The Shattered Greenhouse: How Simple Physics Demolishes the
"Greenhouse Effect".
The Shattered Greenhouse: How Simple Physics Demolishes the
"Greenhouse Effect".
Timothy Casey B.Sc. (Hons.)Consulting Geologist
First Uploaded ISO: 2009-Oct-13Revision 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 107C, 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 rntgen 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
0.125C, or one eighth of a degree Celsius at the earth's surface,
offset by a cooling of 0.125C 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 0.004C.
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 bodyWi = Radiation (heat flux) in
Wm-2 incident upon the body in questionWe = Radiation (heat flux)
in Wm-2 emitted by the body in questionT = Absolute Temperature in
K of the body in question = Emissivity = Absorption / (Absorption +
Reflection) of the body in question = Stefan's Constant =
0.000000056704Wm = Mean incidence of radiation over the entire
surface of the body in Wm-2Ax = Mean cross-sectional area of
radiation incident on the body in m2At = Topographical area of the
body in m2Wb = T4 Stefan's Law relating black body radiation to
temperature (Stefan, 1879)We = Wb Emissivity is the proportion of
hypothetical black body radiation emittedWb = Wi And at thermal
equilibrium, black body radiation is equal to incident radiationWe
= Wi Ergo emissivity is also the proportion of incident radiation
emittedWe = T4 As the Stefan-Boltzmann Equation (Boltzmann, 1884)
elaborates on emitted radiation:Wi = T4Thus a body's temperature
response to incident radiation is entirely independent of
emissivity, such that
Wi = T4This 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 = T4Wm = WiAx/AtWm = T4As 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 65C or 338K (Wood, 1909). Applying the Stefan-Boltzmann
equation as shown above, to the relationship between incident
radiation and body temperature we may determine from:Wm = T4That:Wm
= 0.000000056704 x 3384Wm = 740 Wm-2Now, 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/}0.25Given Wm = 888 Wm-2:T = {888/0.000000056704}0.25 = 353.8K
= 80.6C
As you can see, Arrhenius' hypothetical backradiation should
raise the glass greenhouse temperature 15C 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 55C or 328K.
Thus the radiation incident on the bottom of the halite greenhouse
is as follows:Wm = T4That:Wm = 0.000000056704 x 3284Wm = 656
Wm-2Allowing for additional 20% of backradiation gives us Wm = 788
Wm-2 in the glass greenhouse, predicting:T = {Wm/}0.25Given Wm =
788 Wm-2:T = {788/0.000000056704}0.25 = 343.3K = 70.2C
Once again, the backradiation hypothesis predicts a temperature
difference of 15C 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 (Frhlich & 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 = T4T4 = Wm/T = {Wm/}0.25Given Wm = 342:T =
{342/0.000000056704}0.25 = 278.7K = 5.5C
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
5.5C 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 -7C 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 11C per mile, and we all know that the
average surface temperature is 15C (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 4C or 277K. This,
via the reasoning above, extends to an observed average absorbing
mass temperature for planet earth of 4C or 277K. This is slightly
cooler than the mean absorbing mass temperature calculated above
from the solar constant (278.7K, 5.5C) even if we do allow for 0.5
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 11C per mile we got
from Vallier-Talbot (2007) above, our temperature (278.7K, 5.5C),
calculated from the Stefan-Boltzmann Equation using the Solar
Constant, yields a calculated surface temperature of around 16.5C.
The fact that this is warmer than the observed mean surface
temperatures of Arrhenius and Burroughs (15C) 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 (16.50.5C corresponding to 16-17C) 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 20.9C higher than
that yielded by a calculation such as this, owing to the carbon
dioxide in the atmosphere. The observed surface temperature of 15C
(Arrhenius, 1896; Burroughs, 2007) is actually 1-2C lower than the
calculated mean surface temperature of 16-17C. 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 15C mean surface temperature and the 113C
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/}0.25Given Wm = 1368:T = {1368/0.000000056704}0.25 =
394.1K = 121.0C
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 394.1K or 121.0C 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 ArrheniusWhose physics were rather
erroneousHe recycled raysIn peculiar waysAnd 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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