Letting the Hot Air out of the Greenhouse: Historical Falsification of the Greenhouse Effect.

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

Uploaded ISO: 2010-June-07

Abstract

This article explores the greenhouse effect and the related science in historical literature. The "Greenhouse Effect" is first described by Arrhenius as a radiation trap, which he falsely attributed to Fourier, who asserted that the mechanism of greenhouses worked by presenting a barrier to convective cooling rather than comprising any form of heat trap. Fourier consequently rejected the mechanism of greenhouses as an explanation of the earth's surface temperature, stating that in order for the eath's atmosphere to behave as a greenhouse, it would have to be immobilised by solidification. Closer inspection of Arrhenius' work reveals not so much the radiation trap that he claimed but an energy creation mechanism, which duplicates the radiative portion of total heat flow from the surface to the atmosphere. This "Greenhouse Effect" forms the basis of Anthropogenic Global Warming, yet it presents us with a litany of error, misunderstanding, misinterpretation, misattribution, and outright pseudoscience. It comes as no surprise that it long since fell prey to the most casual refutation by Robert Wood in 1909 and is currently no more valid or true than it was then. The "Greenhouse Effect", like a real greenhouse, thus deprived of its ability to contain hot air, can no longer function as intended. This leaves the notion that Global Warming is Anthropogenic entirely without foundation.

 

Introduction

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) 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 definition remains largely unchanged and the Concise Oxford English Dictionary (11^th Edition) still preserves most of the original root meaning of the term as defined by Arrhenius:

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.

Thus the "Greenhouse Effect" is not some vague notion of constricted heat flow with a definition for every occasion. The "Greenhouse Effect" is a specific claim that is entirely dependent on a chain of three included principles, each of which may be verified or falsified by experimentation.

1. That a substantial proportion of light is converted to infrared by relay (ie. by absorption & re-emission).
2. That radiative transfer plays the dominant role in the transfer of heat from the surface to the atmosphere - to the near exclusion of other modes of heat transfer.
3. That the CO₂ in the atmosphere is substantially more transparent to incoming radiation than to outgoing radiation

• Thus, as a consequence of surface warming due to back-radiation from atmospheric CO₂, removing atmospheric CO₂ would reduce surface temperature.

The "Greenhouse Effect" can therefore be falsified experimentally by the demonstrated failure of the claim or by the demonstrated failure of any one of the underlying principles. Likewise, the "Greenhouse Effect" can be verified by the repeatable confirmation of the claim and all three underlying principles.

The historical approach to examining the "Greenhouse Effect" was inspired by a number of problems I have observed in the literature discussing this hypothesis. Firstly, the science is treaed as some sort of gospel or infallible writ. It is neither and is the product of limited and finite human endeavour. Often, a major scientific idea is undepinned by another idea which is later toppled and in the resulting chaos, it is a commonplace occurence that authors neglect to consider the impact of historical context. The historical context of a discovery or idea is crucially important because therein lie the influences, misperceptions, and errors of the time - and past misconceptions often play a large role in the shaping of contemporary hypotheses. What many popular authors (from both sides of the argument) leave out is the historical context of the "Greenhouse Effect" and the ideas and discoveries leading to its proposition. For example, the discovery and publication of Fourier's Law in 1822, described the relationship between thermal conductivity, temperature variation, conducting surface area, and thickness of the body between heat source & sink. When extended by conservation of energy, this relationship also defines the conduction of heat between two bodies of different materials in thermal contact, but with the additional consideration of thermal contact conductivity. Moreover, authors such as Fourier, Tyndall, and Arrhenius operated under the assumption that light, as a wave, could only be propagated through a material medium and to explain the propagation of light and heat in a vacuum or across space, the medium of "aether" was postulated. Not to be confused with the organic chemical solvent, "ether", aether as the very substance of the void, received its first formal scientific hypothesis at the hands of Newton (1704), itself a modification of an earlier proposition made by Hooke (Whittaker, 1910, p. 17). The idea of aether, with it's roots in the Cartesian definition of matter and original proposition by Rene Descartes (Whittaker, 1910, p. 4), wasn't decisively refuted until the results of the Michelson & Morley (1887) experiment were published. However, the idea of different types of heat that are transmitted differently by transparent materials such as glass dates back to long before Isaac Newton and Hooke, when Edme Mariotte (1686) demonstrated, using concave mirrors, that while the heat of the sun was almost completely transmitted by glass, the heat of a flame was not.

It is of considerable relevance that prior to 1884, only a single mode of heat transfer was recognised. Herschel (1800d, p. 491) states, "iron is a substance that transmits invisible heat very readily;". This is the same usage of transmission as to describe light transmitted by glass. Fourier (1827, p. 579) points out that the temperature of space is similar to the temperature of the poles. He then goes on to explain that the surface temperature of the earth is inexplicable if the lower temperature of space (ie aether in thermal contact with the atmosphere) is the only direct source of heat (Fourier, 1827, p. 582) - and it is in his attempt to resolve this paradox that Fourier makes a proposition that is misunderstood and misapplied by Arrhenius in 1896. Moreover, prior to Maxwell (1864), radiation strictly referred to the indirect conduction of heat via an intermediary medium such as air or aether. It is this particular diction that persists in works such as Tyndall (1864), Tyndall (1867) can be found in some of Clausius' work concerning the first and second laws of thermodynamics that leads to the confusion of radiation and conduction to such an extent that modern authors (Gerlich & Tscheuschner , 2007, 2009) state that radiation cannot propagate against the prevailing heat flow. So in this historical vein, I continue the exploration of the "Greenhouse Effect" based on the sequential discovery of the underlying and undermining elements that relate to the idea.

