Download And by using, the classical solution (equation 2a) in plane geometry

Rebuttal of the “Radiative Greenhouse Effect” Equations
by Pierre Beslu
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«Radiative Greenhouse Effect» (RGE) is based on the fact that the Infra-red radiation
(IR) emitted by the cold gas from the troposphere in direction of the earth surface
contribute to its warming [1]. But it is not because this process that the air inside an
actual greenhouse is warmer than the air outside. It’s the reason why, I precise
“radiative” when I spoke about the IPCC model. In spite of this naming mistake, for a
lot of people, this RGE is indispensable and their ultimate argument used in its favour
consists of saying that without it, the huge software (GCMs) are unable to explain the
warming observed. For the following, let us concede this argument even though it’s
logically insufficient.
In addition the scientists supporters of the theory declare that the simple models
presented even by them have not to be considered as being the truth; they are “just
pedagogical to explain to the “vulgum pecus” the RGE. Most of specialists recognize
that the described mechanisms are unable to explain the warming by the human
greenhouse gas emission. The main reason invoked by these devotees is the
precedence of the water (vs CO2) and the saturation of the phenomena. They
substitute a new model which does no longer appeal to the IR backscattering: the
“effective emission height” associated with the lapse rate. Despite this fundamental
change, not only they persist to call the process “greenhouse effect” but they don’t
change anything in the equations used in their more sophisticated models n GCMs1.
For them, there is finally no link between what they describe and the equations used
in the calculation models! The lack of modifications in the adopted equations or in the
limit conditions or in the input data “justify” from their point of view to not change an
(already) inadequate name! Philosophical questions: How do we manage to
establish equations that didn’t correspond to the description of the phenomena?
So it deserve to look closely at these equations if we don’t want to be in the same
situation than the Delphi pilgrims at the Apollo priests’ mercy to interpret what the
Pythia said.
2 The Classical equations of the Radiative Greenhouse
Effect (RGE)
The equations used in the GCMs model are the classical equation of radiative
transfer established in astrophysics for stellar atmosphere studies. They are applied to
the earth atmosphere without any adaptation.
Of course it’s a 3D problem and only a powerful computer is able to solve it numerically.
It is, in particular, impossible to avoid using it, if we want to obtain local results
(temperature, rain, sea level etc..) at a given time. But it is possible for the
understanding, to get trends and to approach average and global values, in using some
particular situations or limit cases as considering average values in space and time for
which we are very close to the equilibrium and in reducing the problem at two or one
dimensions to end at analytical solutions reflecting correctly the physical mechanisms
1
Giuseppe Tomasi di Lampedusa would say “Everything change in order to nothing change”!
1
taken into account. This way of doing generally allows the validation or the refutation of
the used models.
The premise generally adopted through these equations is that the heat exchange
driving the global equilibrium inside the troposphere, is radiative. In addition, the use of
the stellar troposphere approach leads to consider our atmosphere to be semi-infinite
with his origin at his Top (TOA).
To relate the total IR absorber amount to the flux densities the most suitable parameter is the
total IR flux optical depth [2]. We can derive this optical depth from the Planck law.
Unfortunately, this “works only with very small monochromatic optical depths. In the
Earth atmosphere the infrared monochromatic optical depth is varying many orders of
magnitude, therefore, the required criteria for the application of the Planck mean is not
satisfied. This problem can be eliminated without sacrificing accuracy by using the
simulated flux optical depth” [2]. With this approximation, the wave length dependence
doesn’t exist anymore and we can use the vertical mean optical depth in the equations.
Such optical depths may be computed from monochromatic directional transmittance by
integrating over the hemisphere. They tuned their line-by-line radiative transfer code [2], [3]
for an extreme numerical accuracy. And so it is possible to derive the negative natural
logarithms of these high accuracy Planck weighted hemispheric: A (TA)
τ is the optical thickness and the optical depth is generally defines by χ=χs-τ
(1)
with χs=τ∞. τ∞=∞ when we consider the atmosphere as semi-infinite and consequently
totally absorbent. If not, we substitute τA to τ∞.
Practically, the stratosphere can be ignored since most of the greenhouse gases (and
almost all of the most efficient of them, the water) is contained in the troposphere.
In addition, at the tropopause level, the entering IR flux (except for the one coming
directly from the sun) is negligible.
In a non-scattering atmosphere and applying the “gray approximation” with which the
mean vertical gray-body optical depth  takes the place of the “monochromatic” optical
depth the relationship between the source function B() and thenet radiative flux 
is given by
𝑑𝐵()
𝑑
=
3
4
(2)
The solution of this differential equation is 𝐵()
=
3
4
 + 𝐵0 a
Since an atmosphere layer is assimilated to a black body, its emission law is given as for the
earth surface, by B(T)=-1T4
(3)

