Posts Evaluating Earth Energy Budget Problems

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:

Using Heat Transport Powers of the NASA Earth Energy Budget to Prove that Carbon Dioxide has an Insignificant Effect on Surface Temperatures, 15 June 2018

A Summary of Some of the Physics Errors of the NASA Earth Energy Budget, 8 June 2018

Water Vapor and Gravity Act Together to Warm the Earth, 19 June 2017

The Settled Science of Catastrophic Man-Made Global Warming Violates the Laws of Physics, 10 June 2017

mgh, Not Just Greenhouse Gases, Provides a Warm Earth, 23 May 2017

Greenhouse Gases Warmed the Earth Somewhat, but Additions Now Cool the Earth, 27 July 2015

Why Greenhouse Gas Theory is Wrong -- An Examination of the Theoretical Basis, 7 March 2015

Back-Radiation Insignificance for the Equilibrium Surface Temperature, 14 March 2014

The Stefan-Boltzmann Law at a Non-Vacuum Interface: Misuse by Global Warming Alarmists, 6 April 2013

The Unsettled Earth Energy Budget, 24 February 2013

Back-Radiation and the Highly Fallacious Kiehl-Trenberth Energy Budget, 10 July 2012

NASA Finally Produces A Realistic Energy Budget for the Earth, 26 May 2011

The Nested Black Body Shells Model and Extreme Greenhouse Warming

And Lessons from this Model that Show Us How Limited the Greenhouse Effect Actually Is

In a previous post, Critique of The Steel Greenhouse by Willis Eschenbach, I wrote about the Willis Eschenbach thought experiment model of a perfectly conducting sphere closely surrounded by a concentric perfectly conducting shell in which these bodies behave like black body radiators and the only energy loss mechanism is thermal radiation.  That black body thought experiment was not presented as a good model of the greenhouse gas effect for the Earth.  It was presented to illustrate that there is a warming effect due to thermal radiation absorption in the atmosphere, which many call the greenhouse gas effect.  I pointed out that Eschenbach is right that the surrounding shell causes the inner sphere to have a higher temperature than it would if it were only surrounded by vacuum at T = 0 K because it loses radiant energy more slowly.

But Eschenbach makes a very serious error in common with almost all scientists because he believes the surrounding shell radiates the surface of the inner sphere with the same radiation that the outer shell radiates from its outer surface toward T = 0 K surroundings.  I have explained why this is an error in my post Solving the Parallel Plane Black Body Radiator Problem and Why the Consensus Science is Wrong.  By making this error, he multiplies the photon energy density by a factor of 3 in the space between the sphere and the shell, making this one of many ways that the catastrophic man-made global warming advocates greatly strengthen the greenhouse gas effect.  I pointed out that the current NASA Earth Energy Budget amplifies the photon energy density in the atmosphere even more by a factor of 12.8!  This is critical because the warming effect due to greenhouse gases is proportional to the photon energy density at a wavelength times the absorption cross section at that wavelength.  Consequently, increasing the photon energy density by a factor of 12.8 increases the warming energy by a factor of 12.8 at all wavelengths at which absorption occurs for the gas molecule.

In this post, I will provide the radiative equilibrium solution for a black body sphere with 2 surrounding black body shells.  This might seem important because the mean free path length for absorption of longwave infrared photons that can be absorbed by water vapor and carbon dioxide is very short at the primary absorption wavelengths, though it can be much longer in the wings of those primary absorption wavelengths.  The solution will then be generalized to N surrounding black body shells since the absorption of photons of different wavelengths by a greenhouse gas in the atmosphere can take different numbers of spheres in a model.  In fact, for a given infrared-active molecule, the number of shells is a function of the absorption cross-section as a function of the wavelength because the mean free path length varies over orders of magnitude from the main absorption wavelengths out into the tails or wings of those principal absorption peaks.

Having developed this nested shell model for black body absorbers/radiators, I will then generalize this model to account for a sphere surface which has an emissivity different from the emissivity of the shell surfaces.  Because the absorption of greenhouse gases is over a substantially smaller range of frequencies than is that of the black body material, one might expect a major change in the result for the inner sphere equilibrium temperature based on the effective emissivity/absorptivity of the inner sphere surface and of the nested shell surfaces that might be an analog to greenhouse gases.  This result proves to be very interesting.

