**From about 11,000 to 9,000 years ago the summer solar irradiance absorbed by the Earth’s surface has been estimated to be 40-60 W/m² greater than today from latitudes 40°N to 70°N (****Ullman et al., 2015****). These values seriously undermine the claim CO2 is the driver of climate change.**

###### Image Source: **Ullman et al., 2015**

Despite these much higher insolation values, surface temperatures have been estimated to be only a few degrees warmer than today at these latitudes during the Early Holocene.

At 77°N in High Arctic Svalbard, for example, summers were estimated to be 7°C warmer than today from 10,000 to 9,000 years ago due to this higher radiative forcing (**van der Bilt et al., 2019**).

###### Image Source: **van der Bilt et al., 2019**

So if an additional 60 W/m² radiative forcing only elicits a 7°C surface temperature change, the effective sensitivity of a 1 W/m² perturbation to the surface energy imbalance would be about 0.12°C.

This formula (1 W/m² produces 0.12°C surface warming) has been reproduced by NASA and other scientists using satellite observations.

For example, the Mount Pinatubo eruption produced a surface temperature drop of -0.5°C to -0.6°C associated with a -4 W/m² decline in radiative forcing (**Self et al., 1993**). This is amounts to a 0.12°C to 0.15°C temperature sensitivity per W/m².

###### Image Source: **Self et al., 1993**

Other scientists (**Douglass and Knox, 2005**) have also computed a “0.15 ± 0.06 K/(W/m²)” radiative forcing-temperature sensitivity.

###### Image Source: **Douglass and Knox, 2005**

Anthropogenic global warming advocates suggest it takes an increase of 22 ppm CO2 (about 10 years) to produce a surface forcing change of 0.2 W/m² (**Feldman et al., 2015**).

###### Image Source: **Feldman et al., 2015**

So, using this formula, it would take 110 ppm (40-50 years) to produce a positive 1 W/m² surface forcing imbalance. This would only produce a temperature change of, at most, 0.15°C.

Bellamy and Barrett (**2007**) have likewise suggested the doubling of CO2 could only represent a temperature change of “0.6 – 0.8°C” with the addition of 280 ppm CO2 since the pre-industrial era. This estimate uses the assumption that doubling CO2 produces a 3.7 W/m² top-of-atmosphere (TOA) forcing.

###### Image Source: **Bellamy and Barrett, 2007**

Dr. Kimoto (**2015**), in contrast, suggests using the the *surface* radiative forcing value (1.1 W/m²) for doubling CO2 from 280 to 560 ppm rather than the TOA value (3.7 W/m²) due to the physical reality of water vapor, not CO2, dominating the infrared absorption in the lower atmosphere. He also computes a surface climate sensitivity of 0.13°C per 1 W/m².

Consequently, with doubled CO2 only yielding a 1.1 W/m² surface forcing perturbation to Earth’s energy imbalance, the climate sensitivity from doubling CO2 from 280 to 560 ppm may only be 0.14 to 0.17°C

###### Image Source: **Kimoto, 2015**

In sum, none of these values even remotely suggest CO2 can be a driver of climate change.

[…] Glaring Inconsistency In Estimating CO2 vs. Solar Forcing Suggests CO2 Impacts Are Wildly Exaggerate… […]

“In sum, none of these values even remotely suggest CO2 can be a driver of climate change.” As stated earlier on several occasions: Show me ONE (1) article describing the causal relation between CO2 and global temperature.

Still waiting.

I’ve still got some carbon offset certificates for sale. Special discount for NoTrickZone readers.

The effect of CO2 (ECS) is unknown.

It is refreshing to read estimates that have a reasonable relationship with observations rather than obvious scaremongering that says the future effect of CO2 will be much worse than the past effect … when no one knows the exact past effect, except observing it was harmless.

Unfortunately, the article starts with a red herring statement:

“From about 11,000 to 9,000 years ago the summer solar irradiance absorbed by the Earth’s surface has been estimated to be 40-60 W/m² greater than today from latitudes 40°N to 70°N (Ullman et al., 2015). These values seriously undermine the claim CO2 is the driver of climate change.”

No one claimed CO2 drove natural climate change 11,000 to 9,000 years ago. In fact, the Vostok ice cores showed that temperature peaks happened before CO2 peaks, by an average of 800 years.

The actual current claim is that man made CO2 emissions from burning fossil fuels controlled the climate in the past 50 to 100 years. No evidence of that from 1880 to 1975, so let’s say after 1975. We did have global warming and rising CO2 after 1975.

With perhaps 10 climate change variables, no one knows exactly what the effect of CO2 was. It’s a reasonable guess that CO2 caused some “warming” since 1975. Claiming that CO2 controls the climate requires ignoring all natural causes of climate change … which the IPCC has done since 1975. That’s junk science.

