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Four billion years ago the Sun’s radiative output was 30% less than it is today.

(i) If we assume the radius of the sun is the same, and that the Earth’s atmosphere was the same as it is now (that is, the atmosphere absorbs 10% of the incoming solar radiation and 80% of the outgoing terrestrial radiation), estimate the average surface temperature of the Earth four billion years ago using a single layer atmosphere.

(ii) In fact, the Earth’s atmosphere was drastically different 4 billion years ago (15-20% CO2, 0% O2). Suppose the atmosphere absorbed 5% of the incoming radiation but 95% of the outgoing radiation. What would be the temperature of the early Earth surface and its atmosphere?

The models that you need are described here:
http://www.scienceinschool.org/2008/issue9/climate

That is as far as I am prepared to go helping you with this. Perhaps another teacher will be able and willing to pursue it further.

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