The results will inform us of interesting properties of an energy loss problem dominated by radiation loss and absorption.  However, this model is not a good model of the Earth’s greenhouse gas effect.  Energy loss and transport from the Earth’s surface is not dominated by radiant energy loss and absorption.  It is dominated instead by the effects of the Earth’s gravitational field moderated by convection and the evaporation-condensation cycle of water.  The temperature of the Earth’s surface and of each successively higher layer of air in which an infrared-active molecule will absorb the longwave radiation from the Earth’s surface or a lower layer of air is not determined primarily by radiation transport of energy, but by gravity, convection, and the water cycle.

One has to remember that there are many competing effects in determining the Earth’s climate, including many cooling effects by both water vapor and carbon dioxide that are too often underestimated.  Radiative cooling of the surface is much less than NASA and the UN IPCC claim it is.  The alarmist rendition of greenhouse gas warming does everything it can to amplify that effect, to ignore the many cooling effects, and to over-emphasize the role to carbon dioxide relative to that of water vapor.  Finally, I will adapt a portion of the shell model to make an estimate of the total greenhouse gas effect in the real world of the Earth’s climate.  I will then proceed to make an estimate for the size of the greenhouse effect for the first 400 ppm of carbon dioxide in the atmosphere and discuss briefly what one can expect as one adds higher concentrations of carbon dioxide to the atmosphere.  These estimates are not precise, but they are of the proper scale and will inform us that the warmer Earth surface compared to its overall radiative temperature as seen from space is in very little part due to the absorption of longwave radiation by carbon dioxide.  It also makes it clear that the infrared-absorbing effect due to water vapor is also a small fraction of the 33K effect normally attributed to greenhouse gases, though that effect is many times the effect due to carbon dioxide.

The inner core sphere section of unit area has a power input of Q, the temperature of the sphere is T_S and the power per unit area of surface it emits is P_S.  The first closely surrounding concentric shell has no power input except that radiated by the sphere.  Its own temperature is T_O1, which when the power to the sphere is turned on is 0 K and the shell is only then warmed by radiation from the sphere which travels at the speed of light to it.  It radiates no photons toward the sphere, but does radiate photons as its temperature rises toward the second shell with power P_O1.  The second concentric shell has the same parameters but with a 2 in the subscript, rather than a 1.  It also starts from T=0K.  Only vacuum exists between the sphere and the planes so that there are no heat losses except by means of thermal radiation.

When the power Q to the sphere is first turned on, the sphere has an initial temperature of T_SI, given by the Stefan-Boltzmann Law, since the sphere is at that instant surrounded by T = 0K.

Q = P_SI = σT_SI⁴

Let the thermal equilibrium values of each parameter be denoted with the addition of an E in the subscript, then at thermal equilibrium:

Q = P_SE = P_O1E = P_O2E

Q = σ T_SE⁴ – σ T_O1E⁴ = σ T_O1E⁴ – σ T_O2E⁴ = σ T_O2E⁴

We can see that

T_SI = T_O2E

From the right side of the equilibrium equation we see that

T_O1E⁴ = 2 T_O2E⁴

Then plugging this value in the part of the equilibrium equation involving T_SE, we have

T_SE⁴ – T_O1E⁴ = T_O2E⁴

T_SE⁴ – ( 2 T_O2E⁴ ) = T_O2E⁴

T_SE⁴ = 3 T_O2E⁴ or T_SE = 3^0.25 T_O2E = 3^0.25 T_SI  = 1.3161 T_SI, since T_O2E = T_SI

With one surrounding shell, the equilibrium temperature of the enclosed sphere was given by

T_SE = 2^0.25 T_SI = 1.1892 T_SI

Thus the second shell causes a sufficient reduction in the cooling rate that the equilibrium temperature of the sphere is 1.067 times higher than it would be with one surrounding shell.  The rise in the sphere temperature is less with each added shell.

The Nth surrounding shell results in a radiative equilibrium sphere temperature of

T_SE = (N+1)^0.25 T_SI

Thus,

For 10 shells: T_SE = 1.8212 T_SI

For 100 shells: T_SE = 3.1702 T_SI

For 1000 shells: T_SE = 5.6282 T_SI

Imagine modeling the absorption of surface radiation by water vapor using such a model.  Of course, water vapor is not a black body absorber or radiator of longwave infrared radiation.  For most of the radiation that it absorbs, it has a mean free path for absorption which is short, though in the wings of an absorption maximum, the absorption cross section can be much lower and the corresponding mean free path is much longer.  But for a crude model, one might say that the absorption mean free path is something like 10 meters.  One might then say that to account for water vapor absorption out to 8000 meters altitude, one needs 800 shells.  Of course, one would think each shell would absorb only a fraction of the power that a black body would and it would emit only a fraction of that energy also.  Carbon dioxide has a longer mean free path and it absorbs a smaller fraction of the power that a black body would compared to water vapor, but it also does not have a relatively sharp cut-off in its density at higher altitudes in the atmosphere.  One might model it with a much smaller fraction of absorption compared to water with a shell every 40 meters but with 300 shells to get to an altitude of 12000 meters.

