Empirical values of branching ratios in the three-body recombination reaction for O( ¹ S) and O ₂ (0,0) airglow chemistry

The branching ratios ε and α in the three-body recombination reaction for O( ¹ S) greenline and O ₂ (0,0) atmospheric band airglow chemistry represent the fraction of O ₂ that branch into the b ¹ ∑ _g ⁺ and c ¹ ∑ _u ^- electronic states, respectively. In the present work, the empirical values of these branching ratios have been deduced using a numerical optimization approach. They were obtained using the optimization scheme known as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with our MACD-00 model and simultaneous volume emission rate (VER) measurements of the O( ¹ S) greenline and O ₂ (0,0) atmospheric band emissions. The CMA-ES was employed as the optimization algorithm that would match the O( ¹ S) and O ₂ (0,0) VER profiles simulated by the MACD-00 model to observations made by OXYGEN/S35, S310.10, NASA Flight 4.339, ETON flights P229H and P230H, OASIS, SOAP/WINE, MULTIFOT, and WINDII. We found that most of the values deduced for ε were in the [0.1, 0.3] range, while most of the values of α were in the [0.01, 0.03] range. Excluding the outliers, the average branching ratio values involving the production of O ₂ (b ¹ ∑ _g ⁺ ) and O ₂ (c ¹ ∑ _u ^- ) were determined to be ε = 0.15 ± 0.02 and α = 0.018 ± 0.004, respectively. Overall, the simulations showed good agreement with the observations albeit with some discrepancies in the peak altitudes and shape of the profiles, possibly due to small perturbations in the observed VER profiles that are not considered in our simulations.