Radical New Hypothesis on the Effect of Greenhouse Gases
CLIMATE is complex but in an attempt to understand the effects of increasing levels of atmospheric carbon dioxide on global temperatures simplified General Circulation Models (GCMs) have been developed and are used by the United Nation’s Intergovernmental Panel on Climate Change (IPCC). Al Gore, in his famous movie ‘An Inconvenient Truth’, explained that as the concentration of carbon dioxide increases in the atmosphere, more energy is trapped, warming the planet. This assumption is central to the GCMs and the current consensus on climate change.
Some sceptics complain that the GCMs do not realistically simulate climate because there are many processes that can’t be adequately modelled including cloud formation. Michael Hammer, an engineer who specializes in spectroscopy, is also sceptical of the GCM but his criticism is more fundamental. In the following paper, using the basic laws of spectroscopy, he shows that a significant portion of energy loss from the Earth’s surface is by direction radiation to space at wavelengths not absorbed by carbon dioxide and other greenhouse gases. This is in direct contrast to the IPCC explanation that there is low radiation from the Earth’s surface to space and potentially high radiation from the atmosphere to space.
Science is a process of getting it wrong and hopefully learning – on this single issue Michael Hammer and the IPCC can’t both be right.
AN ANALYSIS OF THE EFFECT OF GREENHOUSE GASES IN THE ATMOSPHERE
By Michael Hammer
Kiehl and Trenberth in 1997 published a global mean energy budget for Earth. This budget has significant implications for the proposed greenhouse mechanism and indirectly leads to the concept of an equivalent radiation altitude for Earth which changes with greenhouse gas concentrations. The K&T and similar models form a basis for the global circulation models used in climate science.
This analysis derives a partial global energy budget based on an analysis of the observed atmospheric lapse rate, and basic laws of spectroscopy, which is at considerable variance with the K&T findings. The differences have significant implications for the greenhouse mechanism and suggest that the concept of an equivalent radiation altitude has no meaning.
It also suggests that the amount of positive feedback attributed to water vapour by these global circulation models is impossible and thus that the temperature rise postulated from the predicted increase in carbon dioxide concentration is greatly exaggerated.
Greenhouse gases in the atmosphere act entirely through radiative processes. Earth’s net energy balance is also entirely due to radiative processes since a planet in space can only gain or lose energy by this means. For these reasons, this paper is primarily concerned with an analysis based on radiative effects.
While this paper specifically mentions the Kiehl & Trenberth model in some detail (since it is the model used by the IPCC), it is recognised that there are other models also used in modelling, for example, the one quoted in “An introduction to Three-Dimensional Climate Modelling” by Warren Washington and Claire Parkinson ISBN 0-935702-52-0 University Science Books. While they show some differences compared to the K&T model they seem to share the same basic structure of low radiation from the surface to space and high radiation from the atmosphere to space. This is the dominant issue being questioned and the K&T model is used here as a convenient example.
3. THE ROLE OF CONVECTION AND LATENT HEAT
This paper is primarily concerned with radiative processes. This should not be taken as denying the role played by convection and latent heat. Clearly these processes have enormous effect within the troposphere and indeed are a dominant cause of our weather. They are also extremely significant in distributing heat around the planet and especially in energy transport from the equator to the poles.
Convection and latent heat effects impact on energy loss to space by changing the temperature versus altitude and latitude profiles within the atmosphere. The variation in height and temperature of the tropopause with latitude is an example of this. These represent perturbations superimposed on radiative processes. While their effects are reduced by averaging over the planet, it is acknowledged that the impact does not entirely cancel out because of the non linear relationship between temperature and energy radiated. Ignoring these effects thus introduces approximations which reduce the precision of the results obtained.
None the less, it is claimed that the mechanisms discussed in this paper are the dominant mechanisms controlling heat loss from this planet and the conclusions following from the analysis are extremely relevant in assessing the impact of green house gases in the atmosphere.
