These are two MODTRAN generated emission spectra, the higher one is for the full atmosphere with 380 ppmv of CO₂ and the lower one is exactly the same except for the removal of all the CO₂. The two spectra make obvious the overlapping of the water and CO₂ spectra in the 600-750 cm^-1 range.

This section concentrates on CO₂ since it is the most important greenhouse gas whose concentration in the atmosphere is changing because of fossil fuel burning [an important subject dealt with subsequently]. The important region in the Earth's emission spectrum shown in the higher diagram on the previous page is outlined and lies between 580-750 cm^-1. Whereas the majority of the emission spectrum lies roughly along a curve which approximates to a blackbody curve, the emission in the specified region is of a much lower intensity. The 'well' in the curve occurs because CO₂ absorbs strongly in that region and only emits radiation to space from a much lower temperature that the emissions from the rest of the spectrum. Much of the CO₂ emission originates from the atmosphere at a temperature of about 218 K [-55 ^oC]. This part of the atmosphere is around 15 km altitude and is known as the tropopause, the top of the troposphere in which around 90% of the atmosphere occurs. The tropopause is the dividing layer between the tropopause and the stratosphere. You have probably noticed when flying long-haul that the outside temperature is around -55 ^oC and that is because the plane is operating around the tropopause. Emission from the CO₂ occurs at that level because the air is 'thin' and does not absorb radiation to anything like the same extent as it does at sea level.

   The lower diagram shows that the 'well' is filled to a large extent when CO₂ is absent. The atmosphere is less opaque to radiation in the 580-750 cm^-1 range and more radiation escapes than when CO₂ is present.

One important conclusion is that CO₂ restricts the passage of radiation from the surface to space; an important characteristic of a greenhouse gas.

To reach the second important conclusion requires a calculation.

The energy flux values are derived by the MODTRAN programme. The flux leaving the troposphere when we have the full atmosphere is 246.5 W m^-2 [watts per square metre]. When the CO₂ 'block' is removed the flux rises to 285.6 W m^-2, an increase of 39.1 W m^-2. If this did come about the radiation balance of the atmosphere would be upset. To redress this imbalance and bring the outgoing flux of energy back to 246.5 W m^-2 the temperature of the surface would have to be reduced and the extent of the reduction may be estimated by using the Stefan-Boltzmann equation.

New temperature = Fourth root [(288.2⁴ x 246.5/285.6] = 277.8 K

This is 288.2 - 277.8 = 10.4 K lower than the surface would be in the presence of the CO₂!

The second important conclusion is that the presence of CO₂ causes the surface of the Earth to be 10.4^oC warmer than it would be in its absence; it is a greenhouse gas.

The next simulated spectra are those for 380 ppmv and 760 ppmv of CO₂ respectively looking down from an altitude of 70 km and hopefully show the slight broadening of the 'well' that is crucial to the understanding of why more CO₂ leads to a little more warming, even though such warming might not be measureable.

The 'well' on the right hand spectrum is broader then the one on the left side because the increased concentration of CO₂ has caused the emission height to increase in some of the weaker absorption bands. This means that the emission arises from colder regions. It is of some interest that the emission in the centre of the absorption band is at slightly higher temperatures and this is consistent with the emissions [corresonding to very strong absorptions] occurring in the startosphere where the temperature increases with increasing altitude.

To convince yourself of the broadening of the 760 ppmv spectrum you could print the spectra on a piece of paper and do some origami to show that the 'well' is larger in the 760 ppmv case.