4, and more days) and chaotic regimes of behavior of minor gas constituents may exist at the heights of the mesopause region (80-90 km). Note that diurnal variation of solar radiation is the key mechanism of the Sun's influence on the chemical process in the entire atmosphere of the Earth.…”