Investigation of the dynamic equilibrium of atmospheric CO2 concentrations

One of the major issues of our time is environmental pollution, environmental protection, and climate change, which are all interconnected. A key characteristic of climate change is the variation in the temperature of the atmosphere, oceans, and land, known as global warming. Science has identified the increase in greenhouse gases as one of the causes of global warming. As is well known, CO₂ is one of the most important greenhouse gases. In our paper, we introduce new global models to examine the temporal changes in atmospheric CO₂ concentration. These models have an input-output structure and are mathematically first-order, constant coefficient linear inhomogeneous differential equations. We also presented a convolution integral equation derived using Duhamel’s theorem, which allows for the examination of the most complex time functions of CO₂ emissions. The models are mathematically easy to evaluate and also allow for the identification of parameters in the balance equations. The solutions to the mathematical models are analytical, continuous explicit functions that can be graphically displayed. Our models provide the opportunity to adjust the time constant of CO₂ absorption and to separate the atmospheric inflow of CO₂ from natural and anthropogenic sources. This facilitates the examination of future CO₂ changes and the impact of renewable energy sources, the green transition, and the reduction of anthropogenic emissions. We validate the model with measurement data from the Mauna Loa Observatory. We prove the dominance of natural CO₂ emissions and absorption and the subordinate role of anthropogenic emissions. Furthermore, we demonstrate that under constant CO₂ emissions, the atmospheric CO₂ concentration stabilizes. The atmospheric CO₂ concentration can be determined for any scenario. We can analyze the role of anthropogenic CO₂ emissions in the magnitude of global warming with these models. We can provide forecasts on whether the replacement of fossil fuels with renewable energies can stop or mitigate global warming.