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Timothy Casey B.Sc.(Hons.): Consulting Geologist   


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The Shattered Greenhouse: How Simple Physics Demolishes the "Greenhouse Effect".

Timothy Casey B.Sc. (Hons.)
Consulting Geologist

First Uploaded ISO: 2009-Oct-13
Revision 5 ISO: 2011-Dec-07

Some former elements of this article such as the laser experiment, radiation budget commentary, and the UHI implications are to be later reproduced in an additional article concerning the mid-20th century revival of the "Greenhouse Effect". This notice will be removed when the new article is uploaded.

Abstract

This article explores the "Greenhouse Effect" in contemporary literature and in the frame of physics, finding a conspicuous lack of clear thermodynamic definition. The "Greenhouse Effect" is defined by Arrhenius' (1896) modification of Pouillet's backradiation idea so that instead of being an explanation of how a thermal gradient is maintained at thermal equilibrium, Arrhenius' incarnation of the backradiation hypothesis offered an extra source of power in addition to the thermally conducted heat which produces the thermal gradient in the material. The general idea as expressed in contemporary literature, though seemingly chaotic in its diversity of emphasis, shows little change since its revision by Svante Arrhenius in 1896, and subsequent refutation by Robert Wood in 1909. The "Greenhouse Effect" is presented as a radiation trap whereby changes in atmospheric composition resulting in increased absorption lead to increased surface temperatures. However, since the composition of a body, isolated from thermal contact by a vacuum, cannot affect mean body temperature, the "Greenhouse Effect" has, in fact, no material foundation. Compositional variation can change the distribution of heat within a body in accordance with Fourier's Law, but it cannot change the overall temperature of the body. Arrhenius' Backradiation mechanism did, in fact, duplicate the radiative heat transfer component by adding this component to the conductive heat flow between the earth's surface and the atmosphere, when thermal conduction includes both contact and radiative modes of heat transfer between bodies in thermal contact. Moreover, the temperature of the earth's surface and the temperature in a greenhouse are adequately explained by elementary physics. Consequently, the dubious explanation presented by the "Greenhouse Effect" hypothesis is an unnecessary complication. Furthermore, this hypothesis has neither direct experimental confirmation nor direct empirical evidence of a material nature. Thus the notion of "Anthropogenic Global Warming", which rests on the "Greenhouse Effect", also has no real foundation.

 

1.0 Introduction: What on Earth Is the "Greenhouse Effect"?

Confusion and Lack of Thermodynamic Definition

Although the "Greenhouse Effect" is of crucial importance to modern climatology and is the putative cornerstone of the Anthropogenic Global Warming hypothesis, it lacks clear thermodynamic definition. This forecasts the likelihood that the name is misapplied. Even general descriptions of the "Greenhouse Effect" may seem confused when compared to one another. In the first year university geology text by Press & Siever (1982, p. 312) we read:

"The atmosphere is relatively transparent to the incoming visible rays of the Sun. Much of that radiation is absorbed at the Earth's surface and then reemitted as infrared, invisible long-wave rays that radiate back away from the surface (Fig. 12-14). The atmosphere, however, is relatively opaque and impermeable to infrared rays because of the combined effect of clouds and carbon dioxide, which strongly absorbs the radiation instead of allowing it to escape into space. This absorbed radiation heats the atmosphere, which radiates heat back to the Earth's surface. This is called the 'greenhouse effect' by analogy to the warming of greenhouses, whose glass is the barrier to heat loss."

This explanation is fundamentally confusing because it is seemingly contradictory, as impermeable materials cannot absorb on the minute to minute timescale that applies to the "Greenhouse Effect", even if such an impermeable material has a very high fluid storage capacity or porosity. According to Press & Siever's explanation above, the atmosphere is relatively impermeable due to the presence of clouds and carbon dioxide, which are part of the atmosphere. How then, can the part of the atmosphere that makes it impermeable to infrared, simultaneously facilitate infrared absorption? Moreover, the idea of thermal permeability is a product of the 19th century pseudoscientific notion that heat was actually a fluid (called "caloric"). This led to a great deal of misunderstanding amongst the scientifically illiterate when it came to the findings of Fourier (e.g. Kelland, 1837). We may compare this description of the "Greenhouse Effect" with that of Whitaker (2007, pp. 17-18), which lacks the misplaced 19th century usage:

"The incoming solar radiation that the earth absorbs is re-emitted in the form of so-called infra-red radiation - this is where the vital 'greenhouse effect' begins. Because of the chemical structure of the greenhouse gases in the atmosphere, they absorb the infra-red radiation from the Earth, and then emit it, into space and back into the atmosphere. The atmospheric re-emission helps heat the surface of the Earth - as well as the lower atmosphere - and keeps us warm."

This explanation describes the "Greenhouse Effect" as "vital", perhaps because, as Whitaker points out, it warms the earth's surface. Wishart (2009, p. 24) explains that this "Greenhouse Effect" is useful for a completely different reason:

"The Moon is another excellent example of what happens with no greenhouse effect. During the lunar day, average surface temperatures reach 107ºC, while the lunar night sees temperatures drop from boiling point to 153 degrees below zero. No greenhouse gases mean there's no way to smooth out temperatures on the moon. On Earth, greenhouse gases filter some of the sunlight hitting the surface and reflect some of the heat back out into space, meaning the days are cooler, but conversely the gases insulate the planet at night, preventing a lot of the heat from escaping."

In Wishart's explanation above, the Greenhouse Effect" is no longer a warming mechanism but a thermal buffer that moderates the extremes of temperature. In fact, Plimer (2001) uses the term "greenhouse" to denote interglacial periods (e.g. Plimer, 2001, p. 80). In describing the conditions when life evolved on earth 3800 million years ago, Plimer (2001, p. 43), like Wishart, is more reminiscent of Frankland (1864) and Tyndall (1867):

"The Earth's temperature had moderated because the atmosphere was rich in carbon dioxide and water vapour created a greenhouse."

