The concentration of CO2 in the atmosphere rose as the last ice age ended, and then stabilized for thousands of years, until humans became serious about changing the atmosphere with the start of the industrial revolution. Suppose that we succeed in raising the CO2 concentration in the atmosphere to a level twice as high as occurred for the thousands of years after the ice age and before the industrial revolution, and then we hold the concentration constant at that new, higher level for the next thousand years. What would happen to the average temperature of the planet?

Question

BlackTom AI · Accepted Answer

Doubling atmospheric CO2 produces a radiative forcing of roughly 3.7 W/m^2, which, given the climate system’s sensitivity, translates into a global mean surface warming of a few degrees Celsius once the system equilibrates.

1) Relevant knowledge points and concepts
- Radiative forcing: the change in energy balance at the top of the atmosphere caused by increased greenhouse gases. For CO2, ΔF ≈ 5.35 · ln(C/C0).
- Climate sensitivity: equilibrium global mean temperature change per doubling of CO2, commonly estimated ≈ 3°C (likely range ~1.5–4.5°C).
- Response timescales: the surface and atmosphere respond in years to decades, but full equilibrium (including deep ocean heat uptake and slow feedbacks) takes centuries to millennia.

2) Step-by-step reasoning
- For a doubling, C/C0 = 2, so ln(2) = 0.693.
- Radiative forcing: ΔF = 5.35 · ln(2) = 5.35 · 0.693 ≈ 3.71 W/m^2.
- Using the typical climate sensitivity (S ≈ 3°C per doubling) or λ ≈ S/ΔF ≈ 3°C / 3.71 W/m^2 ≈ 0.81 °C per (W/m^2), the equilibrium temperature change is:
  ΔT = λ · ΔF ≈ 0.81 × 3.71 ≈ 3.0°C.
- Over the next thousand years with CO2 held constant, the climate would approach this equilibrium warming as oceans and other components equilibrate.

3) Calculations (intermediate steps shown)
- ln(2) = 0.693
- ΔF = 5.35 × 0.693 = 3.71 W/m^2
- λ = 3°C / 3.71 W/m^2 ≈ 0.81 °C/(W/m^2)
- ΔT = 0.81 × 3.71 ≈ 3.0°C

4) Why the correct answer is correct
The calculated equilibrium warming from a CO2 doubling is about 3°C (a “few degrees”), and holding CO2 constant allows the climate to approach and then stabilize near that higher temperature over centuries, matching the described outcome.

5) Why other choices are incorrect
- New ice age (large cooling): opposite sign; added CO2 warms, not cools.
- Small drop a few degrees: wrong direction (CO2 causes warming).
- Remain the same: contradicts well-established radiative forcing and climate sensitivity.
- Increase 30–40°C: far larger than plausible for a CO2 doubling; would require forcing orders of magnitude greater than 3.7 W/m^2.

6) Conclusion
Therefore the correct choice is: "The temperature would increase to a few degrees above the pre-industrial-revolution level, and then stabilize at that new, warmer level." This matches the provided answer.

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