\subsection{Different versions of the atmospheric greenhouse conjecture}
\label{Sec:Versions}
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%
\subsubsection{Atmospheric greenhouse effect after M\"oller (1973)}
%
In his popular textbook on meteorology\TschSpace%
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\cite{Moeller1973a,Moeller1973b}
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M\"oller claims: 
%
\begin{quote}
\lq\lq
In a real glass house (with no additional heating, 
i.e.\ no greenhouse) the window panes are transparent 
to sunshine, but opaque to terrestrial radiation. 
The heat exchange must take place through 
heat conduction within the glass, 
which requires a certain temperature gradient. 
Then the colder boundary surface of the window 
pane can emit heat. In case of the atmosphere 
water vapor and clouds play the role of the glass.\rq\rq \end{quote}
%
\textbf{Disproof:}
The existence of the greenhouse effect is considered 
as a necessary condition for thermal conductivity. 
This is a physical nonsense.
Furthermore it is implied that the spectral transmissivity
of a medium determines its thermal conductivity
straightforwardly. 
This is a physical nonsense as well.
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%
\subsubsection{Atmospheric greenhouse effect after Meyer's encyclopedia (1974)}
%
In the 1974 edition of Meyer's Enzyklop\"adischem Lexikon 
one finds under \lq\lq glass house effect\rq\rq\TschSpace%
%
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\cite{Meyers1974}:
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%
\begin{quote}
\lq\lq
Name for the influence of the Earth's atmosphere 
on the radiation and heat budget of the Earth,
which compares to the effect of a glass house:
Water vapor and carbon dioxide in the atmosphere
let short wave solar radiation go through
down to the Earth's surface with a relative weak 
attenuation and, however, reflect the portion of
long wave (heat) radiation  which is emitted from the 
Earth's surface (atmospheric backradiation).\rq\rq
\end{quote}
%
\textbf{Disproof:}
Firstly, 
the main part of the solar radiation 
lies outside the visible light.
Secondly, 
reflection is confused with emission. 
Thirdly, 
the concept of atmospheric backradiation relies
on an inappropriate application of the formulas 
of cavity radiation. This will be discussed in
Section~\ref{Sec:Radiation}
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%
\subsubsection{Atmospheric greenhouse effect after Sch\"onwiese (1987)}
%
The prominent climatologist Sch\"onwiese
states\TschSpace% 
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\cite{Schoenwiese1987}:
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%
\begin{quote}
\lq\lq
$\dots$ we use the picture of a glass window
that is placed between the Sun and the Earth's surface.
The window pane lets pass the solar radiation unhindered 
but absorbs a portion of the heat radiation of the Earth.
The glass pane emits, corresponding to its own temperature,
heat in both directions: To the Earth's surface and to the
interplanetary space. Thus the radiative balance of the
Earth's surface is raised. 
The additional energy coming from the glass pane 
is absorbed almost completely by the Earth's surface
immediately warming up until a new radiative equilibrium
is reached.\rq\rq
\end{quote}
%
\textbf{Disproof:}
That the window pane lets pass the solar 
radiation unhindered is simply wrong.
Of course, some radiation goes sidewards.
As shown experimentally in 
Section~\ref{Sec:Experiments},
the panes of the car window are relatively cold.
This is only one out of many reasons, 
why the glass analogy is unusable.
Hence the statement is vacuous.  
%
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%
\subsubsection{Atmospheric greenhouse effect after Stichel (1995)}
\label{Sec:Stichel1995}
%
Stichel
(the former deputy head of the German Physical Society)
stated once\TschSpace%
% 
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\cite{Stichel1995}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
\begin{quote}
\lq\lq
Now it is generally accepted textbook knowledge 
that the long-wave infrared radiation, emitted 
by the warmed up surface of the Earth, is 
partially absorbed and re-emitted by ${\rm CO}_2$ 
and other trace gases in the atmosphere. 
This effect leads to a warming of the lower 
atmosphere and, for reasons of the total 
radiation budget, to a cooling of the 
stratosphere at the same time.\rq\rq
\end{quote}
%
\textbf{Disproof:}
This would be a 
\textit{Perpetuum Mobile of the Second Kind}.
A detailed discussion is given in 
Section~\ref{Sec:Thermodynamics}.
Furthermore, there is no total radiation budget,
since there are no individual conservation laws 
for the different forms of energy participating 
in the game. The radiation energies in question 
are marginal compared to the relevant geophysical 
and astrophysical energies.
Finally, the radiation depends on the temperature
and not \textit{vice versa}.
