Here is a list of some of the posts in which I discuss some of the many problems in the Earth Energy Budgets put forth by the advocates of catastrophic man-made global warming:
Showing posts with label Earth energy budget. Show all posts
Showing posts with label Earth energy budget. Show all posts
06 December 2018
15 June 2018
Using Heat Transport Powers of the NASA Earth Energy Budget to Prove that Carbon Dioxide has an Insignificant Effect on Surface Temperatures
In my recent post A Summary of Some of the Physics Errors of the NASA Earth Energy Budget, I discussed a number of problems with the energy budget shown below in which heat transport powers are given as a percentage of the solar insolation at the top of the atmosphere. I demonstrated in that post or referred to earlier posts that demonstrated that the following NASA heat transport power values were very wrong:
1) Back radiation of 100%, which is fictitious when the atmosphere is cooler than the surface
2) Surface Infrared Emission of 117%, which is hugely exaggerated
3) The Surface Absorbed Solar Radiation minus Surface Convection Loss minus Water Evaporation Surface Cooling = 48% - 5% - 25% = 18% in this energy budget. If those values are correct then this sum is also equal to the Surface Infrared Emission. However, I went on to show that this 18% value is too high and/or the 12% of the Earth’s surface radiation emitted through the atmospheric window into space is too low, because it implies that even if the atmosphere were a black body absorber, its temperature would have to be lower than any temperature found in the atmosphere to absorb such a large fraction of the surface emitted infrared radiation.
In conclusion there is virtually no heat transport power in the NASA Earth Energy Budget which is correct. However, given the stridency with which the so-called settled science of the catastrophic man-made global warming hypothesis is said to be unquestionable, let us run through an exercise using some of their own heat transport powers to prove that carbon dioxide at its present atmospheric concentration has a negligible effect on surface temperatures and that increases in that concentration will also have negligible effects on the surface temperature. Remember that this calculation that I will be doing is based on the values provided as an integral and essential part of the so-called consensus science which also is often claimed to be the settled science.
I am going to ask the question what would the surface temperature be if there were no infrared-active gases in the atmosphere, these being the gases commonly called greenhouse gases. When we have removed all such infra-red active gases from the atmosphere, including carbon dioxide and water vapor and the clouds that result from water vapor, we will calculate an equilibrium average surface temperature. There will be no surprise in that result. We will then add carbon dioxide back into the atmosphere and recalculate the surface temperature. The change in temperature will be the temperature effect of the current carbon dioxide atmospheric concentration on the surface temperature. This is where the surprise relative to the effect prescribed by the advocates of catastrophic man-made global warming will be seen. In fact, this result will also surprise the lukewarmers as well.
In order to remove the infra-red active or greenhouse gases, we need to look at another somewhat earlier NASA schematic diagram of heat transport in the atmosphere so that we can separate out the solar insolation reflected from the atmosphere and that part reflected from clouds. We must also be able to use NASA values to separate the portions of the solar insolation absorbed by the atmosphere from that part absorbed by clouds. Of course we expect this alternative NASA Energy Budget to agree with the one above because when the energy budget was promulgated it was already being claimed that the science was settled.
In order to remove the infra-red active or greenhouse gases, we need to look at another somewhat earlier NASA schematic diagram of heat transport in the atmosphere so that we can separate out the solar insolation reflected from the atmosphere and that part reflected from clouds. We must also be able to use NASA values to separate the portions of the solar insolation absorbed by the atmosphere from that part absorbed by clouds. Of course we expect this alternative NASA Energy Budget to agree with the one above because when the energy budget was promulgated it was already being claimed that the science was settled.
Note that 51% is absorbed by the surface instead of 48%, that the sum of the solar insolation reflected from clouds and the atmosphere is 26% instead of 23%, that 19% of solar insolation is absorbed by the atmosphere or by clouds rather than 23%, that solar insolation reflected from the surface is 4% instead of 7%, that conduction is 7% instead of 5%, that water evaporation is 23% instead of 25%, that the surface radiation emitted through the atmospheric window into space is 6% rather than 12%, and that the surface infrared radiation absorbed by the atmosphere is 15% instead of 105%. The second schematic was the viewpoint before that of the first schematic. One has to wonder what the claimed consensus does agree upon and how that agreement is deemed sufficient to make the scientific issues so settled.
If one removes water vapor from the atmosphere, there are no clouds and the mechanism of putting water vapor into the atmosphere has to be removed, namely the evaporation of water. Some solar insolation will still be reflected from the atmosphere or scattered from it with little loss of energy, but most of the reflection is from clouds. The second energy budget tells us that 6%/26% = 0.23 is the fraction of atmospheric reflection not by clouds. The total reflection of both clouds and the atmosphere in the first energy budget is 23%, so the percentage still reflected by the atmosphere with no clouds is (0.23)(23%) = 5.3%. Thus the portion of the solar insolation no longer reflected by clouds is 23% - 5.3% = 17.7%. The fraction of the atmosphere plus clouds absorption of solar insolation which is absorbed by the clouds is 3%/19% = 0.158. The portion of the solar insolation absorbed by clouds is then (0.158)(23%) = 3.6%. Thus the portion of the solar insolation still absorbed with no clouds is 23% - 3.6% = 19.4%.
The removal of the infrared-active gases from the atmosphere also requires us to remove the absorption of incoming solar radiation in the atmosphere by the infrared-active gases. We need additional information to estimate the fraction of the solar insolation absorbed by the infrared absorbing gases. Let us consider these two graphics:
It appears that of the total absorption of solar insolation by the atmosphere, about one-third is absorbed by the infrared-absorbing gases. We just determined that the atmosphere absorbs about 19.4% of solar insolation when we remove clouds, but still have water vapor and other infrared-active gases in the atmosphere. One-third of this is about 6.5%.
Now let us add up the solar insolation power incident upon the surface, PSI, based on the power values of the first NASA Earth Energy Budget:
PSI = 55% + 17.7% + 3.6% + 6.5% = 82.8%,
so the solar insolation incident upon the surface when water vapor, clouds, and all infrared-active gases are removed is much increased relative to the current 55% with them present.
