The presented work investigates a surface dielectric barrier discharge (SDBD) operated dry synthetic air as the working gas using a combination of experimental measurements and simulations. The primary objective is to characterize the production and consumption dynamics of reactive oxygen and nitrogen species to enhance the understanding of their formation and facilitate control of the discharge for applications. Densities of O3, NO2, and N2O5 are measured under varying gas flow rates, utilizing optical absorption spectroscopy as the diagnostic method. A semi-empirical chemical kinetics model is developed based on a compilation of reactions from previous studies on similar types of discharges. The results reveal two previously known and distinct operating modes, with a mode transition occurring between the modes as the flow rate is varied. The results indicate the dependency of the mode transition on the density of sufficiently vibrationally excited nitrogen molecules, which is represented in the model by an increased vibrational temperature at lower gas flow rates. Furthermore, key reactions responsible for the production and consumption of ozone and nitrogen oxides are identified, providing insight into the importance of macroscopic parameters, such as gas temperatures and different time constants, that influence the non-linear balance of these reactions.