%
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%
\subsubsection{Atmospheric greenhouse effect after Anonymous 1 (1995)}
\label{Sec:WaterPot}
%
\begin{quote}
\lq\lq
The carbon dioxide in the atmosphere lets the radiation
of the Sun, whose maximum lies in the visible light, 
go through completely, while on the other hand 
it absorbs a part of the heat radiation emitted by the Earth 
into space because of its larger wavelength. 
This leads to higher near-surface air temperatures.\rq\rq
\end{quote}
%
\textbf{Disproof:}
The first statement is incorrect 
since the obviously non-neglible infrared part of the 
incoming solar radiation is being absorbed
(cf.\ Section~\ref{Sec:SunBlackBody}).
The second statement is falsified
by referring to a counterexample
known to every housewife:
The water pot on the stove.
Without water filled in, the bottom of the pot
will soon become glowing red. Water is an excellent
absorber of infrared radiation. However, with water
filled in, the bottom of the pot will be substantially 
colder. Another example would be the replacement of the 
vacuum or gas by glass in the space between two panes.
Conventional glass absorbs infrared radiation pretty well,
but its thermal conductivity shortcuts any thermal isolation. 
%
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%
\subsubsection{Atmospheric greenhouse effect after Anonymous 2 (1995)}
%
\begin{quote}
\lq\lq
If one raises the concentration of carbon
dioxide, which absorbs the infrared light 
and lets visible light go through, in the 
Earth's atmosphere, the ground heated by the 
solar radiation and/or near-surface air 
will become warmer, 
because the cooling of the ground 
is slowed down.\rq\rq 
\end{quote}
%
\textbf{Disproof:}
It has already been shown in 
Section~\ref{Sec:Background}
that the thermal conductivity is changed
only marginally even by doubling the 
${\rm CO}_2$ concentration in the Earth's
atmosphere. 
%
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%
\subsubsection{Atmospheric greenhouse effect after Anonymous 3 (1995)}
%
\begin{quote}
\lq\lq
If one adds to the Earth's atmosphere a gas,
which absorbs parts of the radiation of the 
ground into the atmosphere, the surface temperatures 
and near-surface air temperatures will become
larger.\rq\rq
\end{quote}
%
\textbf{Disproof:}
Again, the counterexample is the water pot on the stove;
see 
Section~\ref{Sec:WaterPot}.
%
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%
\subsubsection{Atmospheric greenhouse effect 
               after German Meteorological Society (1995)}
%
In its 1995 statement, the German Meteorological Society says\TschSpace%
% 
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\cite{DMG1995}:
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%: 
%
\begin{quote}
\lq\lq
As a point of a departure the radiation budget 
of the Earth is described. 
In this case the incident unweakened solar radiation 
at the Earth's surface is partly absorbed and partly 
reflected.
The absorbed portion is converted into heat and 
must be re-radiated in the infrared spectrum. 
Under such circumstances simple model calculations 
yield an average temperature of about $-18^\circ{\rm C}$
at the Earth's surface
$\dots$
Adding an atmosphere, the incident radiation 
at the Earth's surface is weakened only 
a little, because the atmosphere is essentially 
transparent in the visible range of the spectrum. 
Contrary to this, in the infrared range of the 
spectrum the radiation emitted form the ground 
is absorbed to a large extent by the atmosphere 
$\dots$ 
and, depending on the temperature, re-radiated 
in all directions.
Only in the so-called window ranges 
(in particular in the large atmospheric window 
$8$\,-\,$13$\,$\mu{\rm m}$) 
the infrared radiation can escape into space. 
The infrared radiation that is emitted downwards 
from the atmosphere (the so-called back-radiation) 
raises the energy supply of the Earth's surface.   
A state of equilibrium can adjust itself 
if the temperature of the ground is rises and, 
therefore, a raised radiation according to 
Planck's law is possible. 
This undisputed natural Greenhouse effect 
gives rise to an increase temperature of the 
Earth's surface.\rq\rq
\end{quote}
%
\textbf{Disproof:}
The concept of an radiation budget 
is physically wrong.
The average of the temperature 
is calculated incorrectly. 
Furthermore, an non-neglible 
portion of the incident solar radiation 
is absorbed by the atmosphere. 
Heat must not be confused with heat radiation.
The assumption that if gases emit 
heat radiation, they will emit it  
only downwards is rather obscure. 
The described mechanism of re-calibration 
to equilibrium has no physical basis.
The laws of cavity radiation do not apply 
to fluids and gases.
