03-23-24, 09:05 PM
(This post was last modified: 06-29-24, 10:39 AM by Morpheus.

*Edit Reason: update link to the downloadable file*)
Ok, this is going to be long and in-depth... I'll do my best to lay it out clearly and concisely. It won't be easy, as there's no easy method of inputting formulae, so I'll just make them plain text, rather than LaTeX.

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.

CAGW (Catastrophic Anthropogenic Global Warming, due to CO2) is nothing more than a complex mathematical scam. This isn't stated as opinion, but as mathematically-precise and provable fact. It's not that we should be discussing the severity of the temperature increase due to CO2, it's that we should be laughing anyone who claims that any polyatomic molecule causes 'heat trapping' off the stage.

Ok, the basics first...

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.

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).

Temperature is equal to the fourth root of radiation energy density divided by Stefan's Constant (ie: the radiation constant), per Stefan's Law.

e = T^4 a

a = 4σ/c

e = T^4 4σ/c

T^4 = e/(4σ/c)

T = 4^√(e/(4σ/c))

T = 4^√(e/a)

q = ε_h σ (T_h^4 – T_c^4)

[1] ∴ q = ε_h σ ((e_h / (4σ / c)) – (e_c / (4σ / c)))

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))

[2] ∴ q = (ε_h c (e_h - e_c)) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 (ΔJ m-3)) / 4

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.

[3] ∴ q = (ε_h * (σ / a) * Δe)

Canceling units, we get W m-2.

W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)

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.

You will note that σ = (a * c) / 4… the S-B Constant equals Stefan’s Constant multiplied by the speed of light in vacua divided by 4.

[4] ∴ q = (ε_h * ((a * c) / a) * Δe) / 4 = (ε_h * c * Δe) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 * ΔJ m-3) / 4

Note that [2] and [4] are identical, arrived at via two different avenues.

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.

Assume:

288 K planet

255 K atmosphere

ε = 0.93643 (per NASA ISCCP program)

σ = (2 π^5 k_B^4) / (15 h^3 c^2) = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4

where:

σ = Stefan-Boltzmann Constant

k_B = Boltzmann Constant (1.380649e−23 J K−1)

h = Planck Constant (6.62607015e−34 J Hz−1)

c = light speed (299792458 m sec-1)

e = T^4 a

where:

e = energy density (J m-3)

T = temperature (K)

a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4

Using the Idealized blackbody form of the S-B equation:

Surface To Atmosphere Radiant Exitance:

q = 0.93643 * 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * (288^4) = 365.30616894307 W m-2

Atmosphere To Surface Radiant Exitance:

q = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * (255^4) = 239.757641819 W m-2

Net: 365.30616894307 W m-2 - 239.757641819 W m-2 = 125.54852712407 W m-2

Now, that seems to make sense, right? Except that the 'atmosphere to surface' radiant exitance (aka 'backradiation') violates the fundamental physical laws... energy does not and cannot spontaneously flow up an energy density gradient. And applying emissivity to the idealized blackbody form of the S-B equation is a misuse of the S-B equation (remember that it assumes ε = 1).

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.

Using the Graybody form of the S-B equation:

Surface Radiant Exitance:

q = 0.93643 * 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * ( (288^4) - (255^4)) = 140.78992041451 W m-2

Now, how can we ascertain which is correct?

Well, we can calculate the energy density of each, then perform the calculations.

e = T^4 a

a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4

Surface Energy Density:

e = (288^4) * 7.5657332500339284719430800357226e-16 J m-3 K-4 = 5.20500290293e-6 J m-3

Atmosphere Energy Density:

e = (255^4) * 7.5657332500339284719430800357226e-16 J m-3 K-4 = 3.1989816343e-6 J m-3

Energy Density Gradient:

5.20500290293e-6 J m-3 - 3.1989816343e-6 J m-3 = 2.0060212686e-6 J m-3

Surface To Atmosphere Radiant Exitance:

σ / a * Δe * ε_h = W m-2

5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 * 2.0060212686e-6 J m-3 * 0.93643 = 140.78992041246 W m-2

Atmosphere To Surface Radiant Exitance:

5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 * -2.0060212686e-6 J m-3 * 0.93643 = -140.78992041246 W m-2

In other words, 'Atmosphere To Surface' radiant exitance is zero (there can't be negative radiant exitance). The negative denotes that energy is flowing from surface to atmosphere.