Let us see what happens in this simple model if we assign an emissivity to the sphere surface, ɛ_S, and an emissivity to shells representing absorptions by a greenhouse gas, ɛ_G.  The equations for a two-shell model then become:

Q = ɛ_S σ T_SI⁴

At equilibrium,

Q = ɛ_S σ T_SE⁴ - ɛ_G σ T_O1E⁴ = ɛ_G σ T_O1E⁴ - ɛ_G σ T_O2E⁴ = ɛ_G σ T_O2E⁴

ɛ_S σ T_SI⁴ =  ɛ_G σ T_O2E⁴, so T_O2E = (ɛ_S/ɛ_G)^0.25 T_SI

T_O1E⁴ = 2 T_O2E⁴

ɛ_S T_SE⁴ = 3 (ɛ_G T_O2E⁴) = 3 (ɛ_S T_SI⁴)

T_SE = 3^0.25 T_SI, the same solution for the equilibrium sphere temperature we had for the black body emitters and absorbers.

Consequently, for N greenhouse gas shells we have:  T_SE = (N + 1)^0.25 T_SI just as with N black body shells.

So, the greenhouse gas hypothesis is looking as though it could indeed cause a disastrous increase in the Earth’s surface temperature even though greenhouse gases are far less efficient absorbers and emitters than are black body absorbers, right?

Wrong.  There is a fatal flaw in the model.  That fatal flaw is the assumption that the only way that heat is transported from the surface of the Earth is by means of thermal radiation.  In reality, much more heat is transported up through the atmosphere by means of the water evaporation and condensation cycle and by convection currents.  Let us look once again at the NASA Earth Energy Budget:

There is no back radiation of 100% and the surface radiation given as 117% in terms of the top of the atmosphere solar insolation is hugely exaggerated by NASA.  The real thermal radiation from the surface is the difference between these values or 17%.  This is perhaps a decent value for the loss from the surface itself and of this 12% is lost immediately to space.  This leaves only 5% of thermal radiation from the surface that is absorbed by the atmosphere along with 5% attributed to convection and 25% lost by water evaporation.  So, in this energy balance only 5% / (5% + 5% + 25%) = 0.143 of the surface energy is absorbed by the atmosphere as radiation from the surface.

Even this is a huge overstatement of the fraction of the surface energy carried off by means of transport by radiation from shell to shell.  This is the fraction that is absorbed by the first shell of the many-shell model.  Once that first absorption occurs, the absorbing greenhouse gas molecule passes off the absorbed energy to the nitrogen and oxygen molecules and the argon atoms that collide with it 6.9 billion times a second at sea level and 2.1 billion times a second at 10 Km altitude in the U.S. Standard Atmosphere of 1976.  Yes, the greenhouse gas molecule very quickly comes into temperature equilibrium with the molecules in the same layer of air with it.  These greenhouse gas molecules can radiate thermal energy to the layer of air just above which is slightly cooler, but the time between such radiation events is extremely long compared to the gas collision frequency.  Water molecules radiate only about every 0.2 seconds and carbon dioxide molecules radiate only about once a second.

Consequently, almost all of the 5% of surface energy that is radiated to the first shell and absorbed is thereafter transported by convection.  The assumption in the model above that all energy is transported through the atmosphere as radiation and in stages could not be more wrong.  In fact, while the little bit of further radiation transport from one layer of air to a cooler layer of air a short distance above it would be handled in the nested shell model as a further warming of the surface.  But, this should actually be viewed as a cooling effect, because any energy transported from air layer to air layer is transported to higher altitude faster compared to the alternative transport mechanism of convection.  These realizations constitute a good lesson in the need to check your premises!

