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The Greenhouse Effect

Greenhouse_effect.pdf  14 October 2019

The First Assessment Report of the UN IPCC, 1991, stated, page xi:
“Executive Summary
We are certain of the following:
               there is a natural greenhouse effect which already keeps the Earth warmer than it would otherwise be
               emissions resulting from human activities are substantially increasing the atmospheric concentrations of the greenhouse gases carbon dioxide, methane, chlorofluorocarbons (CFCs) and nitrous oxide ……….”

At page xiii, under ‘What natural factors are important’ it states:
“ One of the most important factors is the greenhouse effect, a simplified explanation of which is as follows Short-wave solar radiation can pass through the clear atmosphere relatively unimpeded But long-wave terrestrial radiation emitted by the warm surface of the Earth is partially absorbed and then re-emitted by a number of trace gases in the cooler atmosphere above”

These statements are deceptive and grossly misleading. The fact is that 51% of the Sun’s radiation is in the long-wavelength, infrared part of the spectrum as is all of the Earth’s emitted radiation. On arrival at the Earth’s orbital distance from the Sun, the incoming infrared energy is more than twice that emitted from the Earth’s surface. Consequently the solar infrared is also partially absorbed and re-emitted by the radiative gases in the atmosphere thereby heating both the atmosphere and the Earth’s surface.

As a result, if there was a Greenhouse Effect, the Earth would get colder as the concentration of greenhouse gases increased due to the back-radiation of part of the incoming Sun’s energy out into space being greater than the internal back-radiation of the Earth’s heat.

Further, in the First Assessment Report, page xiv, it states:
“How do we know that the natural greenhouse effect is real?
The greenhouse effect is real: it is a well understood effect, based on established scientific principles. We know that the greenhouse effect works in practice, for several reasons. Firstly, the mean temperature of the Earth’s surface is already warmer by about 33°C (assuming the same reflectivity of the earth) than it would be if the natural greenhouse gases were not present. ……….”

This statement completely ignores the gravity induced thermal gradient in the atmosphere, as pointed out by Doug Cotton [ref. 14], thereby providing a justification for the introduction of the imaginary greenhouse effect. If the accepted atmospheric absorption of 23% had been applied, the resulting temperature would be 232.1°K i.e. -41°C, or a greenhouse effect of 56°C.

The model used to determine the Greenhouse Effect took the incoming Solar constant of 1370 Watts per square metre and spread that across the whole spherical surface of the Earth, that is, 342.5 W/m^2, as the average irradiance. Using an albedo of 0.3, this gives the Earth’s average temperature to be 255° Kelvin (-18° Celsius ) for an Earth with no component of atmospheric absorption. That is, the model had no night or day, no polar ice caps or Equatorial tropical zone and no atmosphere, simply the same irradiance causing the same constant temperature everywhere. This effectively means a non-rotating, non-orbiting, rocky, waterless planet Earth receiving equal radiation from all directions of the three dimensional Universe. Hence a lifeless barren planet with no vegetation and no oceans.

This is manifestly different to reality, whereby, at any instant in time there is only one spot potentially receiving the full irradiance of 1370 W/m^2, equivalent to a temperature of 394.25 degrees Kelvin ( 121.25 degrees Celsius). Allowing for an albedo of 0.3 (reflection) gives a temperature of 360.6 degrees Kelvin (87.6 degrees Celsius) for an Earth without an atmosphere. Assuming the atmosphere absorbs 23%, further reduces the surface temperature to 328°K i.e. 55°C, for an emissivity of 1. This would apply to a flat surface perpendicular to the incoming radiation and in thermal equilibrium, i.e. neither heating nor cooling, which is a reasonable maximum temperature level for the Equatorial zone without having to introduce a Greenhouse Effect. For an emissivity of 0.9, typically a sand or brick surface, the temperature would be 337°K or 64°C, for an emissivity of 0.8, the temperature would be 347°K or 74°C, typically coal, anodised aluminium, black enamel paint or oxidised steel, and for an emissivity of 0.7, for example basalt rock, the temperature would be 359°K or 86°C.

The MODIS satellite measured a maximum temperature at the Earth’s surface of 70.7°C in 2005 over the Lut Desert in Iran where the Gandom Baryon Plateau consists of dark lava with sand dunes, indicating that there is no need to invoke a greenhouse effect to account for the Earth’s temperature maxima.

The Sun’s heat spot circumnavigates the globe every 24 hours along a different path each time, always within the Equatorial zone. The remainder of that part of the globe facing the Sun receives the Solar constant reduced by the sine of the angle of inclination of the surface with respect to the incoming radiation. This diminishes to zero along the circumference of the plane facing the Sun and over all of the surface facing away from the Sun. That is, the temperature is always fluctuating back and forth between daily maxima and minima and these constantly change as the Earth orbits the Sun.