 

Herschel and the Discovery of Dark Rays

In 1800, Herschel reported the observation of an invisible colour he described as "calorific rays", that had a powerful effect on the temperature of a thermometer (Herschel, 1800a, 1800b, 1800c, 1800d). Although the alcohol thermometer (Ferdinand II de Medici, 1754) was invented some sixty years before the mercury thermometer (Daniel Gabriel Fahrenheit), Herschel used the latest equipment and, in his initial experiments, went to the trouble of blacking his quicksilver thermometer bulbs to ensure better absorption of visible light (Herschel 1800a, p. 260). Herschel conducted an experiment in which he diffracted sunlight through a glass prism (Herschel, 1800d, p. 445) to cast a spectrum of separated wavelengths on a table. Into bands of this spectrum, he immersed a number of thermometer bulbs. He recorded the peak temperature beyond the red of the spectrum, with temperatures decreasing towards the violet end of the spectrum. The experimental setup depicted in Herschel (1800b) presents us with the thermometer bulb being run successively deeper into the spectrum from the red end, such that the infrared band strikes the stem of the thermometer as the bulb passes into the visible spectrum. This could partly explain the gradual diminishment of temperature response as the thermometer bulb traversed the visible spectrum from red to violet. Aware of this, Herschel (1800c, 1800d) modified the experiment to further prevent band contamination by passing the band of interest through a slit and shading the rest of the equipment from the other bands. The temperature response still decayed from red to violet and the temperature response of the entire visible spectrum was roughly equal to that of the invisible colour band. Consulting Nicolau & Maluf (2003), we may learn something that was not known at the time of Herschel's experiment. Refractive index varies markedly with wavelength in the visible spectrum, whereas throughout the infrared spectrum the variation of refractive index is almost negligible. As a consequence, the entire infrared spectrum refracted by glass (700nm-2900nm) spans a band as wide as one of the seven colour bands of the visible spectrum (400nm-700nm). Additionally, Herschel's focus on rays rather than heat renders his closing hypothesis unsurprising. Herschel (1800d, p. 521) argues that even within the visible bands, such as the red band where he observed the strongest overlap of lighting and heating, the rays that occasion light must be separate and distinct from the rays that occasion heat. He underpinned this argument with his observation of the almost complete transmission of red light through a red filter with a significant loss of temperature gain due to the red light. I refer to this observation as Herschel's paradox.

Irrespective of some of the apparent irregularities arising from Herschel's work, Herschel (1800c, 1800d) establishes that roughly half of the heat occasioned by sunlight transmitted through glass is detectable in the visible band. By this, we may confirm the first underlying principle of the "Greenhouse Effect" that the absorption of light results in a substantial increase in the heat of the absorbing material.

 

Fourier, Heat Flow, and What Greenhouse Exactly?

Jean Baptiste Joseph Fourier is famous for quantifying the flow of heat through a body and through multiple bodies in contact. In fact, the linnear relationship between heat flux (in watts per square metre, just like radiation) and the negative multiple of thermal conductivity and temperature gradient is known as Fourier's Law. This cornerstone of thermodynamics, first published by Fourier (1822), quantifies the total flow of heat by all means through a body or a series of bodies in thermal contact. As it was not until more than four decades later that elecromagnetic radiation was discovered by Maxwell (1864) or nearly six decades later when Maxwell's hypothesis was confirmed by Heaviside (1881), Fourier had no empirical means of distinguishing between kinetic heat transfer and radiative heat transfer within a body. Thus he could only build the relationship defined by Fourier's Law based on the total heat flow observed as a consequence of both kinetic and radiative modes of heat transfer. Thus Fourier's Law of thermal conduction describes the summed heat flow of both kinetic and radiative means within a body or bodies in thermal contact.

There is some confusion as to the origin of Fourier's memoirs and remarks on the temperature of the earth, and so it is worth explaining here. Fourier's first verifiable article on the subject is Fourier (1824) in Annales de Chimie et de Physique. This article received international acclaim and was translated by Burgess in 1837. Fourier (1827) makes an appearance, almost as an afterthought, in Memoires de l'Acadeémie Royale des Sciences, for which Fourier was Secretary for life. Although 'tome VII' or volume seven of this journal was published in 1827, there are typesetter's marks from what might be a previous print run in 1824 (lower left of each page) with page numbers (lower right, consecutive) corresponding to another unidentified publication begining at page 72. Many authors (eg. Gerlich & Tscheuschner, 2007, 2009; IPCC) consider Fourier's memoir to be an 1824 publication, when in fact there exists no defnitive evidence to confirm this fact. As the 1824 publication that hosted the original printing of Fourier's 1827 memoire can neither be identified nor reproduced, it is incorrect to use any of the details of this earlier printing, in the context of the later printing. This is especially true considering the possibility that the earlier print run may have been set up and set aside when it was decided not to publish volume seven in 1824. Suffice it to say, that there is nothing remotely related to Fourier on page 72 of volume seven in the Memoires de l'Acadeémie Royale des Sciences, and there is, to date, no publication in which Fourier's memoire may be found to begin on page 72. It is in this mess that we find Fourier's commentary regarding the temperature at the surface of the earth and his explanation of why atmospheric temperature is typically less than that found in hotboxes such as de Saussure's experimental aparatus.

According to Spratt & Sutton (2008, p. 30), John Mercer is credited with the phrase, 'greenhouse effect' in the 1960s. However, according to Weart (2003), Flannery (2005), and Archer (2009), the idea of a "greenhouse" effect was first proposed by Fourier in 1824. In fact, Fourier actually goes out of his way to refute the idea that air is like the glass of a greenhouse, as examined by de Saussure. Fourier (1827, p. 586) and Fourier (1824; as translated in Burgess, 1837, p. 11) describes the results of H. B. de Saussure's experiment in which the temperature of still air is found to increase with proximity to an absorbing body. De Saussure separated several layers of air between black cork and the atmosphere with panes of glass. This experiment consistently yielded a temperature gradient measured across the still air between the warmer absorbing body and the atmosphere, which is much cooler due to convection. It seems that Fourier (1824, 1827) was using these experimental results to demonstrate the relevance of his earlier work (ie. Fourier, 1822) to the temperature of the air (Fourier, 1824; as translated in Burgess, 1837, p. 12) and the atmosphere (Fourier, 1824; as translated in Burgess, 1837, p. 13). Thus, Fourier (1827, p. 586) explained that the elevated temperatures in the vicinity of the absorbing mass were the consequence of restricting airflow without restricting the entry of the sun's rays. Fourier (1827, p. 586-587) then contrasts this mechanism of restricted airflow with the convection of the atmosphere:

In effect, if all the levels of the air of which the atmosphere is formed were to retain their density and transparency, and lose only their mobility, this mass of air thus becoming solid, being exposed to the rays of the sun, would produce an effect of the same type as that which one has just described.

