Questions: Radiative Transfer in the Atmosphere

Question 1

According to the Beer-Lambert law, if an absorbing gas doubles in concentration in an atmospheric layer, the transmittance of that layer:

• A. Decreases linearly (halves)
• B. Decreases exponentially
• C. Increases, since more absorption means more re-emission back down
• D. Remains the same because transmittance depends only on path length

Answer: (B)

Transmittance is T = exp(−τ), where optical depth τ is proportional to concentration. Doubling concentration doubles τ, which exponentially reduces T. This nonlinearity means that adding more of an already-abundant absorber (like CO₂ near its saturation bands) produces diminishing returns — a logarithmic forcing relationship rather than a linear one.

Question 2

Greenhouse gases absorb outgoing infrared radiation uniformly across most infrared wavelengths, so nearly every part of the infrared spectrum is equally attenuated.

• T. True
• F. False

Answer: False

Molecular absorption occurs only at specific wavelengths (vibrational and rotational transition bands), not uniformly. CO₂ absorbs strongly near 15 μm; water vapor has bands across a wide range; but the 8–12 μm atmospheric window is relatively transparent. This spectral selectivity is why the window exists and why different gases have different radiative forcing efficiencies.

Question 3

What is the atmospheric window, and why is it climatically significant?

Model answer: The atmospheric window is the spectral range (~8–12 μm) where the major greenhouse gases (water vapor, CO₂) absorb only weakly, allowing surface-emitted longwave infrared radiation to escape directly to space. It is a primary pathway for planetary cooling; without it, Earth's surface would need to be substantially warmer to maintain energy balance.

This is a commonly overlooked feature. Students often think greenhouse gases block all outgoing IR, but the window allows significant direct cooling of the surface. Clouds and some minor gases (ozone, halocarbons) absorb within the window, which is why clouds strongly affect nighttime cooling and why even trace greenhouse gases with absorption bands in the window (e.g., SF₆) are highly potent warmers.