Statistical Theory on Variation of Carbon Dioxide Concentration in Global Warming

Abstract To comprehend the relationship between global warming and CO₂ emissions more comprehensively, we simulated historical data. This endeavor aimed to discern the underlying patterns governing the fluctuation of CO₂ concentration and annual CO₂ emissions. Our analysis revealed a consistent pattern: both variables followed time-dependent exponential functions characterized by positive feedback mechanisms. Expanding our investigation, we integrated these findings with the framework of five Shared Socio-economic Pathways (SSPs). Extending our simulations from 2015 to 2500, we uncovered a shift in CO₂ concentration dynamics. While exponential growth persisted in earlier periods, a transition to negative feedback mechanisms became evident in later stages. We devised a modified exponential function to model CO₂ concentration variation to capture this transition, facilitating the transition from positive to negative feedback. Subsequently, we explored the correlation between temperature anomalies and CO₂ concentrations. Our analysis revealed a linear relationship between these variables and demonstrated that their physical correlation manifests only over the long term. Leveraging this relationship, we formulated predictions for global temperature anomalies up to 2500. Furthermore, we examined the impact of land-use changes as a strategy to mitigate CO₂ emissions partially. By introducing an illustrative example, we elucidated the potential effectiveness of such measures. Finally, we delved into the short-term evolution of the climate system, focusing on peak series in CO₂ concentration and temperature anomalies. This analysis provided valuable insights into the immediate trajectories of these critical variables.