Thus by way of explaining how the surface of the earth is generally warmer than the aether of space, Fourier (1827, p. 597-598) drops entirely the atmosphere's transparency to light and opacity to heat. He acknowledges the minor roles played by the dissipation of the earth's "original heat" and that of the stars and luminous bodies of the universe to which he attributes the temperature of space and the poles. The primary mechanism of surface heating acknowledged in Fourier's conclusion is that which occurs by absorption of light at the surface of the earth. Specifically, Fourier (1827, p. 597-598) states in his conclusion,

The Earth receives the Sun's rays, which penetrate its mass and are there converted into the dark heat;
it also possesses an original heat retained from its origin, and which continually dissipates at the surface;
finally the planet receives rays of light and heat from innumerable stars amongst which the solar system is placed.
These are the three general causes which determine the terrestrial temperatures. The third, the influence of the stars, is equivalent to the presence of an immense encircling region closed in all parts, whose constant temperature would be a little less than that which we would observe in the polar countries of the earth.

It remains an interesting fact that Fourier (1827) argues that "bright heat" penetrating the earth looses the property of light but retains the property of heat (eg. Fourier, 1827, p. 586) without any attribution to Herschel. Fourier's consistent contrasting of bright heat and dark heat shows a different approach to the subject than that inferred by Herschel's contrast of "the rays that occasion light" with "the rays that occasion heat". The key difference is that Herschel (1800d) considers heat and light to be separate ovelapping spectra, whereas Fourier regards light and heat as both being forms of heat. In essence, Fourier was either unaware of Herschel's work or had entirely rejected Herschel's theory that light and heat comprise separate overlapping spectra.

It is worth noting that the theory of aether is very important to Fourier's Hypothesis. Without aether, there is nothing into which terrestrial heat may be conducted, and no means by which the rays of the sun may reach the earth. It was not until an alternative mode of heat transfer was quantified, that the reign of aethereal wave propagation could be challenged. In light of this possibility, Fourier (1897, p. 598) and Fourier (1824; as translated in Burgess, 1837, p. 19) actually suggested that an alternative means of heat propagation in space might be discovered on the basis of mechanisms he and his contemporaries were not, as yet, capable of measuring. From Fourier (1824) we read:

We might, doubtless, suppose radiating heat to possess properties hitherto unknown, which might, in some way, take the form of this fundamental temperature, which we attribute to space. But in the present state of physical science, all known facts are naturally explained without having recourse to other properties than those derived from actual observation.

This speculation later proved to be prophetic, and Fourier's idea of science remains unchanged in later scientific philosophy, which still embraces Ockham's Razor.

 

Waterson: How Heat as a Mode of Motion led to the Ideal Gas Law

In 1843, while in India, James Waterson connected the idea of heat as a mode of molecular motion with gas temperature and pressure. Although the idea of heat as a mode of motion is much older (Bernoulli, 1738; Herapath, 1821), it still faced considerable resistance at the time. Waterson (1843) used the conservation of kinetic energy to derive the Ideal Gas Law, in the form:

PV/T = K

Where:
P = Pressure
V = Volume
T = Absolute Temperature K = Constant later determined to be the product of Avagadro's constant and the number of moles of gas

Waterson submitted this finding in a paper to the Royal Society in late 1845, only to be rejected by the peer reviewer on the grounds that it was "nothing but nonsense". Waterson (1846) appears to have made the abstracts of the Royal Society for that year. However, it was not until long after Krönig, Clausius & Tyndall had professed the idea of heat as a mode of motion that Lord Raleigh retrieved and published the article in 1892. By the time the Royal Society finally corrected its error, Waterson had been dead for nine years.

 

Krönig, Clausius, Tyndall & Frankland: Heat as Motion and the Thermal Opacity and Emissivity of CO₂

In 1859, John Tyndall conducted a series of experiments examining the nature of heat and light. Heat as a mode of motion was not a new idea, and it had been broached by numerous authors such as Bernoulli (1738), Herapath (1821), Waterson (1843), Krönig (1856), & Clausius (1857). Tyndall (1867, p. 416) describes heat as the vibration of atoms and molecules:

We must not only figure our atoms suspended in the medium, but vibrating in it. In this motion of the consists what we call their heat.

Tyndall (1867, p. 416) goes on to build the image in which rays of light and heat are propagated as waves of this motion through the medium at tremendous speed:

Well, we must figure this motion communicated to the medium in which the atoms swing, and sent in ripples through it, with inconceivable velocity, to the bounds of space. Motion in this form, unconnected with ordinary matter, but speeding through the interstellar medium, receives the name of Radiant Heat; and if competant to excite the nerves of vision, we call it Light.

Tyndall is best known for conducting the first experiments on the thermal transmissivity of various gases. Although Tyndall frequently uses the term, "absorption", he failed in all of his experiments to differentiate absorption and opacity because he makes absolutely no measurement of reflection. This is clearly indicated by the experimental diagrams used to depict Tyndall's apparatus (eg. Tyndall, 1861, Frontispiece; Tyndall, 1864, p. 415; Tyndall, 1867, p. 401). It is only possible for Tyndall to confuse opacity with absorption in this way if he made the major error of assuming that absorption was the compliment of transmission. Both Arrhenius (1896, 1906b) and Weart (2003, p. 3) neglect to mention this rather important fact when describing how Tyndall's work "underpins" the "Greenhouse Effect". The fact that Tyndall failed to differentiate absorbed heat from otherwise reflected heat renders Tyndall's conclusions regarding the thermal absorption of carbon dioxide, purely speculative.

