Question

If co2 is instantaneously doubled, the greenhouse effect is enhanced, and the surface and troposphere receive about 4 w/m? of radiation. use the stefan-boltzmann law again to calculate the temperature that earth's surface has to rise to (in degrees k) in order to balance this radiative forcing. then estimate the total warming that occurs from the co2 doubling by subtracting the original temperature of the planet (288 k)

Answer 1

Doubling atmospheric CO₂ to 560 ppm leads to a radiative forcing of around 3.7 W/m². Using a climate sensitivity factor of 0.8°C per W/m², the increase in Earth's temperature would be approximately 3.0°C.

Step-by-step explanation:

If the concentration of CO₂ in the atmosphere is doubled and results in a radiative forcing of 4 W/m², we can calculate the new equilibrium temperature of the Earth using the Stefan-Boltzmann law. This law states that the power radiated per unit area of the surface of a black body is proportional to the fourth power of its thermodynamic temperature. The Earth, to a first approximation, can be considered a black body. It thus requires an increase in temperature to balance out the additional energy from the radiative forcing.

Pre-industrial CO₂ levels were 280 ppm and doubling it would therefore be 560 ppm, resulting in a radiative forcing of approximately 3.7 W/m². With a climate sensitivity factor of 0.8°C per W/m2, the expected temperature rise due to doubling CO2 would be around 3.0°C. As the original temperature of the planet is 288 K, the new equilibrium temperature would be 288 K + 3 K = 291 K, showing a total warming of 3°C from CO2 doubling. This is a simplified calculation that does not take into account various feedback mechanisms that can either amplify or mitigate the initial temperature rise.