4. SOME BASIC SPECTROSCOPY
If a material absorbs light, one might intuitively expect the amount of light absorbed to be proportional to the concentration of the material, so that doubling the concentration doubles the amount of light absorbed. This is not the case as can be seen by a simple thought experiment. Imagine we have a piece of material which absorbs 50% of the light incident on it transmitting the other 50%. Doubling the concentration of material is exactly equivalent to adding a second identical piece of the material behind the first piece. The first piece absorbs 50% of the light incident on it transmitting the remaining 50%. The second piece being identical does exactly the same, absorbing 50% of the light that passed through the first piece and transmitting 50%. Thus the net light passing through the two pieces is not 0 but 25%. If we have n identical pieces the transmission will be 0.5n.
The relationship between concentration and light absorbed is not linear. Spectroscopists use the term absorbance to define the degree to which a sample absorbs a particular wavelength of light. Absorbance is defined by the equations;
Fraction of energy transmitted = 10 –absorbance
Fraction of energy absorbed = 1 – 10 –absorbance
If a sample has an absorbance of 1, it means that it absorbs 90% of the light incident on it, transmitting the remaining 10%. The absorbance of a sample is directly and linearly proportional to the amount of absorbing material in the light path (Beers law). Thus if a particular sample has an absorbance of 1 then doubling the concentration of the absorbing species for the same path length or doubling the path length with the same concentration will change the absorbance to 2.
5. THE SIGNIFICANCE OF EMISSIVITY
All material substances both absorb radiant energy incident on them, and emit radiant energy at a rate dependent on their temperature. The degree to which they absorb incident energy is often called the absorptivity and the degree to which they emit energy is often called the emissivity. However from Kirchoff’s law of thermal radiation the emissivity and absorptivity must be equal to each other.
The absorptivity/emissivity is a property of the substance and its form. A highly polished surface absorbs and emits less energy than a dull surface and a white surface absorbs and emits less energy than a black surface. What Kirchoff’s law is stating is that absorption of radiant energy and emission of radiant energy are reciprocal processes, a material that does not absorb will also not emit and vice versa. The same factor governs both to an equal extent.
Most of the atmosphere is made up of nitrogen and oxygen which do not significantly absorb infrared energy because their emissivity in this portion of the electromagnetic spectrum is exceptionally low. This means they also do not emit significant infrared – they are not greenhouse gases. Other gases however have a very strong ability to absorb energy at some wavelengths between 4 and 50 microns (the approximate range of emission wavelengths from earth’s surface). They are the greenhouse gases and the most significant is water vapour followed by carbon dioxide and then methane and ozone. Because their emissivity is high at the absorption wavelengths and low at other wavelengths they also selectively radiate energy at these same absorption wavelengths.
5. AN ANALYSIS OF THE KIEHL AND TRENBERTH MODEL
This model is documented at;
(from Bull Amer. Meteor Soc, 78, 197-208 1997).
There is an update dated 2008 at;
both documents specify very similar numbers. The K&T model (2008 update) specifies the following energy flows all with the units watts/m2.
Incoming solar radiation 341
Reflected solar radiation 102
Energy radiated from earth’s surface 396
Surface radiation absorbed by the atmosphere 356
Energy radiated from surface directly to space 40
Energy emitted by atmosphere to space 169
Energy emitted from clouds to space 30
Energy transported to atmosphere via
Convection and latent heat of water vapour 97
Solar radiation directly absorbed by atmosphere 78
This data shows that energy input to the atmosphere via radiative processes = 356 + 78 = 434 watts/m2. Energy input via convective processes = 97 watts/m2. Thus energy input to the atmosphere is dominated by radiative processes (82% radiative and 18% convective).
It should also be noted that the global circulation models GCM’s use a concept called the equivalent radiation altitude. This is a hypothetical altitude from which it is assumed long wave radiation back out to space emanates. Changes in greenhouse gas concentrations are assumed to change the equivalent radiation altitude. Changes to this equivalent radiation altitude together with the known lapse rate through the atmosphere are used to calculate changes in surface temperatures.
There is a well known and documented temperature versus altitude data (lapse rate) for Earth’s atmosphere. This temperature profile is established and maintained by the need for energy balance at every altitude.
The lapse rate consists of an almost linear decrease in temperature with altitude from the surface (+14C) to the top of the troposphere – the tropopause (at between 10 – 14 km altitude) where the temperature is between about -60 and -80 C depending on latitude. Above the tropopause (in the stratosphere) the temperature rises, again almost linearly, to a maximum of about -20C at an altitude of about 50 km.
