The diagram below shows a simple energy balance climate model in which the atmosphere and the Earth’s surface are treated as two bodies.
The Earth’s surface receives both solar radiation and radiation emitted from the atmosphere.
At current atmospheric greenhouse gas concentrations, the temperature of Earth’s atmosphere is set to increase by 6 K.
Data for this model:
Use this data to estimate the increase in temperature of the Earth’s surface.
Step 1: List the known quantities
Step 2: Calculate the solar power absorbed at the Earth’s surface
Ps = e × Pa
Ps = 0.720 × 344 = 247.68 = 248 W m–2
Step 3: Write the equation for the power emitted by a body
P = eσT4
Step 4: Calculate the new power radiated by the atmosphere
P = 0.720 × (5.67 × 10–8) × 2484 = 154.43 = 154 W m–2
Step 5: Calculate the new power absorbed by the Earth’s surface
New power, Ps = 248 + 154 = 402 W m–2
Step 6: Calculate the new temperature of the Earth’s surface
Ps = σTs4
400 = (5.67 × 10–8) × Ts4
Step 7: Determine the increase in temperature
ΔT = 290 – 288 = 2 K
In simplified climate models, you can generally assume the Earth’s surface and the atmosphere: