Greenhouse Gases and Radiative Forcing

Introduction

Nitrogen and oxygen make up 99% of dry air, yet they are almost transparent to the infrared radiation Earth emits. The warming of the planet is controlled instead by trace gases — water vapour, carbon dioxide, methane, nitrous oxide, ozone and halocarbons — present at parts per million or less. This page connects the molecular spectroscopy of these gases to the planetary energy balance, and introduces the quantities scientists use to compare their effects: radiative forcing and global warming potential.

Core explanation

Infrared activity. A vibration absorbs infrared radiation only if it changes the molecule's dipole moment. Homonuclear diatomics (N₂, O₂) have no dipole in any vibration, so they are infrared-inactive. CO₂ is linear and non-polar, but two of its vibrational modes change the dipole:

- the symmetric stretch (about 1340 cm⁻¹) keeps the molecule symmetric and is inactive; - the asymmetric stretch (2349 cm⁻¹, 4.3 µm) is strongly active; - the doubly degenerate bend (667 cm⁻¹, 15 µm) is active.

The 15 µm bend lies near the peak of Earth's thermal emission, which is why CO₂ is so effective. Water vapour absorbs strongly across wide bands and through its pure rotational spectrum; CH₄ absorbs near 7.7 µm; N₂O near 7.8 µm and 17 µm; O₃ near 9.6 µm, inside the atmospheric window. Halocarbons such as CF₂Cl₂ absorb within the 8–13 µm window where little else does, so each molecule is very potent.

The energy balance. Earth absorbs sunlight averaged over its surface: S(1 − α)/4, where S ≈ 1361 W m⁻² is the solar constant and α ≈ 0.30 the albedo, giving about 240 W m⁻². In balance, Earth must emit the same flux as infrared. From the Stefan–Boltzmann law, σT⁴ = 240 W m⁻² gives an effective emission temperature of about 255 K (−18 °C). The actual mean surface temperature is about 288 K (15 °C). The 33 K difference is the natural greenhouse effect.

How the greenhouse effect works. Greenhouse gases absorb surface infrared and re-emit it in all directions, including downwards. Because temperature falls with height in the troposphere, radiation escaping to space comes from a colder, higher level and is weaker. Adding more absorber raises the effective emission height to even colder levels, reducing outgoing radiation; the system then warms until balance is restored.

Radiative forcing. Radiative forcing (RF) is the change in net downward flux at the top of the atmosphere caused by a perturbation, before surface temperatures respond. For CO₂, the forcing is approximately logarithmic in concentration because the centre of the 15 µm band is already saturated and extra CO₂ acts mainly in the band wings:

ΔF ≈ 5.35 ln(C/C₀) W m⁻²

Global warming potential. GWP compares gases per kilogram emitted, integrating forcing over a time horizon (usually 100 years) relative to CO₂. It combines radiative efficiency per molecule with atmospheric lifetime. Approximate GWP₁₀₀ values: CO₂ 1, CH₄ about 28, N₂O about 270, SF₆ over 20 000. Emissions multiplied by GWP give "CO₂-equivalent".

Formulae

Absorbed solar flux = S(1 − α)/4. Stefan–Boltzmann: F = σT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. CO₂ forcing: ΔF ≈ 5.35 ln(C/C₀) W m⁻². CO₂-equivalent = mass emitted × GWP.

Step-by-step reasoning

To judge whether a gas is a significant greenhouse gas:

1. Check whether any vibrational mode changes the dipole moment. 2. Locate its absorption bands relative to Earth's emission peak near 10–15 µm and the window at 8–13 µm. 3. Consider whether the bands are already saturated by existing gases. 4. Combine per-molecule efficiency with atmospheric lifetime to assess its GWP. 5. Multiply by emission rate to judge its total contribution.

Visual explanation

Draw the smooth blackbody curve for 288 K against wavelength from 5 to 50 µm, peaking near 10 µm. Overlay a jagged curve of radiation actually leaving the top of the atmosphere: a deep bite centred at 15 µm (CO₂), a notch at 9.6 µm (O₃), and water-vapour absorption at the short and long ends, with most escape through the 8–13 µm window.

