Questions: Energy Balance Models of Climate

Question 1

In a zero-dimensional energy balance model, if Earth's surface albedo increases (e.g., due to expanding ice cover), what happens to the equilibrium temperature?

• A. It increases, because ice reflects energy back into the atmosphere and warms it
• B. It decreases, because more incoming solar radiation is reflected away and less energy is absorbed
• C. It stays the same, because the model enforces energy balance by definition
• D. It increases, because outgoing longwave radiation decreases proportionally

Answer: (B)

Higher albedo means a greater fraction of incoming solar radiation is reflected rather than absorbed. With less energy input, the equilibrium temperature must decrease for outgoing infrared radiation (which scales as T⁴) to balance the reduced absorbed solar flux. This is the physical basis of the ice-albedo feedback: more ice → higher albedo → lower equilibrium temperature → more ice.

Question 2

In an energy balance model, achieving 'equilibrium' means Earth's surface temperature is perfectly constant and does not fluctuate over time.

• T. True
• F. False

Answer: False

Equilibrium in an EBM means the long-term average energy input equals the long-term average energy output — not that temperature is instantaneously static. Real climate exhibits year-to-year variability, seasonal cycles, and transient fluctuations even around an equilibrium state. EBMs describe the mean state toward which climate tends, not a moment-by-moment balance.

Question 3

In the zero-dimensional EBM, why is the incoming solar flux divided by 4 when computing Earth's equilibrium temperature?

Model answer: Earth intercepts solar radiation as a disk of area πR², but radiates infrared energy from its entire spherical surface of area 4πR². Dividing by 4 spreads the intercepted solar energy over the full surface, giving the effective solar input per unit area as S/4.

The solar constant S (watts per square meter) is measured at Earth's orbital distance facing the Sun. To find the energy absorbed per unit of Earth's surface, you must account for the geometry: only the cross-section (πR²) faces the Sun, but the whole sphere (4πR²) radiates. The ratio 4πR²/πR² = 4 is where the factor comes from. Without this, you would compute an equilibrium temperature much too high.