Some proposed solutions to this problem, known as the faint young Sun problem, include an atmospheric composition with higher concentrations of greenhouse gases, higher atmospheric pressure, increased cloud droplet size, and changes in land distribution and Earth's rotation rate.
Charnay et al. used a three-dimensional global climate model coupled to a dynamic ocean model to examine these possible solutions. They find that an atmosphere that had 100 millibars of carbon dioxide and 2 millibars of methane 3.8 billion years ago, and 10 millibars of carbon dioxide and 2 millibars of methane 2.5 billion years agolevels corresponding to 25 to 250 times the present level of carbon dioxide and 1000 times the present level of methanewould have made it possible for Earth to have had a temperate climate with a mean surface temperature between 10 and 20 degrees Celsius (50 and 68 degrees Fahrenheit), close to the current climate. The authors suggest that these levels of greenhouse gases are consistent with geological data, making such an atmospheric composition a viable solution to the faint young Sun problem. Cloud feedbacks were also shown to prevent a full snowball Earth from developing during that time period. The authors find that some of the other potential solutions could have produced some warming during the Archean, but none individually produced enough warming to avoid widespread glaciation.
Source: Journal of Geophysical Research-Atmospheres, doi:10.1002/jgrd.50808, 2013 http://onlinelibrary.wiley.com/doi/10.1002/jgrd.50808/abstract
Title: Exploring the faint young Sun problem and the possible climates of the Archean Earth with a 3D GCM
B. Charnay, F. Forget, J. Leconte, E. Millour, F. Codro
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