I   cos d and F  
I   cos d be the upward flux and
Let us F 


hémispèreinf
hémisphèresup
downward flux, we have   F   F  

  I  cos dd
0
with  also the Eddington
4
flux
In a stationary phase, purely radiative, the net outgoing flux is equalto the entering visible
flux
=S0(1-A)/4.

the Kirchhoff law leads to the equation (4)
F    T 4  'e   d '
'
and (5)
We have also :
2
0
= F  + F 
4 
s
F  T e

  T 4  'e   ' d '
0
then ddand ddBSince we are in a stationary phase,dd
So we get =2B.
dd gives
Cte
And by using, the classical solution (equation 2a) in plane geometry, the source function for
a radiative transfer in an semi-infinite medium is B=2Cte=2B0
The limit condition is given by the situation that exists at the Top of the troposphere since
we know at this place the outgoing IR radiation flux. We have there F  =0 and also 
These conditions allow the determination of the constant B0 since we have : then
B0=Cte=et it comes the relatively simple equation
B

  1 (6)
2
In astrophysics, this expression is the Schwarzschild solution using the Eddington
approximation. With such references, we understand that the people who use this
solution, hesitate to reconsider it and they would be right if the earth was a star! Bur our
planet is not equivalent to the sun and this cannot be without consequences as we will
see it later.
From the previous equation, it comes for the temperature TA of the atmosphere at an
 
  1
altitude corresponding to  TA  
 2

1/ 4
surface temperature we get
(7), for the average earth
(8)
and for the air temperature
at the contact of the surface, we have of course
(9)
These equations, taught as driving the RGE, show effectively a direct dependence
between the earth surface and troposphere temperatures and the optical depth and
therefore with the anthropogenic Carbon dioxide.
But what is the value of the equations for our atmosphere? What do they
forecast with that?
With the most common data - the heat flux density received from the sun  and the one
emitted by the system «earth+atmosphere»i.e. the Outgoing Long Radiation:
OLR=S (1-A)/4=239,4 w/cm2, for the optical depth of the χ =1,868- the numerical
application gives :
0
T =300 °K= 27.7°C et
s
s
T =279°K=6°C
AS
The discrepancy with the observed surface temperature is significant.
But mainly, we must note the discontinuity between the soil and the atmosphere
temperature measured very close to -in contact with- the soil (or the sea surface). The
discrepancy is very large, 21.7°C !
Let us remark that if the medium is semi-infinite with the limit at its top, by definition there
is no boundary at any bottom! The position of considering nevertheless the earth surface
(soil and seas) as an inferior limit is therefore odd. We will return to that later.
3
The IR flux leaving the atmosphere namely the Outgoing Long wave Radiation( OLR ) at
TOA is given by the equation
OLR  T 4e
s



 '