Natural causes of changing CO2 levels from ocean CO2 absorption and outgassing thousands of years ago are unrelated to adding CO2 to the troposphere by burning fossil fuels in the past 50 years.

[…] Glaring Inconsistency In Estimating CO2 vs. Solar Forcing Suggests CO2 Impacts Are Wildly Exaggerate… […]

[…] Glaring Inconsistency In Estimating CO2 vs. Solar Forcing Suggests CO2 Impacts Are Wildly Exaggerate…! .. and in the real world there’s something called convection, convection render all theories of magical, human CO2 irrelevant due to the fact: If you can’t measure it, – you can’t prove (or observe) it either. Convection can be measured, calculated and observed and we understand both what and why. […]

That paper is available here:

https://sci-hub.se/10.1038/nature14240

“thoroughly corroborated radiative transfer calculations [4]”

And [4] is:

https://sci-hub.se/10.1029/2011jd016821

Those “thoroughly corroborated radiative transfer calculations” are yet another instance of the climastrologists misusing the S-B equation and it still doesn’t fully take into account clouds and aerosols for IR. They’ve become so retarded that even the satellites and FTIR spectrometers they use misuse the S-B equation, so while their measurements are at least somewhat consistent, they are all consistently

wrong.In fact, their Figure 11a in reference [4] above shows a negative column-of-atmosphere forcing for CO2 and SW TOA… and rather than change their stance, they merely noted that there was “an issue regarding the sign of the SW TOA forcing”

And that’s not even taking into account that every bit of their blather violates 2LoT… an object cannot emit radiation which then is reabsorbed and warms that same object. Energy does not flow up an energy density gradient without external energy being required to pump that energy up the gradient (2LoT in a nutshell, in the Clausius Statement sense), and if there is no gradient, energy will not spontaneously flow (which is why thermodynamic equilibrium is known as a quiescent state, the minimum of Helmholtz Free Energy; and why entropy doesn’t change at thermodynamic equilibrium… no energy flows at TE). If they’re attempting to claim that a colder atmosphere can re-emit energy to the warmer surface, that yet again violates 2LoT… a warmer object will have higher energy density at all wavelengths than a cooler. And it is the energy density gradient which regulates energy flow in all cases.

The below is from my prior writings…

“Trust the science!”, they say… “The science is settled!”, they say… yeah, well, even physicists are wrong sometimes, and the climate activists in white lab coats masquerading as climatologists (which we know as climastrologists) are seemingly intentionally so, seemingly paid to be so in order to push a leftist narrative.

Here’s a modern example of a physicist being wrong. He lost a $10,000 bet.

https://www.youtube.com/watch?v=yCsgoLc_fzI

We’re losing our rights and freedoms. Object lesson:

Don’t be wrong.Arrhenius completely discounted convection, advection, specific heat capacity and latent heat of vaporization (which transit ~76.2% of all energy away from the planet’s surface) in formulating his incorrect radiative CO2-warming hypothesis upon which hangs the entire modern CAGW charade; and his experiments used 9.7 µm radiation (while CO2 absorbs mainly at 14.98352 µm) and he over-estimated the absorption coefficient of CO2 by 253%, forcing him to later revise his estimate (which was still wrong) of temperature forcing from CO2…

Maxwell in his “Theory of Heat” (starting on p. 320) predicted that a column of atmosphere would be isothermal, and indeed claimed a column of atmosphere forming a gravitationally-induced thermal gradient would violate 2LoT (proven incorrect… Loschmidt was correct, a lapse rate always evolves due to gravitational auto-compression in an atmosphere dense enough to be gravitationally compressed)…

Boltzmann sided with Maxwell that no lapse rate could exist…

Carnot erred in assuming that heat is never consumed as work…

Clausius in his first memoir erred in attributing ‘heat’ to the energy density of an object (‘heat’ is definitionally an energy flux, ‘temperature’ is a measure of energy density)…

Kirchhoff in formulating his original version of Kirchhoff’s Law of Thermal Radiation used the term ’absorptive power’ when he actually meant ’absorptivity’; and in attempting to expand Kirchhoff’s Law from idealized blackbody cavities to all materials he cheated a bit by using a graphite or carbon thermalizer in perfectly-reflecting cavities (which cannot otherwise exhibit a blackbody spectrum). Further, he took the ideas of Balfour Stewart (published a full year before Kirchhoff published) without attribution, only receiving recognition because he cheated enough (by utilizing a graphite or carbon thermalizer in perfectly-reflecting cavities) to get his mathematics to work, whereas Stewart hadn’t yet fleshed out his mathematics (because he couldn’t, because he didn’t cheat as Kirchhoff did).