At present, 7%/55% is reflected according to the first NASA energy budget above. Let us assume this fraction of reflected solar incident radiation is unchanged, so that the power of solar insolation now absorbed by the surface, PABS, is:
PABS = (1 - {7%/55%})(82.8%) = 72.3%
This power absorbed by the surface is now going to be dissipated by convection and by radiation. In the NASA Earth Energy Budget, 5% is dissipated by convection. Given that water evaporation is not now occurring, it would be reasonable to think the energy dissipation rate by means of convection might go up, but let us do the calculation with a 5% value. The power radiated by the surface to space, PSRS, is then
PSRS = 72.3% - 5% = 67.3%
Now apply the Stefan-Boltzmann Law with an emissivity of 0.95 for the surface and we have
PSRS = (0.673)(340 W/m2) = (0.95) σ TS4,
where TS is the surface temperature with no clouds and no greenhouse gases. Solving for TS,
TS = 255.30 K
Which is the effective radiation temperature of the Earth today with clouds and infrared-active gases in the atmosphere. So, if the NASA power numbers we used from the NASA Earth Energy Budget are right, then water vapor and clouds and other infrared active gases cause the Earth to be 33K warmer than it would be without them. This is consistent with a common claim of the so-called settled science.
Now I will put carbon dioxide back into our atmosphere and observe the effect of doing so.
Nearly all of the absorption of solar insolation by the atmosphere in the infrared spectrum is due to water vapor. How much is absorbed by carbon dioxide is little addressed by the settled science beyond a determination to ignore this cooling effect. To eye-ball the last figure above, it appears that the absorption by CO2, is about one-fifteenth that by water vapor. Since the total infrared absorption of solar insolation by the atmosphere was estimated above to be 6.5%, the part due to carbon dioxide is then about one-sixteenth of that or 0.41%. However, about 7/55 of this is reflected and not absorbed by the surface, leaving about 0.36% less surface absorption.
In the first NASA Earth Energy Budget above, the infrared radiation from the surface absorbed by the atmosphere is given by (117% - 100%) - 12% = 5%, where the difference of the first two powers in parentheses is the real surface infrared emission and 12% is lost through the atmospheric window into space. Most of the 5% of the atmospheric absorption of the surface infrared emission is due to water vapor. It is also important here to only add in that part of the surface emission absorption that carbon dioxide adds to that absorption normally done by water vapor if we would find the relevant net effect of carbon dioxide. From the figure immediately above, this additional CO2 absorption effect relative to that of water vapor is about one-eighth. The fraction of the 5% of surface emission absorbed by the atmosphere is then one-ninth of 5% or 0.56%.
I am looking to modify the calculation for the surface temperature that we did above after removing water vapor, clouds, and carbon dioxide from the atmosphere to accommodate the return of carbon dioxide to the atmosphere to see how the surface temperature changes. It is clear that one needs to subtract the insolation power lost to surface absorption due to CO2 absorbing it in the atmosphere and one wants to add some power due to some additional absorption in the atmosphere of the longwave radiation emitted from the Earth’s surface. Using the full value of the atmospheric absorption of the Earth's infrared emission is actually going to make the warming effect on the surface temperature larger than it is. Most of the heating in the atmosphere stays in the atmosphere and does not cause the surface heat supply to change. It is also likely that the cooling effect on the surface operates at a greater efficiency than does the warming effect. Consequently, what we will be calculating here is an exaggerated, upper limit on the magnitude of the effect of having CO2 in the atmosphere and may even have the wrong sign.
Upon subtracting the insolation power lost by CO2 absorption and adding the power of surface infrared emission absorbed by the atmosphere, we get
PSRS = (0.673 - 0.0036 + 0.0056)(340 W/m2) = (0.95) σ TS4,
and we must observe that each of the cooling and warming effects of carbon dioxide are already the equivalent of mere rounding errors and the difference between them is still more piddling. Nonetheless, let us carry out the calculation to obtain what is surely an upper limit on the surface temperature:
PSRS = (0.675)(340 W/m2) = (0.95) σ TS4,
TS = 255.49 K,
making the total warming effect of carbon dioxide all of about 0.19 K at most at its present concentration. This implies that a doubling of the present CO2 concentration in the atmosphere will produce a temperature increase much smaller than 0.19 K due to the logarithmic decrease of absorption with increased concentration. Even at this upper limit of a 0.19 K temperature increase due to the present levels of CO2 in the atmosphere, the fraction of the greenhouse gas warming due to carbon dioxide is only about
0.19 K / (288.15 K - 255.30 K) = 0.0058 or 0.58%
Meaning that the so-called greenhouse effect is about 99.4% attributable to water vapor and the clouds that result from water vapor.
What is more, in the real world in which there is water vapor, there is a negative, not a positive, feedback response by water vapor which would erase a portion of the fraction of 0.19 K that a doubling of the carbon dioxide concentration in the atmosphere would produce according to these approximations using NASA Earth Energy Budget values.
As I have maintained since 2010, the net effect of carbon dioxide on the surface temperature is entirely negligible. Great increases in the carbon dioxide concentration in the atmosphere will have no significant effect on the surface temperature of the Earth. For all intents and purposes, only water vapor has significant effects on the surface temperature of the Earth and most of its effect is due to clouds and the water evaporation-condensation cycle. There is no real reason for alarm about the effects of using fossil fuels based on added emissions of CO2.
It is unfathomable that after governments around the world have spent well over $100 billion on the catastrophic man-made global warming hypothesis that relatively few scientists are pointing out the errors and contradictions that riddle the so-called settled science. It would appear that government funding of science corrupts science absolutely and/or makes scientists incompetent. It is an interesting parallel to what government power does to government employees.
Updated 2 July 2018.
It is unfathomable that after governments around the world have spent well over $100 billion on the catastrophic man-made global warming hypothesis that relatively few scientists are pointing out the errors and contradictions that riddle the so-called settled science. It would appear that government funding of science corrupts science absolutely and/or makes scientists incompetent. It is an interesting parallel to what government power does to government employees.
Updated 2 July 2018.
