IB DP Physics: HL复习笔记8.2.5 Earth's Surface–Atmosphere System

Earth's Surface–Atmosphere System

  • 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

Worked Example

The diagram below shows a simple energy balance climate model in which the atmosphere and the Earth’s surface are treated as two bodies.

8-2-5-we-energy-system_sl-physics-rn

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:

  • Current mean temperature of the Earth’s atmosphere = 242 K
  • Current mean temperature of the Earth’s surface = 288 K
  • Solar power per unit area at top of the atmosphere = 344 W m–2
  • Emissivity of the atmosphere, e = 0.720
  • Albedo of the atmosphere, a = 0.280

Use this data to estimate the increase in temperature of 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

Exam Tip

In simplified climate models, you can generally assume the Earth’s surface and the atmosphere:

  • Act as black bodies - this means the emissivity of the surface will be equal to 1!
  • Remain at a constant temperature

 

 

 

 

 

转载自savemyexams

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