Based on almost all of the 5% of surface radiation being absorbed by the first shell and then thereafter being transported by convection, about what surface temperature might we expect?  Recall that in the one shell case, the surface equilibrium temperature is given by

T_SE = 2^0.25 T_SI = 1.189 T_SI

At a thermal radiation fraction of 0.143, the greenhouse gas effect temperature rise would be about 0.143 (0.189) = 0.027 times T_SI.  If one takes T_SI = 255 K, the radiative temperature of the Earth system as a whole with respect to space, then the change of temperature attributable to the greenhouse gas effect for our present atmosphere is 

ΔT = 6.9 K

Note that 6.9 K is only 21% of the 33K difference of the surface temperature with respect to the Earth’s effective radiative temperature as seen from space.  Consequently, the claim that this temperature difference is due to the absorption of longwave infrared radiation emitted from the Earth’s surface is exaggerated by nearly a factor of 5.

Almost all of this 6.9K warming effect is due to water vapor, not the 400 ppm of carbon dioxide in the atmosphere.  The absorption by carbon dioxide compared to that by water vapor is about 8 times less.  Thus the portion of the total infrared warming effect due to carbon dioxide is one ninth of 6.9 K, which is 0.8 K.  My recent post Using Heat Transport Powers of the NASA Earth Energy Budget to Prove that Carbon Dioxide has an Insignificant Effect on Surface Temperatures, estimated that the present 400 ppm of CO2 in the atmosphere causes a temperature increase of only 0.2 K, but this is the result of a different approach to the issue and it took into account the increased absorption of solar insolation caused by carbon dioxide in the atmosphere.  The fraction of the 6.9 K net greenhouse gas temperature increase that can be attributed to carbon dioxide overall is then about 3%.

Given that the 0.2 K net warming effect of carbon dioxide is already mostly saturated, additions of further carbon dioxide to the atmosphere will have very little effect on the surface temperature of the Earth.  What is more, the feedback effect of water vapor at present common levels of water vapor is more likely negative than positive and is certainly very small.

The reason that the surface of the Earth is about 33 K warmer than the effective radiative temperature of the Earth system as a whole as seen from space is because most of the energy dissipated by the Earth’s surface and through the troposphere (the lower atmosphere) is transported upward by a combination of water evaporation and convection.  It is very important that transport by thermal radiation is a much more minor actor in the transport of heat in the troposphere.  It is critically important that most of the Earth’s heat is radiated to space from the upper part of the troposphere which is at temperatures that are close to those of the Earth system as observed from space.  This actually forces the air at the altitudes where most of the radiation to space occurs to be near and slightly lower than this low effective radiative temperature of the Earth system.  Once that is a given, then the temperature gradient in our troposphere due to the Earth’s gravitational field dictates the surface temperature with adjustments due to such cooling mechanisms as convection and the effects of the water cycle and clouds.

Critique of The Steel Greenhouse by Willis Eschenbach

Willis Eschenbach made a guest post entitled The Steel Greenhouse at Watts Up With That in November 2009 that reduces a critical aspect of the catastrophic man-made global warming hypothesis to a very simple model.  Some critics of catastrophic man-made global warming claim his model is incorrect and others embrace it.  In this post I will solve the same problem he does, but with fewer assumptions and I will not violate the energy density conservation rules of equilibrium electromagnetic fields given by Stefan’s Law in the simple limit of black body cavities and more generally given by electromagnetic field theory as Eschenbach does.  I will follow the mathematics from a non-equilibrium case to the radiative equilibrium case.

In one very important respect, Eschenbach produces a correct result, yet in another very important respect he buys into an error that causes a huge amplification of the effects of infrared-active or greenhouse gases when that concept of thermal radiation is applied to real climate issues.  If you have not read my prior post on thermal radiation physics which I reference below, you are a most unusually astute scientist if you really know and understand what Eschehbach’s widely shared error is.

I have previously discussed the fundamentals of black body thermal radiation and how it applies to real life materials in several postings.  The best single post to read to understand why it is improper to think about black body and thermal radiation generally as most scientists do is:

Solving the Parallel Plate Thermal Radiation Problem Correctly Provesthe Settled Science of Man-Made Global Warming Wrong

The Eschenbach model for his discussion of a fundamental aspect of the greenhouse gas warming effect is to imagine the Earth as a perfectly conducting sphere with black body emission closely surrounded by a perfectly conducting shell which also has surfaces that act as though they are black body absorbers and radiators.  Effectively, his model takes there to be only vacuum between the surface of the inner sphere and the surrounding shell and only vacuum and a T=0 K universe beyond the surrounding shell.  The only means for energy to flow in the system between the inner sphere and the outer shell is by thermal radiation, as it is also beyond the shell.  The very small correction for the different surface areas of the inner sphere and the outer shell will be ignored as Eschenbach did.  The geometric surface area correction is less than one part in a thousand.  This is not meant to be an accurate model of the Earth and its atmosphere.  It is a useful thought experiment.