   T 4e

d '
0
(10)
And with another definition of RGE given by several authors, the difference between the flux
emitted by the earth surface and the flux send in the space would be :
but
This last inequality is attributed at a missing flux due to the backscattering of the IR and
their absorption by the surface of the earth (and the surface of the oceans): with this
definition «The RGE blocks the outgoing IR radiation» and with the supposed
atmospheric feedback establish an actual cover regarding the IR flux. Thus due to the
reduction of the earth’s cooling, our planet is warming. Unfortunately, for this affirmation,
the satellite observations (ERBS) show the opposite!
In addition, with this “new” definition of the RGE given by G, for an isotherm atmosphere
and at a temperature of the surface (T =T ), the IR emission toward the space is the
same that the one without absorption: So there is no greenhouse effect for an isotherm
atmosphere. We are in presence of an inconsistency: RGE doesn’t exist if the
atmosphere is isotherm and this even if its temperature is warmer than our present
atmosphere, but it does exist if the atmosphere temperature slow down with altitude, all
other things being equal!!
s
A
The classical hypotheses and equations lead therefore to discrepancies and more to
several incoherencies called “modestly” paradoxes !
It’s clear than the basic equations used in the models presented by IPCC in their reports
don’t lead to valid and precise results. And their introduction in a 3D software that treats
a lot of others meteorological equations in general chaotic, will not change something at
these conclusions..
3 The general equation of radiative transfer
First let us note that our actual atmosphere is limited in the space and therefore is a finite
and semi-transparent medium (at least with the definition given for the average optical
depth). This is in agreement with the reality but in complete contradiction with the
classical approach. It’s also clear, the thermodynamic equilibrium being reached, at the
interface surface/air, both temperatures ts, tAS are equal : ts=tAS .
The equation (2) used in the classical model is always valid as well as the conditions at
TOA which require an entering IR flux F  =0 and also χ=0. On the contrary, a condition
at the inferior boundary is now perfectly defined and given by τa and ts=tAS. But this leads
to have two boundary conditions when we want to determine the complete solution of the
equation (2). This can be problematic if Bs is considered as an arbitrary parameter. To
solve this difficulty, we must impose a constraint to Bs.
Ferenc Miskolczi, in his paper « Greenhouse effect in semi-transparent planetary
Atmospheres »[2] solved the new equations which take into account these actual
conditions.
In [2], Ferenc Miskolczi writes (𝜏𝑎 )
4
= 2⁄(1 + 𝜏 + 𝑒 −𝜏𝑎 )
𝑎
(11)
where τa is the optical thickness of the atmosphere. He ends to the equation (12) which
is a little more complicated than the equation (2).
(12)
Miskolczi [2] call “general”, this equation because not only it has respect for the actual
boundary conditions but it also includes asymptotically the classical solution used in the
models (GCMs) with a semi-infinite atmosphere ; for τa=τ∞=, we find again the
equation (2).
Another essential characteristic is now that the IR flux (as the temperatures of the
atmosphere and in particular those of the TOAthe tropopause) given by B0 are linked with
the flux at the earth surface Bs(T)= Ts4.
Let us note that Bs can includes external energy source and therefore doesn’t depend
only upon the radiative exchanges. But, at the equilibrium, it must absolutely respect
the total energy balance of the system. It is, there, the constraint mentioned above.
To observe this requirement about Bs which is present in the second term of the
equation (6), we have to iterate.
3.1 Use of the general equation in purely radiative mode
In a first time, let us accept the main IPCC postulate and let us consider that the heat
exchange are purely radiative inside the atmosphere: To do so, apply the equation (12)
with an IR flux density emitted by the earth surface of 390 w/m 2[1] ; the excess (150
w/m2) compared to the solar irradiation (240 w/m 2) is therefore attributed at the IR
feedback of the troposphere that is to say the RGE.
The surface temperature then obtained from this application of the equation (12) is 9.5
°C which is less than the Global Average Annual Temperature given by all the institutes
(14.5-15°C). Moreover the energy balance is not equilibrated. To reach the required
equilibrium, the modification of Bs in equation (12) by iteration leads very quickly toward
a convergence and the final result gives a new flux density Bs=366.3 instead of 390 (or
396 value proposed by Trenberth in 2009) that is to say 24 to 30 w/m2 less! The
corresponding temperature at the earth surface (as the air temperature in contact) is
10.3°. The temperature at the Tropopause is 6 °C warmer than the one given for the
standard atmosphere by ISA at an altitude of 11km.
If there is no longer inconsistency, we are always far from the observed values.
In spite of these discrepancies and always with the hypothesis of a purely radiative
greenhouse effect, let us determine what increase of temperature the equation (12)
calculates for a CO2 atmospheric concentration doubling (from 400 to 800 ppm).
