Using a detailed atmospheric radiative transfer model, we derive macroscopic relationships of downwelling and outgoing longwave radiation which enable determining the partial derivatives thereof with respect to the explanatory variables that represent the greenhouse gases. We validatethese macroscopic relationships using empirical formulae based on downwelling radiation data, commonly used in hydrology, and satellite data for the outgoing radiation. We use the relation-ships and their partial derivatives to infer the relative importance of carbon dioxide and water vapour in the greenhouse effect. The results show that the contribution of the former is 4% – 5%, while water and clouds dominate with a contribution of 87% – 95%.

The minor effect of carbon dioxide is confirmed by the small, non- discernible effect of the recent escalation of atmospheric CO₂ concentration from 300 to 420 ppm. This effect is quantified at 0.5% for both downwelling and outgoing radiation. Water and clouds also perform other important functions in climate, such as, regulating heat storage and albedo, as well as cooling the Earth’s surface through latent heat transfer, contributing 50%. By confirming the major role of water on climate, these results suggest that hydrology should have a more prominent and more active role in climate research.