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%
\subsubsection{Atmospheric greenhouse effect after Gra\ss l (1996)}
%
The former director of the 
World Meteorological Organization (WMO)
climate research program, 
Professor Hartmut Gra\ss l, 
states\TschSpace%
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\cite{Grassl1996}:
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%
\begin{quote}
\lq\lq
In so far as the gaseous hull [of the Earth] obstructs 
the propagation of solar energy down to the planet's surface 
less than the direct radiation of heat from the surface 
into space, the ground and the lower atmosphere must 
become warmer than \textit{without this atmosphere}, in order 
to re-radiate as much energy as received from the Sun.\rq\rq
\end{quote}
%
\textbf{Disproof:} 
This statement is vacuous, even in a literal sense.
One cannot compare the temperature of a planet's 
lower atmosphere with the situation where a planetary 
atmosphere does not exist at all. 
Furthermore, as shown in
Section~\ref{Sec:SunBlackBody}
the portion of the incoming infrared is larger 
than the portion of the incoming visible light.
Roughly speaking, we have a fifty-fifty relation.
Therefore the supposed warming from the bottom
must compare to an analogous warming from the top.
Even within the logics of Gra\ss l's oversimplified 
(and physically incorrect) conjecture one is left 
with a zero temperature gradient and thus a null effect.
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%
\subsubsection{Atmospheric greenhouse effect after 
               Ahrens (2001)}
%
In his textbook 
\lq\lq Essentials in Meteorology:
       In Invitation to the Atmosphere\rq\rq\
the author Ahrens states\TschSpace%
%
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\cite{Ahrens2001}:
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%
\begin{quote}
\lq\lq 
The absorption characteristics of water vapor, 
${\rm CO}_2$,
and other gases such as methane and nitrous oxide
$\dots$
were, at one time, thought to be similar to the
glass of a florist’s greenhouse. In a greenhouse, 
the glass allows visible radiation to come in, 
but inhibits to some degree the passage 
of outgoing infrared radiation. 
For this reason, 
the behavior of the water vapor and 
${\rm CO}_2$,
the atmosphere is popularly called the greenhouse
effect. However, studies have shown that the warm air
inside a greenhouse is probably caused more by the air’s
inability to circulate and mix with the cooler outside air,
rather than by the entrapment of infrared energy. Because
of these findings, some scientists insist that the
greenhouse effect should be called the atmosphere effect.
To accommodate everyone, we will usually use the term
atmospheric greenhouse effect when describing the role
that water vapor and 
${\rm CO}_2$,
play in keeping the earth’s
mean surface temperature higher than it otherwise
would be.\rq\rq
\end{quote}
%
\textbf{Disproof:}
The concept of the Earth's 
mean temperature is ill-defined.
Therefore the concept of a rise 
of a mean temperature 
is ill-defined as well.
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%
\subsubsection{Atmospheric greenhouse effect after 
               Dictionary of Geophysics, Astrophysics,
               and Astronomy (2001)}
%
The Dictionary of Geophysics, Astrophysics,
and Astronomy says\TschSpace%
%
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\cite{DictionaryGeophysicsAstronomyAstrophysics2001}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{quote}
\lq\lq 
Greenhouse Effect: The enhanced warming
of a planet’s surface temperature caused by the
trapping of heat in the atmosphere by certain
types of gases 
(called greenhouse gases; primarily
carbon dioxide, water vapor, methane,
and chlorofluorocarbons). 
Visible light from the sun 
passes through most atmospheres and is absorbed
by the body'’s surface. The surface reradiates
this energy as longer-wavelength infrared
radiation (heat). If any of the greenhouse gases
are present in the body'’s troposphere, the atmosphere
is transparent to the visible but opaque to
the infrared, and the infrared radiation will be
trapped close to the surface and will cause the
temperature close to the surface to be warmer
than it would be from solar heating alone.\rq\rq
\end{quote}
%
\textbf{Disproof:}
Infrared radiation is confused with heat.
It is not explained at all what is meant by 
\lq the infrared radiation will be trapped\rq\rq.
Is it a MASER, 
is it \lq\lq superinsulation\rq\rq,
i.e.\ vanishing thermal conductivity,
or is it simple thermalization?
%  
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%
\subsubsection{Atmospheric greenhouse effect after 
               Encyclopaedia of Astronomy and Astrophysics (2001)}
%
The Encyclopaedia of Astronomy and Astrophysics 
defines the greenhouse effect as follows\TschSpace%  
%
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\cite{EncyclopaediaAstronomyAndAstrophysics2001}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{quote}
\lq\lq
The greenhouse effect is the radiative influence exerted by
the atmosphere of a planet which causes the temperature
at the surface to rise above the value it would normally
reach if it were in direct equilibrium with sunlight 
(taking into account the planetary albedo). 