The tropopause is thus a cold region sandwiched between warmer regions above and below. For this situation to be stable (and it is stable), the tropopause must have a way of losing energy to a colder sink – otherwise it would warm up due to energy input from the adjacent regions. The only colder region available is space itself and the only energy transfer mechanism available is radiative loss.
Thermal emissions from the tropopause will all be in the 5 micron to 50 micron wavelength range (governed by the temperature of the emitter) and can only occur at the characteristic absorption/emission lines of the green house gases. There is however a problem with this scenario. Ten percent of Earth’s atmosphere is above the tropopause in the stratosphere and the greenhouse gases in this region would normally absorb the emissions from the tropopause.
Further, since the air in the stratosphere is warmer, the downwards radiation onto the tropopause would exceed the upwards radiation from it leading to net energy gain not loss. Yet the tropopause is colder than the stratosphere so it must have a mechanism for losing energy.
A solution to this apparent paradox is that there is an abrupt change in the greenhouse gas composition at the tropopause such that the tropopause can radiate at wavelengths which the stratosphere is not capable of absorbing. The tropopause represents a temperature inversion which greatly inhibits convection and when that is coupled with the fact that water vapour is carried up from Earth’s surface principally by convection, one would immediately suspect water vapour as the variable component – high concentration in the troposphere and low concentration in the stratosphere. This suspicion is confirmed by the two quotes taken from the following link;
“The atmosphere is well mixed below 100 km, and apart from its highly variable water vapour and ozone contents, its composition is as shown below”
“As well as a noticeable change in temperature, the move from the troposphere into the stratosphere is also marked by an abrupt change in the concentrations of the variable trace constituents. Water vapour decreases sharply, whilst ozone concentrations increase. These strong contrasts in concentrations are a reflection of little mixing between the moist, ozone-poor troposphere and the dry, ozone-rich stratosphere.”
This information explains how the tropopause can remain colder than the air above and below. It also explains why temperature rises in the stratosphere. Ozone is a strong absorber of ultraviolet energy from the sun and such absorption will warm the stratosphere. The energy gained will be re-emitted as thermal infrared energy at the absorption/emission lines of the greenhouse gases present, mainly CO2 and methane. The energy absorption by ozone is greatest at around 50 km altitude which is why the temperature peaks at this point and the temperature profile down to the tropopause is essentially an upside down version of what happens in the troposphere.
It should be noted that the tropopause radiates at all wavelengths corresponding to greenhouse gas absorption/emission lines but those greenhouse gases present in the stratosphere also radiate back down onto the tropopause and since they are warmer, the downward radiation exceeds the upwards radiation. Thus the only net energy loss from the tropopause occurs at the wavelengths corresponding the water vapour absorption/emission lines.
Since the tropopause can radiate relatively strongly at the water vapour absorption/emission lines (strongly enough to keep itself cold) it follows that the emissivity at these lines must be relatively high which also means that the absorptivity is also high for the reasons discussed in the earlier section titled “the significance of emissivity”. Couple that with the fact that water vapour concentration is higher at lower altitudes and it follows that the tropopause (possibly together with a small region immediately below it) will be opaque to radiation at the water vapour absorption/emission lines. That means that emission from lower in the atmosphere directly to space becomes impossible at the water vapour absorption/emission lines because the energy is re-absorbed by the region at or immediately below the tropopause.
The implication is that thermal energy from the surface can escape to space in only two ways. First, by surface emission escaping directly to space at wavelengths which the greenhouse gases do not absorb. Second, by emission from the tropopause at wavelengths corresponding to the water vapour absorption/emission lines.
It is possible to gain at least some idea of the relative magnitude of these two emission mechanisms.
Ozone absorbs essentially all radiation below 290 nanometers (UVC radiation) . It further absorbs approximately 90% of radiation between 290 and 320 nanometers (UVB radiation) plus a decreasing amount of UVA radiation up to about 350 nm. The amount incoming solar radiation in these wavelength ranges can be determined by solving Planck’s equation for a 5800K emitter (scaled to 341 watts/m2 total) at wavelength increments of, say, 5 nanometers and then numerically integrating over each wavelength range. The result is 8.3 watts/m2 for UVC, 6.3 watts/m2 for UVB and 8.3 watts/m2 for UVA up to 350 nm. The total absorbed by ozone is 8.3 + 0.9*6.3 + 0.5*8.3 = 18.1 watts/m2 . It should be noted that ozone absorption peaks at around 50 km altitude which should be above most of the albedo effects.