Eschenbach posits that the inner sphere has its own source of heat which he sets at a thermal power density of 235 W/m² at the surface of the sphere.  Since this is the only source of heat, at equilibrium, the only very slightly larger shell around the sphere must radiate energy into space at a power of 235 W/m².  So far he is right.

He posits that the outer shell is a great conductor, so there is no temperature gradient in the shell between the inner and outer surfaces.  Now he applies standard issue knowledge of thermal radiation and says that if the two sided outer sphere is radiating power on the outside surface at 235 W/m², then it must be doing so also from the inner surface which has the same temperature, because the relationship between the power of radiation and the temperature is given by P = σT⁴, where P is the power per unit area, T is the temperature of the surface in Kelvin, and σ is a constant.  This relationship is the Stefan-Boltzmann law.  If the inner surface were radiating into a vacuum at T = 0K, this would be a correct application of the Stefan-Boltzmann Law.  This is not the case for the inner surface, though we will imagine that it is for the outer surface since space has an average temperature relatively close to absolute zero compared to an Earth surface temperature near 288 K.

Eschenbach goes on to observe that since the shell is radiating energy back to the inner sphere at 235 W/m² and the sphere surface already had a supply of power of 235 W/m², the sum of the two powers is now 470 W/m².  Putting a shell around the core sphere has doubled the radiating power of the core sphere.  This is the real greenhouse effect he says.  His solution is based on a flux of photons at 470 W/m² flowing outward from the sphere surface and a flux of photons at 235 W/m² flowing downward from the shell to the sphere surface.

Some people are bothered by the failure here to conserve energy, but not very many, because most people think it is only important to conserve energy at the sphere and at the shell.  Most people seem to examine this and say, well, the 470 W/m² radiating out from the inner sphere surface minus the 235 W/m² radiating into the inner sphere surface from the inner surface of the shell is still 235 W/m² which is supplied by the internal power supply of the core sphere.  QED, energy is conserved.  Never mind the fact that the energy of the photons issuing forth at the rate of 470 W/m² and the energy of the photons from the inside wall of the shell at 235 W/m² must add, not subtract, when we examine the energy density of the volume between the outer shell and the inner core sphere.  I will discuss this somewhat further on in this post, but the reference I gave above will be a much more thorough discussion of this critical issue.

Let us step back from this and talk a moment about black body cavity thermal radiation.  The principal characteristic of a black body cavity is that it is at thermal equilibrium and the energy density inside the cavity is everywhere the same and given by Stefan’s Law.  If the energy density is e, then e = a T⁴, where a is Stefan’s constant.  Within the cavity in equilibrium, there are just as many photons traveling in one direction as in its opposite direction.  If photons traveling in opposite directions had energies that cancelled one another out, then the energy density inside a black body cavity would be zero and would not be given by Stefan’s Law.

If you return to Jackson’s Classical Electrodynamics, you will also find that two oppositely directed electromagnetic plane waves will simply pass through one another and reappear as normal plane waves after their very brief interaction.  They most certainly do not sum up to zero energy.

Let us simplify the problem even more by just looking at two facing planes, one of which has a supply of power Q per unit surface area and only radiates that power from the surface facing the other plane which has two sides that can radiate power.  Imagine these to be a small section out of the Eschenbach inner core of a unit area of surface and of a unit area of outer shell.  This simplification of the model with its parameters for thermal radiation is shown below:

The power into the left plane representing a unit surface area of the inner core causes it to radiate power at a rate of P_S, when the power to the sphere is first turned on.  We will assume that the surrounding shell on the right of the drawing was at T=0 K when the power to the inner core was turned on.  Let us either assume that it has a finite heat capacity so that it has to warm up to its equilibrium temperature or we count on the finite speed of light to create a delay.  We are making this assumption so that we are not too quick to leap to false assumptions.  What is the general case before and when equilibrium is reached?  It is obvious that T_O will increase.  What will happen to T_S?

The power transferred from the inner core to the outer shell is P_S. The power radiated from the outer surface of the shell section will be P_O and that surface is in vacuum facing nothing but T = 0 K space.  For simplicity and in order to be strictly correct in applying the Stefan-Boltzmann Law, the space between the powered inner core and the spherical shell is in vacuum.  We have

Q = P_S  = σ T_S⁴ - σ T_O⁴

P_O = σ T_O⁴

At equilibrium, P_S = P_O, so

T_SE⁴ - T_OE⁴ = T_OE⁴, where the added E in the subscripts designates the equilibrium values.

