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

Abstract

Abstract. The mechanism of generation of 2-day photochemical oscillations in the mesopause region (80-90 km) has been studied analytically. The initial system of equations of chemical kinetics describing the temporal evolution of O, O 3 , H, OH and HO 2 concentrations with allowance for diurnal variations of solar radiation has been simplified successively to a system of two nonlinear first-order time equations with sinusoidal external forcing. The obtained system has a minimum number of terms needed for generation of 2-day oscillations. Linearization of this system near the perioddoubling threshold permits separating explicitly a particular case of the Mathieu equationẍ+α·sin ωt ·x = 0, in which the first sub-harmonic (ω/2) of the exciting force starts to grow exponentially when the amplitude of external forcing (α) exceeds its threshold value. Finally, a system of two simplest differential equations with power-law nonlinearity has been derived that allows analytical investigation of the effect of arising of reaction-diffusion waves in the mesospheric photochemical system.

Nighttime Ozone Chemical Equilibrium in the Mesopause Region

“…Kulikov et al () showed by numerical calculations that in the second and third equations of system , the first terms are the most important at heights between 80 and 90 km. In particular, these terms provide the nontrivial nonlinear dynamic properties of system mentioned in section 1.…”

Boundary of Nighttime Ozone Chemical Equilibrium in the Mesopause Region From SABER Data: Implications for Derivation of Atomic Oxygen and Atomic Hydrogen

“…The local values of O 3 and O 3 eq are close to each other ( O 3 ( t ) ≈ O 3 eq ( t )), when , where is the local characteristic time of O 3 eq : As shown in Kulikov et al (), can be defined from a simplified photochemical model describing the O x ‐HO x evolution in the mesopause region (Feigin et al, ; Kulikov et al, ), so the criterion for validity of the NOCE can be written in the form: where k i are the corresponding reaction constants from Table .…”

“…As shown in Kulikov et al (2018), τ O3 eq can be defined from a simplified photochemical model describing the O x -HO x evolution in the mesopause region (Feigin et al, 1998;Kulikov et al, 2012), so the criterion for validity of the NOCE can be written in the form:…”

“…A more detailed discussion of the criterion derivation can be found in Supporting Information S1 (Allen et al, 1984;Andronov & Pontryagin, 1937;Brasseur & Solomon, 2005;Feigin, 2002;Feigin et al, 1998;Feigin & Konovalov, 1996;Konovalov & Feigin, 2000;Kulikov et al, 2012Kulikov et al, , 2018Mlynczak et al, 2013;Smith et al, 2008).…”

Technical note: Evaluation of the simultaneous measurements of mesospheric OH, HO<sub>2</sub>, and O<sub>3</sub> under a photochemical equilibrium assumption – a statistical approach

“…Complemented with Henry's law (e.g., Djouad et al, 2003;Tulet et al, 2006) in multiphase models, this approach markedly saves calculation time and increases the overall stability of the numerical scheme. Moreover, use of the photochemical equilibrium condition to simulate fast component dynamics reduces the phase space dimension of box models significantly (e.g., Kulikov and Feigin, 2014), allowing a comprehensive analysis of nontrivial nonlinear dynamic properties of various atmospheric photochemical systems (e.g., Feigin and Konovalov, 1996;Feigin et al, 1998;Konovalov et al, 1999;Konovalov and Feigin, 2000;Kulikov et al, 2012).…”