In the second edition of his work, Tyndall (1867, p. 415) adds, as an appendix to his absorption experiments, an extract from his discourse, Radiation through the Earth's Atmosphere, in which he discusses the impact of thermal opacity on atmospheric temperature. Here, Tyndall (1867, p. 416) discusses the kinetic storage of heat in molecular vibration. On page 417, he describes how heat waves speeding from the earth "dash against" molecules of oxygen, nitrogen, and aqueous vapour - to be intercepted predominantly by the aqueous vapour. It is worth noting how Tyndall uses the words absorption and opacity interchangeably. On the opacity of water vapour, Tyndall (1867, p. 417) states:

No doubt can exist of the extraordinary opacity of this substance to the rays of obscure heat; particularly such rays as are emitted by the earth, after being warmed by the sun.

Then, still on the subject of water vapour, Tyndall (1867, p. 418) states:

It has been said that, atom for atom, the absorption of an atom of aqueous vapour is 16,000 times that of air. Now the power to absorb and the power to radiate are perfectly reciprocal and proportional. The atom of aqueous vapour will therefore radiate with 16,000 times the energy of an atom of air.

Notwithstanding the unexplained switch from opacity to absorption, you may recognise in this statement an expression of Kirchhoff's Law. As you can see, this, evidently played a role in Tyndall's later work. Tyndall (1867, p. 419) uses an experiment conducted by Frankland (1864, p. 326) that confirmed the tendency of aqeuous vapour to radiate strongly. Frankland (1864, p. 326), who credits Tyndall with the experiment, argues the case for strong radiative cooling of water vapour as a significant part of the mechanism by which vapour condenses to cloud and rain. Tyndall (1867, p. 419) makes the same argument and goes on to use the opacity or "absorbing power" of aqueous vapour to underpin a mechanism that moderates planetary temperature. Tyndall (1867, p. 419) suggests that heat loss at night and heat gain during the day are reduced or moderated by the presence of aqueous vapour, underpinning the claim by comparing the relative stability of tropical climates with the temperature extremes of dry continental climates. Inasmuch as substances opaque to radiant heat warm the earth's surface at night, they cool the earth's surface by day.

As it turns out, the radiative emission experiment of Frankland (1864) dates back to a similar experiment conducted by Tyndall (1861, p. 277-280). This experiment measured heat emitted by air (producing a deflection of 60 degrees) and, removing the effect of radiation emitted by air via calibration, found that in the presence of roughly the same amount of heat, carbon dioxide raised emission by meagrely a further 18 degrees of deflection (30%). However, the opacity of air taken from Tyndall (1861, p. 176-177) at a deflection of 1 degree or 0.33% presents a minute fraction when compared with much more dramatic results with carbon dioxide (Tyndall, 1861, p. 274). Evidently, the opacity and emissivity of carbon dioxide differ greatly when compared to a control sample such as air. Moreover, the difference in emissivity of air and carbon dioxide in Tyndall's experiment approximate the difference in conductivity of air and cabon dioxide. This is significant in light of Tyndall's comments about the relationship apparent between conductivity and absorptivity, especially given the thermal contact between the atmosphere and the surface of the earth. Not only did Tyndall's experimental results demonstrate a clear difference between opacity and absorption, but Tyndall failed to recognise this crucial difference, both in his experimental results and in his habit of using terms such as absorption and opacity almost interchangeably.

Tyndall was well acquainted with the work of Herschel, as he would reproduce Herschel's experiments at his lectures (Tyndall, 1864, p. 267-269). Thus a failure to account for reflection when attempting to determine absorption may appear to infer incompetence given that Herschel (1800b) demonstrated the reflection of heat. However, we might tenuously speculate that gaseous materials may have been considered an exception. Such assumptions might seem quite natural in light of the fact that Tyndall thought waves of light and heat were transmitted by aethereal propagation (Tyndall, 1864, p. 264-265). It follows from this hypothesis that light and heat can only be conducted via a material medium and the way Tyndall (1864, p. 266) uses the word radiation to indicate conduction of heat affirms this early perspective.

I withdraw the pile from the source of heat, and now I place this slab of ice in front of the pile. You have a deflection in the opposite direction, as if rays of cold were striking the pile. But you know that in this case the pile is the hot body; it radiates heat against the ice; the face of the pile is thus chilled, and the needle, as you see, moves up to 90º on the side of cold. Our pile is therefore not only available for the examination of heat communicated to it by direct contact, but for the examination of radiant heat.

If, rather than taking Tyndall's mid 19^th Century usage at it's 21^st Century meaning, we examine the circumstances of the experiment more closely, we may discover that what Tyndall and his contemporaries often meant by radiation and what we come to understand by radiation in modern usage are two very different things. What we call radiation is omnidirectional and does not preferentially seek out cold objects. Conducted heat, as we understand it, does preferentially flow along the steepest temperature gradient, such as the shortest path from a hot body to a cold body in a homogenous medium (eg. air in Tyndall's lecture hall). Once the thermopile loses its recently acquired heat and falls below room temperature inn Tyndall's ice slab experiment, it is immediately clear that the heat of the thermopile was conducted preferentially by the air to the slab of ice, and yet Tyndall employs the verb, "radiates" to describe this directed example of conduction. We may see from the usage of authors such as Herschel, Clausius, and Tyndall that prior to Maxwell's discovery of electromagnetic radiation in 1864, radiation was used to describe indirect conduction that occurs via an intermediary medium such as liquid, gas or aether. This older usage persisted for some decades. In spite of the updated definition of radiation presented by Tyndall (1867, p.417), this older usage also persists in the same work (Tyndall, 1867, p. 270).

Tyndall's ice slab experiment also demonstrates the predominance of kinetic heat transfer over radiative heat transfer at normal atmospheric temperatures, even via a poor conductor such as air. Without a predominance of kinetic heat transfer, the thermopile in Tyndall's ice slab experiment could not be chilled significantly below room temperature unless the ice slab was placed in contact. By this we may refute the second claim of the "Greenhouse Effect" that radiative transfer plays the dominant role in the transfer of heat from the surface to the atmosphere - to the near exclusion of other modes of heat transfer. Evidently, the heat is conducted in accordance with Fourier's Law and any purely radiative transfer is superfluous to this.

