Greenhouse gases emissions modify the radiative balance of the Earth, causing changes in its climate. Climate Change is considered one of the greatest threats to economic and social stability. Aviation is responsible for around a 2.5% of greenhouse gases emissions. This contribution is steadily increasing, thus the interest of assessing the impacts that different policies might have on it. The simple feedback model proposed here was intended as a tool in order to investigate the stabilization issue. The model was based on the relationship between the number of air traffic passengers and the associated CO₂ emissions. It incorporated a representation of the feedback of the technological innovation on the emissions rate and of those of the socioeconomic response to the climatic impact on the passengers number. The model parameters were estimated using data from a variety of robust air traffic sources. However, it was found that neither of the feedback terms succeeded at stabilizing the emissions, although they might slow down their growth. In addition, there is also a nonlinear version of the model that includes a representation of the passengers perception of insecurity, similar to the one experienced in the current pandemic. This model favors the stability of both, the number of passengers and CO₂ emissions, as it would also be able to control unprecedented situations.

In this study, we introduce a sensitivity analysis of modelled CO${}_2$ aviation emissions to changes in the model parameters, which is intended as a contribution to the understanding of the atmospheric composition stabilization issue. The two variable dynamic model incorporates the effects of the technological innovations on the emissions rate, the environmental feedback, and a non-linear control term on the passengers rate. The model parameters, estimated from different air traffic sources, are subject to considerable uncertainty. The stability analysis of Monte Carlo simulations revealed that, for certain values of the non-linear term parameter and depending on the type of flight, the passengers number at some equilibrium points exceeded its initial value, while the emissions level was below the initial corresponding one. The results of two global sensitivity analyses indicated that the influence of the non-linear term prevailed on the passengers number rate, followed distantly by the environmental feedback. For the emissions rate, the non-linear term contribution dominated, with the technological term influence placing second.

Since 1999, every report released by the International Panel on Climate Change has advocated a decrease in the greenhouse gas emissions associated with aviation in order to preserve the current climate. This study used a two variable differential equations model with a non-linear control term to address several aspects of the emissions stabilization issue. By optimizing the control term parameter, several management alternatives can be obtained based on the properties of the phase plane of the model solutions, as identified by a stability analysis. The system can be stabilised around an equilibrium point that maintains the present number of passengers, or maintains the emissions level or is nearest to its present state. Each of these options entails different issues of growth or reduction in the number of passengers and/or the emissions rate, directly obtained from the model results. The last option seems especially novel and promising, since only short-distance flight passengers are severely reduced, while long-distance and international passengers are allowed to growth, and their associated emissions are reduced to below 50 percent of their actual value. Moreover, in a scenario of slow growth in air traffic, these rates could improve, with fewer reductions in the number of short-distance passengers.