25 March 2018
Solving the Parallel Plate Thermal Radiation Problem Correctly Proves the Settled Science of Man-Made Global Warming Wrong
This is essentially a re-posting of an article of 2 November 2017 which has been edited with additions several times since the original version appeared. The essential physics has not been changed, but I have tried to help the reader understand it more readily along with its implications for the fate of the catastrophic man-made global warming hypothesis.
I will present the Consensus, Settled Science solution to the
parallel plane black body radiator problem and demonstrate that it is
wrong. I will show that it exaggerates the energy of electromagnetic
radiation between the two planes by as much as a factor of two as their
temperatures approach one another. As a result, the calculations of the
so-called Consensus, Settled Science dealing with thermal radiation very often
result in violations of the Law of Conservation of Energy.
Their calculations of thermal radiation greatly exaggerate the density of the infrared photon radiation in the atmosphere and the extent of the absorption of infrared radiation by infrared-active molecules, commonly called greenhouse gases, such as water vapor and carbon dioxide. Their theory of the transport of heat energy between the surface of the Earth and the atmosphere and through the atmosphere is very wrong. It exaggerates the role of thermal radiation greatly and minimizes the role of the water evaporation and condensation cycle and the role of thermal convection. It cannot be emphasized enough how harmful their mishandling of thermal radiation calculations is to their understanding of the critical issues pertaining to the Earth's climate and to man's role in changing the climate through the use of carbon-based (fossil) fuels.
In the case in which the two black body parallel plane radiators have the same temperature, the volume between them becomes that of a black body radiator. The fundamental characteristic of a black body radiator is the constant energy density in the cavity. I will show that the so-called settled science treatment, which wrongly takes the primary characteristic of a black body radiator to be that the power of emission of radiant energy is given by the Stefan-Boltzmann Law, clearly violates the real principal characteristic of a black body cavity, namely that its constant energy density, e, is given by Stefan’s Law as
e = aT4,
where T is the temperature in
Kelvin, a is Stefan’s Constant of 7.57 x 10-16 J/m3K4 , and e
is in Joules per cubic meter.
I have already demonstrated the failure of the settled science
treatment of thermal radiation from black body radiators in the form of
concentric spherical shells in a paper posted on 23 October 2017,
entitled Thermal Radiation Basics and Their Violation by the
Settled Science of the Catastrophic Man-Made Global Warming Hypothesis, but I want to post this
solution with its simpler geometry so that the reason the consensus treatment
is wrong will be even more apparent to thinking readers.
Numerous critics of the consensus science on catastrophic man-made
global warming have argued that the Second Law of Thermodynamics claims that
energy only flows from the warmer body to the colder body, but the consensus
scientists have argued that thermodynamics only applies to the net flow of
energy. I have long argued that the reason that radiant energy only flows
from the warmer to the cooler body is because the flow is controlled by an
electromagnetic field and an energy gradient in that field. I will offer
that proof in this paper with some qualification on the energy flow from the cooler body to the warmer body within a tight constraint. The Second Law of Thermodynamics is not invoked
as the basis of the proof in this paper, but the minimum energy of a system
consistent with the Second Law of Thermodynamics does turn out to be a
consistent solution to the problem of thermal radiation, while the Consensus,
Settled Science theory of thermal radiation does not minimize the system total
energy, does not produce the correct energy density of a black body cavity, and
is not consistent with the Conservation of Energy. I have pointed out its
failure to conserve energy in many prior posts.
In a black body cavity, the electromagnetic radiation is in
equilibrium with the walls of the cavity at a temperature T. The energy
density e is the mean value of
½ E·D + ½ H·B,
where E is the impressed electric field, D is
the displacement, which differs from E when the medium is
polarized (i.e., has dipoles), H is the impressed magnetic
field and B is the magnetic polarization of a medium. If
the cavity is under vacuum, then D = E and B = H in
the cavity volume and |E| = |H|, so e equals |E|2.
The mean value of the energy density of the electromagnetic field in the cavity
depends on the temperature and is created by the oscillating dipoles and higher
order electric poles in the cavity walls. The energy density is independent
of the volume of the cavity. The radiation pressure on the cavity walls
is proportional to the energy density.
This physics may be reviewed by the reader in an excellent
textbook called Thermal Physics by Philip M. Morse,
Professor of Physics at MIT, published in 1965 by W.A. Benjamin, Inc., New
York. Prof. Morse wrote it as a challenging text for seniors and
first-year graduate students. I was fortunate to use it in a
Thermodynamics course at Brown University in my Junior year.
Alternatively, see my post The
Greenhouse Gas Hypothesis and Thermal Radiation -- A Critical Review.
Inside a black body cavity radiator at a temperature T, the energy
density, or the energy per unit volume of the vacuum in the cavity is constant
in accordance with Stefan’s Law. If one opens a small peephole in the
wall of the black body cavity, the energy density just inside that peephole is
the energy density of the black body cavity and that energy density is
proportional to the square of the electric field magnitude there. The
Stefan-Boltzmann Law states that the flow rate of energy out of the peephole
when the black body cavity is surrounded by vacuum and an environment at T = 0
K, is given as the power P per unit area of the peephole as
P = σT4
Note that P = (σ/a) e and that e in the T=0K sink is equal to
zero. A change of energy density in the vacuum volume immediately inside
the peephole into the black body cavity as given by Stefan's Law to a value of
zero in the T=0K outside environment causes a power of thermal radiation
emission out of the peephole to the outside environment as given by the
Stefan-Boltzmann Law.
Why is it that a surface which is not a peephole into a black body
cavity might act like a black body radiator? It has to be that the energy
density very, very close to that surface has the characteristic of the energy
density in a black body cavity radiator, namely that
e = aT4.
Any flow of energy out of the surface due to its temperature T
must be caused by this electromagnetic field energy density at the surface
generated by the vibrational motion of electric charges in the material of the
surface.
Here is the problem of the parallel plane black body radiators
diagrammed, where TC is the cooler temperature and TH is
the warmer temperature:
Let us first consider the case that each plane is alone and
surrounded by an environment of space at T=0. Each plane has a power
input that causes the plane to have its given temperature. Each plane
radiates electromagnetic energy at a rate per unit surface area of
P = σT4.