 

Stewart, Kirchhoff, Stefan, & Boltzmann: The Dawn of Modern Thermodynamics

In the mid 19^th Century, a new approach to heat transfer began to take form. Stewart (1859) showed that in opaque bodies, the compliment of absorptivity was reflectivity. Kirchhoff (1859, 1860) showed that emissivity (as opposed to emission) and absorptivity (as opposed to absorption) were equal and that at thermal equilibrium, absorption and emission were also equal. Thus, in the case of a perfect black body, which cannot reflect any radiation, the radiation emitted at thermal equilibrium is therefore equal to the radiation incident across the entire surface area. Stefan (1879) showed that heat flux or radiation emitted from a perfect black body, in watts per square metre, was proportional to the absolute temperature raised to the fourth power. The Stefan Law, as this became known, is as follows:

W_b = σT⁴

Where:
W_b = Radiation (heat flux) in Wm^-2 emitted by the body in question if it is a perfect black body
W_i = Radiation (heat flux) in Wm^-2 incident upon the body in question
W_e = 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

Boltzmann (1884) drew upon Kirchhoff's Law to quantify the relationship between radiation and temperature beyond the purely hypothetical black body of Stefan's equation. Boltzmann equated emissivity with the proportion of hypothetical blackbody radiation emitted by a grey body:

W_e = εW_b

Boltzmann's subsequent extension of Stefan's Law became known as the Stefan-Boltzmann Equation:

W_e = σεT⁴

These discoveries were not served well by the use of radiation as a term with a technical meaning altered from its contemporary usage. Radiation as the conductive propagation of rays (eg. Herschel, 1800c, 1800d; Fourier, 1824, 1827; Tyndall, 1864, etc.) continued for some time to be understood as such (eg. Tyndall, 1867) when it had actually taken on a separate and distinct meaning that was indicative of a second mode of heat transfer (eg. Kirchhoff, 1859, 1860). Such concepts, though elementary to the conservation of energy principle, are vital to understanding radiative heat transfer. Once it was established that light and heat could be propagated by a means other than by thermal conduction, the conceptual need for a medium to carry the vibrations of heat and light evaporated. A few short years later, in 1887, Michelson and Morley conducted the experiment that refuted aether and revolutionised the way we look at the universe - or rather it revolutionised the way some of us look at the universe.

 

De Marchi and the Relationship between Atmospheric Transparency and Surface Temperature

De Marchi (1895) examines a number of hypothetical mechanisms for the variation of glacial and interglacial periods from a meteorological perspective. Rejecting all contemporary hypotheses, De Marchi proposes that the heating of the earth's surface depends on the transparency of the atmosphere. Although there are strains of this idea in Fourier (1824) and Fourier (1827), de Marchi was the first to suggest the role of atmospheric transparency variation in the variation of global climate:

a lowering of this transparency would effect a lowering of the temperature on the whole earth, slight in the equatorial regions, and increasing with latitude into the 70^th parallel, nearer the poles again a little less. Further, this lowering would, in non-tropical regions, be less on the continents than on the ocean and would diminish the annual variations of temperature.

At the time, the relationship between volcanic ejecta, atmospheric transparency on the global scale, and mean surface temperature was yet to be remarked. Although well known historical eruptions coinciding with cold spells included Krakatoa in 1883, Tambora in 1815, and Laki in 1783; it was not until 1913 that the recent Katmai eruption was associated with climate by Abbot (1913). Back in 1895 De Marchi went on to remark:

This diminution of the air's transparency ought chiefly to be attributed to a greater quantity of aqueous vapour in the air, which would cause not only a direct cooling but also copious precipitation of water and snow on the continents.

We can see immediately that De Marchi's idea is sound in principle. Although water vapour and mist absorb and emit much more heat than carbon dioxide, cloudy and misty days are invariably colder than clear sunny days of roughly the same time of year. What made ice ages "difficult to explain" via the cause of water vapour was the fact that neither De Marchi nor his contemporaries could have been aware of the increased seeding of low level cloud by increases in cosmic radiation, which wasn't discovered until more than 60 years later by Ney (1959). Nonetheless, the effect of volcanic ejecta was later to confirm the influence of atmospheric transparency on the atmospheric temperature at the surface.

 

Erroneous Arrhenius: Pseudoscience underpinned by a Litany of Error

In 1896, Svante Arrhenius published a paper on the effect of carbon dioxide on atmospheric temperature. Although some of his methods encompass a better understanding of statistics than I have often seen demonstrated in modern sciences, Arrhenius makes some remarkable statements. On the very first page of Arrhenius (1896) 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.

Now compare Arrhenius' claim with this statement of Fourier's taken from Fourier (1824; as translated in Burgess, 1837, p. 12):

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.

Fourier (1824; as translated in Burgess, 1837, p. 12) & Fourier (1827, p. 586-587) actually pointed out that for the air to act like the glass of De Saussure's experimental apparatus, based on reduced thermal conductivity relative to high visible transparency, layers of it would have to solidify so that it could restrict circulation. It is by this suppression of circulation, mentioned in Fourier (1824, 1827), that greenhouses retain their heat. Fourier (1824, 1827) does not even mention greenhouses much less attribute their mechanism to the heating of the atmosphere. Not only did Arrhenius (1896) misunderstand the mechanism of greenhouses, but he attributed his own misunderstanding to Fourier. Arrhenius (1906a) published in defense of his greenhouse theory, and the same year, Arrhenius (1906b) is much more carefully worded:

That the atmospheric envelopes limit the heat losses from the planets had been suggested about 1800 by the great French physicist Fourier. His ideas were further developed afterwards by Pouillet and Tyndall. Their theory has been styled the hot-house theory, because they thought that the atmosphere acted after the manner of the glass panes of hot-houses. Glass possesses the property of being transparent to heat rays of small wave lengths belonging to the visible spectrum; but it is not transparent to dark heat rays, such, for instance, as are sent out by a heated furnace or by a hot lump of earth. The heat rays of the sun now are to a large extent of the visible, bright kind. They penetrate through the glass of the hot-house and heat the earth under the glass. The radiation from the earth, on the other hand, is dark and cannot pass back through the glass, which thus stops any losses of heat, just as an overcoat protects the body against too strong a loss of heat by radiation. Langley made an experiment with a box, which he packed with cotton-wool to reduce loss by radiation, and which he provided, on the side turned towards the sun, with a double glass pane. He observed that the temperature rose to 113 (235 F.), while the thermometer only marked 14 or 15 (57 or 59 F.) in the shade. This experiment was conducted on Pike's Peak, in Colorado, at an altitude of 4200 m. (13,800 ft.), on September 9, 1881, at 1 hr. 4 min. p. M., and therefore at a particularly intense solar radiation. Fourier and Pouillet now thought that the atmosphere of our earth should be endowed with properties resembling those of glass, as regards permeability of heat. Tyndall later proved this assumption to be correct.