The above quotes demonstrate a confusing array of "Greenhouse Effect" definitions, including the first one which seems to contradict itself. Plimer (2009, p. 365) really describes this situation very well when he writes:

"Everyone knows what the greenhouse effect is. Well ... do they? Ask someone to explain how the greenhouse effect works. There is an extremely high probability that they have no idea. What really is the greenhouse effect? The use of the term 'greenhouse effect' is a complete misnomer. Greenhouses or glasshouses are used for increasing plant growth, especially in colder climates. A greenhouse eliminates convective cooling, the major process of heat transfer in the atmosphere, and protects the plants from frost."

The "Greenhouse Effect" was originally defined around the hypothesis that visible light penetrating the atmosphere is converted to heat on absorption and emitted as infrared, which is subsequently trapped by the opacity of the atmosphere to infrared. In Arrhenius (1896, p. 237) we read:

"Fourier maintained that the atmosphere acts like the glass of a hothouse, because it lets through the light rays of the sun but retains the dark rays from the ground."

This quote from Arrhenius establishes the fact that the "Greenhouse Effect", far from being a misnomer, is so-called because it was originally based on the assumption that an atmosphere and the glass of a greenhouse are the same in their workings. Interestingly, Fourier doesn't even mention hothouses or greenhouses, and actually stated that in order for the atmosphere to be anything like the glass of a hotbox, such as the experimental aparatus of de Saussure (1779), the air would have to solidify while conserving its optical properties (Fourier, 1827, p. 586; Fourier, 1824, translated by Burgess, 1837, pp. 11-12).

In spite of Arrhenius' misunderstanding of Fourier, the Concise Oxford English Dictionary (11th Edition) reflects his initial opening description of the "Greenhouse Effect":

"Greenhouse Effect noun the trapping of the sun's warmth in the planet's lower atmosphere, due to the greater transparency of the atmosphere to visible radiation from the sun than to infrared radiation emitted from the planet's surface."

These descriptions of the "Greenhouse Effect" all evade the key question of heat transfer. Given that the "Greenhouse Effect" profoundly affects heat transfer and distribution, what are the thermodynamic properties that govern the "Greenhouse Effect" and how, exactly, is this "Greenhouse Effect" governed by these material properties? Moreover, all of the elements expressed in the preceding quotations can be found in Arrhenius' proposition of the "Greenhouse Effect". While Arrhenius credits Tyndall with the thermal buffer idea expressed in Plimer (2001) and Wishart (2009), he then goes on to express the more complicated idea described in Press & Siever (1982) and Whitaker (2007). The "atmospheric re-emission" that "helps heat the surface of the earth" of Whitaker (2007, pp. 17-18) is the key to Arrhenius' original proposition, which revolves around the backradiation notion first proposed by Pouillet (1838, p. 42; translated by Taylor, 1846, p. 61). However, Pouillet used this idea to explain rather than add to the thermal gradient measured in transparent envelopes while, as we shall see, Arrhenius treated backradiation as an addition to the conductive (i.e. net) heat flow indicated by the thermal gradient.

 

2.0 How the "Greenhouse Effect" Is Built upon Arrhenius' Legacy of Error: Misattribution, Misunderstanding, and Energy Creation

Arrhenius' first error was to assume that greenhouses and hotboxes work as a radiation trap. Fourier explained quite clearly that such structures simply prevent the replenishment of the air inside, allowing it to reach much higher temperatures than are possible in circulating air (Fourier, 1824, translated by Burgess, 1837, p. 12; Fourier, 1827, p. 586). Yet, as we have seen in the previous quotation of Arrhenius, this fundamental misunderstanding of greenhouses is attributed by Arrhenius to Fourier.

 

2.1 Misattribution versus What Fourier Really Found

Contrary to what Arrhenius (1896, 1906b) and many popular authors may claim (Weart, 2003; Flannery, 2005; Archer, 2009), Fourier did not consider the atmosphere to be anything like glass. In fact, Fourier (1827, p. 587) rejected the comparison by stipulating the impossible condition that, in order for the atmosphere to even remotely resemble the workings of a hotbox or greenhouse, layers of the air would have to solidify without affecting the air's optical properties. What Fourier (1824, translated by Burgess, 1837, p. 12) actually wrote stands in stark contrast to Arrhenius' claims about Fourier's ideas:

"In short, if all the strata of air of which the atmosphere is formed, preserved their density with their transparency, and lost only the mobility which is peculiar to them, this mass of air, thus become solid, on being exposed to the rays of the sun, would produce an effect the same in kind with that we have just described. The heat, coming in the state of light to the solid earth, would lose all at once, and almost entirely, its power of passing through transparent solids: it would accumulate in the lower strata of the atmosphere, which would thus acquire very high temperatures. We should observe at the same time a diminution of the degree of acquired heat, as we go from the surface of the earth."

A statement to the same effect can be found in Fourier (1827, p. 586). This demonstrates the sheer dissonance between these statements and what proponents of the "Greenhouse Effect" claim that Fourier says in their support. Moreover, I am not the first author to have discovered this fact by reading Fourier for myself (e.g. Fleming, 1999; Gerlich & Tscheuschner, 2007 and 2009). Furthermore, in his conclusion, the optical effect of air on heat is dropped by Fourier (1824, translated by Burgess, 1837, pp. 17-18) and Fourier (1827, pp. 597-598) which both state:

"The earth receives the rays of the sun, which penetrate its mass, and are converted into non-luminous heat: it likewise possesses an internal heat with which it was created, and which is continually dissipated at the surface: and lastly, the earth receives rays of light and heat from innumerable stars, in the midst of which is placed the solar system. These are three general causes which determine the temperature of the earth."