Therefore, T_SE⁴ = 2 T_OE⁴ or T_SE = 1.189 T_OE and

P_S = σ ( 2 T_OE⁴ - T_OE⁴ ) = σ T_OE⁴.

But Q = P_S always, so when the shell was still at T=0 K, Q = P_S = σ T_SI⁴ , where T_SI was the initial temperature of the surface of the sphere when Q was first turned on and all the sphere surface saw as a T=0 K environment.  Consequently,

T_OE = T_SI

At equilibrium, the outward facing surface of the shell radiates energy at the same rate the initial core spherical surface did when it was surrounded by T=0 K.  The shell temperature has become what the initial core sphere surface temperature was.  Very importantly, the inner core surface temperature has increased to be

T_SE = 1.189 T_OE = 1.189 T_SI

Putting the shell around the inner core has sufficiently retarded its rate of cooling that with the same input power to the inner core, its temperature has increased by a factor of 1.189 or the one-quarter root of 2.  The reason for this is that the powered inner core is emitting energy from a surface of unit area 1, while the surrounding shell is retarding its emission with a surface of unit area 1 and emitting a power equal to the initial power emitted from the sphere from its outer surface of unit area 1.  In the similar problem with two planes both of which have two black body surfaces and one of which is supplied with power, the equilibrium condition has both planes at the T_SI temperature.  They create a black body cavity between them and the photon emission from the two facing inner surfaces is P = 0.  There is only P = σ T⁴ emission from the outward facing surfaces of each plane and the interior energy density is given by Stefan’s Law as

e = a T⁴

Let us return to Eschenbach’s post.  His inner sphere had a power of its own of 235 W/m² and the shell radiated 235 W/m² down upon the inner sphere, so he says the inner sphere surface radiates power away from its surface equal to the sum of the internal power and the radiated power from the surrounding shell, which is 470 W/m².  Applying the Stefan - Boltzmann Law:

P_S = 470 W/m² = σ T_SE⁴

T_SE = 301.74 K

In my case,

P_S = σ T_SI⁴ = 235 W/m²

T_SI = 253.73 K

T_SE = 1.189 T_SI = 301.68 K

So, both Eschenbach and my calculations yield the same, higher inner core surface temperature. 

Our important difference is that he supposes the vacuum between the inner core and the surrounding shell has a photon density corresponding to (470 + 235) W/m² = 705 W/m², while my photon density corresponds only to those emitted from the inner core surface and there are no photons emitted from the inner surface of the surrounding shell.  The reasons for this are given at length in my first reference above.  Consequently, the real photon density between the sphere and the shell is actually that corresponding to 235 W/m².  Eschenbach has multiplied the photon density by a factor of 3.

Why is the photon density critical when one more realistically addresses the catastrophic man-made global warming hypothesis?  One way one calculates the longwave infrared absorption warming attributed to greenhouse gases is with an experimentally measured absorption cross section for each frequency of photon energy for each greenhouse gas molecule such as water vapor and carbon dioxide.  One then multiplies the number of photons of each frequency times the value of the absorption cross section for that frequency to calculate the number of absorption events.  A factor of 3 exaggeration in the number of photons at each frequency is an important exaggeration of the greenhouse gas effect.

It is actually even worse than this when the proponents of the catastrophic man-made global warming hypothesis with a similar misconception set to work.  Let us look once again at the NASA Earth Energy Budget:

NASA has a surface radiation of 117% here and a back radiation of 100%.  This produces a corresponding photon density of 217%.  In reality, the photon density is 117% - 100% = 17%.  Consequently, NASA has amplified the photon density by a factor of 217% / 17% = 12.8.  This is the equivalent of amplifying the greenhouse gas effect by a factor of 12.8.

There are many who believe that the radiative forcing caused by a doubling of carbon dioxide in the atmosphere is 3.7 W/m².  Divide that radiative forcing value by 12.8 to account for the greatly exaggerated effect caused by an exaggeration of the number of photons that carbon dioxide can absorb and one gets a radiative forcing value of only 0.29 W/m².  This alone would make it much harder to experimentally document the warming effect of carbon dioxide and would explain why the global climate models have been exaggerating the effects of carbon dioxide so long and why it has been so hard for them to find that elusive hot spot in the upper troposphere in the tropics they predicted.

