In reality, Water only spontaneously flows down a
pressure gradient (downhill). Energy only spontaneously flows
down an energy density gradient (from high to low).

In the domain of theology, original sin refers to Adam and Eve choosing to trust the serpent’s lies rather than natural truth placed by God in the Garden of Eden.  In legal proceedings, a similar concept concerns evidence obtained under false pretences.  “The fruit of a poisonous tree” refers to analyses, interpretations or conclusions that must be excluded because they started with a falsehood.

This post delves into a fraud at the root of consensus Climate Science™, illustrated by the image above showing how both water and energy flow down their respective gradients.  William Happer alluded to the problem in a recent presentation: (See Happer: Cloud Radiation Matters, CO2 Not So Much)

As we shall see below, mischief is a very polite term for a math and science error that has poisoned most all thinking and discussion about changes in climate and weather.  In a previous post, I summarized an important empirical experiment by Thomas Allmendinger proving that a parcel of pure CO2 and a parcel of ordinary air warm exactly the same when exposed to both SW and LW radiation.  (See Experimental Proof Nil Warming from GHGs).

So we know the notion is empirically wrong, now let’s discuss how GHG theory went off the rails from the beginning.  For that I provide below a synopsis of commentary by blogger Morpheus which he posted at Tallbloke’s Talkshop.  Excerpts in italics with my bolds and added images. (Title in red is link to blog)

CAGW (Catastrophic Anthropogenic Global Warming, due to CO2)
is nothing more than a complex mathematical scam.

The takeaways:

1) The climatologists have conflated their purported “greenhouse effect” with the Kelvin-Helmholtz Gravitational Auto-Compression Effect (aka the lapse rate).

2) The climatologists purport the causative agent for their purported “greenhouse effect” to be “backradiation”.

3) The Kelvin-Helmholtz Gravitational Auto-Compression Effect’s causative agent is, of course, gravity.

4) “Backradiation” is physically impossible because energy cannot spontaneously flow up an energy density gradient.

5) The climatologists misuse the Stefan-Boltzmann (S-B) equation, using the idealized blackbody form of the equation upon graybody objects, which manufactures out of thin air their purported “backradiation”. It is only a mathematical artifact due to that aforementioned misuse of the S-B equation. It does not and cannot actually exist. Its existence would imply rampant violations of the fundamental physical laws.

6) Polyatomic molecules are net atmospheric radiative coolants, not “global warming” gases. Far from the ‘global warming gas’ claimed by the climatologists, water acts as a literal refrigerant (in the strict ‘refrigeration cycle’ sense) below the tropopause. CO2 is the most prevalent atmospheric radiative coolant above the tropopause and the second-most prevalent (behind water vapor) below the tropopause. Peer reviewed studies corroborating this are referenced in the paper at the end of this post.

As you can see, there are two forms of the Stefan-Boltzmann (S-B) equation… one for idealized blackbody objects, one for graybody objects.

The idealized blackbody form of the S-B equation assumes emission to 0 K and ε = 1 by the very definition of idealized blackbody objects. ( ε is the term for emissivity from 0 to 1).

Idealized Blackbody Object (assumes emission to 0 K and ε = 1 by definition):
q_bb = ε σ (T_h^4 – T_c^4) A_h
= 1 σ (T_h^4 – 0 K) 1 m^2
=    σ  T^4

The graybody form of the S-B equation assumes emission to > 0 K and ε < 1.

Graybody Object (assumes emission to > 0 K and ε < 1):
q_gb = ε σ (T_h^4 – T_c^4) A_h

The ‘A_h’ term is merely a multiplier, used if one is calculating for an area larger than unity [for instance: >1 m^2], which converts the result from radiant exitance (W m-2, radiant flux per unit area) to radiant flux (W).

One can see from the immediately-above equation that the Stefan-Boltzmann (S-B) equation is all about subtracting the radiation energy density of the cooler object from the radiation energy density of the warmer object.

So radiant exitance at its most simplified (and thus the S-B equation at its most simplified) is just the emissivity of the warmer object (because emissivity only applies to objects which are emitting, and only the warmer object will be emitting… the colder object will be unable to emit in the direction of the warmer object because energy cannot spontaneously flow up an energy density gradient) multiplied by the speed of light in vacua, multiplied by the energy density differential, all divided by 4.

For graybody objects, it is the radiation energy density differential between warmer object and cooler object which determines warmer object radiant exitance. Warmer objects don’t absorb radiation from cooler objects (a violation of 2LoT in the Clausius Statement sense and Stefan’s Law); the lower radiation energy density gradient between warmer and cooler objects (as compared to between warmer object and 0 K) lowers radiant exitance of the warmer object (as compared to its radiant exitance if it were emitting to 0 K). The radiation energy density differential between objects manifests a radiation energy density gradient, each surface’s radiation energy density manifesting a proportional radiation pressure.