In addition to the misunderstanding and misattribution evinced, particularly by the last sentence in the quotation above, Arrhenius failed to acknowledge that Tyndall had confused opacity and absorption in his experimental design (eg. Tyndall, 1861, Frontispiece; 1864, p. 415; 1867, p. 412) and used the words interchangebly in his expression. Consequently Tyndall's experimental results, in not allowing for reflection, provide no empirical support for the degree of "absorption" claimed. Consequently this support Arrhenius claimed for his "Greenhouse Effect" does not exist in Tyndall's work beyond the observation that carbon dioxide is 30% more emissive than air (Tyndall, 1861, pp. 278-279). Moreover, Arrhenius' use of the overcoat analogy speaks to the insulative properties of an overcoat, which is precisely what De Saussure's experiment attributes to air via the thermal gradient observed. This is linked with conductive heat transfer rather than radiative transfer. It might seem that Arrhenius was still thinking of heat transfer strictly in terms of thermal conduction, as Herschel and Fourier did before him. Yet, instead of using Fourier's Law to calculate temperature via the conductive transfer of heat, Arrhenius (1896, p. 255) uses a variant of the Stephan-Boltzmann equation to calculate temperature variations via the radiative transfer of heat. Perhaps Arrhenius' understanding of the word, "radiation", lagged behind the evolution of this term's diction or perhaps Arrhenius believed that radiative heat transfer replaced Fourier's Law. He was keen to point out the obsolescence of Pouillet's work without so much as specifying what work he was referring to. In spite of Arrhenius' insistence on clinging to the long refuted idea of aethereal wave propagation (Arrhenius, 1906, pp. 154, 225), he takes Langley's figure for the temperature of space at absolute zero. Evidently, the nature of aether had changed since its refutation. In fact, the flurry of ad hoc arguments that accompanied the fragmentation of the aether hypothesis, after its refutation in 1887, led Trowbridge (1910) to exclaim that there was an aether for everything. Perhaps this rapid evolution of contemporary science played a role in the chaotic and seemingly contradictory melange of ideas that accompany Arrenius' work.

What is interesting, is that Arrhenius then shows that he completely understands Tyndall's error when he states:

Provisionally, we regard the air as a uniform envelope of the temperature θ and the absorption-coefficient α for solar heat; so that if A calories arrive from the sun in a column of 1 cm² cross section, αA are absorbed by the atmosphere and (1- α) reach the earth's surface. In the A calories there is, therefore, not included the part of the sun's heat which by means of selective reflexion in the atmosphere is thrown out towards space.

Arrhenius, in 1896, fully understands the significance of the reflected component of incident light, and so had to know that Tyndall erred by neglecting reflection in describing the opacity of carbon dioxide as "absorption". Determining the reflected component is essential because this, along with absorbed component, defines the emissivity of the material. Moreover, emissivity is what takes the Stephan-Boltzmann Equation beyond the imaginary black body of hypothetical physics. Arrhenius goes on to postulate a means of calculating the grey-body temperature of the crust, eliminating air temperature as "having no considerable interest" (Arrhenius, 1896, p. 256). Here, Arrhenius makes several unsubstantiated assumptions considering the values of coefficients, including the assignment of black body emissivity (unity) to the subaerial lithosphere of the earth. This is clearly incorrect, as the rocks and soils of the earth are neither all nor even mostly black. In fact, this particular assumption may reflect a confusion of opacity and absorptivity on the part of Arrhenius, as the crust is completely opaque on the scale considered.

Arrhenius (1896) goes on to add to that total conductive heat transfer, the radiative transfer component of total conductive heat transfer between the surface and the atmosphere, which already accounts for both kinetic and radiative components of heat flow. In doing so, he duplicates the component of heat flux radiated from the earth's surface to the atmosphere. This counterfeiting of energy allows the overall system heat flux to exceed the amount of overall heat flux available. In defending his work, Arrhenius (1906a) elaborates on this energy creation mechanism without addressing the fact that it is the consequence of duplicating a component of heat flux. This component of heat flux was already accounted for by the simple fact that Fourier's Law could not be isolated to purely kinetic heat transfer. If it is not enough that Arrhenius can't seem to address the basic physics, consider the following statement:

Die Ansicht, dass eine Kohlensaureabnahme der luft die Temperatur einer Eiszeit erklaren kann, wird nicht eher als unhaltbar erweisen, als bis man zeigt, dass das vollkommene Verschwinden der Kohlensaure aus der Atmosphare nicht genugend ware, um eine Temperaturabnahme von vier bis funf Grad hervorzurufen.

Gerlich & Tscheuschner (2007, p. 56) translate this passage as follows:

The opinion that a decrease of carbonic acid in the air can explain ice-age temperatures is not proved wrong until it is shown, that the total disappearance of carbonic acid from the atmosphere would not be sufficient to cause a lowering of temperatures about four to five degrees.

It is unscientific to say that an idea is true until such time as it is proven wrong and to suggest an unmeetable condition for falsification of a scientific idea is extreme sophistry. The onus of proof rests firmly upon the proposer of a hypothesis, not with it's refutation. Every scientist understands this, and arguing as Arrhenius did in the above quotation, without the repeated confirmation of the idea (as opposed to its underlying principles) constitutes not just fallacy or sophistry, but scientific dishonesty. Moreover, the conditions Arrhenius has set for the refutation of his idea are scientifically impossible to achieve, unless by some dark art it is possible to remove all atmospheric carbon dioxide from the planet. Arrhenius, by imposing an impossible condition for falsification has tacitly admitted that his "Greenhouse Effect" is not falsifiable. We may take this statement of Arrhenius (1906a) as a clear indication that the "Greenhouse Effect" is simply not science. In fact, this is the first clear evidence that the "Greenhouse Effect" is a hoax.