That's nearly exact (except for rounding error... in the case of the Hyperphysics website, the rounding of σ and the rounding of the end result... in the linked paper, I account for the rounding of σ on that site and arrive at a precision of 3.8 parts per 100 trillion) to the full graybody S-B equation (because it is the full graybody S-B equation, stripped to its most basic).

The Hyperphysics website:

http://hyperphysics.phy-astr.gsu.edu/hba...an.html#c3

As you can see, the proper method of calculating radiant exitance for graybody objects is by subtracting the energy density of the cooler object from the energy density of the warmer object to arrive at the energy density gradient, which determines radiant exitance of the warmer object.

The cooler object cannot emit in the direction of the warmer object because energy cannot spontaneously flow up an energy density gradient. To claim that it can is directly analogous to claiming that water can spontaneously flow uphill (ie: up a pressure gradient).

Most people cannot think in terms of energy, energy density and energy density gradient. We need to analogize to something they’re familiar with. Thus, just as, for instance, water only spontaneously flows down a pressure gradient, energy only spontaneously flows down an energy density gradient. That’s 2LoT in the Clausius Statement sense, in a nutshell. So one tack to take is to ask people if water can ever spontaneously flow uphill. Of course they’ll say, “No, water cannot flow uphill on its own.” Then show them dimensional analysis.

mass (M), length (L), time (T), absolute temperature (K), amount of substance (N), electric charge (Q), luminous intensity ©

We denote the dimensions like this: [Mx, Lx, Tx, Kx, Nx, Qx, Cx] where x = the number of that dimension

We typically remove dimensions which are not used.

Force: [M1 L1 T-2] /

Area: [M0 L2 T0] =

Pressure: [M1 L-1 T-2] /

Length: [M0 L1 T0] =

Pressure Gradient: [M1 L-2 T-2]

Explain to them that Pressure is Force / Area, and that Pressure Gradient is Pressure / Length. Remind them that water only spontaneously flows down a pressure gradient (ie: downhill). Then introduce energy. Tell them that energy is much like water. It requires an impetus to flow, just as water requires an impetus (pressure gradient) to flow. In the case of radiative energy, that impetus is a radiation energy density gradient, which is analogous to (and in fact, literally is) a radiation pressure gradient.

Energy: [M1 L2 T−2] /

Volume: [M0 L3 T0] =

Energy Density: [M1 L-1 T-2] /

Length: [M0 L1 T0] =

Energy Density Gradient: [M1 L-2 T-2]

Explain to them that Energy Density is Energy / Volume, and Energy Density Gradient is Energy Density / Length. Highlight the fact that Pressure and Energy Density have the same units (bolded above). Also highlight the fact that Pressure Gradient and Energy Density Gradient have the same units (bolded above).

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.

In fact, the highest pressure ever attained was via lasers increasing energy density in nuclear fusion experiments.

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 to push a Marxist One World Government “Build Back Better” agenda.

“But they’ve measured backradiation!”, some may claim. Yeah, no.

https://claesjohnson.blogspot.com/2011/0...meter.html

As Professor Claes Johnson shows in that article on his website, pyrgeometers (the instrument typically used to ‘measure’ backradiation) utilize the same sort of misuse of the S-B equation as the climatologists use. The bastardized form of the S-B equation used by pyrgeometers [ usually some form of q = (σ T_h^4 – σ T_c^4) or equivalently L_d = U_emf/S + σT_b, as outlined in the documentation for the instrument, with U_emf/S being negative in sign ] apriori assumes a subtraction of 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, which as has been shown, is fallacious.

Do remember that photons, each a quantum of energy, are considered the force-carrying gauge bosons of the EM interaction.