Consequently, if neither plane were in the presence of the other
and each plane has a surface area of A on each side and PCO , PCI , PHO , and PHI are all radiation
powers per unit area, we have
PC = APCO + APCI =
2AσTC4
And
PH = APHO + APHI =
2AσTH4 ,
since in equilibrium the power input is equal to the power output
by radiation.
In the consensus viewpoint, shared by many physicists and by
almost every climate scientist, the parallel plane black body radiators above
are believed to emit photons from every surface of each plane even in the
presence of the other plane with a power per unit area of
PH = σTH4 and PC = σTC4,
just as they would if they were not near one another and they only
cast off photons into a sink at T = 0 K. This viewpoint takes the emitted
radiation as a primary property of the surfaces rather than an electromagnetic
field with a known energy density as the primary property of the surfaces.
Thus, when these planes are in one another's presence this consensus viewpoint says that
PC = APCO + APCI -
APHI = 2AσTC4 - AσTH4
PH = APHO + APHI -
APCI = 2AσTH4 - AσTC4
Note that PC becomes zero at TC =
0.8409 TH and below that temperature PC is
negative or a cooling power in addition to radiative cooling. If TH =
288K, then TC = 242.2K, the effective radiative temperature of
the cooler plane to space if the cooler plane is thought of as the atmosphere
and the warmer plane is the surface of the Earth, both the atmosphere and the
surface act like black body radiators, and the atmosphere receives only radiant
energy from the surface. This is in agreement with calculations I have
presented in the past and is a result which I believe to be correct under the
assumptions, even though in some critical respects this consensus viewpoint is
wrong.
If these planes were isolated from one another and each plane
faced only that T = 0 K vacuum, then one would have
eH = aTH4 and eC =
aTC4,
because these are black body radiator surfaces.
eH = aTH4 in this case.
Unlike the case of concentric spherical shells, which I considered
in Thermal
Radiation Basics and Their Violation by the Settled Science of the Catastrophic
Man-Made Global Warming Hypothesis, there is no divergence or convergence
of the photons emitted from either surface. The relationship of the
radiative power P to the energy density due to that electromagnetic radiation
is always e = (a/σ) P as one traverses the distance between the
planes.
Consequently, the energy density between the planes is
e = (a/σ) PHI + (a/σ) PCI = aTH4 +
aTC4
anywhere between the two planes, because photons have energy no
matter which direction they are traveling and they do not annihilate one
another based on their direction of travel. The total energy between the
planes is that of the electric field or it is the sum of the energy of all the
photons in the space between the planes. The energy density e would then
be the total energy of all the photons divided by the volume of vacuum between
the planes.
Now, let us imagine that these planes are very close together and
the ends are far away and nearly closed. Let us have TC → TH,
then
e → 2aTH4,
but this space between the planes is now a black body cavity in
the limit that TC → TH, and we know by Stefan’s
Law that
e = aTH4
in this case. In addition, we have created a black body
cavity radiator here and P for the walls inside the cavity is actually zero
because the interior is in a state of equilibrium and constant energy density.
P is only P = σ T4 just outside the peephole facing
an environment at T = 0 K. In the above consensus viewpoint case, each
plane surface is emitting real photons, but these cannot annihilate those
photons of the opposite plane. There are no negative energy
photons. These respective photon streams simply add to the total energy
density.
If we did insist on claiming that oppositely directed photons had cancelling energies as is commonly done, then the energy density inside a black body cavity would be zero, not the finite energy given by Stefan's Law. Given the thermal equilibrium in a black body cavity, there are just as many photons traveling in one direction as in the opposing direction, yet their respective energies must be added when determining the energy density. Stefan's Law insists that all photons have positive energy.
If we did insist on claiming that oppositely directed photons had cancelling energies as is commonly done, then the energy density inside a black body cavity would be zero, not the finite energy given by Stefan's Law. Given the thermal equilibrium in a black body cavity, there are just as many photons traveling in one direction as in the opposing direction, yet their respective energies must be added when determining the energy density. Stefan's Law insists that all photons have positive energy.
The consensus treatment of black body thermal radiation doubles
the energy density in a black body cavity, in clear violation of the principal
characteristic of a black body cavity upon which their treatment must be
based. Their treatment greatly increases the energy density between the
planes whenever TC is anywhere near TH, such as is
the case of the temperatures in the lower troposphere compared to the Earth’s
surface temperature. Consequently, the sum of PHI and PCI must
be much smaller than they are thought to be in the consensus treatment of this
problem or in the similar concentric spherical shell problem.
Let us now examine the correct solution to this parallel plane
black body radiators problem. It is the electromagnetic field between the
two planes that governs the flow of electromagnetic energy between the
planes. Or one can say it is the energy density at each plane surface
that drives the exchange of energy between the planes due to the energy density
gradient between the two planes. The critical and driving parameter here
is
Δe = eH - eC = aTH4 –
aTC4 ,
where each black body radiator surface maintains its black body
radiator requirement that the energy density at the surface is given by
Stefan’s Law.
Electromagnetic energy flows from the high energy surface to the
low energy surface, as is the case in energy flows generally.
PHI = (σ/a) Δe = (σ/a) (aTH4 –
aTC4 ) = σ TH4 – σ TC4
PCI = 0,
which is consistent with experimental measurements of the rate of
radiant heat flow between two black body radiators. Note that as TC approaches
TH, PHI approaches zero as should be the case inside
a black body cavity in thermal equilibrium. There is no thermal emission
from either of the black body cavity walls then, except with the absorption of a photon of equal energy. Note also that when TC =
0 K, PHI is given by the Stefan-Boltzmann Law
PHI = σ TH4.
