B.2.1 Conservation of energy in Earth’s atmosphere Notes

Energy Balance: Emissivity and Albedo

The Earth’s energy balance is a delicate equilibrium between the energy it receives from the Sun and the energy it radiates back into space.

Two key concepts, emissivity and albedo, play critical roles in this balance.

Emissivity: How Efficiently a Surface Radiates Energy

1. A black body is a perfect emitter with an emissivity of 1, meaning it radiates the maximum possible energy at a given temperature.
2. Real surfaces have emissivity values between 0 and 1.
3. The formula for emissivity is: $$
   e = \frac{\text{Power radiated per unit area}}{\sigma T^4}
   $$ where:
   1. $e$ is the emissivity.
   2. $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, \text{W m}^{-2} \text{K}^{-4}$).
   3. $T$ is the absolute temperature of the surface in Kelvin.

How Emissivity Affects Radiation

1. High emissivity: Surfaces with emissivity close to 1, like black bodies, radiate energy efficiently.
2. Low emissivity: Surfaces with emissivity near 0, like polished metals, radiate much less energy.

Emissivity in the Real World

Different surfaces have varying emissivity values:

1. Oceans: High emissivity (~0.8), radiating energy efficiently.
2. Ice: Low emissivity (~0.1), radiating less energy.

Albedo: How Much Energy is Reflected

1. It is the fraction of incoming radiation that is reflected back into space.
2. The formula for albedo is: $$
   \alpha = \frac{\text{Total scattered power}}{\text{Total incident power}}
   $$

Albedo values range from 0 (no reflection) to 1 (all radiation is reflected).

How Albedo Affects Energy Balance

1. High albedo: Surfaces like snow and ice reflect most of the incoming radiation, contributing to cooler temperatures.
2. Low albedo: Surfaces like oceans and forests absorb more radiation, contributing to warmer temperatures.

Factors Influencing Albedo

1. Surface Type: Snow and ice have high albedo, while forests and oceans have low albedo.
2. Cloud Cover: Clouds increase albedo by reflecting sunlight.