Clive Best

A radical but rather elegant theory has been proposed by a Hungarian Physicist Ferenc Miskolczi (see refs) that the Earth maintains a maximised greenhouse effect  to allow the Earth to cool as efficiently as possible. This self-regulation arises  because  70% of the Earth’s surface is water allowing both cooling through evaporation (latent heat) but also warming  through H20 being a greenhouse gas. Unlike CO2 the concentration of H2O in the atmosphere is governed by thermodynamic processes. Local thermodynamic equilibrium in the atmosphere ensures equality between the absorbed IR energy by all greenhouse gases from the surface and the  IR  energy emitted back to the surface by those same gases. Water evaporation and convection drives the Earth’s weather systems. Water Vapour also dominates the greenhouse effect of the Earth but has two  subtle feedbacks. Firstly evaporation mainly from oceans is a very efficient way for the surface to loose heat through latent heat. However cloud formation then leads to a higher albedo and to night time heat retention so there is a play-off beween this and the greenhouse effect of H2O. Miskolczi and Zagoni argue that the total average greenhouse effect on Earth depends only on the input energy of the sun plus a small geothermal component. This simple conclusion is backed up by  detailed radiation transmission model calculations and data comparisons.

The total greenhouse effect remains exactly what is needed to maximise cooling of the Earth. Any man-made CO2 increases are simply offset by a small decrease in water vapour so as to maintain thermodynamic equilibrium. They claim that the data show there has been a small 1% decrease in global humidity to offset all CO2 increases caused by  human emissions. The following slides try to explain the energy balance arguements they make. The crucial proposal is that the water content of greenhouse concentrations (H2O + CO2 + CH4) are maintained to be such that half the IR energy radiated from the surface is emitted into space from the top of the atmosphere while another roughly 60 watts/m passes clean through the IR wavelength window. The physics motivation for this first proposal is the virial theorum which states that the kinetic energy (heat) of the atmosphere is half the (gravitational) potential energy. The effective radiative kinetic energy is associated with the IR radiation emitted from the atmosphere to space(Te**4). The effective potential energy is associated to the IR radiation emitted from the surface (Ts**4). The second proposal is that the amount of energy emitted back to the surface is equal to that absorbed by the atmosphere. This is based on an assumption of overall local thermodynamic equilibrium (Kirchoff law). With these two assumptions the normalised greenhouse factor is and will remain equal to  1/3. The Earth’s temperature remains fixed unless the input energy changes through volcanic or human induced aerosols,  or through changes in the Earth’s orbit. The temperature  is however independent of any anthropogenic CO2 increases.

Global Circulation models assume that  rises in CO2 concentration lead to an enhanced greenhouse effect with rising temperatures causing yet more evaporation of H2O leading to an enhanced warming . This is the positive feedback which leads IPCC to give scary predictions of 3-7 degrees rise in global temperatures in the next 50 years or so. The effect of CO2 increase on the greenhouse effect alone would lead to less than a 1 degree rise.

The Saturated Greenhouse theory says that exactly the opposite happens. The Earth has an infinite amount of greenhouse gas available to it in the form of water, but the average relative humidity today at the surface is 78% and just 37% at 9000 m. So why isn’t it 100% ? The reason Miskloczi argues is that energy balance between the surface and the atmosphere (Kirchoff: ED = AA ) plus a requirement that the kinetic energy of the atmosphere = 2* the potential gravitational energy (Virial theorum: EU = 2SU) causes a saturated greenhouse effect therefore limiting the Earth’s temperature to its current level. The normalised greenhouse effect = 1/3 and will always remain so and the Earth’s temperature remains constant unless the external energy parameters change (solar). Therefore to compensate for any  rises in CO2 levels the Earth will adjust the relative humidity to maintain the same thermal equilibrium.

The super El Nino effect in 1998 led to a rise in global temperatures. If it were the case that a temperature rise causes more water vapor through evaporation, causing yet more temperature rise, then one would expect temperatures to continue to rise after 1998, and result in a run-away effect. But the opposite happened, because temperatures fell as the greenhouse equilibrium mechanism restored the balance. The extra greenhouse gases rained out to restore the equilibrium. Miskolczi is arguing that exactly the same effect is happening now as has happened in the past with any sudden  perturbation in  CO2 levels. Energy balance of the Earth/Atmosphere  will cause water vapour content to increase or decrease in order to maintain an equilibrium situation with a saturated greenhouse effect g=1/3. In order to offset a potential  doubling of atmospheric CO2 levels caused by human activity the relative humidity would reduce by 3%. Miskolczi claims that existing data show that already a global reduction of 1% in relative humidity has occurred over the last 100 years. Data from NOAA Earth System Research Laboratory for the upper atmosphere  show that relative humidity has indeed been falling.