Fourier's fame has, in fact, nothing to do with any theory of atmospheric or surface temperature. This fame was earned years before such musings, when Fourier derived the law of physics that governs heat flow, and was subsequently named after him. About this, Fourier (1824, p. 166; Translation by Burgess, 1837, p. 19) remarks:

"Perhaps other properties of radiating heat will be discovered, or causes which modify the temperatures of the globe. But all the principle laws of the motion of heat are known. This theory, which rests upon immutable foundations, constitutes a new branch of mathematical sciences."

As you can see, Fourier admits that his work is constrained to the net movement of heat. In fact, nowhere does Fourier differentiate between radiative and, for example, "kinetic" heat transfer, because the means to tell the difference were not available when Fourier studied heat flow. What this tells us is that Fourier's Law, and only Fourier's Law, can describe the transfer of heat between bodies in thermal contact. Thus the distribution of heat between the atmosphere and the surface of the earth, with which it has thermal contact, cannot be correctly calculated using the radiative transfer equations derived from Boltzmann (1884) because the thermal contact of these bodies makes this a question of Fourier's Law. However, to better understand this it is necessary to explore the motion of heat and the modes of heat transfer more thoroughly than did Arrhenius.

 

2.2 Aethereal Misunderstanding versus Subatomic Heat Transfer

Arrhenius (1906b, pp. 154 and 225) still clung to the aether hypothesis, which refers to the unspecified material medium of space. Arrhenius' adherence to this hypothesis remained firm in spite of its sound refutation by Michelson & Morley (1887). This leaves the conceptual underpinning of radiation in Arrhenius' "Greenhouse Effect" to Tyndall (1864, pp. 264-265; 1867, p. 416), who ascribes communication of molecular vibration into the aether and communication of aethereal vibration to molecular motion. This interaction conceptually separates radiated heat from conducted heat so that radiation remains separate and distinct from conductive heat flow - effectively isolating conductive heat flow from the radiative mode of heat transfer. Thus no consideration is made for internal radiative transfer as a part of conductive transfer, in the context of aethereal wave propagation. However, Arrhenius' contemporaries, having moved beyond the debunked aether hypothesis, had a much more realistic perspective of the interactions between radiation, heat, and subatomic particles.

During the life of Arrhenius' "Greenhouse Effect", the scientific community understood that radiation was electromagnetic (Maxwell, 1864; Heaviside, 1881; Hertz, 1888), and by the time Arrhenius first published on the subject of the "Greenhouse Effect", Thompson (1896) had extended his idea of electrons to photoelectric effects on gases due to ionizing radiation, known then as röntgen rays. The photoelectric effect, by which a current or charge could be generated in certain materials by their exposure to electromagnetic radiation, was a matter of inquiry at the time. The emission of radiation in discrete quanta, though first suggested by Boltzmann in 1877, was mathematically formalised by Planck (1901). Einstein (1905) experimentally confirmed Planck's Equation after adapting it to the photoelectric effect, which was the subject of his study. However, ideas concerning the internal structure of the atom and it's relationship to ionisation, magnetism, photoelectric interactions, and discrete quanta of electromagnetic radiation were under intense development at the time (Thomson, 1902; Thomson, 1903; Thomson, 1904). By the time Bohr (1913) corrected the problems in Thomson's atomic model, the relationship between changes in electron shell (i.e. orbit) potential and photoelectric emission of radiation were a foregone conclusion. The relevance of these discoveries to the question of heat transfer is that unlike the notion of aethereal heat transfer, emission of electromagnetic energy quanta by atoms and molecules in materials confirmed that the radiative mode of heat transfer was as much a part of thermal conduction as any other mode of heat transfer.

In order to understand how heat moves through materials, we must first examine the structure and behaviour of the material media at a sub-atomic level. An atom comprises a nucleus within a shell. The shell is due to "Thomson's corpuscles", later known as electrons, which are negatively charged particles that orbit a nucleus with a positive charge corresponding to the number of these electrons. These orbital paths are also known as electron shells and, when shared by more than one atom, electron shells form the chemical bond between those atoms. When a "photon", or rather an electromagnetic wave pulse, passes through the electron shell -which is the region defined by the corresponding mathematical function called an orbital- one of a number of things may occur. It may pass through the "shell", it may be deflected by the "shell", or it may be absorbed by an electron in the "shell". When an electromagnetic wave pulse or 'photon' of light or heat is absorbed by an electron, the energy imparted to the electron is converted to kinetic energy, which moves the electron out to an orbital level commensurate with the energy gained. If we consider, from the mass of both electron and nucleus, that the centre of mass is somewhere between the electron and the nucleus, then this centre of mass does not coincide with the centre of positive charge, about which the electron orbits. Imagine a circumstance in which this centre of mass remains static, while the nucleus revolves around it. As the electron shell is centred on the nucleus, then in this case the shell and the entire atom or molecule is thus seen to wobble or vibrate about a particular point. The higher the electron shell, the more intense this wobble or vibration becomes. As a consequence, the absorption of electromagnetic radiation by a material manifests itself as what appears to be a corresponding net increase in the kinetic energy of constituent molecules.