Going back to dimensional analysis:

We start with Energy: [M1 L2 T−2] -

Force: [M1 L1 T-2] *

Length: [M0 L1 T0] = [M0 L0 T0]

We are left with nothing on the 'transmitting' end... [M0 L0 T0]. In other words, that Energy is used to apply a Force along a Length. It’s obvious then, that if an equal and opposing Force were applied along that Length, no energy can flow… this is just as true radiatively as it is mechanically.

Aside:

That Force applied along a Length gives us (on the 'receiving' end):

Force: [M1 L1 T-2] *

Length: [M0 L1 T0] =

Work: [M1 L2 T-2]

You'll note that Energy and Work have the same units:

Work: [M1 L2 T-2] = Energy: [M1 L2 T−2]

For those who want to put it in terms of Momentum:

Momentum: [M1 L1 T−1] *

Velocity: [M0 L1 T-1] =

Work: [M1 L2 T−2]

That means Energy Expended = Force * Length = Momentum * Velocity = Work

There's a reason for that. Free Energy is defined as that energy capable of performing work. This is reflected in the equation for Free Energy (represented here as a single object and its environment):

F = U – TS + PV

Where: F = Free Energy; U = internal energy; T = absolute temp; S = final entropy; TS = energy the object can receive from the environment; PV = work done to give the system final volume V at pressure P

If U > TS + PV, F > 0… energy must flow from object to environment.

If U = TS + PV, F = 0… no energy can flow to or from the object.

If U < TS + PV, F < 0… energy must flow from environment to object.

Of course, if we were talking about a system with only two objects with the same physical parameters and nothing else in the system, we could represent the Free Energy as: F = U_1 – U_2

Which is better represented as internal energy over volume to get energy density (since internal energy is an extensive property), converting the calculation to that of an intensive property and thus allowing us to compare dissimilar-sized objects: F = U_1 / V_1 – U_2 / V_2 = e_1 - e_2

And that’s exactly what the S-B equation does. Remember that temperature is a measure of radiation energy density, equal to the fourth root of radiation energy density divided by the radiation constant (Stefan’s Constant). Remember that I wrote above:

q = (ε_h * c * (e_h - e_c)) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 (ΔJ m-3)) / 4

Or equivalently:

q = ε_h * σ / a * (e_h - e_c)

Canceling units, we get W m-2.

W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)

One can see that the S-B equation is all about subtracting the radiation energy density of the cooler object from the radiation energy density of the warmer object (to arrive at the radiation energy density gradient) because Free Energy is all about subtracting the energy density of one object from the energy density of the other object (no matter the form of that energy).

"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.

I state "approximately 288 K" because the angle of collision of two atmospheric atoms or molecules can be from any angle, and thus it's nearly impossible to calculate an exact temperature. We could, of course, use statistical probability to lump the calculations into ranges of angles, then aggregate the results of each range of angles, but the basic idea still holds.

You will note that while the graphic above only addresses CO2 and N2, the same applies to all atmospheric gases due to the Equipartition Theorem.

The Boltzmann Factor (for air at 288 K and for the combined translation mode (kinetic) energy of two colliding particles (atoms or molecules) necessary to excite CO2's lowest vibrational mode quantum state) is ~0.8461... in other words, for every 100 air particles at the Most Probable Speed (MPS), ~84 other particles will have sufficient combined translational mode (kinetic) energy to excite CO2's lowest excited vibrational mode quantum state CO2{v21(1)} during collision.

Polyatomics are 'dual-role' gases... the role they play is dependent upon:

1) The combined translational mode (kinetic) energy of two colliding atoms or molecules.

- and -

2) The lowest excited vibrational mode quantum state energy of the polyatomic molecule.

When 2) > 1), energy flows from vibrational mode to translational mode (ie: thermalization), which is a warming process.

When 1) > 2), energy flows from translational mode to vibrational mode, which is a cooling process. Due to the energy density gradient, that energy cannot flow back to translational mode, and is instead radiatively emitted. Emitted radiation that goes out to space represents a loss of energy for the system known as 'Earth' and is thus a cooling process.

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:

The refrigeration cycle (Earth) [AC system]:

A liquid evaporates at the heat source (the surface) [in the evaporator], it is transported (convected) [via an AC compressor], it gives up its energy to the heat sink and undergoes phase change (emits radiation in the upper atmosphere, the majority of which is upwelling owing to the mean free path length / altitude / air density relation) [in the condenser], it is transported (falls as rain or snow) [via that AC compressor], and the cycle repeats.