The ultraviolet energy absorbed by ozone is not capable of being re-emitted at the same wavelengths because the gas is too cold. Instead it will be re-emitted as long wave radiation at the CO2 and methane absorption/emission lines. For a maximum stratosphere temperature of about -20C the black body radiation between 14 and 15.5 microns is 17.5 watts/m2 which is in reasonable agreement with the calculated energy absorption by ozone.
The remaining incoming solar energy is either reflected back out to space (due to Earth’s albedo) or is absorbed lower in the atmosphere or at the surface.
The overall albedo of Earth is 0.3 so 341 * 0.3 = 102 watts/m2 is reflected back to space leaving 341 – 102 – 18.1 = 221 watts/m2 to be absorbed at or below the tropopause. All of this must be radiated back out to space as long wavelength radiation if thermal balance is to be maintained.
There are many water vapour absorption lines below 8 microns. Between 14 microns and 15.5 microns carbon dioxide absorbs strongly and above 15.5 microns water vapour again has many absorption lines. Between 8 and 14 microns there is a window where the atmosphere offers little if any impediment to direct radiation to space from the surface.
Retrieved from http://en.wikipedia.org/wiki/Atmospheric_windows
“The atmospheric window refers to those parts of the electromagnetic spectrum that are, with the earth’s atmosphere in its natural state, not absorbed at all. One atmospheric window lies approximately at wavelengths of infrared radiation between 8 and 13 or 14 micrometres.”
 ISBN 0521339561 Houghton, J.T. The Physics of Atmospheres
Retrieved from “http://en.wikipedia.org/wiki/Water_absorption”
Cotton, William (2006). Human Impacts on Weather and Climate. Cambridge: Cambridge University Press. ISBN 0521840864. “Little absorption is evident in the region called the atmospheric window between 8 and 14 μm”
Solving Planck’s equation on a spreadsheet for a 288 K source at wavelength increments of 0.2 microns and then numerically integrating yields energies as follows;
Below 8 microns 45 watts/m2
8 microns to 14 microns 143 watts/m2
14 microns to 15.5 microns 28 watts/m2
Above 15.5 microns 174 watts/m2
Interestingly, the energy radiated by Earth’s surface over the strong carbon dioxide absorption band between 14 and 15.5 microns is 28 watts/m2 which is in good agreement with the value typically claimed for the energy retained by carbon dioxide.
It is also important to note that the regions below 8 microns and above 15.5 microns are not totally opaque. There are multiple absorption lines but there are gaps between these lines where substantial energy can escape to space, especially in the wavelength region above 15.5 microns. If this were not the case, line broadening through increasing concentrations of green house gases would have little if any impact on incremental energy retention (discussed in more detail later). This substantially adds to the 143 watts/m2 calculated above.
6. THE IMPACT OF CLOUDS
The above numbers do not allow for the impact of clouds. Clouds are droplets of liquid water and in the thermal infrared, water has an emissivity very close to 1 (hence the high emissivity of earth’s surface at these wavelengths). It is therefore reasonable to expect clouds to act as grey or black body absorbers with an emissivity approaching 1 as the clouds get thicker. This would mean that thick clouds would absorb all the thermal infrared energy incident on them and in turn emit energy as a black body from the cloud top. Since the cloud top is colder than the surface, the energy emitted over the atmospheric window will be lower. How much lower is easy to calculate by integration of Planck’s law given the known atmospheric lapse rate of 6.5C per kilometer and the height of the cloud.
Thin clouds with an emissivity less than 1 would have a smaller impact.
Only a portion of the Earth’s surface at any given time is cloud covered and much of the dense cloud is low altitude cloud, thus a reasonable estimate for the Earth as a whole would be that clouds reduce the energy escaping to space in the atmospheric window by no more than about 15% to 20%.
The radiation from the cloud tops is admittedly no longer radiation directly from earth’s surface but it is still black body radiation and the fraction in the atmospheric window (and in the gaps between the lines at other wavelengths) can still escape directly to space without impediment from green house gas effects. Thus, while clouds do cause some attenuation, their action does not negate the basis of the hypothesis being presented in this paper.