Planck (a former student of Kirchhoff and his successor as lecturer at Berlin’s Friedrich Wilhelms University) erred in confusing ‘temperature’ and ‘heat’ in The Theory of Heat Radiation [5, § 46], and in failing to properly validate Kirchhoff’s Law (from which he derived his equation). His attempt at validating Kirchhoff’s Law in his book is filled with errors… he had to redefine blackbodies to be predicated upon transmissivity (except idealized blackbodies by definition are opaque, zero transmissivity); he ignored absorptivity at the interface of the blackbody (he claimed that the state of photons on the surface and inside the material were identical, and that as a photon traversed through a material, it was successively absorbed); he used polarized light in his experiments (whereas thermal radiation is never polarized) and thus misused Brewster’s Law; and he, like Kirchhoff, cheated a bit by using a small chunk of graphite or carbon as a thermalizer (what he called a ‘catalyst’) in a perfectly reflecting cavity (which cannot otherwise exhibit a blackbody spectrum). In short, Planck held a weird view of what photons were and how they interacted with matter. His definition of a blackbody didn’t even coincide with Kirchhoff’s definition (nor with the standard definition). Planck also erred in clinging to a long-debunked radiative model (Prevost Theory of Exchanges and its core tenet, Prevost’s Principle), and his follow-on assumptions stemming from that led to his treating real-world (graybody) objects as though they radiatively emit willy-nilly without regard to the energy density gradient.

Planck correctly stated:

Do remember that temperature is equal to the fourth root of energy density divided by Stefan’s Constant…

temperature is a measure of energy density.In other words, Planck correctly stated that energy can only flow (the definition of ‘heat’) via conduction if there is a temperature (and therefore an energy density) gradient.

Where Planck erred is in his clinging to the Prevost Theory Of Exchanges (and its core tenet, the Prevost Principle) in regard to radiative energy, which led him to eschew scientific reality (that energy only flows if there is an energy density gradient), to wit:

The immediate corollary to Prevost’s Principle is that E = e… that the actual emission is equal to the disposition to emit, which is false, implying that an object must emit all energy it absorbs (the definition of idealized blackbody objects, which do not and cannot exist).

A further corollary to Prevost’s Principle is that A = I * a… that the actual absorption is equal to the intensity of the incident beam times the disposition to absorb, which is again false, implying that excited quantum states have the same disposition to absorb as do unexcited quantum states (again, the definition of idealized blackbody objects, which do not and cannot exist). Of course, Prevost, in 1791, didn’t know of quantum states, so he couldn’t have known that the corollaries to Prevost’s Principle were incorrect.

Prevost’s Principle was used by Gustav Kirchhoff to develop Kirchhoff’s Law of Thermal Radiation, which is likewise false because it is based upon a false premise (see below). Likewise, much of what Planck developed based upon Kirchhoff’s Law of Thermal Radiation loses its universal application, specifically Planck Length, Planck Time, Planck Mass and Planck Temperature are now merely human-invented units of measure, rather than fundamental units of reality.

The long-debunked Prevost Theory of Exchanges (first replaced by the Kinetic Theory of Heat, then by Quantum Thermodynamics) assumed that energy flowed without regard to energy density gradient, because only an object’s internal state determined radiant exitance. This led Planck to make the further incorrect assumption in keeping with the Prevost Theory of Exchanges:

He correctly stated that energy transfer via conduction was predicated upon there being an energy density gradient, but for radiative energetic exchange, he clung to the Prevost Principle (core tenet of the Prevost Theory of Exchanges, a long-debunked hypothesis from 1791 which was predicated upon the long-debunked Caloric Theory and which postulated that radiant exitance of an object was solely determined by that object’s internal state, thus that energy could flow willy-nilly without regard to energy density gradient).

Except the Prevost Principle would only work for an idealized blackbody object, and they don’t actually exist… they’re idealizations. And the object would have to be in an isolated system, and they don’t actually exist… they’re idealizations.

A graybody object’s radiant exitance isn’t solely determined by that object’s internal state, as the S-B equation plainly shows:

https://i.imgur.com/QErszYW.gif

Idealized Blackbody Object (assumes emission to 0 K and ε = 1):

qbb = ε σ (T_h^4 – T_c^4) Ah

= 1 σ (T_h^4 – 0 K) 1 m2

= σ T4

Graybody Object (assumes emission to > 0 K and ε 1 m2], 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 energy density divided by Stefan’s Constant (ie: the radiation constant).

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)

Since we’re using the Kelvin temperature scale, which has its base at 0 K, we can calculate temperature (and thus energy density) as above. Energy density at 0 K is zero, thus temperature at zero energy density is, of course, 0 K.

q = ε σ (T_h^4 – T_c^4)

∴ q = ε σ ((eh / (4σ / c)) – (ec / (4σ / c))) Ah

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)))

∴ q = (ε c (eh – ec)) / 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

For graybody objects, it is the energy density differential between warmer object and cooler object which determines warmer object radiant exitance. The climate alarmists misinterpret the S-B radiant exitance equation for graybody objects. Warmer objects don’t absorb radiation from cooler objects (a violation of 2LoT in the Clausius Statement sense and Stefan’s Law); the lower 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 energy density differential between objects manifests an energy density gradient, each surface’s energy density manifesting a proportional radiation pressure.

