Math Confirms The Foolishness Of The Climate Cult

Their calculation still relies upon assumptions, leaving it open to error and inaccuracy. And it buys into the very premise of the warmists.

I prefer hard numbers. It leaves the alarmists with no wiggle room. And I prefer to utterly demolish the warmist blather about physically-impossible “backradiation”, a wholly fictive “greenhouse effect, and the poorly-told and easily-disproved climate fairy tale of CAGW.

If the climate alarmists were serious about reducing temperature, they’d advocate for removing all Ar… it serves no biological purpose, it’s used in industry so we need stocks of it, it has a higher concentration than CO2 and thus would be easier to remove, its removal wouldn’t destroy all life on the planet (as CO2’s total removal would) and its removal would absolutely lower the lapse rate by:

Ar: 18.846929895790 K km-1 * 5.105 km * 0.00934 = 0.8986348102821 K

Even if we increased CO2 concentration to 1000 ppm, removing all Ar would still reduce the lapse rate by:

CO2 (430 ppm): 11.683426182319 K km-1 * 5.105 km * 0.00043 = 0.0256468729841 K

CO2 (1000 ppm): 11.683426182319 K km-1 * 5.105 km * 0.001 = 0.0596438906607 K

0.0596438906607 K – 0.0256468729841 K = 0.0339970176766 K

0.8986348102821 K – 0.0339970176766 K = 0.8646377926055 K

Whereas removing all CO2 from the atmosphere (which would kill all life on the planet) would only reduce temperature by:

11.683426182319 K km-1 * 5.105 km * 0.00043 = 0.0256468729841 K

“No one is advocating for removing all CO2 from the atmosphere! That’s just ridiculous!”, some screeching loon will invariably bleat.

Ok, let’s assume they draw it down from 430 ppm to 280 ppm. That would lower temperature by:

CO2 (430 ppm): 11.683426182319 K km-1 * 5.105 km * 0.00043 = 0.0256468729841 K

CO2 (280 ppm): 11.683426182319 K km-1 * 5.105 km * 0.00028 = 0.016700289385 K

0.0256468729841 K – 0.016700289385 K = 0.008946583599 K

Less than 1/100th of a degree. For trillions of dollars wasted.

So while trillions of dollars are being squandered on the non-solution of removing CO2, the above represents a lucrative business opportunity which would absolutely show profound effects upon the climate, and would provide industry with plentiful Ar gas as an additional income stream, without killing industry (and potentially all life on the planet) as would the restriction of CO2.

And do remember, removing CO2 removes the predominant upper atmospheric radiative coolant, which means the upper atmosphere warms, which translates down through the lapse rate to a warmer surface. But being diametrically opposite to reality is the natural state of leftists, their broken brains pretty much guarantees it. LOL

———-

Let’s calculate the Specific Lapse Rate due to each constituent atomic or molecular species of the atmosphere.

Idealized dry gas molar heat capacity lapse rate:
If we take ϒ = 1.404, g = 9.80665 m s-2, R = 8.31446261815324 J mol-1 K-1 and M = 28.9647 g mol-1, then:

dT / dh = -0.4/1.404 * (((28.9647 g mol-1) * 9.80665 m s-2) / 8.31446261815324 J mol-1 K-1) = -9.7330377706482238008458858152373 K km-1

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

∴ Molar Heat Capacity / 7 * 2 = Specific Gas Constant

dT / dh = -0.4/1.404 * (((Molar Mass) * 9.80665 m s-2) / Specific Gas Constant) = Specific Lapse Rate

The below data is taken from the model atmosphere I constructed in my paper at:

https://www.patriotaction.us/showthread.php?tid=2711

… to calculate the Specific Lapse Rate below:

Symbol: Molar Mass: Molar Heat Capacity: Specific Lapse Rate (SLR):
H2 | 2.01588 g mol-1 | 28.82 J mol-1 K-1 | 0.6859482857817 K km-1
He | 4.002602 g mol-1 | 20.7862 J mol-1 K-1 | 1.8883738683977 K km-1
H2O | 18.01528 g mol-1 | 75.327 J mol-1 K-1 | 2.3453681364178 K km-1
CH4 | 16.04246 g mol-1 | 35.69 J mol-1 K-1 | 4.4080355942551 K km-1
N2 | 28.0134 g mol-1 | 29.12 J mol-1 K-1 | 9.4339738283240 K km-1
CO | 28.0101 g mol-1 | 29.1 J mol-1 K-1 | 9.4393555726775 K km-1
Ne | 20.1797 g mol-1 | 20.7862 J mol-1 K-1 | 9.5205114453312 K km-1
O2 | 31.9988 g mol-1 | 29.38 J mol-1 K-1 | 10.680770320623 K km-1
N2O | 44.0128 g mol-1 | 38.6 J mol-1 K-1 | 11.181816712950 K km-1
CO2 | 44.0095 g mol-1 | 36.94 J mol-1 K-1 | 11.683426182319 K km-1
O3 | 47.9982 g mol-1 | 39.22 J mol-1 K-1 | 12.001569302138 K km-1
NO2 | 46.0055 g mol-1 | 37.2 J mol-1 K-1 | 12.127952596066 K km-1
SO2 | 64.0638 g mol-1 | 39.87  J mol-1 K-1 | 15.757493460485 K km-1
Ar | 39.948 g mol-1 | 20.7862 J mol-1 K-1 | 18.846929895790 K km-1
SF6 | 146.06 g mol-1 | 93 J mol-1 K-1 | 30.187357269247 K km-1
Kr | 83.798 g mol-1 | 20.95 J mol-1 K-1 | 39.225663804284 K km-1
I2 | 253.80894 g mol-1 | 54.43 J mol-1 K-1 | 45.728742264382 K km-1
Xe | 131.293 g mol-1 | 21.01 J mol-1 K-1 | 61.282460659191 K km-1

