**HITRAN CH4 absorption spectrum**

For this study, a spectrum for methane, CH_{4}, was calculated using the HITRAN web site facility [Ref.1] with the parameters of temperature of 15.5̊C and pressure 1.0 atmosphere, being the estimated average conditions at sea level. The isotopologue ^{12}CH_{4} was selected as its abundance is 0.988. The result is shown in Figure 1.

The calculated HITRAN spectrum listing gave the major peaks as:

- a: wavenumber 1327.07 cm-1 , that is, wavelength 7.5354 microns, frequency 39.785 Tera Hz, amplitude 1.001 x 10-19 cm/mol,
- b: wavenumber 3057.69 cm-1 , that is, wavelength 3.27045 microns, frequency 91.667 Tera Hz, amplitude 2.173 x 10-19 cm/mol, spectrum maximum,
- c: wavenumber 4315.68 cm-1 , that is, wavelength 2.3171 microns, frequency 129.38 Tera Hz, amplitude 5.63 x 10-21 cm/mol,

From inspection of the HITRAN listing, the absorption bands were chosen by taking one thousandth of the peak line intensity of the most intense line as their outer limits, that is, a line intensity greater than 2.173 x 10-22. This gave the absorption band limits to be:

- a. 7.158 to 8.411 microns,
- b. 3.141 to 4.117 microns, and
- c. 2.161 to 2.437 microns.

**Earth’s thermal radiation**

Applying these values to the Planck function for an average Earth temperature of 288.5̊K ( 15.5̊C ) gave the following energy values for the respective absorption bands:

- a. energy density 3.595 x 10-7 Joules per cubic metre, being 0.0686 of the total surface emission and a photon density of 1.364 x 10+13 photons per cubic metre, being 98.85% of the total absorption,
- b. energy density 9.67 x 10-9 J/cu. m., being 0.00185 of the total surface emission and a photon density of 1.592 x 10+11 photons per cu. m., being 1.15% of the total absorption,
- c. energy density 9.357 x 10-12 J/cu. m., being 1.79 x 10-6 of the total emission and a photon density of 1.092 x 10+8 photons per cu. m., being 0.000008% of the total absorption,

giving a total photon density of 1.38 x 10+13 photons per cu. m. of which the 7.5 micron band dominates with 98.85% of the total. The energy density for all wavelengths from a source at 288.5̊K is 5.241 x 10^-6 Joules per cubic metre of which 7.044% (3.692 x 10-7 J/cu. m) is in the above-chosen CH4 absorption bands. Figure 2 illustrates the Planck spectrum for a source at 15.5̊C, the estimated average Earth surface temperature, with the three main absorption bands for CH_{4} marked, plus the spectrum for a source at 40̊C.

The photons emitted from the Earth’s surface and absorbed by atmospheric CH_{4} molecules activate each molecule into a vibrational mode dependent on the energy of the absorbed photon. The molecule then returns to its ground state by either releasing a photon of the original frequency in a random direction or transferring some or all of the energy into kinetic energy of motion on collision with another atmospheric molecule and changing to a lower energy vibrational state or emitting a photon of that lower energy, lesser frequency. Consequently the energy density of the radiation directed back towards the Earth’s surface will be less than one half of the outgoing energy, that is, less than 1.846 x 10-7 J/cu.m which is less than 3.52% of the surface radiance.

The laws of thermodynamics mandate that the temperature of a surface can only be increased by receiving radiation from a source whose temperature is greater than that of the surface. The response for a source at 40̊C in Figure 1 illustrates that radiant heating from any hotter source requires that source to have a peak radiance of a shorter wavelength, higher frequency, than the receiving surface and have a greater total spectral radiance. The back-radiation from atmospheric methane molecules at less than 3.52% of the surface radiance does not meet these essential conditions. A household thermos flask is a practical example of the fact that back-radiation from a source does not cause that source to increase in temperature.

**Sun’s radiation**

Applying the same absorption bands to the Planck function for the Sun’s radiation at 5772̊K adjusted by a divisor of 46,240 to provide for the decrease in intensity by the square of the distance apart, gave the following energy values for the respective absorption bands at the Earth’s average distance from the Sun:

- a. energy density 1.781 x 10-7 Joules per cubic metre, being 9.81 x 10-3 of the Sun’s total emission and one half of the Earth’s radiation in that band,
- b. energy density 1.279 x 10-8 J/cu.m., being 7.043 x 10-4 of the total emission and 1.323 times the Earth’s radiation in that band,
- c. energy density 2.394 x 10-7 J/cu.m., being 1.318 x 10-2 of the total emission and 2,559 times the Earth’s radiation in that band’

for a total energy density of 4.303 x 10^-7 J/cu.m. from the Sun, absorbed by the atmospheric CH_{4} compared to 3.692 x 10^-7 J/cu.m. from the Earth’s surface. Consequently, if there was a greenhouse effect it would cause the Earth to cool as the concentration of atmospheric CH_{4} increased due to an increase in the amount of the Sun’s radiation emitted back into space before it could warm the Earth, as is the case for atmospheric CO_{2}.

**Conclusion**

The absorption by atmospheric CH_{4} gas of part of the Earth’s surface radiation causes less than 3.52% of the surface radiation to be re-emitted back towards the surface. This radiation, directed towards the surface, is not from a source hotter than the surface so it cannot increase the surface temperature. The kinetic energy induced by collision between CH_{4} molecules in vibrational mode and other atmospheric molecules becomes part of the normal process of convection that continually cools the surface.

The absorption of some of the incoming Sun’s radiation by the atmospheric CH_{4} gas will warm the atmosphere thereby adding to the normal convection with some energy re-radiated back into space. This energy has been shown to be greater than that of the re-radiated surface energy and should cause cooling of the Earth as the concentration of atmospheric CH_{4} gas increases. This has not been shown to happen, consequently there is no basis for the UN IPCC claim of dangerous warming of the Earth due to the release of CH_{4} gas from its surface.

A more accurate analysis requires a detailed consideration of the line by line spectrum of CH_{4} gas however the current analysis in terms of absorption bands should show the appropriate relativities between the various responses.

In claiming that there is a greenhouse effect caused by the Earth’s atmospheric radiative gasses, it would appear that the UN IPCC has failed to account for an identical effect on the incoming Sun’s radiation. In addition, the UN IPCC has totally ignored the well established gravity induced atmospheric temperature-pressure gradient which mandates that, via the Ideal Gas Laws, the temperature is greatest where the pressure is greatest, namely, at the Earth’s surface and fully explains the fictitious 33°C Greenhouse Effect.

**Reference:**

- HITRAN website, https://hitran.ioa.ru , a collaboration between

Harvard-Smithsonian Center for Astrophysics (CFA), Cambridge, MA, USA,

V.E. Zuev Insitute of Atmosperic Optics (IAO), Tomsk, Russia

National Research Tomsk State University (TSU), Tomsk, Russia.