Let us recalculate PH and PC in
this correct formulation of the problem:
PC = APCO + APCI -
APHI = AσTC4 + 0 – [AσTH4 -
AσTC4] = 2AσTC4 - AσTH4
PH = APHO + APHI -
APCI = AσTH4 + [AσTH4 -
AσTC4] - 0 = 2AσTH4 - AσTC4
And we see that the power inputs to each plane needed to maintain
their respective temperatures as they cool themselves by thermal radiation are
unchanged in this correct energy density or electromagnetic field centered
viewpoint from the consensus viewpoint. Experimentally, the relationship
between the power inputs to the thermal radiation emitting planes at given
temperatures are exactly the same. This fact causes the proponents of the
consensus viewpoint to believe they are right, but they nonetheless violate the
energy density requirements of electromagnetic fields and of black body
radiation itself.
Because PCI = 0, back radiation
from a cooler atmosphere to the surface is also either zero or accompanied by an offsetting decrease in the emission from the surface and not 100% of the top of
the atmosphere solar insolation as in the current NASA Earth Energy
Budget. Because PHI = σ TH4 – σ TC4 , the Earth's
surface does not radiate 117% of the top of the atmosphere insolation
either. If the net energy flow by radiation between the surface and the atmosphere is 17%, then any actual back radiation from the atmosphere would be offset by a reduction of radiation from the surface below the 17% level. In other words, if there were a 2% back radiation from the atmosphere, then the surface radiation would be limited to 15% in order to preserve the proper energy density. The NASA radiation flows are hugely exaggerated as are the similar Earth Energy Budgets presented in the UN IPCC reports. See
the NASA
Earth Energy Budget below:
This is very important because reducing these two radiant energy
flows of infrared photons reduces the effect of infrared-active gases, the
so-called greenhouse gases, drastically. Many fewer photons are actually
available to be absorbed or emitted by greenhouse gases than they
imagine. This is a principal error that should cause the global climate
computer models to greatly exaggerate the effects of the greenhouse gases, just
as they have.
As I have pointed out in the past, one fatal consequence of the
exaggeration of thermal radiation from the surface of the Earth is readily
calculated from the fact that even if the atmosphere acted as a black body
absorber, which it does not, it can only absorb the thermal radiation said to
be emitted from the surface at an absurdly low atmospheric temperature.
Observe that the power of infrared radiation from the surface which is absorbed
by the atmosphere PSA is
PSA = σ ( TS4 – TA4)
PSA = (1.17 – 0.12) (340 W/m2)
The first equation is from the discussion above with TS the
surface temperature and TA the temperature of the atmosphere.
The second is according to the NASA Earth Energy Budget above. If one
takes TS to
be 288K, then the temperature of the atmosphere required to absorb as much
infrared energy as NASA claims is absorbed is 155.4K. There is no such
low temperature in the Earth’s atmosphere. To find so low a temperature,
one has to go far out into the solar system many times the radius of Earth’s
orbit. That being the case, any such thermal radiation absorbed by matter
at such a low temperature is as much lost in the Earth Energy Budget as is the
power equal to 12% of the solar insolation emitted from the Earth’s surface
which NASA allows passes through the atmospheric window into space. It
should be apparent to the reader that the NASA Earth Energy Budget is nonsense.
It is not at all surprising that physics adheres to a minimum
total energy in the system. The total flow of photons from the warmer and the
colder bodies are constrained by the energy density requirement between the
bodies. The presence of two bodies in
equilibrium at non-zero temperatures causes a reduction in the total photon
generation in the system of the two bodies.
The normal radiation of each body compared to its being alone in a T=0K
environment is reduced. By means of the electromagnetic field between these two planes, the photon
emission of the planes is coupled and affected by the presence of the other
plane. This is in no way surprising for an electromagnetic field
problem. One needs to remember that photons are creatures of
electromagnetic fields. Opposing streams of photons do not
annihilate one another to cancel out energy, they simply add their
energies. Treating them as though one stream has a negative energy and
the other a positive energy is just a means to throw the use of the
Conservation of Energy out the window. That is too critical a principle
of physics to be tossed out the window.
Extending the Solution to Gray Body Thermal Radiators
and Other Real Materials:
Many real materials do not behave like black body radiators of
thermal radiation. Those that do not radiate as black body materials
would, radiate less than the black body radiator would. Why would they
radiate less? This is because they do not create as high an
electromagnetic field energy density at their surfaces as does a black body
radiator. From Stefan’s Law for a black body radiator, the energy density
at the surface is
e = aT4
but for a gray body radiator the energy density at each wavelength
λ is
e(λ) = εaT4.
This means the energy
density at any given frequency is a constant fraction ɛ of that of a black body
radiator, with 0 ≤ ɛ ≤ 1.
In general, a material
may not behave like either a black body or a gray body radiator at a particular
wavelength. In that case,
e(λ) = ε(λ)aT4,
where the fraction of the black body output at wavelength λ is
variable.
An isolated material surrounded by vacuum and a T=0 K environment
then has a power per unit area output of
P(λ) = εσT4 for a gray body and ε is seen to be
the emissivity, and
P(λ) = ε(λ)σT4, for a general material, such as carbon
dioxide or water vapor, where the absorption and emission become variable
fractions of that of a black body as a function of wavelength.
For our two parallel plates above, if both are gray bodies, then
between the plates
Δe = eH – eC = εH a TH4 – εC a
TC4
PHI = (σ/a) Δe = εH σ TH4 – εC σ TC4
PCI = 0.
Here we see that the emissivity which determines the electromagnetic field energy density at the surface is also playing the role of the absorptivity at the absorbing colder surface. So of course, Kirchhoff’s Law of thermal radiation that the emissivity equals the absorptivity of a material in a steady state process applies. There is really nothing at all to prove if one starts with the primary fact that the energy density is the fundamental driver of the thermal radiation of materials and we know its boundary conditions.
Update: Clarified that any
emission from a cooler body in equilibrium with a warmer body results in still
less emission from the warmer body on 3 September 2018.
02 November 2017
Solving the Parallel Plane Black Body Radiator Problem and Why the Consensus Science Is Wrong
I will present the Consensus, Settled Science solution to
the parallel plane black body radiator problem and demonstrate that it is wrong. I will show that it exaggerates the energy of
electromagnetic radiation between the two planes by as much as a factor of two
as their temperatures approach one another. As a result, the calculations of the so-called Consensus, Settled Science dealing with thermal radiation very often result in violations of the Law of Conservation of Energy.
