This page is about the definition and understanding of saturation of absorption in the atmosphere by GHGs
Saturation in the Greenhouse
There is considerable debate and some misunderstanding about the term ‘saturation’ with regard to the absorption characteristics of the greenhouse gases (GHGs).
There are the ‘bottom-uppers’ who claim that, because almost all of the Earth’s emitted radiation is absorbed by the lowest 100 m of the atmosphere, apart from the 10% or so that escapes to space directly through the infrared ‘window,’ an increase in the concentration of the GHGs cannot lead to more warming. This is a common misapprehension and ignores what might happen in the rest of the atmosphere. The absorbed energy from the surface still has many kilometres to go before it has the opportunity to escape to space. Although the lowest 100 m of the atmosphere appears to be almost saturated, the thermal energy produced by the absorption in that layer is further hindered in its progress to space by the GHGs and the hindering is made more severe by increases in GHG concentration. If there are notional layers in the atmosphere, each successively higher layer is less populated by molecules of all sorts and become more and more transparent to the thermal radiation travelling upwards from the adjacent lower layer. The transmission of the thermal radiation becomes more efficient as altitude increases until the emission levels of the various frequencies are reached. With higher concentrations of GHGs the emission levels move to higher altitudes because the transmission through the layers is made less efficient.
If the consequences of the notional layers are taken into consideration, the bottom-up approach gives the correct answer to the enhancement of warming by the increased GHG concentrations. The route to the understanding of the enhancement is by a top-down approach which is more readily calculable.
The ‘top-downers’ argue, quite properly, that strong absorbers can have zero effect on the warming of the troposphere, but can have a cooling effect in the stratosphere. This is the same conclusion as the bottom-up approach applied properly, but is more easily understood.
It measures the optical density of each ‘line’ in the atmospheric spectrum separately on the basis of an optical path from the top of the atmosphere. The top of the atmosphere is difficult to define absolutely, but for the purpose of the argument put forward it is anywhere where the number density of the GHGs is so small so as to have zero effect on the measurement of optical density. Taking the starting point of the optical path at an altitude where this condition is fulfilled means, in practical terms, above 70 km. At each frequency, as the optical path is extended downwards towards the Earth’s surface, the number densities of the GHGs increase and the relevant optical density increases.
The definition of optical density arises from the Beer-Lambert law of light absorption, applicable to individual frequencies:
I = I0exp(−εcl)
I is the intensity of radiation transmitted by the ‘sample’ of atmosphere containing an absorber with an absorption coefficient, ε, and which has a concentration,c, through a path of length,l. Strictly, this applies to a sample with a fixed concentration and has to be modified for application to the atmosphere where there are concentration gradients.
Rearrangement of the above equation after taking natural logarithms gives a more useful equation:
ln(I0/I) = εcl
The triple product εclis called variously the Absorbance, Optical Density or Optical Path of the particular sample. It varies linearly with concentration of the absorber and the path length, but that has to be modified for the atmosphere as referred to above.
Assuming that the estimation of optical density of the relevant part of the atmosphere is obtainable by calculation or measurement, its value for any particular frequency will increase as the path length from the top of the atmosphere increases.
One method of defining the optical density that refers to the emission level of a particular frequency is to use a value of 0.67 for radiation emerging from a hemisphere to take into account all directions rather than just those photons on a path normal to the surface. That value gives a ratio of I/I0is 0.51; a 51% chance of the photon reaching space. The OD = 0.67 can be scaled down to 0.67 × 3/5 = 0.4 for photons normal to the surface which would have an I/I0value of 0.67; a 67% chance of reaching space.
Without going into actual detail, it is certain that these criteria for the definition of emission level require the level to be at a higher altitude if the GHG concentration increases. The particular level might be in the troposphere at low concentrations of the GHG and progress into the stratosphere as its concentration increases.