Thus, the climastrologists cling to the long-debunked Prevost Principle (whether they know it or not… and if they don’t know it, then they really have no business being anywhere near anything related to science) when they claim that energy can radiatively flow without regard to energy density gradient… and that leads to all manner of unscientific drivelry… ‘backradiation’, ‘Global Warming Potential’, ‘carbon footprint’, the incorrect usage of the S-B equation in the K-T (Kiehl-Trenberth) diagram and even in instruments such as pyrgeometers and FTIR spectrometers, and ultimately in their core narrative: CAGW.

Even worse is that they then further misuse the S-B equation by converting it into what they call a “forcing formula”:

4 ε σ T^3

… which builds-in a warming trend:

———-

For 288 K, a 1 K negative temperature change, ε=0.93643 (ref: NASA ISCCP program):

4 ε σ T^3 = 5.07369679087621 W m-2

For 288 K, a 1.00525093764635 K negative temperature change, ε=0.93643 (ref: NASA ISCCP program):

q = ε σ T^4 = 5.07369679087621 W m-2

———-

For 288 K, a 1 K positive temperature change, ε=0.93643 (ref: NASA ISCCP program):

4 ε σ T^3 = 5.07369679087621 W m-2

For 288 K, a 0.99474906235365 K positive temperature change, ε=0.93643 (ref: NASA ISCCP program):

q = ε σ T^4 = 5.07369679087621 W m-2

———-

So their bastardized equation gives the result for a warming of 0.99474906 K while claiming it’s a warming of 1 K, and gives the result for a cooling of 1.00525093 K while claiming it’s a cooling of 1 K.

And that’s likely why they bastardized the S-B equation… to hide the fact that they continue to treat real-world graybody objects as idealized blackbody objects, and to build-in whatever warming trend they possibly could in order to help sustain their alarmist narrative.

It further stretches credulity when they claim that CO2 removal from the atmosphere will result in the environment continuing to absorb CO2 at the same rate for some time after CO2 atmospheric concentration decreases due to some purported “inertia”… as if Henry’s Law and partial pressure have “inertia”… it’s almost as if they’re wholly incognizant of the fact that pressure is an instantaneous measure… or they don’t even know why the oceans absorb / outgas CO2 in accord with Henry’s Law.

It is all based upon mathematical fraudery, none of it is correct, none of it is physical, none of it is scientific. CAGW is nothing but a complex mathematics-based scam. It is little more than a rigged mathematical game of thimblerig, and few are quick-witted enough to catch the climastrologists palming the pea as they shuffle the thimbles.

1)The climate alarmists are, as usual,provably diametrically opposite to reality.———-

The climate alarmists misuse the S-B equation, using the form meant for idealized blackbody objects upon graybody objects:

q = σ T^4

… and slapping ε onto that (sometimes) …

q = ε σ T^4

Their misuse of the S-B equation inflates radiant exitance far above what it actually is for all graybody objects, necessitating that they carry that error forward through their calculations and cancel it on the back end, essentially subtracting a wholly-fictive ‘

cooler to warmer’ energy flow from the real (but calculated incorrectly and thus far too high) ‘warmer to cooler’ energy flow… which leads especially scientifically-illiterate climate alarmists to conclude that energy actually can flow ‘cooler to warmer’ (a violation of 2LoT and Stefan’s Law).https://i.imgur.com/2Bd25TG.png

The S-B equation for graybody objects isn’t meant to be used to subtract a fictive ‘

cooler to warmer’energy flowfrom the incorrectly-calculated and thus too high ‘warmer to cooler’energy flow, it’s meant to be used to subtract cooler objectenergy density(temperature is a measure of energy density, the fourth root of energy density divided by Stefan’s constant) from warmer objectenergy density. Radiant exitance of the warmer object is predicated upon theenergy density gradient.Their problem, however, is that their take on radiative energetic exchange necessitates that at thermodynamic equilibrium, objects are furiously emitting and absorbing radiation (this is brought about because they claim that objects emit only according to their temperature (rather than according to the energy density gradient), thus for objects at the same temperature in an environment at the same temperature, all would be furiously emitting and absorbing radiation), and they’ve forgotten about entropy… if the objects (and the environment) are furiously emitting and absorbing radiation at thermodynamic equilibrium as their insane take on reality must claim, why does entropy not change?

They cite Clausius out of context… Clausius was discussing a cyclical process by which external energy did work to return the system to its original state (for irreversible processes), or which returned to its original state because it is an idealized reversible process… except idealized reversible processes don’t exist. They’re idealizations. All real-world processes are irreversible processes, including radiative energy transfer, because radiative energy transfer is an entropic temporal process.