Their calculations of thermal radiation greatly exaggerate the density of the infrared photon radiation in the atmosphere and the extent of the absorption of infrared radiation by infrared-active molecules, commonly called greenhouse gases, such as water vapor and carbon dioxide. Their theory of the transport of heat energy between the surface of the Earth and the atmosphere and through the atmosphere is very wrong. It exaggerates the role of thermal radiation greatly and minimizes the role of the water evaporation and condensation cycle and the role of thermal convection. It cannot be emphasized enough how harmful their mishandling of thermal radiation calculations is to their understanding of the critical issues pertaining to the Earth's climate and to man's role in changing the climate through the use of carbon-based (fossil) fuels.
In the case in which the two black body parallel plane radiators have the same temperature, the volume between them becomes that of a black body radiator. The fundamental characteristic of a black body radiator is the constant energy density in the cavity. I will show that the so-called settled science treatment, which wrongly takes the primary characteristic of a black body radiator to be that the power of emission of radiant energy is given by the Stefan-Boltzmann Law, clearly violates the real principal characteristic of a black body cavity, namely that its constant energy density, e, is given by Stefan’s Law as
Their calculations of thermal radiation greatly exaggerate the density of the infrared photon radiation in the atmosphere and the extent of the absorption of infrared radiation by infrared-active molecules, commonly called greenhouse gases, such as water vapor and carbon dioxide. Their theory of the transport of heat energy between the surface of the Earth and the atmosphere and through the atmosphere is very wrong. It exaggerates the role of thermal radiation greatly and minimizes the role of the water evaporation and condensation cycle and the role of thermal convection. It cannot be emphasized enough how harmful their mishandling of thermal radiation calculations is to their understanding of the critical issues pertaining to the Earth's climate and to man's role in changing the climate through the use of carbon-based (fossil) fuels.
In the case in which the two black body parallel plane radiators have the same temperature, the volume between them becomes that of a black body radiator. The fundamental characteristic of a black body radiator is the constant energy density in the cavity. I will show that the so-called settled science treatment, which wrongly takes the primary characteristic of a black body radiator to be that the power of emission of radiant energy is given by the Stefan-Boltzmann Law, clearly violates the real principal characteristic of a black body cavity, namely that its constant energy density, e, is given by Stefan’s Law as
e = aT4,
where T is the temperature in Kelvin, a
is Stefan’s Constant of 7.57 x 10-16 J/m3K4
, and e is in Joules per cubic meter.
I
have already demonstrated the failure of the settled science treatment of
thermal radiation from black body radiators in the form of concentric spherical
shells in a paper posted on 23 October 2017, entitled Thermal
Radiation Basics and Their Violation by the Settled Science of the Catastrophic
Man-Made Global Warming Hypothesis, but I want to post this
solution with its simpler geometry so that the reason the consensus treatment
is wrong will be even more apparent to thinking readers.
Numerous critics of the consensus science on catastrophic
man-made global warming have argued that the Second Law of Thermodynamics claims that energy only
flows from the warmer body to the colder body, but the consensus scientists
have argued that thermodynamics only applies to the net flow of energy. I have long argued that the reason that
radiant energy only flows from the warmer to the cooler body is because the
flow is controlled by an electromagnetic field and an energy gradient in that
field. I will offer that proof in this
paper. The Second Law of Thermodynamics is not invoked as the basis of the proof in this paper, but the minimum energy of a system consistent with the Second Law of Thermodynamics does turn out to be a consistent solution to the problem of thermal radiation, while the Consensus, Settled Science theory of thermal radiation does not minimize the system total energy, does not produce the correct energy density of a black body cavity, and is not consistent with the Conservation of Energy. I have pointed out its failure to conserve energy in many prior posts.
In
a black body cavity, the electromagnetic radiation is in equilibrium with the
walls of the cavity at a temperature T. The energy density e is the mean
value of
½ E·D + ½ H·B,
where
E is the impressed electric field, D is the displacement, which differs
from E when the medium is polarized (i.e., has dipoles),
H is the impressed magnetic field
and B is the magnetic polarization
of a medium. If the cavity is under vacuum, then D = E and B = H in the cavity volume and |E| = |H|, so e equals |E|2. The mean value of the
energy density of the electromagnetic field in the cavity depends on the temperature and is created by the oscillating dipoles and higher order electric poles in the cavity walls. The energy density is independent of the volume of the cavity.
The radiation pressure on the cavity walls is proportional to the energy
density.
This physics may be reviewed by the reader in an excellent textbook called Thermal Physics by Philip M. Morse, Professor of Physics at MIT, published in 1965 by W.A. Benjamin, Inc., New York. Prof. Morse wrote it as a challenging text for seniors and first-year graduate students. I was fortunate to use it in a Thermodynamics course at Brown University in my Junior year. Alternatively, see my post The Greenhouse Gas Hypothesis and Thermal Radiation -- A Critical Review.
This physics may be reviewed by the reader in an excellent textbook called Thermal Physics by Philip M. Morse, Professor of Physics at MIT, published in 1965 by W.A. Benjamin, Inc., New York. Prof. Morse wrote it as a challenging text for seniors and first-year graduate students. I was fortunate to use it in a Thermodynamics course at Brown University in my Junior year. Alternatively, see my post The Greenhouse Gas Hypothesis and Thermal Radiation -- A Critical Review.
Inside a black body cavity radiator at a temperature T, the energy density, or the energy per unit
volume of the vacuum in the cavity is constant in accordance with Stefan’s
Law. If one opens a small peephole in
the wall of the black body cavity, the energy density just inside that peephole
is the energy density of the black body cavity and that energy density is
proportional to the square of the electric field magnitude there. The Stefan-Boltzmann Law states that the flow
rate of energy out of the peephole when the black body cavity is surrounded by
vacuum and an environment at T = 0 K, is given as the power P per unit area of the peephole as
P = σT4
Note that P = (σ/a) e and that e in the T=0K sink is
equal to zero. A change of energy density in the vacuum volume immediately inside the peephole into the black body cavity as given by Stefan's Law to a value of zero in the T=0K outside environment causes a power of thermal radiation emission out of the peephole to the outside environment as given by the Stefan-Boltzmann Law.
