Climate change is an important societal issue. Large effort in society is spent on addressing it. For adequate measures, it is important that the phenomenon of climate change is well understood, especially the effect of adding carbon dioxide to the atmosphere. In this work, a theoretical fully analytical study is presented of the so-called greenhouse effect of carbon dioxide. The effect of this gas in the atmosphere itself was already determined as being of little importance based on empirical analysis. In the current work, the effect is studied both phenomenologically and analytically. In a first attempt of energy transfer by radiation only, it is solved by ideal-gas-law equations and the atmosphere is divided into an infinite number of layers each absorbing and reemitting infrared radiation (surpassing the classical Beer-Lambert analysis of absorption). The result is that the exact structure of the atmosphere is irrelevant for the analysis; we might as well keep the two-box model for any analytical approach. However, the results are unsatisfactory in that they cannot explain the profile of the atmosphere. In a new approach, the atmosphere is solved by taking both radiative as well as thermodynamic processes into account. The model fully fits the empirical data and an analytical equation is given for the atmospheric behavior. Upper limits are found for the greenhouse effect ranging from zero to a couple of mK per ppm CO2. It is shown that it cannot explain the observed correlation of carbon dioxide and surface temperature. This correlation, however, is readily explained by Henry’s Law (outgassing of oceans), with other phenomena insignificant. Finally, while the greenhouse effect can thus, in a rudimentary way, explain the behavior of the atmosphere of Earth, it fails describing other atmospheres such as that of Mars. Moreover, looking at three cities in Spain, it is found that radiation balances only cannot explain the temperature of these cities. Finally, three data sets with different time scales (60 years, 600 thousand years, and 650 million years) show markedly different behavior, something that is inexplicable in the framework of the greenhouse theory.
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