Contributed by Georges Geuskens, Ph.D.

__The consensus__

Scientists interested in the climate, quite as many supporters as opponents of an anthropogenic climate change, agree on the following points:

- The climate can change as it has always done and will continue to do
- To maintain a constant temperature the Earth must dissipate the energy received from the Sun and the energy balance of the Earth must take into account all different possible mechanisms.
- Part of the energy is dissipated by the Earth as thermal radiation also called “black body” radiation.
- Some gases in the atmosphere, namely CO2, can absorb a fraction of that thermal radiation.
- CO2 having absorbed a fraction of that radiation could have an influence on the temperature of the Earth’s surface or of the low atmospheric layers.

The debate between supporters and opponents of an anthropogenic climate change would be closed quickly if we could give a __quantitative__ basis to all these phenomena on which there is agreement from a qualitative point of view.

To put the problem in quantitative terms requires the knowledge of:

– the amount of solar energy received by the Earth at the top of the atmosphere,

– the fraction of the energy emitted by the earth as thermal radiation

– the fraction of the thermal radiation absorbed by CO2.

Several of these quantities are not well known and are often contested estimates. To put the problem in quantitative terms, however, it is necessary to accept some estimates __even if uncertain__. Then we will consider these as basic assumptions common to supporters and opponents of an anthropogenic climate change.

__Common basic assumptions__

It is essential to know the amount of solar energy received by the Earth. The value of 340 W/m2 at the top of the atmosphere is generally acknowledged. This value is not measured but calculated assuming a uniform distribution of energy over the entire Earth’s surface without taking account of an unlit hemisphere and a variation with latitude. It is certainly overestimated but a correct value taking into account the speed of rotation of the Earth and the inclination of its axis of rotation would lead to insurmountable computational difficulties. Without anything better we’ll use this value accepted by supporters of an anthropogenic climate change.

The second hypothesis concerns the energy balance of the Earth. The most complete and often cited model is that proposed by NASA. Again it is accepted by the supporters of an anthropogenic climate change. According to that model, 30% of the energy received by the Earth at the top of the atmosphere is reflected by the clouds, the atmosphere and the Earth’s surface (it is the albedo of the Earth). Then the atmosphere and the clouds absorb 19% of the transmitted solar radiation and finally only 51% are absorbed by the land and the oceans. This energy is then dissipated by evaporation of ocean water (23%), by air convection (7%) and thermal radiation (21%). While uncertainty remains high regarding the relative importance of these three mechanisms, we will use this assessment to quantitatively determine the influence of CO2 on the temperature of the Earth’s surface or of the low atmospheric layers.

The third value required to achieve this goal is the fraction of the Earth’s thermal radiation absorbed by this gas. If we consider the Earth as a black body at 15 °C Wien’s law states that the intensity of the emitted radiation should be maximum at 10 µm and Planck’s equation allows calculating that 95% of the spectrum would be between 5 and 40 µm. Among the major atmospheric constituents only CO2 and H2O absorb radiation in that wavelength range. In particular, CO2 has an absorption band centered at 15 µm which enables the excitation of the initially linear molecule to a state of vibration involving deformation. By integrating Planck’s equation between 14 and 16 µm it can be calculated that 9.3% of the thermal radiation of the Earth at 15°C is emitted in that wavelength range. Ultimately CO2 could absorb only 9.3% of 21% or a little less than 2% of the total energy received from the sun at the top of the Earth’s atmosphere and thus about 6 W/m2.

The difference of opinion between supporters and opponents of an anthropogenic climate change is fundamentally about the __deactivation mechanism__ of CO2 molecules excited by absorption of a fraction of the thermal radiation from the Earth. The first, in fact, invoke the theory of the greenhouse effect in support of their thesis whereas the latter dispute this theory.

__The theory of the greenhouse effect__

Let us first recall the definition of the greenhouse effect proposed by supporters of the theory of an anthropogenic global warming

*The greenhouse effect is a radiative phenomenon caused by **gases, such as water vapor or CO2, absorbing a fraction of the infrared radiation emitted by the Earth and then *__re-radiating__* part of it back *

*in all directions including toward*

*the Earth’s surface whose temperature is, therefore, higher than in the absence of infrared absorbing gas. These gases are therefore called*

*“greenhouse gases”*

*.*

If 2% of solar energy absorbed by CO2 is radiated back in all directions, as assumed by supporters of the theory of the greenhouse effect, there would be no more than half that fraction to reach the Earth’s surface i.e. about 3 W/m2. Knowing that a human being at rest dissipates 60-100 W as heat the temperature increase due to a possible greenhouse effect would be much lower than that resulting from the presence of a human being occupying a surface of one square meter.