Their mathematical fraudery is what led to their ‘

energy can flow willy-nilly without regard to energy density gradient‘ narrative (in their keeping with the long-debunked Prevost Principle), which led to their ‘backradiation‘ narrative, which led to their ‘CAGW‘ narrative, all of it definitively, mathematically, scientifically proven to be fallacious.2)CO2 isn’t a ‘global warming’ gas… it acts as a net atmospheric radiativecoolantat all altitudes except a negligible warming at the tropopause.———-

https://i.imgur.com/0DTVYkR.png

The image above is from a presentation given by atmospheric research scientist Maria Z. Hakuba at NASA JPL.

https://i.imgur.com/IYDjzxX.png

That’s adapted from the Clough and Iacono study, Journal Of Geophysical Research, Vol. 100, No. D8, Pages 16,519-16,535, August 20, 1995.

Note that the Clough & Iacono study is for the atmospheric radiative cooling effect, so positive numbers at right are cooling, negative numbers are warming.

Gee… adding more of the predominant upper-atmospheric radiative coolant causes more emitters per unit volume, which causes more emission per unit volume, which causes more emission to space, which causes a larger loss of energy from the system known as ‘Earth’, which causes cooling… who knew? LOL

It is the monoatomics and homonuclear diatomics which are the actual ‘greenhouse’ gases… remember that an actual greenhouse works by

hindering convection.Monoatomics (Ar) have no vibrational mode quantum states, and thus cannot emit (nor absorb) IR. Homonuclear diatomics (O2, N2) have no net magnetic dipole and thus cannot emit (nor absorb) IR unless that net-zero magnetic dipole is perturbed via collision.

In an atmosphere consisting of solely monoatomics and diatomics, 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, byhindering convection.The environmental lapse rate would necessitate that the surface also warms, given that the lapse rate is ‘anchored’ at TOA (that altitude at which the atmosphere effectively becomes transparent to any given wavelength of radiation).

The surface would also have to warm because that ~76.2% of energy…

https://andymaypetrophysicist.files.wordpress.com/2020/09/figure-2.png

… which is currently removed from the surface via convection and evaporation would have to be removed nearly solely via radiation (there would be some collisional perturbation of N2 and O2, and thus some emission in the atmosphere)…. and a higher radiant exitance implies a higher surface temperature.

The chance of any N2 or O2 molecule colliding with water vapor is ~3% on average in the troposphere, and for CO2 it’s only ~0.0415%. Logic dictates that as atmospheric concentration of CO2 increases, the likelihood of N2 or O2 colliding with it also increases, and thus increases the chance that N2 or O2 can transfer its translational and / or vibrational mode energy to the vibrational mode energy of CO2, which can then shed that energy to space via radiative emission. (And yes, t-v and v-v collisional processes do occur from N2 to CO2… if you doubt me, I can post the maths and studies which prove it.)

Thus, common sense dictates that the thermal energy of the ~95.94 – 99.74% (depending upon humidity) 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.

So can anyone explain how increasing the concentration of the major radiative coolant gases (H2O, CO2) in the atmosphere (and thus increasing the likelihood that Ar, N2 and O2 will transfer their energy to those radiative coolant gases and then out to space via radiative emission) will result in more ‘heat trapping’, causing global warming? I thought not.

Maybe that’s why Loschmidt, in the 1860’s, found, using Maxwell’s equations and much to the consternation of Maxwell and Boltzmann, that adiabatic gravitational auto-compression (the tradeoff of gravitational potential energy for enthalpy as a parcel of air descends in altitude, thus producing an increase in pressure, specific internal energy and hence, temperature… what we know today as the lapse rate… finally empirically corroborated in 2007 by Graeff) shows that far from CO2 being the ‘control knob’ of planetary temperature, it has such little effect that its effect upon global temperature is essentially immeasurable. It is adiabatic gravitational auto-compression which largely controls the lapse rate (‘anchored’ at TOA) and hence surface temperature… H2O and CO2 can increase the cooling a bit as detailed in this paper, but only a bit before the lapse rate equilibrates again. Once again the climate alarmists have made a mountain out of a molehill, while chucking trillions of dollars down that mole-hole, and while managing the whole while to be diametrically opposite to reality.

https://article.sciencepublishinggroup.com/pdf/10.11648.j.earth.20170606.18.pdf

3)Water vapor isn’t a ‘global warming’ gas… it acts as a literalrefrigerant(in the strict ‘refrigeration cycle’ sense) below the tropopause.———-

You know, the refrigeration cycle (

Earth) [A/C system]:A liquid evaporates at the heat source(the surface) [in the evaporator],it is transported(convected) [via an A/C compressor],it emits radiation 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 A/C compressor], andthe cycle repeats.That’s kind of why, after all, the humid adiabatic lapse rate (~3.5 to ~6.5 K / km) is lower than the dry adiabatic lapse rate (~9.81 K / km).