If we take the processes we have just examined and apply them to more than one molecule, we may then perceive as Waterson (1843, 1846, 1892) did, that through collisions between molecules, the material must either expand or its internal pressure will increase. By this we may infer the kinetic propagation of heat through a medium by the collision of its molecules, as the momentum of one molecule is transferred to another in the collision. This is not the only consequence of molecular collision. Such a collision may transfer the kinetic energy from an electron of the inbound molecule to an electron of the outbound molecule. It is also possible that the collision may destabilise one or both electron shells resulting in the corresponding drops to lower electron potentials. When an electron falls to a lower orbit or electron shell of lesser potential, a "photon" or pulse of electromagnetic radiation is emitted. That electromagnetic wave pulse then propagates through the material until it is either absorbed by another molecule or escapes from the material. However short-lived, such radiation quanta carry a proportion of heat flow in all materials. Whether we are talking about air, glass, or steel, a component of internal heat transfer is via internal radiation, however short the path of that radiation may be. Ergo, thermal conduction is not solely the kinetic transfer of heat, but also the transmission and reception of radiation within a material or materials in thermal contact. This is confirmed by the fact that conductive heat transfer, as defined by Fourier (1822), is only concerned with total heat flow and therefore describes the sum of both radiative and kinetic transfer without addressing either specifically. This differs markedly from the separation of radiative and kinetic transfer implicit in the ethereal model of heat transfer proposed by Tyndall and favoured by Arrhenius. This divergence of Arrhenius' idea of heat transfer from the facts of contemporary science forecasts a major error in Arrhenius' thermodynamics.

 

2.3 Obfuscated Energy Creation versus "Kirchhoff's Law"

It is an interesting fact that Arrhenius (1896 and 1906b) obfuscates his critical backradiation mechanism of the "Greenhouse Effect" by focusing the reader's attention on the idea he falsely attributed to Fourier, which is now found in the dictionary; namely, that the atmosphere admits the visible radiation of the sun but obstructs the infrared radiation from the earth. However, Arrhenius' calculations are based on surface heating by backradiation from the atmosphere (first proposed by Pouillet, 1838, p. 44; translated by Taylor, 1846, p. 63), which is further clarified in Arrhenius (1906a). This exposes the fact that Arrhenius' "Greenhouse Effect" must be driven by recycling radiation from the surface to the atmosphere and back again. Thus, radiation heating the surface is re-emitted to heat the atmosphere and then re-emitted by the atmosphere back to accumulate yet more heat at the earth's surface. Physicists such as Gerlich & Tscheuschner (2007 and 2009) are quick to point out that this is a perpetuum mobile of the second kind - a type of mechanism that creates energy from nothing. It is very easy to see how this mechanism violates the first law of thermodynamics by counterfeiting energy ex nihilo, but it is much more difficult to demonstrate this in the context of Arrhenius' obfuscated hypothesis.

Suffice it to say that heat is lost at the earth's surface when it is radiated to the atmosphere. The atmosphere having gained this heat loses it when it is re-radiated, half into space and half back to earth because radiation is omnidirectional - being emitted by a molecule in any direction. However, such heat losses are not represented in the "Greenhouse Effect", which recycles this heat instead. According to this hypothesis, this heat joins yet more heat absorbed from direct solar radiation during the relay - much of which is simultaneously emitted and recycled again. The intensity of terrestrial radiation absorbed by the atmosphere is thus increased and, taken in addition to that absorbed by the earth's surface, now totals more than the radiation available from the sun (e.g. Kiehl & Trenberth, 1997; Trenberth et al., 2009). The logic is seductive, yet flawed. Radiation is simply the amount of power per square metre. This power cannot be used and stored at the same time. Power cannot be raised without intensifying the source or adding another source of energy. You can prove this at home by observing the consequences when you unceremoniously unplug the power lead from your amplifier (while listening to some music). Without the additional source of power, it simply cannot amplify the signal from the radio receiver or the DVD pickup.

Authors who defend the "Greenhouse Effect" attempt to characterise it as a form of heat congestion (e.g. Archer, 2009). The problem with this defense is that no amount of heat congestion can result in an average power output exceeding the average power input. The defense is also subject to the limitations of "Kirchhoff's Law". "Kirchhoff's Law" dictates that while emissivity and absorptivity are always equal for a given material or body, the equality of absorption (not absorptivity) and emission (not emissivity) of radiation defines thermal equilibrium between bodies that are not in thermal contact. Even the misconception that selective absorptivity makes it easier for radiation to get in than to escape, breaks down when both the atmosphere and the surface of the earth are treated as a whole body. Regardless of internal complexities, a whole body ultimately can only emit the exact amount of radiation it receives, or a lesser amount corresponding to a lower pre-equilibrium temperature if thermal equilibrium has not been reached. By increasing absorption, emission is increased - which was confirmed experimentally by Stewart (1858, 1860a, 1860b) and Kirchhoff (1859 & 1860). Moreover, this greater emission has a cooling effect on the atmosphere and Frankland (1864, p. 326) asserts that without this loss of heat by emission to space, atmospheric water vapour could not condense into clouds and precipitation. This cooling by radiative emission is further confirmed by Ellsaesser (1989) and Chillingar et al. (2008). Thus surface evaporation and subsequent condensation at altitude has a powerful cooling effect, which in addition to convection, offsets the high degree of heating that occurs at the surface.

Inasmuch as we raise the absorptivity of the atmosphere, we equally raise its capacity to emit radiation to space. This was understood by Tyndall, Frankland and Fourier, as well being experimentally confirmed by Pouillet (1838, p. 44; translated by Taylor, 1846, p. 63). This concept of "Kirchhoff's Law" possibly dates back to the experimental work of Leslie (e.g. 1804, p. 24). However, the inclusion of "Kirchhoff's Law" in Fourier (1822) is highly suggestive of a much earlier source given the abundance of pre-existing qualitative thermodynamic principles that were subsequently quantified by Fourier. The principle that a material's absorptivity is equal to it's emissivity, thus, has a long history with many experimental confirmations. This same law of physics, experimentally conifrmed by numerous scientists, dictates that the temperature of the atmosphere cannot be changed simply by increasing absorptivity. "Kirchhoff's law" thereby functions as the key to understanding the behaviour of passive body temperature in constant incident radiation. Moreover, when Arrhenius (1896, p. 255) added the radiative transfer between the earth's surface and the atmosphere to the conductive transfer between the earth's surface and the atmosphere, he effectively duplicated the radiative transfer quantity, because it was already included in the conductive transfer quantity ("M"). This quantity is representative of net heat flow in accordance with Fourier's Law which, further, does not distinguish between kinetic and radiative modes of heat transfer across a thermal contact.

