Two completely different explanations of the so-called atmospheric greenhouse effect are scrutinized: First, the explanation of the American Meteorological Society (AMS) and the World Meteorological Organization (WMO) quantifying this effect by two characteristic temperatures, secondly, the explanation of Ramanathan et al. (1987) that is mainly based on an energy-flux budget for the Earth-atmosphere system. Both explanations are related to the global scale. In addition, the meaning of climate, climate change, and climate variability is discussed to outline in which way the atmospheric greenhouse effect might be responsible for climate change and climate variability, respectively. In doing so, it is distinguish between two different branches of climatology, namely (a) physical climatology in which the boundary conditions of the Earth-atmosphere system play the most dominant role and (b) statistical climatology that is dealing the statistical description of fortuitous weather events that had been happening in climate periods; each of them usually comprises 30 years. Based on the findings, it is argue that (a) the so-called atmospheric greenhouse effect cannot be proved by the statistical description of fortuitous weather events that took place in a climate period, (b) the description by AMS and WMO has to be discarded because of physical reasons, (c) energy-flux budgets for the Earth-atmosphere system do not provide any evidence that the atmospheric greenhouse effect does exist.