Why is it that a surface which is not a peephole into a
black body cavity might act like a black body radiator? It has to be that the energy density very,
very close to that surface has the characteristic of the energy density in a
black body cavity radiator, namely that
e = aT4.
Any flow of energy out of the surface due to its
temperature T must be caused by this electromagnetic field energy density at
the surface generated by the vibrational motion of electric charges in the
material of the surface.
In fact, while it is commonly claimed that photons inside the cavity are being 100% absorbed on the walls and an equal amount of radiant energy is emitted from the absorbing wall, the actual case is that the radiant energy incident upon the walls can be entirely reflected from the walls. Planck had derived the frequency spectrum of a black body cavity from an assumption of complete reflection from the walls.
In fact, while it is commonly claimed that photons inside the cavity are being 100% absorbed on the walls and an equal amount of radiant energy is emitted from the absorbing wall, the actual case is that the radiant energy incident upon the walls can be entirely reflected from the walls. Planck had derived the frequency spectrum of a black body cavity from an assumption of complete reflection from the walls.
Here is the problem of the parallel plane black body
radiators diagrammed, where TC is the cooler temperature and TH
is the warmer temperature:
Let us first consider the case that each plane is alone
and surrounded by an environment of space at T=0. Each plane has a power input that causes the
plane to have its given temperature. Each plane radiates electromagnetic energy at a rate per unit surface
area of
P = σT4.
Consequently, if neither plane were in the presence of
the other and each plane has a surface area of A on each side and PCO , PCI , PHO , and PHI are all radiation powers per unit area, we have
PC = APCO + APCI = 2AσTC4
And
PH = APHO + APHI = 2AσTH4
,
since in equilibrium the power input is equal to the
power output by radiation.
In the consensus viewpoint, shared by many physicists and
by almost every climate scientist, the parallel plane black body radiators
above are believed to emit photons from every surface of each plane even in the
presence of the other plane with a power per unit area of
PH = σTH4 and PC
= σTC4,
just as they would if they were not near one another and
they only cast off photons into a sink at T = 0 K. This viewpoint takes the emitted radiation as a primary property of the surfaces rather than an electromagnetic field with a known energy density as the primary property of the surfaces.
Thus, when these planes are in one another's presence this consensus viewpoint says that
Thus, when these planes are in one another's presence this consensus viewpoint says that
PC = APCO + APCI - APHI
= 2AσTC4
- AσTH4
PH = APHO + APHI - APCI
= 2AσTH4
- AσTC4
Note that PC becomes zero at TC =
0.8409 TH and below that temperature PC is negative or a
cooling power in addition to radiative cooling.
If TH = 288K, then TC = 242.2K, the effective
radiative temperature of the cooler plane to space if the cooler plane is
thought of as the atmosphere and the warmer plane is the surface of the
Earth, both the atmosphere and the surface act like black body radiators, and the atmosphere receives only radiant energy from the surface. This is in agreement with calculations
I have presented in the past and is a result which I believe to be correct under the assumptions,
even though in some critical respects this consensus viewpoint is wrong.
If these planes were isolated from one another and each
plane faced only that T = 0 K vacuum, then one would have
eH = aTH4 and eC
= aTC4,
because these are black body radiator surfaces.
eH = aTH4 in this case.
eH = aTH4 in this case.
Unlike the case of concentric spherical shells, which I considered in Thermal Radiation Basics and Their Violation by the Settled Science of the Catastrophic Man-Made Global Warming Hypothesis, there is
no divergence or convergence of the photons emitted from either surface. The relationship of the radiative power P to
the energy density due to that electromagnetic radiation is always e = (a/σ) P
as one traverses the distance between the planes.
Consequently, the energy density between the planes is
Consequently, the energy density between the planes is
e = (a/σ) PHI + (a/σ) PCI = aTH4
+ aTC4
anywhere between the two planes, because photons have
energy no matter which direction they are traveling and they do not annihilate one another based on their direction of travel. The total energy between the planes is that of the electric field or it is the sum of the energy of all the photons in the space between the planes. The energy density e would then be the total energy of all the photons divided by the volume of vacuum between the planes.
Now, let us imagine that these planes are very close
together and the ends are far away and nearly closed. Let us have TC → TH,
then
e → 2aTH4,
but this space between the planes is now a black body
cavity in the limit that TC → TH, and we know by Stefan’s
Law that
e = aTH4
in this case. In
addition, we have created a black body cavity radiator here and P for the walls inside the
cavity is actually zero because the interior is in a state of equilibrium and
constant energy density. P is only P = σ T4
just outside the peephole facing an environment at T = 0 K. In the above consensus viewpoint case, each plane surface is
emitting real photons, but these cannot annihilate those photons of the opposite
plane. There are no negative energy
photons. These respective photon streams
simply add to the total energy density.
The consensus treatment of black body thermal radiation
doubles the energy density in a black body cavity, in clear violation of the
principal characteristic of a black body cavity upon which their treatment must
be based. Their treatment greatly
increases the energy density between the planes whenever TC is
anywhere near TH, such as is the case of the temperatures in the
lower troposphere compared to the Earth’s surface temperature. Consequently, the sum of PHI and PCI
must be much smaller than they are thought to be in the consensus treatment of
this problem or in the similar concentric spherical shell problem.
Let us now examine the correct solution to this parallel
plane black body radiators problem. It
is the electromagnetic field between the two planes that governs the flow of
electromagnetic energy between the planes.
Or one can say it is the energy density at each plane surface that
drives the exchange of energy between the planes due to the energy density
gradient between the two planes. The
critical and driving parameter here is
Δe =
eH - eC = aTH4 – aTC4
,
where each black body radiator surface maintains its
black body radiator requirement that the energy density at the surface is given
by Stefan’s Law.
Electromagnetic energy flows from the high energy surface to the low
energy surface, as is the case in energy flows generally.
