Question

If CO2 is instantaneously doubled, the greenhouse effect is enhanced, and the surface and troposphere receive about 4 W/m² 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.

a) 2.24 K
b) 3.12 K
c) 4.08 K
d) 5.03 K

Answer 1

To find the temperature increase that balances a 4 W/m² radiative forcing from doubled CO2, use the Stefan-Boltzmann law with Earth's initial temperature of 288 K and solve for the temperature that equates to a power emission of 244 W/m².

Step-by-step explanation:

The question involves calculating the temperature increase required to balance an extra 4 W/m² of radiative forcing due to a hypothetical instantaneous doubling of CO2. We'll use the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature, given by the equation P = σ*T^4, where σ is the Stefan-Boltzmann constant and T is the temperature in Kelvins.

The Earth's initial equilibrium temperature is 288 K, corresponding to a power emission of 240 W/m². Increasing this power emission by an additional 4 W/m² requires the Earth to increase its temperature to balance this radiative forcing. Let's calculate the new temperature (T_new) that will satisfy the following:

P_initial + ΔP_radiative = σ*T_new^4

240 W/m² + 4 W/m² = σ*T_new^4

Solving this equation for T_new gives the temperature increase required to balance the enhanced greenhouse effect.