# Why we get the same forcing for each doubling of CO2

### Submitter:

Romps, David — Lawrence Berkeley National Laboratory

### Area of research:

Radiation Processes

### Journal Reference:

*Journal of Climate*, , 10.1175/JCLI-D-21-0275.1. ONLINE.

## Science

It is well known that the radiative forcing (i.e., effected decrease in outgoing longwave radiation) from carbon dioxide is approximately logarithmic in its concentration, producing about four watts per square meter of global-mean forcing for each doubling. These are basic facts of climate science that serve as a foundation of our understanding of anthropogenic global warming, yet competing explanations for these basic facts have been given in the literature in recent years. Here, the various pieces of physics that conspire to generate the logarithmic forcing are explored in detail using both line-by-line radiative-transfer calculations and a simple pencil-and-paper model for the forcing. An essential part of the mechanism is the particular distribution of absorption coefficients within the 15-micron band of carbon dioxide.

## Impact

An alternative explanation has been given repeatedly in the literature relying on the particular lapse rate of Earth's troposphere, and that explanation would appear to work for any greenhouse gas. It is shown here that that alternate explanation is incorrect: it is neither necessary nor sufficient to explain the logarithmic forcing of carbon dioxide and it is generally inapplicable to well-mixed greenhouse gases in Earth’s atmosphere.

## Summary

The basic mechanism by which increases in CO_{2} lead to additional radiative forcing is robust. Not only can this forcing be understood with a simple quantitative model, but the model makes clear why the forcing is logarithmic (i.e., why each doubling of concentration gives the same additional forcing) and why its magnitude is around four watts per square meter. This work helps to lay to rest an alternate explanation that has appeared in papers and textbooks.