Statistical Theory on Variation of Carbon Dioxide Concentration in Global Warming

Climate warming is a typical complex, time-varying system. In the absence of complete knowledge of its evolutionary dynamics, future trends can be predicted using time-series data (data-driven prediction). It has been shown that historical CO ₂ concentration data can be well represented by exponential growth. According to Takens' theorem on delay embedding, historical data can be combined with future projections within the framework of the five Shared Socioeconomic Pathways (SSPs). By extending the simulation of CO ₂ concentration changes from 2015 to 2500, we observe a transition from exponential growth to exponential decay in the later stages. A modified exponential function is introduced to model this shift. We then examine the correlation between global temperature anomalies and CO ₂ concentrations, finding that their physical correlation is evident only over the long term. Using this relationship and CO ₂ concentration data, we generate predictions for global temperature anomalies up to 2500, which can be compared with other models in the literature.