The climatologists use:   q = σ T^4… on graybody objects, and sometimes slap ε<1 onto that,
when they should be using:  q = ε σ (T_h^4 – T_c^4)

This has the effect of artificially inflating radiant exitance of all calculated-upon objects.

Essentially, the climatologists are treating real-world graybody objects as though they are idealized blackbody objects… with emission to 0 K and emissivity of 1 (sometimes… other times they slap emissivity onto the idealized blackbody form of the S-B equation while still assuming emission to 0 K… which is still a misuse of the S-B equation, for graybody objects).

This essentially isolates each object into its own system so it cannot interact with other objects via the ambient EM field, which grossly inflates radiant exitance of all objects, necessitating that the climatologists carry these incorrect values through their calculation and cancel them on the back end (to get their equation to balance) by subtracting a wholly-fictive ‘cooler to warmer’ energy flow from the real (but far too high because it was calculated for emission to 0 K) ‘warmer to cooler’ energy flow.

That wholly-fictive ‘cooler to warmer’ energy flow is otherwise known as ‘backradiation’... it is nothing more than a mathematical artifact due to that aforementioned misuse of the S-B equation.

As I show here and in the below-linked paper, the correct usage of the S-B equation for graybody objects is via subtracting cooler object energy density from warmer object energy density to arrive at the energy density gradient, which determines radiant exitance of the warmer object.

So we’re talking about the same concept as water only spontaneously flowing down a pressure gradient (ie: downhill) when we talk of energy (of any form) only spontaneously flowing down an energy density gradient. Energy density is pressure, an energy density gradient is a pressure gradient… for energy.

It’s a bit more complicated for gases because they can convert that energy density to a change in volume (1 J m-3 = 1 Pa), for constant-pressure processes, which means the unconstrained volume of a gas will change such that its energy density (in J m-3) will tend toward being equal to pressure (in Pa). This is the underlying mechanism for convection. It should also have clued the climatologists in to the fact that it is solar insolation and atmospheric pressure which ‘sets’ temperature, not any ‘global warming’ gases.

Since a warmer object will have higher radiation energy density at all wavelengths than a cooler object (because remember, temperature is a measure of radiation energy density, equal to the fourth root of radiation energy density divided by Stefan’s Constant):

… ‘backradiation’ can do nothing to warm the surface because energy cannot spontaneously radiatively flow from lower to higher radiation energy density, and thus CAGW is nothing more than a complex mathematical scam perpetrated to obtain multiple billions of dollars in funding for trough-grubbing line-toeing ‘scientists’ and by perfidious politicians.

“But how does that make CAGW a scam?”, some may ask… well, because we’re being lied to, based upon an unscientific premise.

The climatologists have misused the Stefan-Boltzmann (S-B) equation (and the fundamental physical laws), and in the process, have practically flipped reality on its head… polyatomics (CO2, H2O, etc.) are not “global warming gases”, they are net atmospheric radiative coolants (radiative emission to space being the only way that Earth can shed energy); monoatomics (Ar) are not inert gases that have no effect upon climate, they are the actual “greenhouse gases” (because they cannot emit IR, and thus cannot shed energy to space… they dilute the radiative coolant gases); homonuclear diatomics (N2, O2) are somewhere in between… they can radiatively emit IR (and thus shed energy from the system known as ‘Earth’), but only under certain conditions (collisional perturbation of their net-zero electric dipole, which is why homonuclear diatomic vibrational mode quantum states are meta-stable and relatively long-lived. Collisions happen exponentially less frequently as altitude increases), and thus are “greenhouse gases” like the monoatomics, just not to the same extent.

We live, at the planet’s surface, in what can be analogized to the evaporator section of a world-sized AC unit, with polyatomics being net atmospheric radiative coolants (a higher concentration of them increases thermodynamic coupling between heat source (surface) and sink (space)), and with monoatomics and homonuclear diatomics playing the same role as non-condensable gases would play in an AC unit… diluting the polyatomic radiative gases which transit the majority of the energy, thus reducing the efficiency at which energy is transited from surface to upper atmosphere, then radiatively emitted to space.

Think about it this way… we all know the air warms up during the daytime as the planet’s surface absorbs energy from the sun. Conduction of that energy when air contacts the planet’s surface is the major reason air warms up.

How does that ~99% of the atmosphere (N2, O2, Ar) cool down? It cannot effectively radiatively emit.

Convection moves energy around in the atmosphere, but it cannot shed energy to space. Conduction depends upon thermal contact with other matter and since space is essentially a vacuum, conduction cannot shed energy to space… this leaves only radiative emission. The only way our planet can shed energy is via radiative emission to space. Fully ~76.2% of all surface energy is removed via convection, advection and evaporation. The surface only radiatively emits ~23.8% of all surface energy to space. That ~76.2% must be emitted to space by the atmosphere.