If we adopt the increase of absorption determined par F. Mickolzi in [3], this increase is of
0,46 °C.
Although we use the general equation and the actual boundaries to describe the
atmosphere to calculate the temperature increase provoked by a doubling of [CO 2], the
climate sensitivity is twice less than the one proclaimed by IPCC! Their apocalyptic
prediction become questionable.
5
Even with the new equations which are general and better appropriate, the agreement
between calculation results and observations was not good. These discrepancies reveals
that the choice to consider only radiative exchange is not sufficient to explain the
biosphere temperature. Something is still wrong!
3.2 Insertion of some thermodynamics in the system
It surprising that some physicists could think that heat exchanges between the earth and
its atmosphere could be only driven by the radiations. All the thermal engineers know
that, fluid and gas are much more efficient than radiations to warm or cool an object.
The equation (12) can’t be used on all the height of the troposphere unless the
thermodynamic enter by a way or another. The model of transfer in a pure radiative
mode can be applied without restriction only when the exchange are exclusively radiative
that is at TOA and pratically at the Top of the troposphere.
Of course, the term Bs includes the input of heat coming from the visible light of the sun
(and no reflected that is to say around 240 w.m-2) but we have to determine the origin of
the additional 150/160 w.m-2. We saw that IPCC attributes them to the back radiation
from the troposphere. It’s enough, yet, to look at any Trenberth diagram to observe that
the upward (surface radiation) and downward (back radiation) flux are practically equal:
their sum is almost zero. We observe also that the IR are not alone to exchange heat
between the earth with the atmosphere and inside this atmosphere. And the dependence
of the flux Bs cannot have for origin the radiation emission alone: geothermal flux,
certainly, increases very few Bs (around 0,03%), but the ocean has a much greater
influences and particularly the phenomena like el Niño or its opposite la Niña etc...
More generally, the surface temperature depends not only on the sun light but also on
advection, convection, evaporation, precipitations etc. And it is well known also that the
vertical temperature gradient (lapse rate) inside the troposphere is not determine by
radiative exchanges and is independent of the concentration of carbon dioxide : the
temperature decreases when we go up and when the air becomes rare and when we go
down, the air pressure increases and of course, the air temperature also increases. The
lapse rate Γ results from the first principle of thermodynamics : a gas volume with a mass
m and a temperature T situated at an altitude h has a total energy U which is the sum of
a gravitational and thermal energy. Because, in the troposphere we are in a Local
Thermodynamic Equilibrium (LTE), this amount of energy is constant and we have
therefore:
U=mC T+mgh et
dU= mC .dT+mg.dh=0 d’où dT/dh=-g/C =Γ
p
p
p
With the heat capacity of the dry air Cp=1006 J/(kg.K) and the gravity of earth g = 9,8
m/s², we get a lapse rate value Γ=-9.74 °K/km. In moist air, we have Γ=-g/(C +C ) which
gives for a standard atmosphere -6.5°C/km and -5°C/km for a saturated atmosphere.
The temperature profile as a function of altitude is indeed governed by the
thermodynamics,
p
h
We can take into account in the same time the both phenomena, the radiative transfer and
the thermodynamics , by applying the equation (12) at the superior limit B(0)=B0 and from
that place using the lapse rate responsible of the temperature variation with altitude from
the top of the troposphere to the earth surface.
As it was done for the semi-infinite atmosphere, let us take at TOA
but this time, B0 depend also upon Bs.
6
in the equation (12)
The numerical application of the equation (12) with the following input data, an optical depth
a=1,868 and an heat emission of the earth surface Bs= 385 -396 W/m2, give for the
tropopause temperature a value around of -52 °C. Such a temperature at an altitude of
around 11000 m and a thermal gradient (lapse rate)  of 6,5°C/km imposes a surface
temperature of 19 °C and an unbalanced energy (difference of 15 W/m2). Therefore it’s
necessary to iterate to respect the energy balance. Some iteration are sufficient to converge
to a flux of 407W/m2 which corresponds to a temperature surface of 18°C. The flux emitted
by the earth surface, Bs, is greater (>11 W/m2) than the value published by Trenberth in
2009.The surface temperature (Ts=Tas) differs from the Global Mean Temperature
determined by all the institute by 3 °C. Apparently, it’s yet an important discrepancy. But this
mean temperature determined by the various institutes is more or less an arithmetic
average. Whereas the temperature calculated with the equations (8), (9) or (12) are effective
temperatures for a T4 law. This last data gets a value greater than the global mean
temperature2. Therefore this difference of 3 °C is an argument in favour of our approach. Let
us remark also that the difference is incidentally only 1°C with the temperature resulting from
the de surface flux given by Trenberth en 2009.
In order to evaluate the effect due to the change of surface flux resulting from the
increase of absorbing gas concentration like [CO2] in the atmosphere, the use of the