This theory depends on the two assumptions of local thermodynamic equilibrium (Kirchoff) and the applicability of the Virial theorem to the radiation fluxes from the surface and the top of the atmosphere. Mainstream IPCC scientists have all attacked this but direct measurements do really seem to support these assumptions. The pressure distribution of the atmosphere is a function of gravity and temperature P(h)=Po*exp(-mgh/kT). The effective black body radiation emitted by the atmosphere to space by greenhouse gases is a kind of measure of it’s “greenhouse” temperature and hence its kinetic energy, whereas the radiation emitted from the surface is related to the Po the pressure at height zero and hence the gravitational potential energy. I certainly will need to think harder about this one to be  convinced, but the theory is very attractive and if true would completely overturn mainstream climate change predictions.

References:

Ferenc M. Miskolczi, “Greenhouse Effect in Semi-Transparent Planetary Atmospheres“, Quarterly Journal of the Hungarian Meteorological Journal, Vol. 111, No. 1, January - March 2007.

Explanation by Miklos Zagoni

Model discusion

The saturated greenhouse effect

If our eyes were sensitive to the IR radiation in the main CO2 absorption bands then we would just see fog. The atmosphere is opaque to CO2 at well below pre-industrial levels with an absorption length of about 10 meters. This would be a very thick fog.  By adding more CO2 to the atmosphere man is just reducing a little that aborption length.

The CO2 greenhouse effect is caused by the reduction in IR radiation escaping into space from the higher atmosphere of the earth. As we add CO2 so the height where the fog disperses and radiation escapes increases.  The temperature is lower at these heights reducing the effective energy escaping by a small amount (Blackbody radiation proportional to T**4). The energy balance of solar input radiation to the Earth and heat loss to space by the Earth must remain in balance. Therefore the Earth warms slightly to emit a little more total IR radiation across the spectrum to compensate the small extra energy trapped by extra CO2. However the energy increase is only logarithmic because the absorption is already opaque.

All these effects based on accurate cross-sections have been included in a model of the atmosphere by the US navy. The model is called MODTRAN and has been validated by direct satellite measurements. It is very informative since one can simulate what effect CO2 has on energy output for different regions and by inference how the Earth’s temperature reacts. The atmosphere’s simulated are for different regions with different profiles of water vapour and clouds. Changing the water vapour factor actually has a much larger effect than changing the CO2 concentrations. Current concentrations of CO2 are 375 ppm.

One can also calculate the temperature rise caused by doubling current levels of CO2 from 375 ppm to 750 ppm. We do this by adjusting the Earth’s temperature as input to MODTRAN to give the same net radiated IR energy in watts/sqm as we had at 375 ppm. This is because we always need to balance the incoming solar energy against outgoing IR energy form the Earth at a given temperature and the solar energy doesn’t change. The temperature rise varies slightly from the Tropics to the Arctic and on whether we include clouds or not. However the temperature rise that results varies from about 0.7 to 0.8 degrees C. This is nothing like the predictions of the IPCC which talk of 2.5 to 7 degrees heating but more about that later.

Similarly we can use MODTRAN also to estimate the total greenhouse effect of CO2 on planet Earth. i.e. how cold would it get if there were no CO2 at all in the Earth’s atmosphere ! The results are surprisingly little change in my opinion. The temperature would fall between 5 and 7.5 degrees C i.e. about the same change seen between the  Ice ages and inter-glacial warm periods. How can that be ? The main answer is that the most important greenhouse gas is water vapour and the temperature regulation of the Earth depends far more on small  changes in water vapour than on big changes in CO2.