7. ENERGY RADIATION FROM THE TROPOPAUSE
Earlier discussion suggested that the tropopause can only generate net radiation to space at the water vapour wavelengths which means below 8 microns and above 15.5 microns.
Again solving and numerically integrating Planck’s equation over these wavelengths for a temperature of 213K (-60C) yields a total energy of 82 watts/m 2. Surface/cloud plus tropopause radiation must equal 221 watts/m2 implying the net energy radiated from the surface and cloud tops would have to be about 139 watts/m2. However the presence of gaps between emission lines suggests the tropopause radiation will be somewhat lower and the surface/cloud top radiation higher. When this is taken into account the numbers are entirely consistent with earlier calculations. Purely as a hypothetical example, if we assume cloud cover causes 15% attenuation and 17% of the energy in the below 8 micron and above 15.5 micron ranges is not absorbed we get;
Surface/cloud emission = 0.85 * ( 143+0.17*(45+174)) = 153 watts/m2
Tropopause emission = 0.83 * 82 = 68 watts/m2
Total emission = 221 watts/m2
Water vapour also has very strong absorption bands in the NIR centred at 1.45 microns, 1.95 microns 2.5 microns plus other weaker lines. There is a significant amount of incident solar energy at these wavelengths and that energy will be rapidly absorbed once water vapour concentration becomes appreciable, which means at or close to the tropopause. As a consequence, much of the energy emitted from the tropopause is not energy that has percolated up from the surface but rather energy absorbed directly from incoming solar radiation at or near the tropopause.
8. IMPLICATIONS OF THIS ANALYSIS FOR THE KIEHL TRENBERTH MODEL
The global mean energy budget claimed by K&T suggests the vast majority of the energy radiation to space comes from the atmosphere. It paints a picture of an atmosphere which absorbs almost all surface emissions and then re-radiates a variable amount of this to space. This implies that slight changes in concentration can vary the fraction emitted thus changing temperatures. Hence the concept of an equivalent emission altitude and the prediction of a high sensitivity to changes in greenhouse gas concentrations.
The picture emerging from this analysis suggests the opposite, with most of the energy reaching the ground being radiated directly back to space from the surface or cloud tops in the windows between the atmospheric absorption lines. It implies an atmosphere which blocks almost all the energy radiation from the surface to space at the GHG wavelengths while barely impeding energy radiation to space at other wavelengths. In this scenario, changing GHG concentrations can only affect warming via line broadening.
The concept of an equivalent emission altitude is not needed and indeed has no meaning in this scenario. Energy loss to space from Earth’s surface can only occur directly from the surface/cloud tops or from the tropopause although the relative magnitude of each could change with changing greenhouse gas concentrations.
The very large difference in surface versus atmospheric emission levels predicted from this analysis compared to the Kiehl Trenberth model calls into question the basis of global circulation models based on K&T or other similar data. It also calls into question the reliability of the output from such models and in the predictions flowing from those models.
It is possible to reinforce this finding by a completely different analysis which is shown below.
9. A SPECTRSCOPIC ANALYSIS OF GREEN HOUSE GAS ABSORPTION
Imagine a single greenhouse gas which absorbs energy at only one specific wavelength. As the greenhouse gas absorbs energy it heats up until the energy it emits equals the energy it absorbs. Because it only has significant emissivity at the absorption wavelength the energy will be re-emitted at this wavelength. However, the emitted energy will be emitted in all directions. Since the atmosphere is a thin continuous shell covering the entire earth it has only two surfaces, an inner surface adjacent the planet itself and an outer surface adjacent to space. Radiation leaves the atmosphere through one of these two surfaces. Thus, radiating in all directions in effect means 50% will be emitted towards space and 50% returned to the planetary surface.
A very simplistic first approximation would be to say if the absorbance of the gas column is N then the gas absorbs 1- 10-N per unit of the incident energy and 50% of this is returned to the earth’s surface giving an effective energy retention of
Energy retained = 0.5*(1-10-N). (1)
That may be correct when N is very small (<<1) but is grossly in error for higher absorbances because it ignores repeated re-absorption and re-emission of energy within the gas column.