Thus, common sense dictates that the thermal energy of the constituents of the atmosphere which cannot effectively radiatively emit (N2, O2, Ar) must be transferred to the so-called ‘greenhouse gases’ (CO2 being a lesser contributor below the tropopause and the largest contributor above the tropopause, water vapor being the main contributor below the tropopause) which can radiatively emit and thus shed that energy to space. Peer-reviewed studies corroborating this are referenced in the linked file below.

So, far from being ‘greenhouse gases’ which ‘trap heat’ in the atmosphere, those polyatomic radiative gases actually shed energy from the atmosphere to space. They are net atmospheric radiative coolants.

In short, in an atmosphere sufficiently dense such that collisional energy transfer can significantly occur, all polyatomic radiative molecules play the part of atmospheric radiative coolants at and above the temperature at which the combined translational mode energy of two colliding particles (atoms or molecules) exceeds the lowest excited vibrational mode quantum state energy of the radiative molecule. Below this temperature, they act to warm the atmosphere via thermalization (the mechanism the climate alarmists claim happens all the time), but if that occurs below the tropopause, the net result is an increase of Convective Available Potential Energy, which increases convection, which is a net cooling process. It is a gradation… as temperature increases, so too does the population of vibrationally excited polyatomics, and thus increases radiative emission. For CO2, that ‘transition temperature’ (the temperature at which the molecule transitions from being ‘net warmant’ to ‘net coolant’ and vice versa) is ~288 K.

The climatologists only told people half the story (thermalization by CO2 via vibrational mode to translation mode (v-t) collisional energy transfer processes). They didn’t tell anyone about the inverse (translational mode to vibrational mode (t-v) collisional energy transfer processes, (then that energy being radiatively emitted to space)), which is a cooling process. That didn’t fit their doomsaying narrative, so they left it out.

In other words, the climatologists only told people about the warming part (thermalization), not the cooling part. In order to hew to the fundamental physical laws, one must consider energy flow both to and from the CO2 molecule.

This doesn’t just apply to CO2, however. It applies to all atmospheric polyatomic molecules. In fact, far from the ‘global warming gas’ claimed by the climatologists, water acts as a literal refrigerant (in the strict ‘refrigeration cycle’ sense) below the tropopause:

That’s why, after all, the humid adiabatic lapse rate (~3.5 to ~6.5 K km-1) is lower than the dry adiabatic lapse rate (~9.81 K km-1).

You will note that the dry adiabatic lapse rate is due to the monoatomics and homonuclear diatomics... we’ve removed in this case the predominant polyatomic which reduces lapse rate.

Remember that an actual greenhouse works by hindering convection of energy out of the greenhouse.

In an atmosphere consisting of solely monoatomics and homonuclear diatomics (ie: no polyatomic radiative molecules), the atoms / molecules could pick up energy via conduction by contacting the surface, just as the polyatomics do; they could convect just as the polyatomics do… but once in the upper atmosphere, they could not as effectively radiatively emit that energy, the upper atmosphere would warm, lending less buoyancy to convecting air, thus hindering convection… and that’s how an actual greenhouse works, by hindering convection.

For homonuclear diatomics, there would be some collisional perturbation of their net-zero electric dipole and thus some emission in the atmosphere, but by and large the atmosphere could not effectively emit (especially at higher altitudes, because the probability of collision decreases exponentially with altitude).

Thus the surface would have to radiatively emit that energy (which is currently ~76.2% of all energy removed from the surface via radiation, convection and evaporation) instead… and a higher surface radiant exitance implies a higher surface temperature.

On the contrary, in our actual atmosphere, as temperature increases, (t-v) (translational mode -to- vibrational mode) collisional energy transfer processes increase and thus spectral emission increases only because CO2 is a net atmospheric radiative coolant (transferring translational mode energy to vibrational mode energy, then radiatively emitting it). So they are attempting to claim that CO2 is a “global warming gas” and simultaneously a net atmospheric radiative coolant, a contradiction… which is why their claims make no sense upon close examination.

In fact, removing CO2 would increase upper atmosphere temperature (due to fewer emitters in the upper atmosphere), which would set the starting point of the lapse rate higher, which translates down through the lapse rate to a warmer surface. That doesn’t occur with Ar, because it is a monoatomic, has no vibrational mode quantum states and thus cannot emit (nor absorb) IR in any case, and thus it only dilutes the radiative polyatomics, reducing the efficiency by which energy is transited from surface to space.

Because we don’t live in a ‘greenhouse’ as the climatologists claim… we live in what can be analogized to a world-sized AC unit… the surface is akin to the AC unit’s evaporator section (ie: the heat source); the atmosphere is akin to the AC unit’s working fluid; space is akin to the AC unit’s condenser section (ie: the heat sink); convection is akin to the AC unit’s compressor (ie: the motive force to move the working fluid).

These concepts used to be common knowledge. Somewhere along the way, the concepts got skewed to fit a particular narrative. Eventually, the concepts described herein will be common knowledge again, whereupon CAGW and its offshoots will be dumped on the midden heap of bad scientific ideas.