lapse rate impose to take into account the variation of thickness of the atmosphere and
therefore the variation of the altitude of the IR emission. Let us note that in the purely
radiative case, only the change of the absorptivity is considered.
This altitude change is first caused by the addition of an amount of molecules which is
small compared to those already present in the atmosphere. As an example, the
doubling of the present concentration of carbon dioxide would cause an elevation of the
tropopause of 4.4 m. But we must also take into
account the variation of altitude due to the air
temperature increase. It is given by the ideal gas
law pV=nRT ou pV=rT (dV=rdT/p from which we
deduce easily dz).
On the facing figure, we have an image of this
temperature effect on the height of the
troposphere from the poles to the tropics. The
height of 11 km is only an average allowing to get
a one dimension treatment.
The altitude variation due to the doubling of
atmospheric CO ( from 400 to 800 ppm) taking
into account the both mechanisms (addition of molecules and variation of temperature,
iteration process is there also necessary) leads to an increase of 0.11 or 0.09 °C
according to whether we use the absorptivity calculated by reference [2] or by [3]. It is a
very small climate sensitivity linked to the increase of carbon dioxide concentration
(around 0.1°C instead of 1.2°C claimed by IPCC). But let us remark that IPPC prediction,
even with its largely exaggerated climate sensitivity is catastrophic if and only if a positive
feedback of the water vapour exists to intensify the CO2 effect.
2
So we have to evaluate the effect of the variation of H2O concentration in the atmosphere
resulting from a temperature increase whatever its origin: increase of CO2 concentration,
el Nino phenomenon etc. To do that, we use again the equation (12), and we are going
to study an envelope case: a completely saturated atmosphere. From F. Miskolczi [2],
2
We can determine the effective (following a T 4 law) for a surface divided in 5, 6, 10 zones with temperatures
somehow distributed like the earth’s ones and corresponding to an average temperature of de 15°C. We will
note that the effective temperature of this surface will be greater by at least 2 °C than this value.
7
the saturation is reached for an average concentration in the air of 6.2 per mil or almost
60 kg.m-2 instead of 25 kg.m-2. This leads to an increase of the absorptivity by around
12%. These figures induce an increase of altitude of the tropopause of around 39 m. The
direct application of the (12) equation leads to a tropopause temperature of -51.9 °C
instead of -53.4. This would be there a warming. But since the atmosphere is saturated,
the value of lapse rate is now 5°C/km instead of 6.5 °C/km as a result of the variation of
specific heat capacity of the air. The consecutive surface temperature is then +3.3 °C
instead of +14.5 °C. This time, it’s a great cooling. The variation of the water
concentration in the atmosphere act in the opposite direction to what is claimed by IPCC
and what the models (GCMs) predict: a feedback exist, yes but negative and not
positive. Good News, the system acts as an air-conditioner.
It then appears that the 33 °C of difference, which would exist according to the IPCC and
a lot of scientists between the earth surface temperature of an hypothetic earth with an
atmosphere without greenhouse gas (mainly without H2O and CO2) and the actual
temperature observed on our present earth, don’t come from the RGE. It is the result of
both the amount of H2O inside the atmosphere and the pressure variation with altitude.
At the end, it’s the gravitation and not the "radiative greenhouse gas » which is
responsible of the fact that the earth surface is at a temperature greater than the
troposphere temperature!
Consequently and unlike the reference [2] said any increase of CO concentration
cannot be invoked to explain the global Warming of the climate.
2
4 Discussion
4.1 Mistake
The approximation of a semi-infinite and totally absorbing medium is not adapted to our
atmosphere. The use of a boundary limit at the base of our atmosphere (at the interface
earth/air) is surprising as already noted for something infinite. Anyway this lead to two
different temperatures for the surface in the soil or ocean (T s) and in the air (TAS) given
by the equations (8) and (9).
In the reality we have three medium : medium 1, the
interstellar space which is void, medium 2, the gaseous
atmosphere limited by the medium 1 at its top and
medium 3 the earth (solid or liquid). Each medium, has
its own law of transfer. In the void space, it’s clear that
the transfer is radiative. Normally in the atmosphere, it’s
a mix of several phenomena. For the soil, its only
conduction, for the ocean we must add, convection,
evaporation. For the classical approach defended by
IPCC and reported in the chapter 2, the purely radiative
transfer equations are applied to the second medium,
the atmosphere. They then derived the equation (7) for
the temperature of the atmosphere and (9) for the air
temperature at the earth surface.
But, surprise, they uses also the formalism of the
medium 2 in order to determine one temperature of the medium 3 that is to say the
one named Ts. It’s a first error. Moreover when we look carefully, we realize that they
consider that there is no downward flux in the medium 3 (soil or ocean). Only the upward

