Simplified mathematical model for calculating global warming through anthropogenic CO2

Researchers from Otto von Guericke University Magdeburg, Institute of Fluid Dynamics and Thermodynamics in Germany devised a simplified one dimensional mathematical model for calculating global warming caused by anthropogenic CO₂.

They studied the heat transfer radiations in the atmosphere. Here, the radiation exchange among the gas which contains water vapor and carbon dioxide and the Earth’s surface as well as the clouds is considered. The emissivity of the gases is function of temperature, gas concentration and beam length of the atmospheric layer defined through the model.

The authors modeled and validated with the known average temperature of the Earth. Their model was successful also for analysis of past climate events. For describing the mechanism of the greenhouse effect, the researchers assumed Earth has uniform temperature with no distinction between land and oceans.

In their modelling of the net heat fluxes exchanged according to the Stefane Boltzmann law are considered as is usual in thermal engineering. About 50% of the Earth is covered with clouds. The clouds as well as dust, aerosols, and a shortwave band of H₂O in the atmosphere act as a radiation shield, the total radiation at the Earth’s surface is reduced as well as the heat flow rate.

The researchers calculated the optical thickness for the gas between the Earth and the clouds to be 0.90 bar, for a cloud-free sky and Space to be 2.72 bar and for the gas between the clouds and Space as 1.43 bar. In their model final accumulation was reached at 20 km height which was presumed radiation behavior below such level influences the Earth’s temperature.

This study shows that the temperature of the Earth increases significantly with the CO₂ concentration. While doubling the CO₂ concentration, the temperature of the Earth increases by 0.4 K. This increase lies in the lower range of the complex models of different global climate research institutes. Since 1860, the Earth’s temperature has already risen due to anthropogenic CO₂ emissions by 0.4 K. The measured increase of about 1 K is attributed to side effects caused by the CO₂ related temperature increase. Therefore, using the researchers’ model a temperature increase of more than 0.4 K is predicted for the future.

The findings of this study can estimate how strongly CO₂ influences the climate and to what extent the temperature of the Earth increases with an increase in the CO₂ content.