As the absorbance of the gas column rises, repeated absorption and re-emission becomes very significant. In this context we must again remember that the same emissivity covers both absorption and emission so that emitted energy will be predominantly at the absorption wavelengths thus facilitating repeated absorption and re-emission. By the time the atmospheric absorbance has reached 1, 90% of the energy at the absorption wavelengths is being absorbed which also means that much of the energy emitted by the atmosphere will be re-absorbed within the atmosphere, possibly going through several absorption re-emission cycles within the atmosphere.
To analyse this situation, imagine we treat the entire gas column as stack of 1 absorbance layers. As a first order approximation, assume that each layer absorbs all the energy it receives from above or below and maintains itself in thermal equilibrium by emitting an equal amount of energy, half towards the surface and half away from the surface. The result is shown diagrammatically for an N absorbance atmosphere.
E1 is the total energy absorbed by layer 1
E2 is the total energy absorbed by layer
En is the total energy absorbed by layer n
EN is the total energy absorbed by layer N
Equations (2) to (5) are obtained by summing energy into each layer.
Substituting (2) into (3) gives E2 = 2 * E3 / 3 (6)
Rewriting (4) with n=3 and then
Substituting (6) into it gives E3 = 3 * E4 / 4 (7)
Since equn (9) holds for any n we can replace n by N to get
From (9) EN-1 = N-1/N * EN
Substituting into (5) gives EN = (N-1)/2N * EN +1
And rearranging EN = 2N/(N+1) (10)
If we expand (8) as a series we get;
En = n/n+1 * En+1
= n/n+1 * n+1/n+2 * En+2
= (n/n+1) * (n+1/n+2) * (n+2/n+3) *…* (N-1/N) * EN
Cancelling common terms gives En = n/N * EN (11)
Substituting for EN from equn (10) gives
En = 2n/(N+1)
The energy radiated away to space is 0.5 * E1 = 1/(N+1) (12)
The energy returned to the earths surface is 0.5* EN = N/(N+1) (13)
Equations 1 and 13 are plotted below. Interestingly, even below 1 absorbance equation 13 gives essentially the same result as equation 1 and can thus be treated as a reasonable approximation over the entire absorbance range.
10. INTERPRETATION OF THESE RESULTS
Heinz Hug (http://www.john-daly.com/artifact.htm) has measured the absorbance of the atmospheric column of CO2 at 280 ppm and reports a total absorbance in excess of 2000. The above calculation suggests that the fraction of energy at the absorbing wavelength which is radiated to space is only 1/2001 or 0.05%. This is in agreement with the analysis derived from the temperature versus altitude profile.
In the case of water vapour, it is only necessary to note that Fourier transform infrared spectrometers with an optical path length of well under 1 meter need to be either purged with dry gas or packed with desiccant and sealed in order to avoid unacceptably high energy loss from water vapour absorption and that the troposphere is 10,000 meters thick (more than 10,000 times the path length) to realise that a similar situation exists for water vapour.
11. THE IMPACT OF LINE BROADENING
Both of the above analyses suggest that greenhouse gases almost totally block energy loss to space at their absorption/emission wavelengths. This implies that significant energy loss from the surface or cloud tops is by direct radiation to space at wavelengths where the greenhouse gases do not absorb. Given that, one might be tempted to conclude that since the greenhouse gases already absorb everything they can, further increases in concentration should have no impact. This is not the case because of an effect known as line broadening.
The absorption versus wavelength profile for a green house gas line does not have infinitely steep sides. As concentration rises the line centre will saturate but absorption out in the wings of the line are not yet saturated. Further increases in concentration have no impact on the behaviour at the line centre but do slightly increase absorption out in the wings. In effect the line slowly broadens as the concentration increases. It is this effect that gives rise to the well known logarithmic relationship between concentration and energy absorbed.
In fact, the unsaturated lines of greenhouse gases are so narrow and therefore absorb so little energy, that the overall impact of a greenhouse gas does not become significant until the line centres saturate and the line start to broaden. This means that all greenhouse gases of significance are likely to display the logarithmic relationship between concentration and energy absorbed.
