Know how the temperature of the Earth is affected by factors controlling the balance between incoming radiation and radiation emitted from the Earth's surface

2.3.3 Radiation – Earth’s Temperature and Energy Balance

Learning Objective

Understand how the temperature of the Earth is affected by the factors that control the balance between incoming solar radiation and radiation emitted from the Earth’s surface.

Key Concepts

• Incoming solar radiation (insolation) – energy received from the Sun.
• Outgoing terrestrial radiation – energy emitted by the Earth as infrared radiation.
• Energy balance – when incoming and outgoing energy are equal, the Earth’s average temperature remains constant.
• Greenhouse effect – atmospheric gases that absorb and re‑emit infrared radiation, influencing the outgoing energy.

Factors Controlling Incoming Solar Radiation

1. Solar constant (S) – average solar energy received at the top of the atmosphere per unit area perpendicular to the Sun’s rays. Approx. \$1361\ \text{W m}^{-2}\$.
2. Earth–Sun distance – varies with the elliptical orbit; radiation varies as \$\dfrac{1}{r^{2}}\$.
3. Angle of incidence – radiation per unit area is \$S\cos\theta\$, where \$\theta\$ is the angle between the Sun’s rays and the normal to the surface.
4. Albedo (α) – fraction of incident radiation reflected back to space. Global average albedo ≈ 0.30.

Factors Controlling Outgoing Radiation

1. Surface temperature (T) – governs emitted power via the Stefan‑Boltzmann law:

   \$P = \sigma A T^{4}\$

   where \$\sigma = 5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}\$.

2. Emissivity (ε) – effectiveness of a surface in emitting radiation (0 ≤ ε ≤ 1). Real Earth surface emissivity ≈ 0.95.
3. Atmospheric absorption – greenhouse gases (CO₂, H₂O, CH₄, etc.) absorb infrared radiation and re‑emit it, reducing the net loss to space.
4. Cloud cover – reflects solar radiation (increasing albedo) and also absorbs/emits infrared radiation.

Energy Balance Equation for the Earth

The Earth reaches a steady average temperature when:

\$ (1 - \alpha) \, S \, \frac{\pi R^{2}}{4\pi R^{2}} = \varepsilon \sigma T^{4} \$

where:

• \$\alpha\$ = planetary albedo
• \$S\$ = solar constant

\$R\$ = radius of the Earth (cancels out in the simplified form)

• \$\varepsilon\$ = effective emissivity of the Earth–atmosphere system
• \$\sigma\$ = Stefan‑Boltzmann constant
• \$T\$ = effective radiating temperature (≈ 255 K without greenhouse effect)

How Changes in Each Factor Influence Earth’s Temperature

Illustrative Example

Assume the albedo of the Earth increases from 0.30 to 0.35 due to a large volcanic eruption that injects reflective aerosols into the stratosphere. Using the simplified balance equation:

\$ (1 - \alpha) S = \varepsilon \sigma T^{4} \$

With \$S = 1361\ \text{W m}^{-2}\$ and \$\varepsilon = 0.95\$, the effective temperature drops from about 288 K to roughly 284 K, illustrating a cooling effect of a few degrees Celsius.

Key Points to Remember

• The Earth’s temperature is a result of a delicate balance between absorbed solar energy and emitted infrared energy.
• Albedo, greenhouse gases, and emissivity are the primary controllable factors that can shift this balance.
• Small changes in any factor can lead to noticeable climate variations over time.

Suggested Diagram

Practice Questions

1. Explain how an increase in cloud cover can both cool and warm the Earth.
2. Calculate the change in effective temperature if the solar constant were to increase by 2 % while all other factors remain constant.
3. Describe why the effective radiating temperature of the Earth (≈ 255 K) is lower than the average surface temperature (≈ 288 K).

Summary

Understanding the factors that control the Earth’s radiation balance is essential for explaining climate change and predicting future temperature trends. By analysing how each factor—solar input, albedo, greenhouse gases, emissivity, and orbital distance—affects the incoming and outgoing energy, students can grasp why the Earth’s temperature is not static and how human activities can influence it.