340 watts per square meter of solar energy fall on the Earth
The amount of heat a surface radiates is proportional to the fourth power of its temperature. If temperature doubles, radiated energy increases by a factor of 16 (2 to the 4th power). If the temperature of the Earth rises, the planet rapidly emits an increasing amount of heat to space. This large increase in heat loss in response to a relatively smaller increase in temperature—referred to as radiative cooling--is the primary mechanism that prevents runaway heating on Earth….The atmosphere radiates heat equivalent to 59 percent of incoming sunlight; the surface radiates only 12 percent. In other words, most solar heating happens at the surface, while most radiative cooling happens in the atmosphere. https://www.earthobservatory.nasa.gov/features/EnergyBalance/page4.php
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About 23 percent of incoming solar energy is absorbed in the atmosphere by water vapor, dust and ozone, and 48 percent passes through the atmosphere and is absorbed by the surface.
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The oceans account for 0.022 percent of the total weight of Earth. http://see-the-sea.org/facts/facts-body.htm
The total mass of Earth’s atmosphere is about 5.5 quadrillion tons, or roughly one millionth of Earth’s mass. http://blogs.britannica.com/2012/01/how-much-does-earth-atmosphere-weigh/
.022/.000001 = ~22,000. So oceans are ~22,000 x weightier than entire atmosphere
CO2 makes up .0.0582% of atmosphere by weight. https://micpohling.wordpress.com/2007/03/30/math-how-much-co2-by-weight-in-the-atmosphere/
22,000/.00058 = ~37,900,000. So oceans weigh ~37,900,000 times atmospheric CO2.
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Then there is the geologic factor of Earth's own magma heat to consider also.
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