It has other important consequences as well.  Suddenly the cooling effects of carbon dioxide that are usually ignored with the claim that they are much smaller than the greenhouse gas warming effect are not so small in comparison.  These cooling effects include:

• The absorption of solar insolation in the atmosphere before it can reach the surface to warm the surface
• Carbon dioxide has a higher heat capacity than do nitrogen and oxygen molecules, so more carbon dioxide increases the heat energy carried upward by convection currents
• Because carbon dioxide radiates thermal energy from a warmer layer of air to a cooler layer of air above it and that energy is transported at the speed of light, albeit for a short distance in the troposphere, this is faster transport of energy than is the convection current that would otherwise transport this energy upward           

Even if each of these three cooling effects is smaller than the reduced greenhouse warming forcing effect for carbon dioxide of 0.29 W/m², the sum of the decrease on the net warming forcing effect may be quite significant.  What is more, these cooling effects probably do not saturate as quickly as the greenhouse warming effect does as one increases the concentration of carbon dioxide in the atmosphere from current levels.  Consequently, the small warming effect of 400 ppm of carbon dioxide may be reduced by further additions of carbon dioxide, if not now, then maybe as one adds more to 600 ppm of carbon dioxide in the atmosphere.  At this point, we do not know what happens as CO₂ is added in increments at higher concentrations than 400 ppm.

In addition, the diminished effect of carbon dioxide on warming should cause everyone to have more interest in understanding many natural causes or non-man-made causes of climate variability.  We have far too little knowledge of

• Solar irradiance variations
• Solar wind and the weakening solar magnetic field effects
• Cosmic ray seeding of clouds
• Other causes of cloud variations
• The condensation of water in dew and ground fog surface warming
• Precipitation effects on warming/cooling
• Evaporation of water as a function of temperature and humidity around the world
• Better understanding of the greenhouse effect of water vapor
• Ocean currents and cycles
• Effects caused by the weakening of the Earth's magnetic field
• Effects of aerosols
• Effects of dust
• Other effects not listed

Then there are other man-made effects, primarily man’s use of the land.

I believe that these other effects on climate will in some cases prove to be more important for our understanding of the climate and its changes than are the effects of additions to the carbon dioxide concentration in our atmosphere.  Carbon dioxide has a very small effect on the climate, especially so when one is concerned about the effect of additions to the present levels of carbon dioxide.

Global Warming: Fake News from the Start -- Article by Dr. Tim Ball and Tom Harris

Senator Tim Wirth, scientist James Hansen and others manufactured the climate “crisis”

President Donald Trump announced that the United States would withdraw from the Paris Agreement on climate change because it is a bad deal for America.

He could have made the decision simply because the science is false. However, most of the American and global public have been brainwashed into believing the science is correct (and supported by the faux 97% consensus), so they would not have believed that explanation. 

Canadian Prime Minister Justin Trudeau, and indeed the leaders of many western democracies, support the Agreement and are completely unaware of the gross deficiencies in the science. If they understood those deficiencies, they wouldn’t be forcing a carbon dioxide (CO₂) tax on their citizens. 

Trudeau and other leaders show how little they know, and how little they assume the public knows, by calling it a “carbon tax” on “carbon emissions.” But CO₂ is a gas, the trace atmospheric gas that makes life on Earth possible. Carbon is a solid, and carbon-based fuels are solid (coal), liquid (oil) or gaseous (natural gas).

By constantly railing about “carbon emissions,” Trudeau, Obama and others encourage people to think of carbon dioxide as something “dirty,” like soot, which really is carbon. Calling CO₂ by its proper name would help the public remember that it is actually an invisible, odorless gas essential to plant photosynthesis. 

Canadian Environment Minister Catherine McKenna is arguably the most misinformed of the lot, saying in a recent interview that “polluters should pay.” She too either does not know that CO₂ is not a pollutant, or she is deliberately misleading people.

Like many of her political peers, McKenna dismisses credentialed PhD scientists who disagree with her approach, labelling them “deniers.” She does not seem to understand that questioning scientific hypotheses, even scientific theories, is what all scientists should do, if true science is to advance.

That is why the Royal Society’s official motto is “Nullius in verba,” Latin for “Take nobody's word for it.” Ironically, the Society rarely practices this approach when it comes to climate change.

Mistakes such as those made by McKenna are not surprising, considering that from the outset the entire claim of anthropogenic global warming (AGW) was built on falsehoods and spread with fake news. 

