CO₂ and the Greenhouse Effect: the Physics That Warms the Planet

Earth as an (almost) black body

Every object above absolute zero emits electromagnetic radiation. The wavelength of that radiation depends on the object's temperature, a relationship described by Wien's displacement law: λ_max = b / T, where b = 2.898 × 10⁻³ m·K.

The Sun, with a surface temperature of ~5,778 K, emits mainly in the visible range (λ_max ≈ 500 nm). Earth, with a surface temperature of ~288 K (15 °C), emits mainly in the thermal infrared (λ_max ≈ 10,000 nm = 10 µm). This difference in wavelength between incoming radiation (solar, visible) and outgoing radiation (terrestrial, infrared) is the key to the whole greenhouse effect.

Why CO₂ absorbs infrared and N₂ does not

99 % of the atmosphere is N₂ (78 %) and O₂ (21 %), and neither absorbs infrared radiation to any significant degree. Why? The answer lies in the quantum mechanics of molecular vibrations.

A molecule absorbs infrared radiation only if the vibration being excited produces a change in its dipole moment. Homonuclear diatomic molecules such as N₂ and O₂ are symmetric: however they vibrate (bond stretching), the charge distribution stays symmetric and the dipole moment is always zero. No change in dipole moment means no infrared absorption.

CO₂ is linear and non-polar at equilibrium, yet it has vibrational modes that do change the dipole moment:

Symmetric stretch (ν₁, 1,388 cm⁻¹): both oxygens move towards and away from the central carbon at the same time. The dipole moment does not change (symmetry is preserved), so this mode is infrared-inactive (but Raman-active).

Asymmetric stretch (ν₃, 2,349 cm⁻¹): one oxygen moves in while the other moves out. The charge distribution becomes momentarily asymmetric, so the mode is infrared-active. It absorbs at ~4.3 µm, outside Earth's peak emission range but relevant for absorbing part of the incoming solar radiation.

Bending mode (ν₂, 667 cm⁻¹): both oxygen atoms bend in the same direction relative to the carbon. This creates a transverse dipole moment, so the mode is infrared-active. It absorbs at ~15 µm, right in the middle of Earth's peak infrared emission.

The 15 µm bending mode is the most important for the greenhouse effect because it matches Earth's emission peak almost perfectly. Every CO₂ molecule in the atmosphere acts as a tiny "sponge" that captures 15 µm infrared photons, re-emits them in all directions (including downwards, back to the surface), and warms the lower atmosphere.

The atmospheric window and the greenhouse gases

The absorption spectrum of the atmosphere has "windows": wavelength regions where the atmosphere is relatively transparent. The most important window lies between 8 and 13 µm, a region where neither water vapour nor CO₂ absorbs efficiently.

This window is critical: it is where Earth can "breathe", emitting energy to space. Stratospheric ozone absorbs part of this window (around 9.6 µm), and methane, N₂O and chlorofluorocarbons (CFCs) absorb mainly in this region. That is why these gases have such a high global warming potential (GWP) per molecule: they close the window through which Earth loses heat.

CO₂ concentration: the Keeling curve

Charles Keeling began measuring atmospheric CO₂ at Mauna Loa (Hawaii) in 1958. The result is the Keeling curve, the best-known and least ambiguous climate record in modern science:

• 1958: 315 ppm
• 1988: 351 ppm
• 2015: 400 ppm (the first time above 400 ppm in the instrumental era)
• 2024: ~425 ppm

Pre-industrial CO₂ (estimated from air bubbles trapped in ice cores) was about 280 ppm for the 10,000 years before the industrial revolution. The current level is a 52 % increase in less than 300 years, a rate unprecedented in the 800,000-year ice-core record.

The seasonal oscillation visible in the Keeling curve (about ±4 ppm each year) reflects the metabolism of Northern Hemisphere vegetation: in spring and summer, photosynthesis consumes CO₂ and the concentration falls; in autumn and winter, respiration and decomposition release it and the concentration rises.

Radiative forcing and climate sensitivity

Radiative forcing measures the change in Earth's energy balance caused by a change in the concentration of a greenhouse gas, expressed in W/m². The forcing from CO₂ since pre-industrial times is about +2.1 W/m², as if every square metre of Earth's surface received 2.1 extra watts of energy that used to escape to space.

For CO₂, the relationship between concentration and forcing is not linear but logarithmic: each doubling of CO₂ adds a fixed forcing of ~3.7 W/m². This is because the centres of the CO₂ absorption bands are saturated, and the marginal effect of adding more CO₂ happens on the "wings" of the bands.

Climate sensitivity (how much temperature rises when CO₂ doubles) is one of the most important and most uncertain parameters in climate science. The current consensus (IPCC AR6) puts it at 2.5–4 °C per doubling of CO₂, with a best estimate of about 3 °C.

The carbon cycle: a buffer under strain

The oceans and the land biosphere absorb about 50 % of the anthropogenic CO₂ emitted each year, acting as sinks that slow its build-up in the atmosphere. Without them, CO₂ would already be above 500 ppm.

Dissolved CO₂ forms carbonic acid in seawater, which dissociates into bicarbonate and carbonate. This process, ocean acidification, has lowered average ocean pH from 8.2 to 8.1 since pre-industrial times (a drop of 0.1 pH units means about 26 % more H⁺). For organisms that build calcium carbonate shells (corals, molluscs, sea urchins, some plankton), acidification makes calcification harder and can dissolve existing structures.

The next article climbs into the stratosphere: ozone, the triatomic molecule that shields us from ultraviolet radiation, how CFCs destroy it catalytically, and the story of the greatest success of 20th-century environmental diplomacy.