As the lines broaden they further constrict the wavelengths at which radiation can escape from Earth’s surface to space. For the same energy to be emitted from a narrower window implies higher energy density at the remaining wavelengths which implies a higher surface temperature.
In the case of carbon dioxide, the IPCC in their fourth assessment report stated that the increase from 280ppm to 390 ppm increased energy retained by 1.77 watts/m2. Applying the logarithmic relationship;
1.77 = n * log (390/280)
from which it follows that n = 12.3.
The increase from 390 ppm to 560 ppm (2070 projection from IPCC 4th assessment report) would increase retained energy by 12.3 * log (560/390) = 1.93 watts/m2 . Applying Stefan’s law at 288 kelvin (+14C) we find that each degree rise in temperature takes 5.4 watts/m2 . Thus the direct effect of the rise in carbon dioxide is 1.93/5.4 = 0.36C.
IPCC inflates this to about 3C by assuming massive positive feedback from water vapour. A 3C rise implies an additional 16.2 watts/m2 of which 16.2 – 1.93 or 14.3 watts/m2 must be coming from water vapour. The CRC handbook of chemistry and physics shows that water vapour content at constant humidity rises exponentially with temperature roughly doubling for each 10 K rise in temperature. This can be expressed as
water vapour concentration is proportional to 10 (temperature/33.2)
A 3C rise in temperature increases water vapour concentration by 10 (3/33.2) = 1.23 (23%). Applying the same calculations as for carbon dioxide
14.3 = m * log (1.23) from which m = 159 and each doubling of water vapour changes energy retained by 159 * log(2) = 48 watts/m2 .
The earlier Planck’s law calculations suggested water vapour at +14C retains at most 219 watts/m2 (in fact less when one allows for gaps between absorption lines). Coupling that with the CRC handbook data that water vapour doubles or halves for each 10C change in temperature, a sensitivity of 48 watts/m2 per doubling implies the following;
14C energy absorbed/emitted <219 watts/m2
+4C energy absorbed/emitted < 171 watts/m2
-6C energy absorbed/emitted < 123 watts/m2
-16C energy absorbed/emitted < 75 watts/m2
-26C energy absorbed/emitted < 27 watts/m2
-36C energy absorbed/emitted 0 watts/m2
This is completely incompatible with water vapour radiating substantial amounts of energy at -60C which is necessary to explain a cold tropopause.
Both the analysis from basic spectroscopy and the analysis based on atmospheric lapse rates give similar results and imply that greenhouse gases almost totally block energy loss to space at their absorption/emission wavelengths. That in turn suggests that a very significant portion of the energy loss from Earth’s surface is by direct radiation to space at wavelengths where the greenhouse gases do not absorb.
This is in conflict with the Kiehl & Trenberth model and other similar models which suggest that most of the energy loss to space is from the atmosphere. If the atmosphere emits little energy, and then largely from the tropopause and stratopause, the concept of an equivalent radiation altitude has no meaning. Further, the analysis suggests that most of the radiative energy loss from the atmosphere to space is re-radiation of solar energy absorbed high up in the atmosphere.
Surface temperature will increase with increasing greenhouse gas concentrations due to line broadening. The direct effect of carbon dioxide (in the absence of any feedbacks) using the IPCC quoted sensitivity and their postulated rise in carbon dioxide from 390 ppm to 560 ppm will contribute 0.4 degrees by 2070. The IPCC claim that positive feedback from water vapour will increase that to about 3C would imply a sensitivity of 48 watts/m2 per doubling in water vapour concentration. Such a high sensitivity is not compatible with the observed atmospheric temperature versus altitude profile.
It should be noted that this analysis does not predict no radiation to space at the greenhouse gas absorption lines. There is still energy at these absorption lines emitted to space. For the well mixed greenhouse gases such as CO2 and CH4 this energy largely emanates from the stratosphere and is powered significantly by UV absorption of incoming solar radiation by ozone plus some absorption of surface radiation at 9.6 micron . In the case of water vapour, the energy emanates from near the tropopause and is powered significantly by near infrared absorption of incoming solar radiation by water vapour.
Michael Hammer graduated with a Bachelor of Engineering Science and Master of Engineering Science from Melbourne University. Since 1976 he has been working in the field of spectroscopy with the last 25 years devoted to full time research for a large multinational spectroscopy company.