The

effectiveemission height is ~5.105 km. That also happens to be where atmospheric pressure is 1/2 that at sea level, which isn’t a coincidence.7 – 13 µm: >280 K (near-surface)

>13 – 17 µm: ~260 – ~240 K (~5km in the troposphere)

The emission profile is equivalent to a BB with a temperature of 255 K, and thus an

effectiveemission height of 5.105 km.The lapse rate is said to average ~6.5 K / km. 6.5 K / km * 5.105 km = 33.1825 K.

That is not the ‘greenhouse effect’, it’s the tropospheric lapse rate. The climate alarmists have conflated the two.Polyatomic molecules (CO2, H2O) reduce the adiabatic lapse rate (ALR), not increase it (dry ALR: ~9.81 K / km; humid ALR: ~3.5 to ~6.5 K / km) by dint of their higher specific heat capacity and/or latent heat capacity convectively transiting more energy (as compared to the monoatomics and homonuclear diatomics), thus attempting to reduce temperature differential with altitude, while at the same time radiatively cooling the upper atmosphere faster than they can convectively warm it… they increase thermodynamic coupling between heat source and sink… they are

coolants.9.81 K / km * 5.105 km = 50.08005 K (dry adiabatic lapse rate, due to homonuclear diatomics and monoatomics), which would give a surface temperature of 255 + 50.08005 = 305.08005 K. Sans CO2, that number would be even higher.

Water vapor (primarily) reduces that to 272.8675 K – 288.1825 K, depending upon humidity. Other polyatomics (CO2) contribute to cooling, to a lesser extent. The higher the concentration of polyatomics, the more vertical the lapse rate, the cooler the surface.

Also remember: the atmosphere is stable as long as actual lapse rate is less than ALR… and a greater concentration of polyatomic molecules reduces ALR… thus convection increases.

That’s kind of why, after all, CO2 isn’t used as a filler gas in double-pane windows… if it was such a terrific ‘heat trapping’ gas, it’d be used as such. It’s not. Low DOF, low specific heat capacity monoatomics generally are.

4)Empirical examples:———-

In fact, the Kiehl-Trenberth diagram…

https://i.imgur.com/RJMT26o.png

… does exactly as I stated… it treats a real-world (graybody) surface as if it were an idealized blackbody object, with emission to 0 K ambient and ε = 1. That’s the only way that diagram can get to 390 W m-2 surface radiant exitance.

https://i.imgur.com/nJh4Z7U.png

That’s proof-positive that they’ve misused the S-B equation to fit their narrative. Had they used the actual emissivity, they couldn’t have arrived at 390 W m-2 (see below), and had they used the proper form of the S-B equation for graybody objects, they’d not have even gotten close to 390 W m-2 (see below).

Their use of the wrong formula increases radiant exitance of graybody objects far above what it actually is:

https://i.imgur.com/4ulMbq6.png

… which necessitates that they carry those incorrect values through their calculation and subtract a fictional ‘

cooler to warmer‘ energy flow from the real (but calculated incorrectly and thus too high) ‘warmer to cooler‘ energy flow.Thus, some of the alarmists come to believe that energy actually can flow ‘

cooler to warmer‘ (the basis of their ‘backradiation‘ blather). This violates 2LoT in the Clausius Statement sense… energy cannot flow from lower energy density to higher energy density without external energy doing work upon the system to push that energy against the energy gradient.Do remember that a warmer object will have higher energy density at all wavelengths than a cooler object.The equation for the radiation energy density is Stefan’s Law and a is Stefan’s constant.

e = aT^4

∴ T = 4^√(e/a)

In other words,

temperature is equal to the fourth root of energy density divided by Stefan’s constant. It is a measure ofenergy density.Keep in mind that Stefan’s constant above equals 4σ/c (which is sometimes known as the radiation constant).

Which is why: U = T^4 4σ/c

The above formula is the Stefan-Boltzmann relation between energy density and temperature.

If ΔU = 0, then (ΔU * c/4σ) = 0, thus no energy can flow.

U has the same physical units as pressure (J m-3) and U ∝ T. That is

radiation pressure, which sets up the energy density gradient.This agrees with Planck’s Law: ρ(T) = aT^4 = T^4 4σ/c.

The S-B equation integrates Planck’s Radiation Formula (which calculates the energy density for a given wavelength) over all wavelengths.