Astrophysicist Joseph Postma [ref. 13] has devised a rational model for the Sun warming the Earth which gave a result of +15.5 degrees Celsius for the average surface temperature of the Sun-lit side, an acceptable estimate, without invoking a Greenhouse Effect.

In summary, the UN IPCC model defines an isolated sphere in space exhibiting no change in surface temperature whatsoever in marked contrast to the ever-changing temperature both with time and location across the Earth’s surface. The contrived 33 degree Kelvin Greenhouse Effect is not a property of the atmosphere but a measure of the bias inherent in the artificial model used to estimate the average temperature of the surface of an imaginary Earth.

Specifics:

In calculating the greenhouse effect, the average temperature of the Earth without the greenhouse effect was taken to be 255 degrees Kelvin (-18 deg.Celsius). This is the result obtained by taking one quarter of the Solar constant of 1370 Watts per square metre, namely 342.5 W/m^2 as the average irradiance over the spherical surface of the Earth relative to a circular disk of the same radius – the area of a sphere being four times that of a circular disk of the same radius. This was reduced by a factor of three tenths to account for the albedo, 0.3, of the Earth’s surface giving an amount of 239.8 W/m^2 heating of the surface equivalent to a temperature of 255 deg.K ( -18 degrees Celsius ) from the Stefan-Boltzmann law.

Figure 1

The variation of radiant energy from the Planck law for a source at 255 degrees Kelvin with respect to wavelength is shown in Figure 1. The peak radiant energy is 4.42 Watts per steradian per square metre per micrometer at a wavelength of 11.36 microns. The total energy density over all wavelengths is 3.2 x 10 -6 Joules per cubic metre.

The temperature of the Earth with greenhouse effect was taken to be 288 deg.K (+15 deg.C), the estimated average temperature of the Earth. At this temperature the Stefan-Boltzmann law determines the radiant exitance for an emissivity of 1 to be 390.1 W/m^2, 63% greater than at 255 degrees Kelvin.

Figure 2 shows the variation of radiant energy from the Planck law for a source at 288 degrees Kelvin with respect to wavelength. The peak radiant energy is 8.12 Watts per steradian per square metre per micrometer at a wavelength of 10.06 microns. The total energy density over all wavelengths is 5.2 x 10 -6 Joules per cubic metre. Note that the vertical scale is twice that of Figure 1.

Figure 2

Planck’s formula determines the energy density for a body at 255 deg.K to be 3.199 x10^-6 Joules per cubic metre and for 288 deg.K to be 5.205 x10^-6 J/m^3. The difference of 2.006 x10^-6 J/m^3 must be the energy generated by the greenhouse effect which causes the Earth surface, with greenhouse effect, to be radiating 1.63 times more energy than it would without the greenhouse gases.

Comparison between Figures 1 and 2 shows that the source of higher temperature has its peak radiant energy at a shorter wavelength (higher frequency) and its amplitude is larger at all wavelengths. As heat from a source of higher temperature is required to increase the temperature of a receiving body, that heat must fit these conditions of greater amplitude and a peak at shorter wavelength. Also notable is the fact that the part of the spectrum of shorter wavelength than the peak contains about one quarter of the total radiant energy of a source.

If all of the Earth’s radiant energy at 288 deg.K was to be absorbed and re-radiated by the atmospheric gases, less than one third may be directed towards the Earth surface, namely, less than 1.735 x10^-6 J/m^3. Of this only seven tenths could be absorbed by the surface due to the 0.3 albedo, that is, 1.215 x10^-6 J/m^3, and only one quarter could effectively increase the surface temperature. That amounts to an effective back-radiation of 0.304 x10^-6 J/m^3, almost one seventh of the supposed 2.006 x10^-6 J/m^3 from the greenhouse effect making that effect not physically possible.

Added to that is the fact that only a small proportion of the atmosphere contains radiative molecules and those that are energised by the Earth’s outgoing radiation are likely to transfer that energy to kinetic energy of motion when they collide with other air molecules and the Greenhouse Effect proposition loses all credibility as a source of heat for the Earth’s surface.