This effect stems from the fact 
that certain atmospheric gases have the ability
to transmit most of the solar radiation and to absorb
the infrared emission from the surface. 
The thermal (i.e.\ infrared) radiation 
intercepted by the atmosphere is then
partially re-emitted towards the surface, 
thus contributing additional heating of the surface.
Although the analogy is not entirely satisfactory in
terms of the physical processes involved, it is easy to
see the parallels between the greenhouse effect in the
atmosphere-surface system of a planet and a horticultural
greenhouse: the planetary atmosphere plays the role of the
glass cover that lets sunshine through to heat the soil 
while partly retaining the heat that escapes from the ground.
The analogy goes even further, since an atmosphere may
present opacity \lq windows\rq\ allowing infrared radiation
from the surface to escape, the equivalent of actual
windows that help regulate the temperature inside a
domestic greenhouse.\rq\rq
\end{quote}
%
\textbf{Disproof:}
The concept of the 
\lq\lq direct equilibrium with the sunlight\rq\ 
is physically wrong, 
as will be shown in detail in 
Section~\ref{Sec:RadiativeBalance}.
The description of the physics of a horticultural 
greenhouse is incorrect. Thus the analogy stinks. 
%  
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%
\subsubsection{Atmospheric greenhouse effect after 
               Encyclopaedia Britannica Online (2007)}
%
Encyclopaedia Britannica Online 
explains the greenhouse effect 
in the following way\TschSpace%
%
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\cite{BritanicaOnline2007}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{quote}
\lq\lq
The atmosphere allows most of the visible light 
from the Sun to pass through and reach the 
Earth's surface. As the Earth's surface 
is heated by sunlight, it radiates part 
of this energy back toward space as 
infrared radiation. This radiation, 
unlike visible light, tends to be 
absorbed by the greenhouse gases 
in the atmosphere, raising its temperature. 
The heated atmosphere in turn radiates 
infrared radiation back toward the 
Earth's surface. (Despite its name, 
the greenhouse effect is different 
from the warming in a greenhouse, 
where panes of glass transmit visible 
sunlight but hold heat inside the 
building by trapping warmed air.) 
Without the heating caused by the 
greenhouse effect, the Earth's average 
surface temperature would be only about 
$-{\rm 18}\,^\circ{\rm C}$ ($0\,^\circ{\rm F}$).\rq\rq
\end{quote}
%
\textbf{Disproof:}
The concept of the Earth's average temperature
is a physically and mathematically ill-defined 
and therefore useless concept as will be shown 
in 
Section~\ref{Sec:RadiativeBalance}.
%  
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%
\subsubsection{Atmospheric greenhouse effect after Rahmstorf (2007)}
%
The renowned German climatologist Rahmstorf claims\TschSpace%
%
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\cite{Rahmstorf2007}:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%
\begin{quote}
\lq\lq
To the solar radiation reaching Earth's surface 
$\dots$ 
the portion of the long-wave radiation is added, 
which is radiated by the molecules partly downward
and partly upward. Therefore more radiation arrives
down, and for reasons of compensation the surface 
must deliver more energy and thus has to be warmer
($+15\,^\circ{\rm C}$), 
in order to reach also there down again an equilibrium. 
A part of this heat is transported upward from the surface 
also by atmospheric convection. Without this natural 
greenhouse effect the Earth would have frozen life-hostilely 
and completely. 
The disturbance of the radiative balance 
[caused by the enrichment of the atmosphere with trace gases] 
must lead to a heating up of the Earth's surface, 
as it is actually observed.\rq\rq
\end{quote}
%
\textbf{Disproof:}
Obviously, reflection is confused with emission.
The concept of radiative balance is faulty. 
This will be explained in 
Section~\ref{Sec:RadiativeBalance}.
%
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%
\subsubsection{Conclusion}
%
It is interesting to observe,
%
\begin{itemize}
\item that until today
      the \lq\lq atmospheric greenhouse effect\rq\rq\ 
      does not appear 
      \begin{itemize}
      \item in any fundamental work of thermodynamics,
      \item in any fundamental work of physical kinetics, 
      \item in any fundamental work of radiation theory;
      \end{itemize}
\item that the definitions given in the literature
      beyond straight physics are very different
      and, partly, \textbf{contradict} to each other.
\end{itemize}
%      