F = U – TS

Where:

F = Helmholtz Free Energy (J)

U = internal energy (J)

T = absolute temp (K)

S = system final entropy (J K-1)

TS = energy the object can receive from the environment

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

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

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

Free energy is defined as the capacity to do work. If U = TS, p_photon = u/3 = p_object, energy cannot flow because no work can be done. Helmholtz Free Energy is

zero. Photon chemical potential iszero.So in the real world, the energy density gradient determines radiant exitance, energy does not flow willy-nilly without regard to energy density gradient and 2LoT applies always and everywhere.

https://i.imgur.com/IgxATSg.png

———-

One can use electrical theory to arrive at the same conclusions…

[1]Images of circuit simulator:https://i.imgur.com/6vvuwHb.gif

https://i.imgur.com/sLHKnn1.gif

[2]Circuit simulator:https://tinyurl.com/yzo8hak9

The bottom circuit in the circuit simulator is how reality works… objects interact. That interaction through radiation pressure determines radiant exitance of each object. So while the climate alarmists claim that there’s no way a photon could possibly ‘know’ the temperature of the object upon which that photon supposedly incides, it absolutely does ‘know’ because that photon must pass through the EM field (the photon being nothing but a quantum of EM energy) between objects, and thus the energy density gradient between objects… and if the EM field energy density (ie: the energy density gradient between the objects) is such that the chemical potential of the EM field is higher than the chemical potential of the photon, a photon from a cooler object won’t even reach the warmer object… it will be subsumed into the background EM field (there is no law of conservation for photons).

You’ll note that the top two circuits in the circuit simulator are how the climate alarmists calculate radiant exitance… (ie:

they put each object into its own separate system that doesn’t interact with other objects, and they essentially claim all objects emit to 0 K, equivalent in electrical terms to discharging to ground). That’s not how reality works, and their doing so leads them to conclude that a lower-temperature but higher-emissivity object can radiatively warm a higher-temperature but lower-emissivity object if they stick with their silliness to the bitter end.Only through hand-wavium do they connect the two objects after the fact to subtract a wholly-fictive ‘cooler to warmer’ energy flow from the real but incorrectly calculated and thus too high ‘warmer to cooler’ energy flow.

Now, let’s do it correctly:

T = 4√e/(4σ/c)

e = T^4 4σ/c

e = T^4 a

c = 299792458 m s-1

Th = 600 K

εh = 0.04

eh = 9.8051902920439712996382317262965e-5 J m-3

Tc = 273.15 K

εc = 0.96

ec = 4.2116846355194792664142496540057e-6 J m-3

σ = 5.670374419e−8 W m−2 K−4

a = 7.5657e-16 J m-3 K-4 = 4σ/c = 7.5657332500339284719430800357226e-16 J m-3 K-4

σ / a = 74948114.5 W J-1 mσ / a * Δe = W m-2

9.8051902920439712996382317262965e-5 J m-3 – 4.2116846355194792664142496540057e-6 = 9.3840218284920233729968067608959e-5 J m-3 energy density differential

9.3840218284920233729968067608959e-5 J m-3 energy density differential * 74948114.5 W J-1 m * (εh = 0.04) = 281.3258969889278120384163525 W m-2

https://i.imgur.com/SgvQvLb.gif

Again, the 0.0036929889278120384163525 W m-2 differential is due to rounding on the Hyperphysics webpage.

In fact:

(281.3222048179386 / 5.6703e-8 * 5.670374419e-8) – 281.3258969889278120384163525 = 0.000000000000038296252606814321993545315062695 W m-2

That’s a precision of 3.8 parts per 100

trillion, just by accounting for the rounding of σ on the Hyperphysics page. And the remaining differential isstilldue to rounding (of the final result) on the Hyperphysics page. LOLSo as one can see, if one properly uses the S-B equation and the underlying fundamental physical laws, Catastrophic Anthropogenic Global Warming is shown to be so fallacious as to be laughable.

Richard Greene wrote:

“With perhaps 10 climate change variables, no one knows exactly what the effect of CO2 was.”

It’s far worse than that… we can’t even accurately calculate the effect because the lapse rate equations in both mass heat capacity and molar heat capacity forms are irrevocably broken.

They assume that once energy is convectively and advectively removed from the surface, that energy will definitely make its way out to space… but they don’t properly attribute to which molecules by which that happens. Only the radiative (polyatomic) molecules are radiative coolants, the monoatomics and homonuclear diatomics are warmants. An increasing atmospheric concentration of monoatomics and/or homonuclear diatomics would dilute the molar fraction of polyatomics, lowering radiant exitance from each mol of air. Conversely, an increasing atmospheric concentration of polyatomics would increase radiant exitance from each mol of air, which implies higher radiant exitance to space, which is a cooling process for the system known as ‘Earth’.

The problem is that the two forms of the lapse rate equation don’t take into account whether or not an atom or molecule can radiatively emit its energy to space.

It is the monoatomics and the homonuclear diatomics which are the real ‘greenhouse gases’.