PHI = (σ/a) Δe = (σ/a) (aTH4 – aTC4
) = σ TH4
– σ TC4
PCI = 0,
which is consistent with experimental measurements of the
rate of radiant heat flow between two black body radiators. Note that as TC approaches TH,
PHI approaches zero as should be the case inside a black body
cavity in thermal equilibrium. There is no thermal emission from either of the black body cavity walls then. Note also that when TC = 0 K, PHI is given by the Stefan-Boltzmann Law
PHI = σ TH4.
Let us recalculate PH and PC in
this correct formulation of the problem:
PC = APCO + APCI - APHI
= AσTC4
+ 0 – [AσTH4
- AσTC4]
= 2AσTC4
- AσTH4
PH = APHO + APHI - APCI
= AσTH4
+ [AσTH4
- AσTC4]
- 0 = 2AσTH4
- AσTC4
And we see that the power inputs to each plane needed to
maintain their respective temperatures as they cool themselves by thermal
radiation are unchanged in this correct energy density or electromagnetic field
centered viewpoint from the consensus viewpoint. Experimentally, the relationship between the power inputs
to the thermal radiation emitting planes at given temperatures are exactly the
same. This fact causes the proponents of
the consensus viewpoint to believe they are right, but they nonetheless violate
the energy density requirements of electromagnetic fields and of black body
radiation itself.
Because PCI = 0, back radiation from a cooler atmosphere to the surface
is also zero and not 100% of the top of the atmosphere solar insolation as in
the current NASA Earth Energy Budget. Because PHI = σ TH4 – σ TC4 , the Earth's
surface does not radiate 117% of the top of the atmosphere insolation
either. These radiation flows are hugely exaggerated by NASA and in
similar Earth Energy Budgets presented in the UN IPCC reports. See the NASA
Earth Energy Budget below:
This is very important
because reducing these two radiant energy flows of infrared photons reduces the
effect of infrared-active gases, the so-called greenhouse gases,
drastically. Many fewer photons are actually available to be absorbed or emitted by greenhouse gases than they imagine. This is a principal error that should cause the global
climate computer models to greatly exaggerate the effects of the greenhouse gases, just
as they have.
The first equation is from the discussion above with
TS the surface temperature and TA the temperature of the
atmosphere. The second is according to the NASA Earth
Energy Budget above. If one takes TS
to be 288K, then the temperature of the atmosphere required to absorb as much
infrared energy as NASA claims is absorbed is 155.4K. There is no such low temperature in the Earth’s
atmosphere. To find so low a
temperature, one has to go far out into the solar system many times the radius
of Earth’s orbit. That being the case,
any such thermal radiation absorbed by matter at such a low temperature is as
much lost in the Earth Energy Budget as is the power equal to 12% of the solar insolation
emitted from the Earth’s surface which NASA allows passes through the
atmospheric window into space. It should
be apparent to the reader that the NASA Earth Energy Budget is nonsense.
As I have pointed out in the past, one fatal consequence of the
exaggeration of thermal radiation from the surface of the Earth is readily
calculated from the fact that even if the atmosphere acted as a black body
absorber, which it does not, it can only absorb the thermal radiation said to
be emitted from the surface at an absurdly low atmospheric temperature. Observe that the power of infrared radiation
from the surface which is absorbed by the atmosphere PSA is
PSA = σ ( TS4 – TA4)
PSA = (1.17 – 0.12) (340 W/m2)
Extending the Solution
to Gray Body Thermal Radiators and Other Real Materials:
Many real materials do
not behave like black body radiators of thermal radiation. Those that do not radiate as black body
materials would, radiate less than the black body radiator would. Why would they radiate less? This is because they do not create as high an
electromagnetic field energy density at their surfaces as does a black body
radiator. From Stefan’s Law for a black
body radiator, the energy density at the surface is
e = aT4
but for a gray body
radiator the energy density at each wavelength λ is
e(λ) = εaT4.
This means the energy
density at any given frequency is a constant fraction ɛ of that of a black body
radiator, with 0 ≤ ɛ ≤ 1.
In general, a material
may not behave like either a black body or a gray body radiator at a particular
wavelength. In that case,
e(λ) = ε(λ)aT4,
where the fraction of
the black body output at wavelength λ is variable.
An isolated material
surrounded by vacuum and a T=0 K environment then has a power per unit area
output of
P(λ)
= εσT4 for a gray body and ε is seen to be the emissivity, and
P(λ) = ε(λ)σT4,
for a general material, such as carbon dioxide or water vapor, where the absorption and emission become variable fractions of that of a black body as a function of wavelength.
For our two parallel
plates above, if both are gray bodies, then between the plates
Δe = eH – eC
= εH a TH4 – εC a TC4
PHI = (σ/a) Δe = εH σ TH4
– εC σ TC4
PCI = 0.
Here we see that the emissivity which determines the electromagnetic field energy density at the surface is also playing the role of the absorptivity at the absorbing colder surface. So of course, Kirchhoff’s Law of thermal radiation that the emissivity equals the absorptivity of a material in a steady state process applies. There is really nothing at all to prove if one starts with the primary fact and boundary condition that the energy density is the fundamental driver of the thermal radiation of materials.
Update: Considerable additions were made on 8 November 2017.
Update: Additions made on 12 November 2017.
Update: The extension to gray bodies and other bodies was made on 14 November 2017.
Update: Explanatory additions on 27 November 2017.
Update: Further explanatory text added on 29 November 2017.
Update: Further efforts to help the reader to understand this post and to provide the reader a reason to read it in the introductory paragraphs on 24 March 2018. I am amazed how difficult many readers find it to alter their viewpoint of thermal radiation even when they have no counter argument to my argument presented here.
Update: The extension to gray bodies and other bodies was made on 14 November 2017.
Update: Explanatory additions on 27 November 2017.
Update: Further explanatory text added on 29 November 2017.
Update: Further efforts to help the reader to understand this post and to provide the reader a reason to read it in the introductory paragraphs on 24 March 2018. I am amazed how difficult many readers find it to alter their viewpoint of thermal radiation even when they have no counter argument to my argument presented here.
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