The earth's energy budget
For surface temperature stability the average incoming energy from all sources - which includes direct energy from the sun plus back radiation from the atmosphere - must equal outgoing energy. If incoming energy rises then, EVERYTHING ELSE BEING EQUAL, surface temperatures will rise until a new equilibrium is established at a higher temperature.
Anthropogenic global warming (AGW)
The theory is simple. Add a greenhouse gas, in this case CO2, to the atmosphere and the amount of back radiation increases. Everything else being equal this should result in a rise in average surface temperatures.
There is a simple approximation formula that can be used to calculate the extra back radiation from adding CO2 to the atmosphere:
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Extra radiation (watts / sq. metre) = 5.35 ln(C / C0)
Where ln = natural logarithm
C0 = atmospheric CO2 level in 1750 = 280 parts per million (ppm)
C = current CO2 level = 385 ppm.
Plugging in the numbers gives additional back radiation of 1.7 watts / sq.metre. This translates into an average temperature rise at Earth surface of about 0.3 degrees Celsius. If this was the sum total of AGW there would be nothing to worry about.
What is not equal? Positive and negative feedbacks
Positive feedbacks amplify the effects of adding CO2 to the atmosphere. Negative feedbacks mitigate the effect of additional CO2.
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Unfortunately most feedbacks that have been investigated appear to be positive. I'll confine myself to discussing four.
Water vapour
Water vapour is by far the most important greenhouse gas. Physics theory says that adding CO2 should lead to an increase in the water vapour content of the atmosphere. This appears to be happening. Additional water vapour magnifies the effects of additional CO2.
Albedo
Albedo is a measure of the amount of sunlight Earth surface reflects. The more that is reflected the less heating at Earth surface. Higher temperatures, mainly by shortening the "ice and snow" periods in the northern hemisphere, decrease the Earth's albedo leading to further rises in temperature.
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