Flux F is taken into account. It’s another astonishment since in steady state, the
8
amount of heat entering a section is equal to amount of heat coming out. From that way
of doing, they get in the air
=2B= F  + F  and F  2B  F , and in the soil or
the sea F   2B . So they have created arbitrarily an artificial heat source. All this
gives, at the end, the equation (8). So in all the situation we will have TS>TAS since

1
4
 
 s  2     s  1

 2

 2


1/ 4
We saw before than the temperatures of the air at
the surface calculated in purely radiative mode, are always smaller than the global mean
surface temperature (however measured on earth in the air). Normally, the conclusion
would have been that the radiative process is insufficient to explain the temperature of
the troposphere.
The use of the fake equation (8), allows to obtain a much warmer surface temperature TS
(27.7 instead of 6°C as indicated in the chapter 2). This difference is, of course,
attributed to the RGE. “Quod erat demonstrandum” for them, but it is a serious mistake
And thanks to this trick, in all the situations, they may claim the greenhouse effect
increases always the temperature of the biosphere. In fact they at least exaggerate the
RGE and we may even say they “created” it or more exactly they pulled it out of their hat.
4.2 Arguments
The results presented in the chapter 3 shows that RGE cannot explain the past warming
neither the very important one predicted by IPCC for 2100! We may even propose that
RGE doesn’t exist. But because such a proposition disrupts the “doxa”, an explanation
must be given and we must demonstrate why RGE has no physical basis.
We may reach this objective by different way :
1. In all the classical approaches, there is confusion between the unidirectional
radiative flux and heat transfer. An heat transfer by radiation is given by the
difference between what it is absorbed and what is radiated, net balance is the
only one interesting3 ! The net flux at the surface "emitted minus
absorbed” coming from the air is then negative. The exchange of IR radiation
causes a cooling of the surface ! Of course, a compensation exists to reestablish the balance through the vertical transport of heat by convection and
evaporation/condensation of the water in troposphere.
2. The lower layers of the atmosphere don’t contribute to the incoming or the
outgoing radiation. The IR are trapped in this “dark” zone4 (blind zone for some
people [2]). In that case, the intensity is isotropic and the net flux is zero. The IR
radiation emitted in the cosmos comes from the upper layers of the atmosphere.
The definition of the RGE given in the chapter 2, G  Ts4  OLR is therefore not
correct. And the limit for the IR emission toward the space is, in no case, the earth
surface but is situated in altitude. Of course, this surface varies with the latitude
and with the wave frequency, but in average it may be represented by a surface
situated above the “dark” zone at around 5000m. It’s at this (pseudo) surface that
we may apply the Stephan-Boltzmann law and where the global equilibrium
between the incoming short wave flux and the IR outgoing flux, exists. The
temperature of this surface is therefore of -18 °C which is admitted by everybody
and is even written in the IPCC reports. Then, by applying the lapse rate, we find
again the actual global average surface temperature. Everything is coherent.
3
4
It is what is not done when they derive the equation (8), see chapter 4.1
From an IR point of view
9
3. Moreover, as a lot of physicists highlighted, the RGE mechanism breaks the
second thermodynamics law. But this point is contested by some other scientists;
therefore this contradiction needs to be justified. One way to know if the law is
respected is to see whether or not the IR radiations emitted by the troposphere
toward our planet warm it. First remember the fact that electromagnetic (e.m.)
waves with the matter can take various forms according to the characteristics both
of the wave and the matter. Everybody knows it’s not enough that a wave packet
arrives on a surface to warm it; some material let pass radiation. Matter can also
reflect or deviate a radiation without changing its wave character neither altering
its energy: as the polish metals do, since they are reflectives, in large range of
energy
and
therefore
are
not
warming
when
lighted.
We
must
also
have
in
our
mind
the
particle-wave
duality.
Let us in detail look at our planet. It receives from the sun a radiation spectrum
corresponding quite well with the spectrum of a black body at a temperature
around 5500°C. It is composed mainly by Ultraviolet and visible radiations with a
maximum at 0.5 µm (yellow surface of the figure). The earth absorbs the high
frequencies (the short wave) without emission of radiation in the same range: The
radiations emitted by the earth are in red on the figure; It’s clear that the both
spectra have very few recovering. It’s obvious then that the high frequency
(yellow) is absorbed and dissipated in incoherent heat energy. More precisely, in
