Science 9 July 1971:
Vol. 173 no. 3992 pp. 138-141
DOI: 10.1126/science.173.3992.138
Atmospheric Carbon Dioxide and Aerosols: Effects of Large Increases on Global Climate
1. S. I. Rasool1,
2. S. H. Schneider1
+ Author Affiliations
1. 1Institute for Space Studies, Goddard Space Flight Center, National Aeronautics and Space Administration, New York 10025
Abstract
Effects on the global temperature of large increases in carbon dioxide and aerosol densities in the atmosphere of Earth have been computed. It is found that, although the addition of carbon dioxide in the atmosphere does increase the surface temperature, the rate of temperature increase diminishes with increasing carbon dioxide in the atmosphere. For aerosols, however, the net effect of increase in density is to reduce the surface temperature of Earth. Because of the exponential dependence of the backscattering, the rate of temperature decrease is augmented with increasing aerosol content. An increase by only a factor of 4 in global aerosol background concentration may be sufficient to reduce the surface temperature by as much as 3.5 ° K. If sustained over a period of several years, such a temperature decrease over the whole globe is believed to be sufficient to trigger an ice age.

The factor: ln(C/C0) is obviously dimensionless, but the constant (5.35) is in units of W/m^2.

It is the net change in rate of energy transfer per unit area due to an instantaneous change in CO2 concentrations.

This equation is not an analytical solution to the radiative transfer equations. This equation is an empirical fit to change in CO2 concentrations over a certain range – with the results for this empirical fit derived from the radiative transfer equations – see, for example, Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations.

Steve: I know that it is an “empirical fit”. That was one of the purposes of this post.

What units is this in? K, F, or C?

- I don’t go into the IPCC expression a lot more but there is an extract from the paper Myhre and some background. Feel free to ask a question over at that post..

Just ran into this post tonight. I was wondering if Steve had ever come to a ‘conclusion’ regarding the plausibility of logarithmic forcing.

So, yeah, I appreciate the update. Even by a stranger, passing in the night.

I’ve been doing my own research of old papers for http://scienceofdoom.com and the “source” is clear.

IPCC TAR cites “New estimates of radiative forcing due to well mixes greenhouse gases” Myhre et al 1998.

Their paper, published in GRL, explains clearly what they do. At least, they follow on from a couple of decades of work with “radiative-convective models”, so a few things might be implied rather than explicit.

They are running the RTE (radiative transfer equations) using both LBL (line by line) and well-proven band models. They use the results from a few standardized profiles because the results from one “average” profile have been demonstrated to not match the average of results from many profiles.

And the “simplified expression” – the holy grail – comes from running these averaged 1-d simulations for different CO2 values and plotting the results.

Consequently, they find the new coefficient for the ln(C/Co) formula which best fits.

Delta F = 5.35 ln(C/Co)