Evaluating solutions to the faint young Sun problem
During the Archean eon, between about 3.8 billion years ago and 2.5 billion years ago, the Sun was about 20 to 25 percent fainter than it is today. With less sunlight to warm the Earth, the oceans should have been frozen over, but geological evidence suggests that this was not the case.
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 ago—levels corresponding to 25 to 250 times the present level of carbon dioxide and 1000 times the present level of methane—would 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
Exploring the faint young Sun problem and the possible climates of the Archean Earth with a 3-D GCM
 Different solutions have been proposed to solve the “faint young Sun problem,” defined by the fact that the Earth was not fully frozen during the Archean despite the fainter Sun. Most previous studies were performed with simple 1-D radiative convective models and did not account well for the clouds and ice-albedo feedback or the atmospheric and oceanic transport of energy. We apply a global climate model (GCM) to test the different solutions to the faint young Sun problem. We explore the effect of greenhouse gases (CO2 and CH4), atmospheric pressure, cloud droplet size, land distribution, and Earth’s rotation rate. We show that neglecting organic haze, 100 mbar of CO2 with 2 mbar of CH4 at 3.8 Ga and 10 mbar of CO2 with 2 mbar of CH4 at 2.5 Ga allow a temperate climate (mean surface temperature between 10°C and 20°C). Such amounts of greenhouse gases remain consistent with the geological data. Removing continents produces a warming lower than +4°C. The effect of rotation rate is even more limited. Larger droplets (radii of 17 μm versus 12 μm) and a doubling of the atmospheric pressure produce a similar warming of around +7°C. In our model, ice-free water belts can be maintained up to 25°N/S with less than 1 mbar of CO2 and no methane. An interesting cloud feedback appears above cold oceans, stopping the glaciation. Such a resistance against full glaciation tends to strongly mitigate the faint young Sun problem.