Not only did Arrhenius duplicate heat, thereby invoking an energy creation mechanism to equip carbon dioxide with a power source it does not have, he propagated an erroneous explanation of how greenhouses work, which he falsely attributed to Fourier. Moreover, Arrhenius used this erroneous explanation as an alternative focal point for his "Hothouse Effect". With respect to the "Greenhouse Effect", as it later became known, this misdirection proved most effective in drawing scrutiny away from the weakest proposition of the idea - as attested by its consequent Concise Oxford Dictionary definition. It is upon this litany of error and misdirection that the "Greenhouse Effect" and the implicitly "anthropogenic" nature of global warming and climate change is based. Having ascertained the various mechanisms of the "Greenhouse Effect", we are ready to test this hypothesis against the laws of physics as they apply to real and repeatable experimental results of a physical and material nature.

 

3.0 Elementary Physics versus the "Greenhouse Effect"

Heat distribution amongst materials in thermal contact is controlled by respective thermal conductivities rather than any putative optical properties. The relationship between thermal gradient -the change in temperature per unit length- and heat flux -the rate of energy flow across a unit area- is key to understanding the relationship between thermal conductivity and heat distribution within a material or materials in thermal contact. This is limited by the overall power available via the heat flux, which may come from another body in thermal contact or as radiation from a body isolated by a vacuum. However, the amount of heat available to a system due to increased absorption, is lost to corresponding emission. Thus a change in materials without a change in incident radiation -the radiation that falls on a body- can, at most, alter the distribution of heat within those materials.

 

3.1 The Physics of Nitrogen, Oxygen, and Carbon Dioxide

The relationship between conductivity and net heat transfer explains why physicists, as Gerlich & Tscheuschner (2007 and 2009) point out, only consider the question of heat and temperature in terms of measurable physical properties such as thermal conductivity and heat capacity, unless that heat is being radiated across a vacuum. The latter case presents a question only answered by the Stefan-Boltzmann Equation, explained below. However, in terms of bodies in thermal contact, such as the atmosphere and the surface of the earth, the assertions of Arrhenius with respect to backradiation must necessarily be accompanied by a great variation in thermal conductivity in order to account for a comparably greater change in thermal gradient. This question is addressed in Gerlich & Tscheuschner (2007 and 2009, pp. 6-10), which shows an insufficient difference in the thermal conductivities of carbon dioxide, nitrogen, and oxygen to account for the claims of Arrhenius.

Carbon dioxide does, in fact, have a lower thermal conductivity than either nitrogen or oxygen (by roughly 36%, calculated from the figures of Gerlich & Tscheuschner, 2007 and 2009). So a large increase (i.e. by hundreds of thousands of parts per million) in atmospheric carbon dioxide concentration that would increase the thermal gradient accordingly, could produce a measurable surface warming. As this cannot change the amount of heat flowing through the system, the effect would be manifest by a decrease in atmospheric temperature offset by a corresponding increase in surface temperature. However, a meagre doubling of the presently insignificant levels of atmospheric carbon dioxide cannot have a measurable effect. In fact, geological history records that other factors have a much greater influence on global climate than carbon dioxide.

If carbon dioxide produced the backradiation claimed by Arrhenius, thermal conductivity measurements of carbon dioxide would be so suppressed by the backradiation of heat conducted into this material, that the correspondingly steep temperature gradient would yield a negative thermal conductivity of carbon dioxide. In reality, a 10,000ppm increase in carbon dioxide could, at most, reduce the conductivity of air by 1%. Given the actual difference between the thermal conductivities of carbon dioxide (0.0168) and zero grade air (0.0260), a 10,000ppm increase in carbon dioxide would lower the thermal conductivity of zero grade air by 0.36%. That would represent a 0.36% increase in thermal gradient, or a surface warming of 0.18% and a ceiling cooling of 0.18% of the total difference in temperature between the top and bottom of the affected air mass. In the case of a tropospheric carbon dioxide increase of 10,000ppm, that would correspond to a warming of 0.125ºC, or one eighth of a degree Celsius at the earth's surface, offset by a cooling of 0.125ºC at the tropopause. On the scale of doubling the troposphere's carbon dioxide, the surface warming predicted by this simple and materialistic thermodynamic approach is on the order of 0.004ºC.

 

3.2 Extending the Stefan-Boltzmann Equation to Incidence of Radiation

Beyond the material medium of the atmosphere, heat is transferred across the vacuum of space by electromagnetic radiation. In fact, radiation is the only way heat can cross a vacuum and this radiative transfer of heat is governed by the Stefan-Boltzmann Law. As we shall see, this is critical to calculating body temperature from heat entering an otherwise thermally isolated body. It also dictates the temperature of the ideal greenhouse. However, as the Stefan-Boltzmann Law concerns radiation emitted, we must first extend this law to relate temperature to incident radiation. This is achieved by applying the the principle of equal absorptivity and emissivity best known as "Kirchhoff's Law".