That’s kind of 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.

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.

Now, having gotten through all of that, there is a paper which goes into much more depth.

To date, there's not been a warmist physicist nor a climatologist who has been able to refute the scientific reality contained within that file, though several have tried. The last was physicist Bob Wentworth, who gave up after I backed him into numerous logical traps. Some have even changed their stance because of the information within that file.

That file:

Climate Sanity.pdf (Size: 2.29 MB / Downloads: 83)

Anyone is free to use any of what I write however they wish... rewrite it to make it more easily understandable then publish it under your own name, publish it in whole or in part as-is under your own name, round-file it, whatever. I don't even want any attribution. Let's just work on destroying CAGW before it destroys our way of life.

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.

CAGW (Catastrophic Anthropogenic Global Warming, due to CO2) is nothing more than a complex mathematical scam. This isn't stated as opinion, but as mathematically-precise and provable fact. It's not that we should be discussing the severity of the temperature increase due to CO2, it's that we should be laughing anyone who claims that any polyatomic molecule causes 'heat trapping' off the stage.

Ok, the basics first...

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.

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).

Temperature is equal to the fourth root of radiation energy density divided by Stefan's Constant (ie: the radiation constant), per Stefan's Law.

e = T^4 a

a = 4σ/c

e = T^4 4σ/c

T^4 = e/(4σ/c)

T = 4^√(e/(4σ/c))

T = 4^√(e/a)

q = ε_h σ (T_h^4 – T_c^4)

[1] ∴ q = ε_h σ ((e_h / (4σ / c)) – (e_c / (4σ / c)))

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))

[2] ∴ q = (ε_h c (e_h - e_c)) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 (ΔJ m-3)) / 4

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.

[3] ∴ q = (ε_h * (σ / a) * Δe)

Canceling units, we get W m-2.

W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)

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.

You will note that σ = (a * c) / 4… the S-B Constant equals Stefan’s Constant multiplied by the speed of light in vacua divided by 4.

[4] ∴ q = (ε_h * ((a * c) / a) * Δe) / 4 = (ε_h * c * Δe) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 * ΔJ m-3) / 4

Note that [2] and [4] are identical, arrived at via two different avenues.

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.

Assume:

288 K planet

255 K atmosphere

ε = 0.93643 (per NASA ISCCP program)

σ = (2 π^5 k_B^4) / (15 h^3 c^2) = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4

where:

σ = Stefan-Boltzmann Constant

k_B = Boltzmann Constant (1.380649e−23 J K−1)

h = Planck Constant (6.62607015e−34 J Hz−1)

c = light speed (299792458 m sec-1)

e = T^4 a

where:

e = energy density (J m-3)

T = temperature (K)

a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4

Using the Idealized blackbody form of the S-B equation:

Surface To Atmosphere Radiant Exitance:

q = 0.93643 * 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * (288^4) = 365.30616894307 W m-2

Atmosphere To Surface Radiant Exitance:

q = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * (255^4) = 239.757641819 W m-2

Net: 365.30616894307 W m-2 - 239.757641819 W m-2 = 125.54852712407 W m-2

Now, that seems to make sense, right? Except that the 'atmosphere to surface' radiant exitance (aka 'backradiation') violates the fundamental physical laws... energy does not and cannot spontaneously flow up an energy density gradient. And applying emissivity to the idealized blackbody form of the S-B equation is a misuse of the S-B equation (remember that it assumes ε = 1).

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.

Using the Graybody form of the S-B equation:

Surface Radiant Exitance:

q = 0.93643 * 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 * ( (288^4) - (255^4)) = 140.78992041451 W m-2

Now, how can we ascertain which is correct?

