This page deals with emission levels of the carbon dioxide spectrum, out to space and down to Earth, and the effects of pressure broadening/contacting as altitude in the atmosphere varies.
Emission Levels and Spectra
Any emissions at altitudes in between the emission-to-space level and the emission-to-surface level are re-absorbed by the atmosphere. The GHG molecule will absorb radiation according to the absorption coefficients of its spectra and will emit radiation according to the same absorption coefficients and the local temperature of the atmosphere. Depending upon altitude the emitted radiation might escape to space or hit the surface, otherwise it will be re-absorbed.
Emission to space
The emission-to-space level for any line or band is determined by its associated absorption coefficient, the local temperature and the concentration of the GHG. The level for a strongly absorbing line is likely to be in the stratosphere; where its concentration distribution makes it probable that 50% of the upwardly emitted radiation would escape to space. At lower levels radiation from the same line would be completely re-absorbed independently of the direction of the emission. Such a strongly absorbing line would contribute to the cooling of the stratosphere and because of the positive lapse rate would cause more cooling if the concentration of the absorber increased.
A weakly absorbing line would have an emission level, again where the probability of upward emission reaching space is 50%, somewhere in the troposphere and would contribute to the warming of the troposphere/surface system. Its warming effect would be increased if its concentration increased since the lapse rate in the troposphere is negative. As with a strong absorber, any radiation emitted below the emission-to-space level would be completely re-absorbed.
Thus, it is possible for the various parts of the CO2 spectrum to have a range of emission levels and to have their corresponding brightness temperatures and to contribute to stratospheric cooling or tropospheric warming.
Emission to the surface
The emission levels for radiation that reaches the surface are again determined by the specific absorption coefficient of the particular line or band. Strong absorbers will have lower emission-to-surface levels than weak ones. The levels can again be defined in terms of the probability of the downward emitted radiation having a 50% chance of reaching the surface with any radiation emitted above that level being re-absorbed. The brightness temperatures indicate the associated levels.
Strong absorbers have emission levels close to the surface where the temperature is high and the intensity of emission is consequently high. Weak absorbers have emission levels far from the surface in regions of lower temperatures and their consequent emission intensities are low.
The Q branch of the CO2 spectrum at 667.4 cm-1
The transitions (ΔJ = 0, but not 0 → 0) representing the Q branch of the fundamental bending mode of the CO2 molecule are subject to slight variation from the band centre at 667.4 cm-1 because of the Coriolis effect. The molecular rotation becomes more rapid as the J value increases and the more energetic rotational motion causes the length of the molecule to increase slightly and this alters the wavenumber of the vibrational transition to higher values.
Figure 1 is a typical transmission spectrum of CO2 showing the P (wavenumbers below 667.4 cm-1), Q (the intense peak at around 667.4 cm-1, and the R (wavenumbers greater than 667.4 cm-1) branches. The Q branch is clearly not a smooth curve and shows evidence of some ‘fine structure’ with Q branch centres at different wavenumbers.
Figure 1 A transmission spectrum of CO2
The variation of spectral details with altitude, and therefore concentration and total pressure, are of considerable importance in greenhouse theory. The details of the Q branch are demonstrated with spectra with a better resolution than that of the one shown in Figure 1. Figure 2 shows a transmission spectrum of CO2 with a concentration of 400 ppmv and with a total atmospheric pressure of 1 atmosphere, i.e., that found at sea level. The wavenumber range covers most of the members of the Q branch.
Figure 2 A spectrum of the Q branch of the fundamental bending mode of CO2
Figure 2 indicates that the Q branch is composed of several members that overlap under the conditions of high total atmospheric pressure. The feature at 669.73 cm-1 is the second member of the R branch, the first member is at 668.16 cm-1 and is overlain by the Q branch members. The transmission is not zero at any point on the Q branch and with a longer path length of 10 m the transmission values are very largely zero, i.e., there is total absorption. Figure 3 shows a spectrum similar to that of Figure 2, but with a path length of 10 m. The second member of the R branch at 669.73 cm-1 is again present.
Figure 3 A spectrum of CO2 with a path length of 10 m
At lower total pressures lines become less broad and it is of interest to look at spectra similar to those of Figure 2 and 3, but where the concentration of CO2 is 40 ppmv (the equivalent of 400 ppmv at sea level) and a total pressure is 0.1 atmospheres. Figure 4 shows the spectrum of 40 ppmv CO2 with a total atmospheric pressure of 0.1 atm. Concentrations of 400 ppmv at sea level and 40 ppmv at an atmospheric pressure of 0.1 atm., are identical in terms of numbers of molecules per cubic metre.
Figure 4 A spectrum of CO2 with a total atmospheric pressure of 0.1 atmospheres.
Figure 4 shows the details of the members of the Q branch clearly resolved, but with transmission values that are mainly non-zero. The general appearance is slightly upset by the presence of the two R branch members at 668.16 cm-1 and 669.73 cm-1. The HITRAN database contains details of all the spectral lines of the greenhouse gases and Figure 5 shows how the members of the Q branch of the CO2 spectrum varies with the value of the lower J value of each transition, beginning with a value of 2 which is coincident with the recognized band centre of 667.4 cm-1.
Figure 5 The wavenumbers of the members of the Q branch of CO2 and their variation with lower J value
Figure 5 shows the spread of wavenumbers of the members of the Q branch as the values of J; the lower of the two J values associated with each transition. The variation is sufficient to overlap with the first two members of the R branch whose wavenumbers are 668.16 cm-1 and 669.73 cm-1. Figure 6 is a plot of the intensities of the Q branch transitions.
Figure 6 A plot of line intensity against the wavenumber of the members of the Q branch
Figure 6 shows the relatively rapid increase in intensity of the line as the value of J increases followed by the slow decline to almost zero with the lower J value of 48.
Figure 7 shows the effect of having a 10 m path length on the spectrum of the members of the Q branch at the total atmospheric pressure of 0.1 atm..
Figure 7 A spectrum of CO2 with a path length of 10 m
Figure 7 shows the effect of increasing the path length to 10 m and the consequent reduction in transmission with about half of the Q branch members showing zero transmission. In the full atmosphere there would be complete absorption and the Q branch would appear as an asymmetric band, the top of which would have an emission level in accordance with its brightness temperature in the stratosphere.