"Kirchhoff's Law" can be used to simplify the Stefan-Boltzmann Equation (Boltzmann, 1884) yielding a form that is surprisingly elegant. The significance of Kirchhoff's Law lies in the fact that emissivity not only constrains the proportion absorbed, but the readiness with which the body may emit (Kirchhoff, 1859; Kirchhoff, 1860, translated by Guthrie, 1860). Thus as emissivity decreases for the same emission of radiation, the temperature rises. However, given a constant incident radiation, the proportion by which temperature is raised by lack of emissivity is balanced by the reduced proportion of absorbed radiation. Substituting incident radiation multiplied by emissivity for emitted radiation in the Stefan-Boltzmann Equation arises the following way:

Where:
Wb = Radiation (heat flux) in Wm-2 emitted by the body in question if it is a perfect black body
Wi = Radiation (heat flux) in Wm-2 incident upon the body in question
We = Radiation (heat flux) in Wm-2 emitted by the body in question
T = Absolute Temperature in ºK of the body in question
ε = Emissivity = Absorption / (Absorption + Reflection) of the body in question
σ = Stefan's Constant = 0.000000056704
Wm = Mean incidence of radiation over the entire surface of the body in Wm-2
Ax = Mean cross-sectional area of radiation incident on the body in m2
At = Topographical area of the body in m2

Wb = σT4     Stefan's Law relating black body radiation to temperature (Stefan, 1879)
We = εWb   Emissivity is the proportion of hypothetical black body radiation emitted
Wb = Wi     And at thermal equilibrium, black body radiation is equal to incident radiation
We = εWi    Ergo emissivity is also the proportion of incident radiation emitted
We = σεT4   As the Stefan-Boltzmann Equation (Boltzmann, 1884) elaborates on emitted radiation:
εWi = σεT4

Thus a body's temperature response to incident radiation is entirely independent of emissivity, such that

Wi = σT4

This is confusing because it looks just like Stefan's Law for black bodies. However, as the radiation in question is not the body's emitted radiation as used by Stefan (1879), but is instead the incident radiation, it applies not only to black bodies but in general - as shown by the simple derivation. However, this case is strictly for omnidirectional radiation, which is only incident when all the radiation is diffuse or scattered. Radiation from a given source is directional and when the source is distant, the radiation is measured in a plane perpendicular to incidence. As a body is a three dimensional object with a much larger surface area than the area across which incident radiation falls, the emitted radiation of a body is always correspondingly lower in intensity then the incident radiation. As the area of incidence is less than the area of emission, we must further modify our equation so:

WiAx/At = σT4
Wm = WiAx/At
Wm = σT4

As you can see, the temperature of a body in constant incident radiation cannot be raised by compositional changes, and solely depends on the intensity of the radiation. This confirms the duplication of energy and to some degree, the perpetuum mobile inherent in the "Greenhouse Effect."

 

3.3 Returning to Wood's Experiment to Test Pouillet's Backradiation Hypothesis & Arrhenius' Greenhouse Effect

We may well ask if it is at all possible for backradiation to coexist as a significant process alongside contact transfer. It would certainly seem possible within the limitations of thermal gradients. However, if we revisit the experiment conducted by Robert Wood in 1909, an entirely different picture emerges. Wood constructed two miniature greenhouses identical in all but one respect. One used a plate of halite to transmit light into the interior, while the other used a plate of glass to transmit light into the interior (Wood, 1909). While glass absorbs more than 80% of infrared radiation above 2900nm, halite does not and is regarded as quite transparent to infrared. The point of the experiment was to test whether the halite's lack of absorption and re-emission of infrared radiation relative to that of glass would have any effect on the temperature of the greenhouse.

Taking Pouillet (1838) and Arrhenius (1906a) into account, we may extend the backradiation hypothesis to this particular situation. In this case, the glass lets through the light of the sun but absorbs 85% of the terrestrial infrared radiation radiation returning to space - at least that emitted above 2900nm. We may suppose that this 85% is of the half of the radiation that is absorbed above 2900nm and is augmented by about 15% of the other half of the outgoing infrared radiation based on the numbers from Nicalau and Maluf (2001). That is a total absorption of 50% of the outgoing radiation. This radiation is subsequently emitted from the glass itself; half radiated outside and half radiated back inside the miniature greenhouse. The amount of radiation reaching the bottom of the greenhouse is equal to that directly received from the sun plus the 25% radiated back by the glass. Although halite is more transmissive than glass in the visible spectrum, this is offset by the fact that halite is much more reflective than glass in the visible spectrum (Lane & Christensen, 1998). The difference in light transmission is less than 5%. Thus in the case of this experiment, the glass greenhouse bottom can be said to have received at least 120% (100-5+25) of the radiation received by the halite greenhouse bottom according to the Arrhenius' revision of Pouillet's hypothesis. Thus we expect the temperatures of the respective greenhouses to reflect this significant difference in hypothetical radiation reaching the respective bases.

In Wood's experiment, the halite greenhouse interior temperature rose to 65ºC or 338ºK (Wood, 1909). Applying the Stefan-Boltzmann equation as shown above, to the relationship between incident radiation and body temperature we may determine from:
Wm = σT4

That:
Wm = 0.000000056704 x 3384
Wm = 740 Wm-2

Now, according to the backradiation hypothesis and the measurable optical properties of glass and halite, this 740 Wm-2 should be supplemented, in the glass greenhouse, by 20% in backradiation from the glass. Thus we may surmise, via Arrhenius' variation on Pouillet's backradiation idea, that the radiation at the bottom of the glass greenhouse in the first stage of Wood's experiment was 888 Wm-2. This predicts the temperature of the glass greenhouse as follows:
T = {Wm/σ}0.25

Given Wm = 888 Wm-2:
T = {888/0.000000056704}0.25 = 353.8ºK = 80.6ºC

As you can see, Arrhenius' hypothetical backradiation should raise the glass greenhouse temperature 15ºC above the halite greenhouse temperature, in Wood's experiment. In fact, the first stage of the Wood experiment resulted in the glass greenhouse being slightly cooler than the halite greenhouse. Considering the possibility that this could be due to the fact that the glass filters some of the sun's radiation that is not filtered by the halite, Wood proceeded to conduct a second stage in his historic experiment. This time, he filtered the radiation entering both greenhouses with a sheet of glass. This had the effect of reducing the internal temperature of the halite greenhouse to 55ºC or 328ºK. Thus the radiation incident on the bottom of the halite greenhouse is as follows:
Wm = σT4

That:
Wm = 0.000000056704 x 3284
Wm = 656 Wm-2

Allowing for additional 20% of backradiation gives us Wm = 788 Wm-2 in the glass greenhouse, predicting:
T = {Wm/σ}0.25

Given Wm = 788 Wm-2:
T = {788/0.000000056704}0.25 = 343.3ºK = 70.2ºC

Once again, the backradiation hypothesis predicts a temperature difference of 15ºC but in this second stage of the Wood experiment no significant difference in temperature was recorded between the glass greenhouse and the halite greenhouse. From the recorded results of the Wood experiment, we can only conclude that the backradiation hypothesis of Arrhenius creates heat ex nihilo, but only in theory.