Well, we can calculate the energy density of each, then perform the calculations.

e = T^4 a

a = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4

Surface Energy Density:

e = (288^4) * 7.5657332500339284719430800357226e-16 J m-3 K-4 = 5.20500290293e-6 J m-3

Atmosphere Energy Density:

e = (255^4) * 7.5657332500339284719430800357226e-16 J m-3 K-4 = 3.1989816343e-6 J m-3

Energy Density Gradient:

5.20500290293e-6 J m-3 - 3.1989816343e-6 J m-3 = 2.0060212686e-6 J m-3

Surface To Atmosphere Radiant Exitance:

σ / a * Δe * ε_h = W m-2

Quote:First, take a look at this:

σ / a = 5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 = 74948114.5024 W m-2 / J m-3.

Well, what do you know... that's the conversion factor for radiant exitance (W m-2) and energy density (J m-3)!

It's almost as if the radiant exitance of graybody objects is determined by the energy density gradient, right?

5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 * 2.0060212686e-6 J m-3 * 0.93643 = 140.78992041246 W m-2

Atmosphere To Surface Radiant Exitance:

5.67037441918442945397099673188923087584012297029130e-8 W m-2 K-4 / 7.5657332500339284719430800357226e-16 J m-3 K-4 * -2.0060212686e-6 J m-3 * 0.93643 = -140.78992041246 W m-2

In other words, 'Atmosphere To Surface' radiant exitance is zero (there can't be negative radiant exitance). The negative denotes that energy is flowing from surface to atmosphere.

That's nearly exact (except for rounding error... in the case of the Hyperphysics website, the rounding of σ and the rounding of the end result... in the linked paper, I account for the rounding of σ on that site and arrive at a precision of 3.8 parts per 100 trillion) to the full graybody S-B equation (because it is the full graybody S-B equation, stripped to its most basic).

The Hyperphysics website:

http://hyperphysics.phy-astr.gsu.edu/hba...an.html#c3

As you can see, the proper method of calculating radiant exitance for graybody objects is by subtracting the energy density of the cooler object from the energy density of the warmer object to arrive at the energy density gradient, which determines radiant exitance of the warmer object.

The cooler object cannot emit in the direction of the warmer object because energy cannot spontaneously flow up an energy density gradient. To claim that it can is directly analogous to claiming that water can spontaneously flow uphill (ie: up a pressure gradient).

Most people cannot think in terms of energy, energy density and energy density gradient. We need to analogize to something they’re familiar with. Thus, just as, for instance, water only spontaneously flows down a pressure gradient, energy only spontaneously flows down an energy density gradient. That’s 2LoT in the Clausius Statement sense, in a nutshell. So one tack to take is to ask people if water can ever spontaneously flow uphill. Of course they’ll say, “No, water cannot flow uphill on its own.” Then show them dimensional analysis.

mass (M), length (L), time (T), absolute temperature (K), amount of substance (N), electric charge (Q), luminous intensity ©

We denote the dimensions like this: [Mx, Lx, Tx, Kx, Nx, Qx, Cx] where x = the number of that dimension

We typically remove dimensions which are not used.

Force: [M1 L1 T-2] /

Area: [M0 L2 T0] =

Pressure: [M1 L-1 T-2] /

Length: [M0 L1 T0] =

Pressure Gradient: [M1 L-2 T-2]

Explain to them that Pressure is Force / Area, and that Pressure Gradient is Pressure / Length. Remind them that water only spontaneously flows down a pressure gradient (ie: downhill). Then introduce energy. Tell them that energy is much like water. It requires an impetus to flow, just as water requires an impetus (pressure gradient) to flow. In the case of radiative energy, that impetus is a radiation energy density gradient, which is analogous to (and in fact, literally is) a radiation pressure gradient.

Energy: [M1 L2 T−2] /

Volume: [M0 L3 T0] =

Energy Density: [M1 L-1 T-2] /

Length: [M0 L1 T0] =

Energy Density Gradient: [M1 L-2 T-2]

Explain to them that Energy Density is Energy / Volume, and Energy Density Gradient is Energy Density / Length. Highlight the fact that Pressure and Energy Density have the same units (bolded above). Also highlight the fact that Pressure Gradient and Energy Density Gradient have the same units (bolded above).

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.

In fact, the highest pressure ever attained was via lasers increasing energy density in nuclear fusion experiments.

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 to push a Marxist One World Government “Build Back Better” agenda.