This result is supported by the paper by J. Kauppinen and P. Malmi “No Experimental Evidence For The Significant Anthropogenic Climate Change”, July 13, 2019 [15]

Despite this, the last UN IPCC report AR5, “Climate Change 2014″ under “Summary for Policymakers” stated:

SPM 2. Future Climate Changes, Risks and Impacts
Continued emission of greenhouse gases will cause further warming and long-lasting changes in all components of the climate system, increasing the likelihood of severe, pervasive and irreversible impacts for people and ecosystems. Limiting climate change would require substantial and sustained reductions in greenhouse gas emissions which, together with adaptation, can limit climate change risks. {2}

SPM 2.1 Key drivers of future climate
Cumulative emissions of CO2 largely determine global mean surface warming by the late 21st century and beyond. Projections of greenhouse gas emissions vary over a wide range, depending on both socio-economic development and climate policy.

End of copy.

CO2 Emission Spectrum

Using the facility on the HITRAN website [ref. 12], a listing of the emission spectra for isotopologue 16O12C16O was calculated for a temperature of 280 degrees Kelvin (7 deg. C) and pressure of 0.9 atmospheres, roughly the conditions at an altitude of 1000 metres above sea level. This isotopologue has a natural abundance of 0.984 so is a reasonable representation of the atmospheric CO2 absorption.

Taking a cutoff level of one thousandth of the maximum line strength gave three absorption peaks. These were :
(a) the maximum of 3.687E-18 cm/molecule at wavelength 4.23 microns within the band 4.19 microns to 4.37 microns,
(b) a lessor maximum of 3.106E-19 cm/molecule at wavelength 14.98 microns within the band 14.09 microns to 16.19 microns, and
(c) the third maximum of 6.169E-20 cm/molecule at wavelength 2.68 microns within the band 2.67 microns to 2.8 microns.
The position of the first two bands is shown on Figures 1 and 2 with the 4.23 micron band in red and the 14.98 micron band in blue.

As the wavelength for (b) is greater than that for the peak for the assumed average temperature of the Earth, 10.06 microns, it cannot cause the Earth’s temperature to increase. It is ‘colder’ than the Earth. Only radiation in (a) the 4.23 micron band and (c) the 2.68 micron band can increase the Earth’s temperature, that is, radiation of shorter wavelength than the peak.

For a source at 288 degrees Kelvin, Planck’s law determines that the 2.68 micron band has an energy density of 5.016 x 10^-11 Joules per cubic metre, the 4.23 micron band has an energy density of 5.344 x 10^-9 J/m^3 and the 14.98 micron band has an energy density of 5.053 x 10^-7 J/m^3, making a total of 5.107 x 10^-7 J/m^3 radiated from the Earth’s surface within the CO2 absorption bands. Of this, only the 2.68 and 4.23 micron bands, a total of 5.394 x 10^-9 J/m^3, can increase the temperature of the Earth’s surface. If one third is back-radiated towards the Earth, the surface (due to the albedo) may absorb seven tenths as heating, which is 1.2586 x 10^-9 J/m^3 or one part in 1600 of the supposed Greenhouse Effect. If there is to be a Greenhouse Effect then the UN IPCC needs to explain from where do they source the main component of the back-radiation energy as it cannot be from CO2.

Furthermore, if there is back-radiation of the Earth’s emitted heat energy by the atmosphere, there must also be back-radiation of the incoming Sun’s energy by the atmosphere.

For the radiant energy from a 5772 degrees Kelvin source at the Earth’s distance from the Sun as source, the 2.68 micron band would have an energy density of 7.104 x 10^-8 J/m^3, the 4.23 micron band would have an energy density of 1.9723 x 10^-8 J/m^3 and for the 14.98 micron band 1.861 x 10^-9 . That is, a total of 9.262 x 10^-8 J/m^3. If two-thirds is radiated out into space, that is a loss of 6.175 x 10^-8 J/m^3 or 49 times the supposed energy heating of the Earth’s surface by CO2 back-radiation of the Earth’s outgoing energy. That means that if the Greenhouse Effect is operative then CO2 would be causing cooling of the Earth due to part of the Sun’s incoming radiation being back-radiated into space.

Conclusion:

The mathematical model used to determine the Greenhouse Effect was an entirely inappropriate model so the resulting figure of 33 degrees Celsius is a measure of the bias in the model and does not define anything relevant to the real Earth. If there is a Greenhouse Effect, there may be cooling not warming of the Earth.

The following web pages provide results from the analysis of empirical data that demonstrates the degree to which real world data conforms with the above conclusions. The scene from the head of this page and repeated below shows the reality, namely that there is no Greenhouse Effect. The sunlight has melted the snow in the open areas but not in the hollows that cannot be reached by the Sun’s rays. If there was a Greenhouse Effect it would be radiated down from the sky above and melted the snow in the hollows. This has not happened yet there has been enough sunshine to cause the springtime blossoming of the wildflowers.