 

3.4 Is the "Greenhouse Effect" Really Necessary?

The temperature of the earth's surface is often explained using the "Greenhouse Effect". However, having refuted the "Greenhouse Effect", we may wonder if it was necessary in the first place. The earth orbits the sun in the vacuum of space. There is no aether as Fourier, Tyndall and Arrhenius believed. Moreover, there is no heat capacity or thermal conductivity in space. The only way for heat to escape the planet is by emission to space. That makes the temperature of the absorbing mass of the earth a question of radiative heat transfer. Hereafter, I will refer to the that portion of the earth's mass which absorbs solar radiation as the "solarsphere" because the atmosphere does not include the surface layer warmed by the sun on a day to day basis and there is no other term to encompass both. The method of calculation is to treat the solarsphere as an absorbing body subject to incident radiation from the sun.

Given the solar constant of 1368 Wm-2 (Fröhlich & Brusa, 1981) and the fact that the cross-sectional area of solar radiation incident upon the earth is roughly one quarter of the earth's surface area, it is unsurprising to observe that authors such as Kiehl & Trenberth (1997) arrive at 342 Wm-2 as the mean quantity of solar radiation that falls on the entire surface of the earth. Using this, we may calculate the expected geographical and altitudinal mean temperature of the earth's solarsphere.

Wm = σT4
T4 = Wm
T = {Wm/σ}0.25

Given Wm = 342:
T = {342/0.000000056704}0.25 = 278.7ºK = 5.5ºC

This figure, is an average or mean temperature for all times, latitudes, and altitudes of the the earth's solarsphere. Just as the balance point or centre of gravity is found at the centre of mass, this average temperature may be found at the centre of heat capacity. In materials of similar heat capacity, this can be found near the centre of mass. Thus, in order to determine how well our 5.5ºC result -calculated above- corresponds to observed reality, we must first determine the average observed temperature at the barometric median in the part of the earth penetrated by solar energy.

From the diagrams supplied by Vallier-Talbot (2007, pp. 25-26), we may roughly determine the centre of mass for a one square metre column extending from two metres below the surface to 50 kilometres above the surface. Soils and clays amount to roughly 2 tons per cubic metre, with the atmospheric column having to weigh 10 tons in order to yield a mean barometric pressure of roughly 1000 hectopascals at the surface. The total column weighs 14 tons with the centre of gravity corresponding to the barometric median at 700 hPa. Referring once again to Vallier-Talbot (2007, p. 26) we may determine that on average, this pressure corresponds to an elevation of roughly a mile or 1600m above the surface. Given the observed average atmospheric thermal gradient of -7ºC with every 1000m of elevation above the surface (Vallier-Talbot, 2007, p. 25), we may calculate the average absorbing mass temperature as it occurs at the altitude of the barometric mean for our absorbing column. No doubt you've worked out that the temperature drop over a tropospheric ascent is 11ºC per mile, and we all know that the average surface temperature is 15ºC (Arrhenius, 1896, p. 239; Burroughs, 2007, p. 124). Notwithstanding 100 years of apparently constant mean temperature from Arrhenius to Burroughs, we may determine that the observed temperature at the altitude corresponding to the centre of absorbing mass is 4ºC or 277ºK. This, via the reasoning above, extends to an observed average absorbing mass temperature for planet earth of 4ºC or 277ºK. This is slightly cooler than the mean absorbing mass temperature calculated above from the solar constant (278.7ºK, 5.5ºC) even if we do allow for 0.5º warming over the last century. However, if we were to consider the impact of convective cooling, I think we can agree that the temperature we derive from the Stefan-Boltzmann equation is well within the tolerance we must allow for such tests.

Adding the tropospheric thermal gradient of 11ºC per mile we got from Vallier-Talbot (2007) above, our temperature (278.7ºK, 5.5ºC), calculated from the Stefan-Boltzmann Equation using the Solar Constant, yields a calculated surface temperature of around 16.5ºC. The fact that this is warmer than the observed mean surface temperatures of Arrhenius and Burroughs (15ºC) leaves no room for such dubious free energy mechanisms as Arrhenius' "Greenhouse Effect". The surface temperature of the earth can be much more simply explained without resorting to such complex and unverifiable entities as radiative amplification and power recycling via backradiation of the "Greenhouse Effect". Absorptivity of any of the parts can vary, but that only alters the overall emissivity, which in turn leaves unchanged, the gross power flowing though the system. Once equilibrium is reached it is only the power flowing through a thermally isolated system that controls and maintains mean temperature. This is because comtinuing and ongoing power is required to offset the amount of heat that is lost spontaneously and continuously due to emission of radiation.

