On the Influence of Carbonic Acid in the Air on the Temperature of the Ground, Svante Arrhenius, Philosophical Magazine and Journal of Science, Series 5, Volume 41, April 1896, pages 237-276 now in the public domain, available online at the Royal Society of Chemistry.
This publication was little noticed in its day but has become a center of controversy as the potential impact of Carbon Dioxide, referred to Carbonic Acid in the paper, could have on the surface temperature of the Earth. It is referenced in numerous papers, blogs and the greenhouse equations still include the basic natural log relationship determined by Arrhenius. At issue is if that relationship, that appears to be based on an average atmospheric radiant layer at a temperature of 255K is relevant.
G. S. Chandler, in a latter study determined that a doubling of CO2 would cause approximately 2 degrees per doubling and estimate early 20th century warming to mainly natural(greater than 50%) as of 1934.
The central issue would be that the effective radiant layer would vary with regional temperature and therefore the impact of carbon dioxide would vary with region. The basic natural log relationship does not considered adequately the variation in source temperature.
In order to properly evaluate the performance of climate models, a better understanding of the physical process of the atmospheric effect, not just Carbon Dioxide, needs to achieved. Where the average radiant layer impacted by change in Carbon Dioxide concentration is colder (higher in the atmosphere) that the average layer of water vapor condensation, the Carbon Dioxide impact on the surface would be muted.
A proper physical explanation of the potential impact of CO2 greater than 2C per doubling has not been published. Since modeled values are diverging from observations, it appears past due that a study based on physical principles be published. The first step toward that goal would be to determine what if any validity there is to the above Arrhenius published paper.