Why does the IPCC predict much higher temperature changes than 1 degree for a doubling of CO2 ? This is because they are assuming  positive feedbacks exist which they include in their  climate models. So for example :

• A rise in temperature causes more evaporation from oceans leading to further warming by increasing concentrations of water vapour.  In fact MODTRAN demonstrates that increasing water vapour by just 10% leads to as much warming as doubling CO2 !  Of course the opposite is also true.
• A warming Earth leads to melting of the ice caps leading to a decreasing Albedo (solar energy reflection) leading to more absorbed energy leading to a warmer Earth surface.
• A rise in temperature of the ocean leads to a drop in  CO2 take up because less can be dissolved as temperature rises. However an opposite effect to this for increasing CO2 is that the biosphere will absorb more CO2 as plants and plankton grow faster. This feedback of the carbon cycle with temperature is called gamma (ppmv increase in CO2 per degree C) and is usually assumed to be a positive feedback. It can be adjusted to give big increases in temperature. If we define gamma to be the increase in CO2 (ppm.v) for each degree rise in temperature then plugging large values into climate models lead to much higher temperature rises.

I have been struggling to understand exactly how increasing CO2 levels leads to global warming using  basic physics, and the story is complex. The trapping of certain bands of infrared radiation emitted from the Earth by greenhouse gases is well known. The effective cross-section of CO2 of absorption for CO2 in its rotational bands is also well known (HITRAN). Using the current concentration of CO2 in the atmosphere it is also clear that essentially all the radiation emitted by the surface in these bands is already absorbed by CO2 at pre-industrial levels. In fact spectra from space show that the main CO2 bands are saturated in the lower atmosphere with minimal emission from the high atmosphere. The absorption of radiation follows a logarithmic law with distance assuming a uniform concentration of CO2 in air. All that happens if you double the concentration of CO2 in air is that the absorption length is halved. So more radiant energy is absorbed and reflected back to earth at  lower levels of the atmosphere than before. However the total energy balance would appear at first sight to be almost unchanged. In fact just such an experiment was performed by Herr. Koch and led Angstrom to  dismiss theories of man induced warming already back in the early 20th century (Realclimate: what Angstrom didn’t know).

There are 3 main CO2 bands of IR absorption at wavelengths 1388, 667, 2349 cm-1 (HITRAN) and these are already saturated at current levels of CO2 in the atmosphere. Infra Red measurements from space show that the atmosphere is  opaque at these wavelengths. However at high levels in the atmosphere this is not no longer true and this is the only argument for the enhanced greenhouse warming by CO2 warming which makes sense to me (see below).

Spectra of solar radiation and outgoing Infrared radiation. Note CO2 absorption bands ref: Barry & Chorley.

There is a very interesting paper here : http://brneurosci.org/co2.html which describes the basic physics. The absorption length for the existing concentration of CO2 is around 25 meters i.e. the distance to reduce the intensity by 1/e. All agree that  direct IR radiation in the main CO2 bands is absorbed well below 1 km above the earth. Increasing levels of CO2 merely cause the absorption length to move closer to the surface. Doubling the amount of CO2 does not double the amount of global warming. Any increase could be at most logarithmic, and  this is also generally agreed by all sides.

Lab experiments using tubes filled with CO2 to represent the atmosphere show that the IR transmission is essentially saturated and doubling the amount changes the transmission very slightly . So what is wrong and how are these arguments refuted by the majority of climate scientists? There are two main arguments  why global warming is important despite apparent saturation when man adds CO2 to the atmosphere (see  Realclimate ). The first of these is rather convincing.

1. IR scatters repeatably upward through layers of the atmosphere until at between 5-9 km  the air is so thin that the the atmosphere becomes transparent allowing CO2 emissions here to radiate out into space. At these levels there is little water vapour and CO2 dominates the energy loss. As CO2 concentrations increase so this level shifts to  higher levels in the atmosphere since a critical density must be reached for the radiation to escape.  These levels are colder (until we reach the troposphere) and IR loss is proportional to T**4 (Stefan Boltzman’s law). This means that slightly LESS energy is radiated to space than before and since the total energy must balance, the Earth warms up to radiate more heat to compensate. Don’t forget that there are windows in the IR spectrum with no absorption other water vapour allows easy extra energy loss through evaporation and IR emission. The temperature profile of the atmosphere is called the (adiabatic) lapse rate and is approximately -7 degrees per km falling to -4 degrees per km in the tropics. This is valid up to the Tropopause after which temperature rises again in the stratosphere. So greenhouse warming depends on falling temperature with height, and the anthropic enhanced greenhouse effect due to CO2 emissions is equal to the reduction of IR emissions to space in CO2 bands from the upper troposphere.