Our calculation of mean surface temperature without the "Greenhouse Effect" above (16.5±0.5ºC corresponding to 16-17ºC) is made without considering the effect of carbon dioxide. According to Arrhenius (1906a, translated by Gerlich & Tscheuschner, 2009, pp. 56-57) the observed temperature should be 20.9ºC higher than that yielded by a calculation such as this, owing to the carbon dioxide in the atmosphere. The observed surface temperature of 15ºC (Arrhenius, 1896; Burroughs, 2007) is actually 1-2ºC lower than the calculated mean surface temperature of 16-17ºC. The lower atmosphere will always be warmer than the upper atmosphere because higher material density in the lower atmosphere dictates a much higher thermal conductivity, absorption and density of heat. In contact with an opaque surface warmed by the bulk of the heat absorbed from the sun, it is not difficult to explain why the surface is so much warmer than the altitude corresponding to the centre of mass in the solarsphere. Moreover, the Ideal Gas Law (PV = nRT) dictates that the temperature of a gas containing a given amount of heat invariably increases with pressure. As the highest atmospheric pressure is at the surface, it makes sense that the higher temperature is there, especially if obstruction to radiative outflow decreases with altitude.

Turning our attention to the example of Langley's greenhouse experiment on Pike's Peak in Colorado (mentioned by Arrhenius, 1906b), we may be tempted to ask how it is that a greenhouse can reach such high temperatures. Qualitatively, we may attribute the difference between the 15ºC mean surface temperature and the 113ºC observed in Langley's greenhouse to the fact that noon-time radiation at the surface is three to four times as intense as the mean radiation over the whole of the earth's surface. Repeating our calculation method, this time for the midday conditions of a greenhouse:

T = {Wm/σ}0.25

Given Wm = 1368:
T = {1368/0.000000056704}0.25 = 394.1ºK = 121.0ºC

As you can see, our application of the Stefan-Boltzmann Equation predicts that incident Solar radiation at 1368 Wm-2 should produce a maximum daytime temperature of 394.1ºK or 121.0ºC in a greenhouse fully protected from heat losses to conduction. Although Langley's temperature is lower by eight degrees, it is near enough and, allowing for conductive heat loss, remains a testament to the insulating effectiveness of double glazing.

What is demonstrated in the above examples, is the fact that surface temperature and the temperature in a greenhouse can be explained without resorting to the extraneous entity called the "Greenhouse Effect". This is significant in light of Ockham's Razor, which states:

Entia non sunt multiplicanda praeter necessitatem.

This reads in English as:

Entities are not to be multiplied beyond necessity.

Although the terminology may seem unfamiliar in light of 20th century usage, if we look at the words for what they mean we can, nonetheless, understand this statement. This suggests, in modern palance, that it is simply not valid to hypothesise beyond what is strictly necessary to explain the material evidence we possess. A hypothesis that does go beyond the support of material evidence violates this principle in that the evidence is already explained by a simpler theory. This is one of the most fundamental and definitive principles of science.

 

4.0 Conclusion: a Greenhouse with neither Frame nor Foundation Cannot Stand

In the frame of physics, a "greenhouse effect" as such, can only be used to describe a mechanism by which heat accumulates in an isolated pocket of gas that is unable to mix with the main body of gas. The elimination of convection within the troposphere by stratification, and the consequent temperature rise at the surface, presents us with a natural, if not hypothetical, example of a "greenhouse mechanism" in the frame of physics. Pseudoscience, popular misconception and political misuse of the term "greenhouse effect" have given it quite a different and unrelated meaning.

The Hothouse Limerick

There was an old man named Arrhenius
Whose physics were rather erroneous
He recycled rays
In peculiar ways
And created a "heat" most spontaneous!

Timothy Casey, 2010
Since its original proposition by Arrhenius, the definition of the "Greenhouse Effect" has been chaotic and, as such, has successfully obfuscated the weakest and most important part of that proposition. Namely, that terrestrial heat radiated into the atmosphere is there absorbed and re-emitted back to earth to raise surface temperatures beyond what is possible from the incident radiation alone. In fact the physics, as we have examined them, only allow compositional changes to redistribute heat within the absorbing mass of the earth if no change in mean incident radiation occurs. This predicts that atmospheric warming due to increased opacity can only result in surface cooling, which effectively does no more than alter the thermal gradient, thereby redistributing the heat without adding or subtracting from it. This was confirmed by observations of surface cooling during eruptions that ejected ash and carbon dioxide into the stratosphere (Angell & Korshover, 1985) and by observations of stratospheric warming as a consequence of these same eruptions (Angell, 1997). The "Greenhouse Effect" would predict that backradiation from this warmer stratosphere would instead warm the surface significantly. Evidently, this did not occur. If the power recycling mechanisms that typify the "Greenhouse Effect" really existed, we could build cars that ran on nothing but their own recycled momentum and free energy machines could be built to create energy out of nothing more than spent energy. With a viable "Greenhouse Effect" a windscreen would not need a demister as the heat back-radiated by the glass would prevent ice and water drops from condensing and double-glazed windows filled with carbon dioxide would be self heating. In reality, heat flows and is conducted via two modes of heat transfer. One mode of heat flow is by contact transfer, and the other is by radiative transfer. By taking the radiative transfer part of conductive transfer and adding it to the total amount of conductive transfer between the surface of the earth and the atmosphere, Arrhenius (1896) duplicated a portion of the existing heat pro rata to the degree of absorption by carbon dioxide when, in fact, this portion of radiative transfer is already included in the conductive transfer figure.

In the real physics of thermodynamics, the measurable thermodynamic properties of common atmospheric gases predict little if any influence on temperature by carbon dioxide concentration and this prediction is confirmed by the inconsistency of temperature and carbon dioxide concentrations in the geological record. Moreover, when the backradiation "Greenhouse Effect" hypothesis of Arrhenius is put to a real, physical, material test, such as the Wood Experiment, there is no sign of it because the "Greenhouse Effect" simply does not exist. This is why the "Greenhouse Effect" is excluded from modern physics textbooks and why Arrhenius' theory of ice ages was so politely forgotten. It is exclusively the "Greenhouse Effect" due to carbon dioxide produced by industry that is used to underpin the claim that humans are changing the climate and causing global warming. However, without the "Greenhouse Effect", how can anyone honestly describe global warming as "anthropogenic"?

 

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