The plot to deceive the world about human-caused global warming gathered momentum right after the World Meteorological Organization and United Nations Environment Program (UNEP) created the United Nations Intergovernmental Panel on Climate Change (IPCC) in 1988.

After spending five days at the U.N. with Maurice Strong, the first executive director of UNEP, Hamilton Spectator investigative reporter Elaine Dewar concluded that the overarching objective of the IPCC was political, not scientific. “Strong was using the U.N. as a platform to sell a global environment crisis and the global governance agenda,” she wrote.

The political agenda required “credibility” to accomplish the deception. It also required some fake news for momentum. Ideally, this would involve testimony from a scientist before a legislative committee. 

U.S. Senator Timothy Wirth (D-CO) was fully committed to the political agenda and the deception. As he explained in a 1993 comment, “We’ve got to ride the global warming issue. Even if the theory of global warming is wrong, we will be doing the right thing.…” 

In 1988 Wirth was in a position to jump-start the climate alarm. He worked with colleagues on the Senate Energy and Natural Resources Committee to organize and orchestrate a June 23, 1988 hearing where the lead witness would be Dr. James Hansen, then the head of the Goddard Institute for Space Studies. Wirth explained in a 2007 interview with PBS Frontline:

“We knew there was this scientist at NASA, who had really identified the human impact before anybody else had done so and was very certain about it. So, we called him up and asked him if he would testify.”

Hansen did not disappoint. The New York Times reported on June 23, 1988: “Today Dr. James E. Hansen of the National Aeronautics and Space Administration told a Congressional committee that it was 99 percent certain that the warming trend was not a natural variation, but was caused by a buildup of carbon dioxide and other artificial gases in the atmosphere.”

Specifically, Hansen told the committee, “Global warming has reached a level such that we can ascribe with a high degree of confidence a cause and effect relationship between the greenhouse effect and observed warming…. It is already happening now.”

Hansen also testified: “The greenhouse effect has been detected, and it is changing our climate now…. We have already reached the point where the greenhouse effect is important.”

Wirth, who presided at the hearing, was pre-disposed to believe Hansen and told the committee. “As I read it, the scientific evidence is compelling: the global climate is changing as the earth's atmosphere gets warmer,” Wirth said. “Now the Congress must begin to consider how we are going to slow or halt that warming trend, and how we are going to cope with the changes that may already be inevitable.” 

More than any other event, that single hearing before the Energy and Natural Resources Committee publicly initiated the climate scare, the biggest deception in history. It created an unholy alliance between a bureaucrat and a politician, which was bolstered by the U.N. and the popular press – leading to the hoax being accepted in governments, industry boardrooms, schools and churches all across the world.

Dr. John S. Theon, Hansen’s former supervisor at NASA, wrote to the Senate Minority Office at the Environment and Public Works Committee on January 15, 2009. “Hansen was never muzzled, even though he violated NASA’s official agency position on climate forecasting (i.e., we did not know enough to forecast climate change or mankind’s effect on it). Hansen thus embarrassed NASA by coming out with his claims of global warming in 1988 in his testimony before Congress.”

Hansen never abandoned his single-minded, unsubstantiated claim that CO₂ from human activities caused dangerous global warming. He defied Hatch Act limits on bureaucratic political actions, and in 2011 even got arrested at a White House protest against the Keystone XL pipeline. It was at least his third such arrest to that point. 

Like Trudeau and other leaders duped by the climate scare, Senator Wirth either had not read or did not understand the science. In fact, an increasing number of climate scientists (including Dr. Ball) now conclude that there is no empirical evidence of human-caused global warming. There are only computer model speculations that humans are causing it, and every forecast made using these models since 1990 has been wrong – with actual temperatures getting further from predictions with every passing year.

President Trump must now end America’s participation in the fake science and fake news of manmade global warming. To do this, he must withdraw the U.S. from further involvement with all U.N. global warming programs, especially the IPCC, as well as the agency that now directs it – the United Nations Framework Convention on Climate Change. He should also launch a “Red Team” exercise that lets non-alarmist scientists examine climate cataclysm claims and the purported evidence for them.

Only then will the U.S. have a chance to fully develop its hydrocarbon resources to achieve the president’s goal of global energy dominance and long-term prosperity for America and the world. 

Dr. Tim Ball is an environmental consultant and former climatology professor at the University of Winnipeg in Manitoba. Tom Harris is executive director of the Ottawa, Canada-based International Climate Science Coalition.