Think about it… the dry adiabatic lapse rate is ~9.81 K km-1, whereas the humid adiabatic lapse rate is ~3.5 to ~6.5 K km-1… because in a dry atmosphere, N2 and O2 make up ~99% of all atmospheric constituents, and they’re homonuclear diatomics. They cannot radiatively emit unless their net-zero magnetic dipole is perturbed via collision.

Monoatomics (Ar) have no vibrational mode quantum states, and thus cannot emit (nor absorb) IR. Homonuclear diatomics (O2, N2) have no net magnetic dipole and thus cannot emit (nor absorb) IR unless that net-zero magnetic dipole is perturbed via collision.

In an atmosphere consisting of solely monoatomics and diatomics, 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, byhindering convection.The surface would also have to warm because that ~76.2% of energy…

https://andymaypetrophysicist.files.wordpress.com/2020/09/figure-2.png

… which is currently removed from the surface via convection and evaporation would have to be removed nearly solely via radiation (there would be some collisional perturbation of N2 and O2, and thus some emission in the atmosphere)…. and a higher radiant exitance implies a higher surface temperature.

The chance of any N2 or O2 molecule colliding with water vapor is ~3% on average in the troposphere, and for CO2 it’s only ~0.0415%. Logic dictates that as atmospheric concentration of CO2 increases, the likelihood of N2 or O2 colliding with it also increases, and thus increases the chance that N2 or O2 can transfer its translational and / or vibrational mode energy to the vibrational mode energy of CO2, which can then shed that energy to space via radiative emission. (And yes, t-v and v-v collisional processes do occur from N2 to CO2… if you doubt me, I can post the maths and studies which prove it.)

Thus, common sense dictates that the thermal energy of the ~95.94 – 99.74% (depending upon humidity) 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.

I’m working on a new lapse rate equation which takes all of the above into account, but it’s a slow slog.

Now, obviously, the lapse rate equation (in either of its forms) is flawed. We can ascertain this by doing the lapse rate calculation for the polyatomic H2O (a radiative molecule and literal refrigerant (in the strict ‘refrigeration cycle’ sense) in the troposphere) vs. the homonuclear diatomic H2 (a non-radiative molecule and hence one of the true ‘global warming’ gases):

100% H2O atmosphere (isentropic ratio for 20 C), molar form of the lapse rate equation:

dT / dh = -0.4/1.330 * ((( 0.01801528 kg mol-1) * 9.80665 m s-2) / 21.522 J mol-1 K-1) = -2.4688085646511036442514147090615 K km-1

100% H2 atmosphere (isentropic ratio for 20 C), molar form of the lapse rate equation:

dT / dh = -0.4/1.410 * (((0.00201588 kg mol-1) * 9.80665 m s-2) / 7.0956604559795225906303946663492 J mol-1 K-1) = -0.56054991677662967137690736391597 K km-1

That implies that H2 would dramatically reduce the lapse rate, even more than water vapor would, and thus dramatically cool the surface. But homonuclear diatomics (which H2 is) cannot emit (nor absorb) radiation unless their net-zero magnetic dipole is perturbed via collision. They can pick up energy via conduction by contacting the surface, just as the polyatomics can; they can convect just as the polyatomics can; but once in the upper atmosphere, they cannot effectively radiatively emit that energy to space.

The stated molar isobaric heat capacity for dry air is Cp = 7/2 R: 7 / 2 * 8.31446261815324 J mol-1 K-1 = 29.10061916353634 J mol-1 K-1

Therefore we can use the equation above to calculate the specific gas constant for any mixture of gas.

29.099786225134 J mol-1 K-1 / 7 * 2 = 8.3142246357525714285714285714286 J mol-1 K-1

We can then calculate the molar heat capacity of an atmosphere with a changed mixture, then calculate the specific gas constant, then calculate the lapse rate.

The molar heat capacity above (29.09978…) is derived from my model dry atmosphere with 16 constituent molecular species, with the molar fraction adjusted to cumulate to 100% (if you’ve ever looked at the published percentage concentration of gases in the atmosphere, they add up to more than 100%, so I fixed that).

Further, we over at Joe Postma’s site have been working on something revolutionary… it’s a bit difficult to explain, but there’s a correlation between the number of electrons in a mole of atmosphere and the temperature, which is affected by gravity and thus air density. Given that we can analogize thermodynamics to electrical theory (voltage can be analogized to σ T^4, resistance can be analogized to emissivity, emission to ground can be analogized to emitting to 0 K, etc.), if we hold constant for a 1 eV rise of these bound electrons, we get the same result as the S-B equation for temperature and radiant exitance!

It was originally conceived of by a poster going by ‘Jopo’, whose quirky brain sees these correlations so easily its astounding.

He’s scaled it to the other planets in our solar system, at 1 bar pressure, and arrived at the exact temperatures on those planets and at that altitude.

That definitively kills CAGW.

There are still some things we’re attempting to grasp, so if any of you are able to lend a hand, do please drop by Joe Postma’s site.