“But they’ve measured backradiation!”, some may claim. Yeah, no.

https://claesjohnson.blogspot.com/2011/0...meter.html

As Professor Claes Johnson shows in that article on his website, pyrgeometers (the instrument typically used to ‘measure’ backradiation) utilize the same sort of misuse of the S-B equation as the climatologists use. The bastardized form of the S-B equation used by pyrgeometers [ usually some form of q = (σ T_h^4 – σ T_c^4) or equivalently L_d = U_emf/S + σT_b, as outlined in the documentation for the instrument, with U_emf/S being negative in sign ] apriori assumes a subtraction of 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, which as has been shown, is fallacious.

Do remember that photons, each a quantum of energy, are considered the force-carrying gauge bosons of the EM interaction.

Going back to dimensional analysis:

We start with Energy: [M1 L2 T−2] -

Force: [M1 L1 T-2] *

Length: [M0 L1 T0] = [M0 L0 T0]

We are left with nothing on the 'transmitting' end... [M0 L0 T0]. In other words, that Energy is used to apply a Force along a Length. It’s obvious then, that if an equal and opposing Force were applied along that Length, no energy can flow… this is just as true radiatively as it is mechanically.

Aside:

Quote:As Δe → 0, ΔT → 0, q → 0. As q → 0, the ratio of graybody object total emissive power to idealized blackbody object total emissive power → 0. In other words, emissivity → 0. At thermodynamic equilibrium for a graybody object, there is no radiation energy density gradient and thus no impetus for photon generation.

As Δe → 0, ΔT → 0, photon chemical potential → 0, photon Free Energy → 0. At zero chemical potential, zero Free Energy, the photon can do no work, so there is no impetus for the photon to be absorbed. The ratio of the absorbed to the incident radiant power → 0. In other words, absorptivity → 0.

α = absorptivity = absorbed / incident radiant power

ρ = reflectivity = reflected / incident radiant power

τ = transmissivity = transmitted / incident radiant power

α + ρ + τ = 100%

For opaque surfaces τ = 0% ∴ α + ρ = 100%

If α = 0%, 0% + ρ = 100% ∴ ρ = 100% … all incident photons are reflected at thermodynamic equilibrium for graybody objects.

This coincides with standard cavity theory… applying cavity theory outside a cavity, for two graybody objects at thermodynamic equilibrium, no absorption nor emission takes place. The system reaches a state of quiescence (which is the definition of thermodynamic equilibrium). The photons remaining in the intervening space set up a standing wave, with the wavemode nodes at the object surfaces by dint of the boundary constraints. Nodes being a zero-crossing point (and anti-nodes being the positive and negative peaks), no energy can be transferred into or out of the objects. Photon chemical potential is zero, they can do no work, photon Free Energy is zero, they can do no work... there is no impetus for the photons to be absorbed. Should one object change temperature, the standing wave becomes a traveling wave with the group velocity proportional to the radiation energy density gradient and in the direction of the cooler object.

Now, obviously, if energy cannot spontaneously flow when there is zero energy density gradient (ie: at thermodynamic equilibrium), it certainly cannot spontaneously flow up an energy density gradient.

That Force applied along a Length gives us (on the 'receiving' end):

Force: [M1 L1 T-2] *

Length: [M0 L1 T0] =

Work: [M1 L2 T-2]

You'll note that Energy and Work have the same units:

Work: [M1 L2 T-2] = Energy: [M1 L2 T−2]

For those who want to put it in terms of Momentum:

Momentum: [M1 L1 T−1] *

Velocity: [M0 L1 T-1] =

Work: [M1 L2 T−2]

That means Energy Expended = Force * Length = Momentum * Velocity = Work

There's a reason for that. Free Energy is defined as that energy capable of performing work. This is reflected in the equation for Free Energy (represented here as a single object and its environment):

F = U – TS + PV

Where: F = Free Energy; U = internal energy; T = absolute temp; S = final entropy; TS = energy the object can receive from the environment; PV = work done to give the system final volume V at pressure P

If U > TS + PV, F > 0… energy must flow from object to environment.

If U = TS + PV, F = 0… no energy can flow to or from the object.