Real-world analogy

A greenhouse gas layer acts like adding blankets to a bed. Your body generates heat at a steady rate; each blanket slows its escape, so your skin warms until heat loss again matches production. The blanket does not produce heat — it changes the balance point. Unlike a blanket, the atmosphere traps heat by radiation rather than by stopping convection.

Real-world example

Atmospheric CO₂ has risen from about 280 ppm before industrialisation to over 420 ppm today. Using ΔF ≈ 5.35 ln(420/280) gives about 2.2 W m⁻², consistent with assessment values. Adding methane, nitrous oxide and halocarbons brings well-mixed greenhouse gas forcing to over 3 W m⁻², partly offset by aerosol cooling.

Why?

Why does CO₂'s forcing grow only logarithmically while that of a new halocarbon grows linearly? At the centre of the 15 µm band, the atmosphere is already opaque, so extra CO₂ adds absorption only in the weaker wings. A halocarbon at trace level absorbs in the nearly empty window, so each added molecule contributes fully.

Common misconception

"Greenhouse gases trap heat by reflecting infrared back to Earth." They absorb and re-emit rather than reflect, and the essential point is that emission to space occurs from colder, higher layers. Another error is to confuse the greenhouse effect with ozone depletion; they involve different chemistry and different wavelengths.

Worked example

Question: What forcing results from doubling CO₂ from 280 ppm, and what warming would occur with a climate sensitivity parameter of 0.8 K per W m⁻²?

Reasoning: ΔF = 5.35 ln(560/280) = 5.35 × ln 2 = 5.35 × 0.693 ≈ 3.7 W m⁻². Equilibrium warming ΔT = 0.8 × 3.7 ≈ 3.0 K.

Answer: About 3.7 W m⁻² and roughly 3 K of equilibrium warming.

Quick check

1. Why is the symmetric stretch of CO₂ infrared-inactive while its bending mode is active? Answer: The symmetric stretch keeps the molecule centrosymmetric with zero dipole, whereas bending creates an oscillating dipole moment.

Exam focus

Expect to explain infrared activity using dipole change, derive the 255 K effective temperature from the energy balance, and define radiative forcing and GWP. Know why GWP depends on the time horizon, especially for short-lived methane.

Advanced insight

GWP is a metric choice, not a physical constant. Methane's lifetime is about 12 years, so its GWP over 20 years is about 80 but over 100 years about 28. Alternative metrics such as global temperature-change potential and GWP give different weightings, which matters for policies that trade methane cuts against CO₂ cuts.

Summary

Only molecules whose vibrations change the dipole moment absorb infrared; N₂ and O₂ do not, while CO₂, H₂O, CH₄, N₂O, O₃ and halocarbons do. Earth's effective temperature from the energy balance is about 255 K, and the natural greenhouse effect raises the surface to 288 K. Radiative forcing measures the flux imbalance from a change, logarithmic for CO₂. GWP compares gases per kilogram over a set time horizon.

Practice questions

1. Explain why N₂ is not a greenhouse gas despite being the most abundant atmospheric gas. Answer: N₂ is homonuclear; its only vibration does not change the dipole moment, so it cannot absorb infrared radiation. 2. Calculate Earth's effective temperature given absorbed solar flux 240 W m⁻² and σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. Answer: T⁴ = 240 ÷ 5.67 × 10⁻⁸ = 4.23 × 10⁹, so T ≈ 255 K. 3. Why are gases absorbing in the 8–13 µm region especially potent per molecule? Answer: Little else absorbs in this atmospheric window, so their absorption is not saturated and each molecule blocks radiation that would otherwise escape. 4. A facility emits 10 tonnes of CH₄ per year. Using GWP₁₀₀ = 28, give the CO₂-equivalent. Answer: 10 × 28 = 280 tonnes CO₂-equivalent per year.