With renewed interest in the development of civil supersonic aircraft, their return in the future is becoming more ever more likely. The environmental impact of emissions in the stratosphere on climate and the ozone layer therefore needs to be explored. The stratospheric ozone levels determine the amount of harmful ultraviolet radiation reaching the Earth's surface and thus the level of risk to human health and ecosystems. Ozone response is complex, varying with emission altitude and latitude and we are currently reliant on computationally expensive chemistry-transport models to calculate chemical species concentration changes resulting from supersonic aviation emissions. This paper takes a novel approach to reduce the dependency on these models, creating data-driven dynamical systems that model the global spatiotemporal atmospheric ozone response for different emission scenarios. The dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods are applied to atmospheric ozone data obtained from the GEOS-Chem model, and the evolution of the dominant POD spatial modes are modelled using sparse identification of nonlinear dynamics algorithm (SINDy). We show that DMD models can reconstruct monthly global column ozone changes with root mean square errors less than 0.05 Dobson unit (DU) for a period of three years. Predicting the global mean column ozone changes for the years beyond the period used to construct the models, results in errors less than 0.12 DU. Independent DMD models at two different altitudes can be interpolated to produce estimates for ozone response at an intermediate altitude. These methods can serve as a basis for low dimensional surrogate models that can be used to evaluate chemical species concentrations changes as a result of supersonic aviation emissions.