• It is useful to consider Earth’s energy balance in terms of how much incoming energy from the Sun is used and how much is returned to space
• If incoming and outgoing energy are in balance, the Earth’s temperature will remain constant
• This can be used to create models which can help climate scientists predict temperature fluctuations based on current and increased concentrations of greenhouse gases
  • At it’s simplest, the model involves a one-layer atmosphere above the Earth’s surface

Step 1: List the known quantities

• • Solar power above atmosphere,?Pa?= 344 W m^–2
  • Emissivity of the atmosphere,?e?= 0.720
  • Emissivity of the surface,?e?= 1
  • New temperature of Earth’s atmosphere,?Ta?= 242 + 6 = 248 K
  • Stefan-Boltzmann constant, σ = 5.67 × 10^–8?W m^–2?K^–4
  • Power absorbed at the Earth’s surface =?Ps
  • New temperature of Earth’s surface =?Ts

Step 2: Calculate the solar power absorbed at the Earth’s surface

• • This can be calculated using the emissivity and the solar power above the atmosphere

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

• • The power absorbed by the Earth’s surface is a sum of the solar radiation that reaches the surface plus the power radiated by the atmosphere

New power,?Ps?= 248 + 154 = 402 W m^–2

Step 6: Calculate the new temperature of the Earth’s surface

• • The Earth’s surface can be assumed to be a black body, hence e = 1

Ps?= σTs⁴

400 = (5.67 × 10^–8) ×?Ts⁴

Step 7: Determine the increase in temperature

ΔT?= 290 – 288 = 2 K