This page is a description of the contribution of carbon dioxide to the greenhouse effect

 The Greenhouse action of CO2

Much argument rages about the effect of the 0.039% of carbon dioxide in the atmosphere and its contribution to global warming. This article is devoted to an explanation of how the gas affects the emission spectrum of the planet and causes some of the warming of the surface and cooling of the stratosphere.

Figure 1 is a spectrum of CO2that shows its band structure. In the centre of the band the absorption is almost complete, but the 'side bands' absorb as much as 40% of the radiation at their particular frequencies.

 

Figure 1A spectrum of the main band of CO2for a 1 m path length and a concentration of 330 ppmv

The absorptions occur as the bending mode of the otherwise linear molecule acquires energy from photons of suitable magnitude. The molecule becomes more vibrationally active as a result of the absorptions. At the centre of the band at 667 cm-1the very strong absorption is known as the Q branch. It consists of many overlapping absorptions where the rotational energy does not change, but the vibrational energy changes. At lower wavenumbers there is a set of absorptions with equal spacings that are known as the P branch. In these absorptions the molecule acquires vibrational energy, but loses a varied, quantum controlled amount of rotational energy. The opposite is the case for the set of absorptions at wavenumbers higher than the Q branch. These are known as the R branch and occur when the molecule acquires vibrational energy and a varied, quantum controlled amount of rotational energy.

The whole spectrum is controlled by the quantum rules that specify for a linear molecule in its bending mode that if the vibrational quantum number (v) changes by one unit: v = 0 to v = 1 in this case, the accompanying changes in the rotational quantum number (J) are −1, 0 and +1 respectively for the P, Q and R branches. The structure of the Q branch arises because the transition energy for the vibrational change is slightly altered by the Coriolis Effect; the different rotational energies affect the vibrational energy; the length of the molecule extends if the rotational energy is high.

The behaviour of the Q branch in particular is crucial to the understanding of the warming effect of the gas in the atmosphere. Figure 2A & 2B show portions of ten MODTRAN-generated emission spectra for the clear sky atmosphere. The spectral region of interest is that from 550 to 850 cm-1and includes the P, Q and R branches of the CO2spectrum.

 

Figure 2APortions of the emission spectra of the atmosphere with varying concentrations of CO2(in ppmv as indicated in each portion). The portions of Planck curves are for comparative temperatures; from the top downwards the curves are appropriate for the temperatures 300 K, 280 K, 260 K, 240 K and 220 K. The horizontal axis gives the wavenumbers in cm-1

 

Figure 2BPortions of the emission spectra of the atmosphere with varying concentrations of CO2(in ppmv as indicated in each portion). The portions of Planck curves are for comparative temperatures; from the top downwards the curves are appropriate for the temperatures 300 K, 280 K, 260 K, 240 K and 220 K. The horizontal axis gives the wavenumbers in cm-1

The spectral portions show only the emissions from water vapour and CO2when it is present. Consider the emission when CO2is absent and assume that the global mean temperature is 280 K (7°C). The radiance to space is estimated to be 286.2 W/m2, considerably greater than the value required for radiative balance (235 W/m2). Adding just 1 ppmv of CO2produces a noticeable effect and the Q branch of the spectrum is particularly obvious. The estimated radiance to space is 281.7 W/m2, a reduction of 4.5 W/m2. Such an atmosphere would be radiating less energy to space and the system as a whole would be warmer. Even 1 ppmv of CO2has a warming effect!

The following argument relies on the interpretation of the emission height or altitude and the temperature from where the emission originates. For the 1 ppmv CO2spectrum the emission temperature of the Q branch is 225 K, those of the P and R branches are around 260 K, all within the troposphere at altitudes of 9.5 km and 3.8 km respectively. The physics of absorption spectroscopy indicate that such emission altitudes should increase as the concentration of the greenhouse gas increases, not linearly, but logarithmically. A broad view of the spectra of Figure 2 shows that the emission temperatures of all the bands decrease as the CO2concentration increases. The CO2'well' in the spectra become deeper and broader as the concentration of the gas increases. The emissions are originating in cooler and cooler parts of the atmosphere. Additionally, the radiance to space decreases with increasing CO2concentration and more and more warming of the system is caused. For instance, the radiance to space for the present-day concentration of 390 ppmv is estimated to be 258.7 W/m2, a reduction of 27.5 W/m2compared to the case with zero CO2. Assuming a mean global temperature of 280 K for the CO2-less case, a crude estimate of the temperature when 390 ppmv of CO2are present is [2804× 286.2/258.7]1/4= 287 K, not too far away from the present global mean temperature. If it becomes possible to burn enough fossil fuel to raise the concentration of CO2to 600 ppmv the global mean temperature might become [2804× 286.2/256.92]1/4= 287.7 K These calculations of the effect of CO2is for a cloudless sky, but more sophisticated calculations still produce an answer of 7-8°C global warming contribution from CO2. The increasing concentration of CO2decreases the overall emissivity of the Earth to space and warming must be the result.

Figure 2 shows a more subtle effect, particularly exhibited by the behaviour of the Q branch. For CO2concentrations of 1, 5 and 10 ppmv the sharp Q branch is pointing downwards, but by 30 ppmv it has become reversed and beyond 40 ppmv it is definitely pointing upwards and more so as the concentration increases. As the concentration of CO2increases there is a tendency for all the bands to exhibit lower emission temperatures. This is because their emissions arise from regions where their concentrations are low enough to allow radiance to space without the photons being absorbed. But nowhere do the emission temperatures go below the 220 K Planck curve; that is the minimum temperature existing in the tropopause - the region dividing the troposphere and the stratosphere. From 30 ppmv CO2increasing concentration causes the Q branch and parts of the P and R branches to reverse their early trends and originate from regions of higher temperature. The explanation of this is that their emission heights are now in the stratosphere where temperature increases with increasing altitude. It can also be seen from Figure 2 that more and more emission comes from the stratosphere as the CO2concentration increases. The increase is particularly obvious from the 1000 ppmv spectrum where practically the whole of the P, Q and R structure has gone into reverse and is emitting from the stratosphere at the higher temperatures at its higher altitudes.

This means that in the central portion of the CO2spectrum at the higher concentrations, further increases of CO2don't affect the troposphere, but actually increase the radiance to space from the stratosphere. This secondary effect is to cause the stratosphere to cool, the primary effect being the warming of the surface/troposphere system. A greater fraction of the CO2spectrum is becoming 'saturated' as far as warming the troposphere system is concerned, but is contributing to a greater cooling of the stratosphere. The interplay between the two major energy reservoirs - the surface/troposphere system and the stratosphere - arrange by radiative and other means to satisfy the requirement of giving back to space the 235 W/m2that, on average, the Earth receives from the Sun.

Experimental observations do indicate that the surface and troposphere are warming and the stratosphere is cooling. The other supposed influences on climate and global warming cannot explain such observations, but that does not mean that they are wrong. It means that their influences do not obviate the influence of increasing CO2concentration, the latter being consistent with the spectra presented here.