The question about saturation becomes almost irrelevant when the above definition is adopted. The crucial parameter is the emission level defined as above. If the emission level is in the troposphere, knowing that the lapse rate is negative, the temperature falls as altitude increases, the emission emerges from a colder part of the atmosphere and its intensity will be lower than it would be with a lower GHG concentration. As a contributor to the total output to space, the contribution of the particular frequency will be smaller from the higher GHG concentration and the system will warm up to compensate for the lost output. The opposite is the case if the emission level is in the stratosphere where the lapse rate is positive. There, the higher GHG concentration still raises the emission level, but to a level where the temperature is higher. Such an increased contribution to the total output to space causes the stratosphere to cool until the output is restored to its lower concentration value.
The conclusion from this is that particular frequencies never become saturated. Their emission levels keep rising with increasing concentration. If their emission levels are in the stratosphere they make no contribution to the warming of the troposphere and perhaps they could then be regarded as being saturated.
Experimental measurements of the spectra of GHGs are reproduced by programmes such as MODTRAN and their spectra extracted from the HITRAN database are in full agreement. The use of experimental spectra or those extracted from HITRAN, based upon experimental measurements to judge whether or not any particular ‘line’ or ‘band’ is saturated in the sense of being absorbed completely by a slab of the atmosphere are just a guide to their real action in the warming/cooling argument. The figure below shows the emission from an altitude of 15 km, typical of the top of the troposphere.
This is for 380 ppmv CO2in the Standard Atmosphere with clear sky. The output flux is 261.6 W m-2, somewhat larger than the mean global value of 235 W m-2, but that’s because of the absence of clouds. More importantly, the CO2output between 630-680 cm-1‘flatline’ along the Planck curve at the temperature of ~216 K; that of the tropopause. This means that the central portion of the main 667 cm-1fundamental bending mode is ‘saturated’ within the meaning of that term as far as the troposphere is concerned. That part of the band cannot make the troposphere warmer if the CO2concentration increased. The CO2spectra outside of the 630-680 cm-1range can and must contribute to tropospheric warming if the CO2concentration were to increase. Such spectra range from 580-790 cm-1excluding the central portion. These arise from what are known in the trade as ‘hot bands’ which mean that the transitions are from an already excited state. They are by statistics alone weak bands because the populations of their lower states are considerably smaller than the molecules in their ground states; by 1-3%. The main contributors to these hot bands are shown in the diagram below. There are two levels of hot bands. One set have their lower states as the first excited state of the bending mode. These are much weaker than the fundamental of the bending mode. The second set of hot bands arises from the excited states of the first set and the transitions are much weaker still. The 961 cm-1and 1063.7 cm-1transitions are of the latter category and are obliterated in the atmospheric spectrum by the ozone band centred at 1043 cm-1.
The band centres are given in the arrows in cm-1and the nomenclature of the states is of the formvtype of vibrationpresence or otherwise of rotation around the molecular axis(state). The vibration types are 1: symmetric stretch, 2: bend, 3: anti-symmetric stretch. The rotational quantum numbers for rotation around the molecular axis are 0, 1, 2… The states are also quantum numbers, but for vibrations; 0 is the ground state, 1 is the first excited state, 2 is the second excited state… the higher the quantum number, the more vibrational energy is contained by the molecule.
So, to concentrate exclusively on thev20(0) →v21(1) transition at 667 cm-1is a considerable approximation, verging upon a sizeable error.
The hot bands in the troposphere are nowhere near being ‘saturated’ and contribute considerably to warming that arises from atmospheric injections of CO2. Just how much warming they cause is the big question that is very debatable. Increases in atmospheric concentration of CO2have a warming effect on the troposphere and this is evidenced by the measurable widening and deepening of the 580-780 cm-1‘ditch’ in the global emission spectrum. Similar increases have no effect in the 620-680 cm-1range as far as the troposphere is concerned, but do have a cooling effect in the stratosphere.
The simultaneous warming of the troposphere and cooling of the stratosphere cause some people to get the wrong answer, since they conclude that the resultant warming applies entirely to the troposphere. Any calculation using MODTRAN suffers from the difficulties in separating the effects of GHG concentration changes upon the two regions. A calculation for the troposphere inevitably alters the energy budget of the stratosphere and vice versa. A more sophisticated approach is needed and that takes programming expertise and computer time. Some calculations may be attempted using the MODTRAN facility, but their results should be regarded as indicative of what might happen if the GHG concentrations were to change. They cannot be definitive, although some authors think otherwise.