B.2 Greenhouse effect

The question asks for the definition of the solar constant $S$. This is a fundamental quantity in climate physics.

The solar constant $S$ is defined as the intensity (power per unit area) of solar radiation incident on a surface held perpendicular to the Sun's rays at the top of Earth's atmosphere. Its value is approximately $S\approx 1400{\text{W m}}^{-2}$.

It is not the Sun's total power output $P_{\odot }$ (which is $\approx 3.9\times 10^{26}$ W), nor is it the absorbed intensity (which would require subtracting reflected energy using albedo).

The option stating intensity at a perpendicular surface at the top of the atmosphere precisely matches the definition of the solar constant.

We need the correct definition of the solar constant from four candidate options.

'The total power output of the Sun in watts' is incorrect — this describes the Sun's luminosity $P_{\odot }$, not the solar constant. The solar constant is an intensity (W m⁻²), not a total power.

'The average power absorbed per unit area after accounting for albedo' is incorrect — albedo is not yet applied when defining the solar constant. The solar constant describes incident radiation before any reflection.

'The rate at which Earth radiates infrared energy back into space per unit area' describes Earth's outgoing radiation, not the incoming solar radiation. These are opposite directions of energy flow.

The remaining option — intensity of solar radiation on a perpendicular surface at the top of Earth's atmosphere — correctly defines the solar constant $S\approx 1400{\text{W m}}^{-2}$.

Albedo $\alpha$ is the fraction of incident radiation that is reflected. An albedo of 0.40 means 40% of incoming radiation is reflected back into space.

The fraction absorbed is $(1-\alpha )=1-0.40=0.60$, meaning 60% of incoming solar radiation is absorbed by the planet.

The planet absorbs 60% of incident solar radiation. This is the fraction used in equilibrium temperature calculations: $P_{\text{absorbed}}=(1-\alpha )\cdot S\cdot \pi R^2$.

The question tests understanding of albedo: specifically, whether students know that albedo is the reflected fraction, not the absorbed fraction.

40% is the fraction reflected, not absorbed. Confusing albedo with the absorbed fraction is a common error.

80% has no direct relationship to an albedo of 0.40 — it appears to be $2\times 40\%$ and has no physical basis here.

100% would imply a perfect absorber with zero albedo, which contradicts the given $\alpha =0.40$.

Since 40% is reflected, $(1-0.40)=0.60$, so 60% is absorbed. This is the correct answer.