 

Ångström, Ruben, & Ladenburg: Spectroscopic Saturation

Ångström (1900) describes a variation of Tyndall's experiment with a minor refinement. In this experiment, infrared radiation is passed through a tube of containing significantly less CO₂ than that of an equivalent column extending from top to bottom of the atmosphere. Like Tyndall, Ångström (1900) did not measure reflection and so could not venture a plausible figure for absorption or emissivity. Initially, 90% of the infrared radiation was transmitted by the CO₂, and when the amount of CO₂ was reduced by a third (via pressure variation), the amount of radiation transmitted by the gas mixture increased by less than 0.5% to 90.4%. Ruben & Ladenburg (1905), underpinning Arrhenius (1906a), made a much more detailed study of CO₂ emissivity over a range of combustion temperatures at 100ºC and above. Their results, documenting a maximum CO₂ absorptivity for 100ºC at 0.169 or 16.9%, were later confirmed by Hottel (1954), Leckner (1972), Farag (1976), Farag & Allam (1981), and Lallemant et al. (1996). As it turns out, even 100ºC is a little high for regional tropospheric temperatures, and so the results of Ångström stand.

The results of Ångström's experiment are twofold:

1. CO₂ is transparent to 90% of infrared radiation applicable to temperature variation.
2. Those infrared bands that CO₂ readily obstructs are already almost totally blocked by atmospheric CO₂

This finding shows the insignificance of second claim of the "Greenhouse Effect", which asserts that infrared radiated from the earth is trapped by greenhouse gases. Moreover, the findings of Ångström (1900) demonstrate that adding CO₂ to the atmosphere could not cause a measurable variation in the amount of heat transmitted by the atmosphere, because in the specific infrared bands obstructed by CO₂, the obstruction is already almost total. Thus increasing the amount of CO₂ in the atmosphere cannot measurably change the amount of radiation absorbed by the atmosphere. Thus we may conclude from Ångström's results that adding CO₂ to the present concentrations in the atmosphere will have no measurable effect on infrared radiation levels at the ground, nor on the amount of radiation absorbed by the atmosphere.

 

Robert Wood's decisive Experiment

In 1909, Robert W. Wood conducted an experiment to test the core proposition of the greenhouse hypothesis: that the internal air temperature of a greenhouse is raised by the trapping of long wave radiation converted from the absorption of light passing through the glass. Wood (1909) in a paper titled, “Note on the Theory of the Greenhouse”, is eloquent, concise, clear, and cogent. It is worth reproducing here:

XXIV. Note on the Theory of the Greenhouse
By Professor R. W. Wood (Communicated by the Author)

There appears to be a widespread belief that the comparatively high temperature produced within a closed space covered with glass, and exposed to solar radiation, results from a transformation of wave-length, that is, that the heat waves from the sun, which are able to penetrate the glass, fall upon the walls of the enclosure and raise its temperature: the heat energy is re-emitted by the walls in the form of much longer waves, which are unable to penetrate the glass, the greenhouse acting as a radiation trap.

I have always felt some doubt as to whether this action played any very large part in the elevation of temperature. It appeared much more probable that the part played by the glass was the prevention of the escape of the warm air heated by the ground within the enclosure. If we open the doors of a greenhouse on a cold and windy day, the trapping of radiation appears to lose much of its efficacy. As a matter of fact I am of the opinion that a greenhouse made of a glass transparent to waves of every possible length would show a temperature nearly, if not quite, as high as that observed in a glass house. The transparent screen allows the solar radiation to warm the ground, and the ground in turn warms the air, but only the limited amount within the enclosure. In the "open," the ground is continually brought into contact with cold air by convection currents.

To test the matter I constructed two enclosures of dead black cardboard, one covered with a glass plate, the other with a plate of rock-salt of equal thickness. The bulb of a thermometer was inserted in each enclosure and the whole packed in cotton, with the exception of the transparent plates which were exposed. When exposed to sunlight the temperature rose gradually to 65ºC., the enclosure covered with the salt plate keeping a little ahead of the other, owing to the fact that it transmitted the longer waves from the sun, which were stopped by the glass. In order to eliminate this action the sunlight was first passed through a glass plate.

There was now scarcely a difference of one degree between the temperatures of the two enclosures. The maximum temperature reached was about 55ºC. From what we know about the distribution of energy in the spectrum of the radiation emitted by a body at 55º, it is clear that the rock-salt plate is capable of transmitting practically all of it, while the glass plate stops it entirely. This shows us that the loss of temperature of the ground by radiation is very small in comparison to the loss by convection, in other words that we gain very little from the circumstance that the radiation is trapped.

Is it therefore necessary to pay attention to trapped radiation in deducing the temperature of a planet as affected by its atmosphere? The solar rays penetrate the atmosphere, warm the ground which in turn warms the atmosphere by contact and by convection currents. The heat received is thus stored up in the atmosphere, remaining there on account of the very low radiating power of a gas. It seems to me very doubtful if the atmosphere is warmed to any great extent by absorbing the radiation from the ground, even under the most favourable conditions.

I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention to the fact that trapped radiation appears to play but a very small part in the actual cases with which we are familiar.

The fact that the diathermic greenhouse outperformed the glass greenhouse in the first stage of the experiment shows that heat absorbed by the upper medium is not simultaneously emitted and absorbed to the lower medium, as suggested by Arrhenius (1906a). The glass, by absorbing more heat than the halite, leaves less heat available for the air and cardboard below the glass. Therefore, the temperature of the air in the glass greenhouse is lower than that in the diathermic halite greenhouse. By this, we may infer that increasing absorption in the stratosphere, by injecting more thermally absorbent materials such as volcanic ash, SO₂, water vapour, or even CO₂ will raise upper atmospheric heat by absorbing radiation destined for the surface, thereby reducing the heat at the surface and, as a consequence, causing surface temperatures to fall. Wood's Note on the Theory of the Greenhouse is, far from the shallow exploration he claims, the basis for a devastating refutation of the "Greenhouse Effect".