interacting with the soil or with the ocean, particle aspect of the solar light prevails
over the wave character. That are the photons which now interact with the matter
in such a way that e.m. energy is
transform in particle motions: the
conservation of the total momentum when
the particles collide, leads to an increase
of the velocity of the receiver particles and
at the macroscopic level leads to an
increase of the temperature. It’s clear that
when the incoming radiation owns a
frequency (and a temperature) greater the
illuminated object, then the e.m. energy is
turned into heat.
Let us see now, what’s happen when the
temperature of the incoming radiation is
equal to the temperature of the illuminated
object. The absorption in the form of
particle motions, if it exists yet, can no longer lead to an increase of temperature
since we have equality of the velocities.
And for a smaller incoming radiation temperature, we even must get a cooling
with a particles mechanism. The thermal motions of hot and fast particles are
transmitted to the colder particles and never the inverse. But we see on the figure
for the case (Tincoming<Tobject) we are in the range of the red surface) in the
earth/sun system for which the wave character takes back entirely the
precedence over the particles character. It’s probable that there is no “reduction »
of the wave into particle. The incoming radiation undergoes a Rayleigh, LorentzMie or Thomson diffusion with change of direction but without loss of energy. With
this purely wave reasoning if the incoming radiation has a temperature smaller
than the receptive object, there will never get any warming of the liquid or solid
matter. And in the case for which the emission that follows the interaction of the
IR coming from the troposphere is reinforced by resonance (as in the resonant
amplification of a string musical instrument), we will have a cooling. In the both
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cases, waves and particles, we never can consider a warming if the incoming
radiation temperature is less than the temperature of the lit object. We can also
show that very simply by using the law of the conservation of momentum.
4. Indeed, we can, from this law, demonstrate this inability of RGE to warm the
terrestrial surface. The momentum of a photon p is given by p=h/=h/c where h
is the Planck constant and c the light velocity. Thanks to Wien law, it is possible to
link this momentum to a (radiation) temperature p=hT/ with =2,9.10-3. We
know also, that an object at a temperature T radiates at a frequency T. If the
exchange are purely radiative, the variation of momentum of a collided particle or
an atom of the lit object in thermal equilibrium will be given by
dp=mdv- hT/c+ hi/c where i is the frequency of the incoming radiation
absorbed by the object (by the particle of interest). With v the particle velocity and
m its mass, the quantum momentum leads to the following equation :
dv=(h/(c.m))(i-T)=(h/(.m))(Ti-To) It’s obvious that if we have in this
equation i>T or Ti>To, the velocity of the particles and therefore the object
temperature will increase. It’s the case of the light coming from the sun.
But if now we have i =T or Ti=To; dv=0 and no warming.
And if i<T or Ti<To, dv<0 that means a cooling. In [5], we reach the same
conclusion.
The e.m. radiations conform to the second law of thermodynamic. This is comforting!
All these items refute all the purely radiative approach. And it is not nothing, there is no
conflict between radiation transport, thermodynamics and quantum physic.
5 Conclusion
It has been demonstrated that the purely radiative classical approach with a semi-infinite
atmosphere is an approximation not correct to describe our atmosphere. There is no
congruence with the reality. Such a model must only be applied where and when all the heat
exchanges are (almost) purely radiative. To be in agreement with all the observation, it is
necessary to take in consideration all the mechanism driven by the thermodynamics.
Then it appears the Greenhouse effect is no longer needed to explain the surface
temperature of the earth. There is no room for the RGE! This conclusion agrees with the
second law of thermodynamic. To those who could be surprise, let us add than a
radiation cannot warm its own source. The RGE based on an approximation established
for another case, is a false postulate and is condemned.
6 References
[1]IPCC AR4 WG1 (2007)
[2]
Ferenc
Miskolczi;
“Greenhouse
effect
in
semi-transparent
planetaryatmospheres”IDŐJÁRÁS Quarterly Journal of the Hungarian Meteorological
Service, Vol. 111, No. 1, January–March 2007, pp. 1–40
[4] Rob van Dorland and Piers M. Forster « Rebuttal of Miskolczi’s alternative
greenhouse theory”
[5] Maurice Hadrien, « CO2 : coupable ou non coupable? » Editions Mélibée
[6] J. E. Potsma A discussion on the absence of a measurable greenhouse effect 22
octobre 2012 cité par Camille Veyres
11
[3]J.L Dufresne et J. Treiner« L’effet de serre : plus subtil qu’on ne le croit » La
météorologie N° 72 Fevrier 2011
12