If U < TS + PV, F < 0… energy must flow from environment to object.

Of course, if we were talking about a system with only two objects with the same physical parameters and nothing else in the system, we could represent the Free Energy as: F = U_1 – U_2

Which is better represented as internal energy over volume to get energy density (since internal energy is an extensive property), converting the calculation to that of an intensive property and thus allowing us to compare dissimilar-sized objects: F = U_1 / V_1 – U_2 / V_2 = e_1 - e_2

And that’s exactly what the S-B equation does. Remember that temperature is a measure of radiation energy density, equal to the fourth root of radiation energy density divided by the radiation constant (Stefan’s Constant). Remember that I wrote above:

q = (ε_h * c * (e_h - e_c)) / 4

Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).

W m-2 = (m sec-1 (ΔJ m-3)) / 4

Or equivalently:

q = ε_h * σ / a * (e_h - e_c)

Canceling units, we get W m-2.

W m-2 = ((W m-2 K-4 / J m-3 K-4) * ΔJ m-3)

One can see that the S-B equation is all about subtracting the radiation energy density of the cooler object from the radiation energy density of the warmer object (to arrive at the radiation energy density gradient) because Free Energy is all about subtracting the energy density of one object from the energy density of the other object (no matter the form of that energy).

"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.

I state "approximately 288 K" because the angle of collision of two atmospheric atoms or molecules can be from any angle, and thus it's nearly impossible to calculate an exact temperature. We could, of course, use statistical probability to lump the calculations into ranges of angles, then aggregate the results of each range of angles, but the basic idea still holds.

You will note that while the graphic above only addresses CO2 and N2, the same applies to all atmospheric gases due to the Equipartition Theorem.

The Boltzmann Factor (for air at 288 K and for the combined translation mode (kinetic) energy of two colliding particles (atoms or molecules) necessary to excite CO2's lowest vibrational mode quantum state) is ~0.8461... in other words, for every 100 air particles at the Most Probable Speed (MPS), ~84 other particles will have sufficient combined translational mode (kinetic) energy to excite CO2's lowest excited vibrational mode quantum state CO2{v21(1)} during collision.

Polyatomics are 'dual-role' gases... the role they play is dependent upon:

1) The combined translational mode (kinetic) energy of two colliding atoms or molecules.

- and -

2) The lowest excited vibrational mode quantum state energy of the polyatomic molecule.

When 2) > 1), energy flows from vibrational mode to translational mode (ie: thermalization), which is a warming process.

When 1) > 2), energy flows from translational mode to vibrational mode, which is a cooling process. Due to the energy density gradient, that energy cannot flow back to translational mode, and is instead radiatively emitted. Emitted radiation that goes out to space represents a loss of energy for the system known as 'Earth' and is thus a cooling process.

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:

The refrigeration cycle (Earth) [AC system]:

A liquid evaporates at the heat source (the surface) [in the evaporator], it is transported (convected) [via an AC compressor], it gives up its energy to the heat sink and undergoes phase change (emits radiation in the upper atmosphere, the majority of which is upwelling owing to the mean free path length / altitude / air density relation) [in the condenser], it is transported (falls as rain or snow) [via that AC compressor], and the cycle repeats.

That’s kind of 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.

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.

Now, having gotten through all of that, there is a paper which goes into much more depth.

To date, there's not been a warmist physicist nor a climatologist who has been able to refute the scientific reality contained within that file, though several have tried. The last was physicist Bob Wentworth, who gave up after I backed him into numerous logical traps. Some have even changed their stance because of the information within that file.

That file:

Climate Sanity.pdf (Size: 2.29 MB / Downloads: 83)

Anyone is free to use any of what I write however they wish... rewrite it to make it more easily understandable then publish it under your own name, publish it in whole or in part as-is under your own name, round-file it, whatever. I don't even want any attribution. Let's just work on destroying CAGW before it destroys our way of life.

You take the blue pill…the story ends, you wake up in your bed and believe whatever you want to believe.

You take the red pill…you stay in Wonderland, and I show you how deep the rabbit hole goes.

You take the red pill…you stay in Wonderland, and I show you how deep the rabbit hole goes.