2. It is not completely true that the CO2 absorption bands are saturated as the fine structure is quite complex and in the side bands there is still energy left for the atmosphere to absorb. This is a much smaller effect than the first point. The extra absorption caused by an increase of a factor 4 is just a few percent as shown in the figure. In fact already 95% of the radiant energy is absorbed by CO2 at pre-industrial levels leaving a maximum of just 5% for any increase you like. It is often estimated  that the CO2 green house warming component of  the planet is about  3 degrees C so this extra absorption and emission to the surface  would appear to only add just 0.15 degrees of warming.

Saturation now and @ 4*CO2 levels (note LOG scale)

Therefore the main physics arguement supporting enhanced global warming caused by increasing levels of CO2 is the in height and thereby lower temperature of the effective radiating level of the atmosphere to space. The first comment to make is that we never  hear this crucial explanation in  the popular descriptions of the greenhouse effect. We just hear that more CO2 absorbs more heat radiated from the earth and radiates it back to the surface thereby heating us up just  like a thicker blanket does in bed (blankets actually work by cutting down convection losses). However the real explanation above concerns just the outermost layers of the atmosphere. The enhanced greenhouse effect depends on  a decreasing temperature gradient with height so that as the effective radiating level for IR  by CO2 rises so the energy loss falls and the earth must rise in temperature to compensate. Energy balance demands that there is a perfect match between incoming solar energy and outgoing IR energy. So lets look at this in more detail.

The effective temperature for all IR emissions is around -20 degrees C radiating at a height h of 5km. Now suppose that we double CO2 concentrations and the effective last radiating level rises to say 6 km. The temperature would now be about -27 degrees C as the decrease is almost linear in the troposphere. However the effective surface area is now also greater by an amount 8*PI*R (where R is radius of the Earth = 6350) making 1.6*10**5 sq km larger than at 5 km height.  The IR radiation falls off with temperature as T**4 which gives us a reduction of about 18% relative to before.

However if we just look at the main CO2 emission band and use the measurements from space (taken from Houghton’s book Global Warming - A complete Briefing). It would appear that the effective temperature of CO2 band alone  is -53 degrees C which is almost at the tropopause ( -60 degrees). So with all else remaining the same (water vapour, methane etc.) the drop in energy loss is just 3% in that single band.

CO2 causes the  lower atmosphere to be opaque at the main absorption bands. The mean free path is only  about 25 meters, so at these wavelengths the lower atmosphere is already like a thick fog where IR radiation is scattered in all directions. As we rise up in the atmosphere so the density falls exponentially and only at heights of 8-9 kms  does the atmosphere then become transparent in the main CO2 bands allowing energy loss direct to space. Doubling concentration rises that level nearer to the tropopause  which radiates at a lower temperature. The estimate given for the Earth’s warmng in Houghton’s book is 1.2 degrees for each doubling - so 2.4 degrees would be the heating if  CO2 concentrations were to increase by a factor 4. These figures are based on a radiation reduction of 4 watts/meter**2 caused by this effect of the effective radiation level rising to a colder level. In his book Prof. Houghton says this can easily be proved, but I have not  understood where this figure comes from nor how it has been calculated.

Feedback Effects

The IPCC predictions of future warming are based on model assumptions of positive feedback effects which are supposed to result from the initial warming caused by CO2 emissions. The main feedback effect is that of increased evaporation of the oceans leading to an increased greenhouse effect of water vapour (already 80 - 90% of greenhouse effect). However it is known that cloud cover in general leads to a net cooling effect on the Earth by blocking incident solar radiation. An increase in cloud cover of 10% would be enough to cancel out global warming effcets of increased CO2 ( Barry & Chorley).

Radiative Forcing Update: I have now found this reference to the equations used to derive the 4 watts/sq m radiative forcing by doubling the amount of CO2 in the atmosphere.

rf = f * ln([CO2]/[CO2]prein)/ln(2)    in watts/m ** 2

It would appear that in order to derive the factor f the IPCC assume that all of the 0.6 degrees warming apparently seen since the industrial revoluton is due to CO2 and thereby derive the constant

AF = 5.35 ln(C/Co)

Then we get simply  5.35*ln(2)  = 3.7 watts/sq m for the radiative forcing of  doubling CO2 !

If it is really true that this formula has been derived only by assuming that all “observed” temperature rise since 1750 is caused only by CO2 increases, then I fear this is a circular argument !  Many skeptics argue that the recent rises in temperature is dominated by a natural recovery from the little Ice Age. In order to be convinced that CO2 is the primary cause of recent warming then I would prefer  that this  formula could be derived from basic physical arguments  rather than introducing a fudge factor preset to prove a theory.