*(this paragraph revised after first posting)*Moreover, could the Earth’s surface specifically absorb infrared radiation of wavelength 15 µm radiated back by CO2 ? This could be the case for the surface occupied by the oceans since liquid water has an absorption band at that wavelength but it is not the case for the tip of the Earth’s surface since absorption could occur only between well-defined energy levels due to the quantification of the energy. CO2 could therefore restore the absorbed energy only to 71 % of the Earth’s surface. Reduced to the scale of the planet, this amount of energy is on average about 2 W/m2. As a conclusion the greenhouse effect as defined above could not lead to an appreciable warming of the Earth’s surface.

__The kinetic theory of gases__

Against the theory of the greenhouse effect it can be argued that the probability of radiative deactivation of CO2 (with emission of wavelength 15 µm) is practically nil given the enormous number of collisions between atmospheric molecules at a pressure close to one atmosphere and at a temperature of 15 ° C.

The atmosphere is composed mainly of nitrogen (78%) and oxygen (21%) as bi-atomic molecules N2 and O2. The third component in order of abundance is argon Ar (about 1%). CO2 accounts for only about 0.04%. All these molecules have virtually no interaction between them except that being in constant agitation they come into collision with each other. The kinetic theory of gases allows calculating that at the temperature of 15 ° C atmospheric molecules are moving at speeds of the order of 500 meters per second and at a pressure of one atmosphere each undergoes several billion collisions per second. The kinetic theory of gases also calculates the average kinetic energy of bi-atomic N2 and O2 molecules which is Ec = 5/2 kT (where k is the Boltzmann constant and T the temperature in Kelvin). The energy of the CO2 vibration level is also known: it is Ev = hc / λ (where h is Planck’s constant, c the speed of light and λ the wavelength of the absorbed radiation, in this case 15 µm). A simple calculation shows that this value is only 30% higher than the average kinetic energy of the surrounding molecules. As the latter have a wide distribution of kinetic energy some have enough of it to bring the CO2 molecules to this vibration level during a collision. This conversion of translational kinetic energy of N2 or O2 molecules into vibrational energy of CO2 molecules is reversible. Not always the same CO2 molecules vibrate but their proportion remains constant at a given temperature because a dynamic equilibrium is established as a consequence of numerous collisions. Under these conditions CO2 molecules that have absorbed a fraction of the thermal radiation emitted by the Earth deactivate by collision and transfer of their energy to surrounding molecules and not by radiating back the wavelength of 15 µm. We can therefore conclude that the greenhouse effect, as defined by the supporters of an anthropogenic global warming, does not exist.

Knowing the CO2 absorption coefficient and its content in air it can be calculated that the absorption of wavelength 15 µm is substantially saturated for radiation passing through an atmospheric thickness of 10 m. The absorption of the thermal radiation of the Earth between 14 and 16 microns (6 W/m2) is selective by CO2 molecules but due to collisions with the surrounding molecules that energy is distributed over all the molecules contained in an air column 10 m high. If the perfect gas law is used to calculate the number of molecules in 10 m3 of air at one atmosphere and 15 °C it appears that each molecule will undergo per second an increase of kinetic energy of less than 0.001%. This insignificant amount will increase the air convection movements that also occur in the absence of CO2 and could only lead to a local temperature increase of the order of ten thousandth of a degree. It is important to note that this value is calculated taking into account the totality of atmospheric CO2 and not only the anthropogenic fraction whose effect would be even smaller. Moreover, if the absorption of radiation of wavelength 15 µm is saturated by passing through an atmospheric thickness greater than 10 m the effect would be even smaller because it would be distributed over a greater number of surrounding molecules.

__Conclusion__

From this statement we can conclude that:

- The greenhouse effect, as defined by the supporters of an anthropogenic climate change, does not exist because CO2 molecules that have absorbed a fraction of the thermal radiation of the Earth deactivate by collision and not by back radiation of the wavelength absorbed
- The absorption by CO2 of a fraction of the thermal radiation of the Earth results, as a consequence of numerous collisions with the surrounding molecules, in a very tiny increase of their average kinetic energy corresponding to a local temperature increase of the low atmospheric layers of the order 0.0001°C.
- CO2 can in no way lead to a warming of the Earth’s surface and its influence on the temperature of the low atmospheric layers is insignificant.