 

Abbot Replies to Wood

Wood (1909) drew only a single letter in answer to his Note on the Theory of the Greenhouse, and that was from Abbot (1909). Abbot's response was to corroborate Wood's finding and then attempt to reconcile these with atmospheric conditions via a series of calculations and contemporary observations. Abbot establishes that although the range of variation may increase with loss of absorbing gases, such as carbon dioxide and water vapour, the average temperature would be unaffected. Thus Abbot reconciles the views of Wood with the views of Frankland and Tyndall. Arrhenius' Greenhouse Effect", beyond the temperature moderating concept of Frankland and Tyndall, was implicitly refuted by Abbot (1909). Not one author has since refuted Wood, and those that cite Wood do so to underpin other ideas or confirm Wood's finding. It is significant that Arrhenius, being a subscriber to the same journal as Wood, did not reply to defend his "Greenhouse Effect" against the simple empirical demolition to which it had fallen victim, nor did Arrhenius publically reply to Abbot's more theoretical approach. If anything, the obsolescence of Abbot's method explained the difference between Abbot's calculated average temperature and that observed. Using more accurate information than Abbot had access to, we may now calculate a mean temperature for the absorbing portion of planet earth that is very close to what we actually observe. Arrhenius and his "Greenhouse Effect" were subsequently and politely forgotten by authors in physics (eg. Bejan & Kraus, 2003) and in the history of geology (eg. Hallam, 1989) in spite of the fact that Arrhenius made major claims concerning thermodynamics and the origin of ice ages.

 

Conclusion

Of all the authors associated with the "Greenhouse Effect", Svante Arrhenius stands at the centre of greenhouse debate because the "Greenhouse Effect" was not conceived by Fourier, as Arrhenius (1896) insinuates, but by Arrhenius himself. In fact, Arrhenius attributed his own erroneous mechanism of greenhouse warming to the atmosphere, and then claimed the idea was Fourier's. Yet Fourier considered and rejected the comparison, based on a far sounder understanding of how greenhouses work. My remarks concerning the misquotation of Fourier's work are not the first. In Fleming (1999) we read:

The central role that the theory of terrestrial temperatures played in Fourier's mathematical physics has not received the attention it deserves from historians, although his cryptic allusions to the heating of a greenhouse, taken out of context, have been widely cited by subsequent authors.

Arrhenius went on to claim that Tyndall's findings concerning the so-called "absorption" of heat by CO₂ "proved" this "Greenhouse Effect" when Tyndall's findings simply confirmed the thermal opacity of CO₂ and in the absence of corresponding reflectivity measurements could say nothing whatsoever about the thermal absorptivity of CO₂. By Arrhenius' own admission he knew the significance of the reflected component of radiation (Arrhenius, 1896, p. 255), and so he could not have but understood the irrelevance of Tyndall's findings to his "Greenhouse Effect", given that Tyndall clearly neglects reflection when speculating on absorption as the compliment of transmission. Arrhenius goes on to invoke an energy creation mechanism by duplicating the surface to atmosphere radiative transfer component of the surface to atmosphere heat transfer total, already governed by thermal conductivity via Fourier's Law.

Having reviewed the literature we may revisit and test the three principles and subsequent claim of Arrhenius' "Greenhouse Effect":

1. That a substantial proportion of light is converted to infrared by relay (ie. by absorption & re-emission).
   This is confirmed to a large degree by Herschel (1800c, 1800d).
    
2. That radiative transfer plays the dominant role in the transfer of heat from the surface to the atmosphere - to the near exclusion of other modes of heat transfer.
   This had already been refuted by the results of Tyndall's ice slab experiment (Tyndall, 1864, p. 266), and was subsequently demolished by Wood (1909).
    
3. That the CO₂ in the atmosphere is substantially more transparent to incoming radiation than to outgoing radiation.
   Angstrom (1900) showed that CO₂ has only a minor (<10%) range of opacity to infrared.
    

• Thus, according to Arrhenius, the consequence of these principles is that any reduction in atmospheric CO₂ concentration reduces air temperature - which explains ice ages.
  Kirchhoff (1859, 1860) found that increases in absorbivity equally raise emissivity. Thus, by using Kirchhoff (1859, 1860) to extend Boltzmann (1884) to the effects of incident radiation on temperature, changes in absorptivity or emissivity alone cannot possibly influence body temperature. Thus in a body of two parts, such a system dictates that a temperature increase in one part of the body is accompanied by a temperature decrease in the other part of the body. This predicts that increasing atmospheric absorption will reduce surface temperatures, a fact proposed by de Marchi (1895), confirmed experimentally by Wood (1909), and proven by the impact of volcanic sulphate aerosols on surface temperature, first observed by Abbot (1913). See the simplified falsification of the "Greenhouse Effect" for more information on the standing of the "Greenhouse Effect" in the frame of physics.

Thus is the "greenhouse effect" historically falsified, both in principle and in fact. It should come as no surprise that This hypothesis of ice age mechanisms came to be so casually refuted, that neither it nor it's originator even rate a mention in Hallam (1989), a history of significant geological contoversies with an entire chapter devoted to "The Ice Age". The "Greenhouse Effect" is not even mentioned in passing by Bejan & Kraus (2003), an extensive textbook devoted entirely to the physics of heat transfer. Gerlich & Tscheuschner (2007, 2009), who have surveyed many such textbooks, go on to point out that the "Greenhouse Effect" does not appear in physics textbooks because it does not exist in the frame of physics. It is upon Arrhenius' litany of error, misunderstanding, and misattribution replete with a pseudoscientific reversal of the onus of proof that the cornerstone of Anthropogenic Global Warming is based. After all, without the now shattered "Greenhouse Effect", how can "Anthropogenic Global Warming" be honestly described as Anthropogenic?

 

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