It is easy to calculate the current surface warming at the current CO2 atmospheric concentration due to the lapse rate:
11.683426182319 K km-1 * 5.105 km * 0.00043 = 0.0256468729841 K

Which equates to:
11.683426182319 K km-1 * 5.105 km * 0.000001 = 0.0000596438906607 K ppm-1

And for any given atmospheric concentration:
(1000 ppm): 11.683426182319 K km-1 * 5.105 km * 0.001 = 0.0596438906607 K

So going from current concentration to 1000 ppm CO2 would increase the lapse rate by:
0.0596438906607 K – 0.0256468729841 K = 0.0339970176766 K

So any climate models prognosticating a number greater than that are just flat-out wrong.

Of course, to be absolutely correct, we must account for which atoms or molecules that CO2 is displacing in any given parcel of air, and the SLR of those atoms or molecules.

It is easy to see from the above why the Dry Adiabatic Lapse Rate is stated to be ~9.81 K km-1:

(N2) 9.433973828324 K km-1 * 0.780761158 +
(O2) 10.680770320623 K km-1 * 0.20944121395198 +
(Ar) 18.84692989579 K km-1 * 0.00934 +
(CO2) 11.683426182319 K km-1 * 0.00043 +
(CH4) 4.4080355942551 K km-1 * 0.0000018 +
(Xe) 61.282460659191 K km-1 * 0.0000000869565217391 +
(SF6) 30.187357269247 K km-1 * 0.0000000000115 +
(CO) 9.4393555726775 K km-1 * 0.00000008 +
(I2) 45.728742264382 K km-1 * 0.00000000009 +
(Kr) 39.225663804284 K km-1 * 0.000001 +
(SO2) 15.757493460485 K km-1 * 0.000000015 +
(NO2) 12.127952596066 K km-1 * 0.00000033698 +
(O3) 12.001569302138 K km-1 * 0.0000000003 +
(N2O) 11.18181671295 K km-1 * 0.00000033671 +
(Ne) 9.5205114453312 K km-1 * 0.0000182 +
(He) 1.8883738683977 K km-1 * 0.000005222 +
(H2) 0.6859482857817 K km-1 * 0.00000055 =

(N2) 7.36568033074394 +
(O2) 2.23699350189356 +
(Ar) 0.176030325226679 +
(CO2) 0.00502387325839717 +
(CH4) 0.00000793446406965918 +
(Xe) 0.00000532890962253648 +
(SF6) 0.000000000347154608596341 +
(CO) 0.0000007551484458142 +
(I2) 0.00000000411558680379438 +
(Kr) 0.000039225663804284 +
(SO2) 0.000000236362401907275 +
(NO2) 0.00000408687746582232 +
(O3) 0.0000000036004707906414 +
(N2O) 0.00000376502950541739 +
(Ne) 0.000173273308305028 +
(He) 0.00000986108834077279 +
(H2) 0.000000377271557179935 = 9.78397288330931 K km-1

Above, I’ve adjusted relative concentrations to arrive at 1,000,000 ppm. You’ll note the model atmospheres you find online exceed 1,000,000 ppm, which is impossible and which skews results.

The differential of 0.0260271166906954 K km-1 between the stated value and the calculated value of the Dry Adiabatic Lapse Rate is accounted for by the fact that the model atmospheres typically used for the 9.81 K km-1 stated figure exceed 1,000,000 ppm.

———-

Do keep in mind that we’re replacing primarily homonuclear diatomics (which have a net-zero electric dipole and thus cannot emit unless that dipole is perturbed via collision… collisions occurring exponentially less frequently with altitude) with a radiative polyatomic. The homonuclear diatomics dilute the radiative polyatomics (which radiatively cool the upper atmosphere by absorbing solar IR, then re-emitting it spaceward (ie: down the energy density gradient)). Do remember that a molecule can only emit when that energy can spontaneously flow down the energy density gradient, so it’s not going to be emitting earthward (ie: up the energy density gradient)… the highest probability of emission is when the molecule’s dipole moment is perpendicular to the maximum energy density gradient… this increases emission probability in two ways: maximum energy density gradient; and when an atom or molecule emits a photon, there is a probability distribution of emission direction, with maximum emission probability perpendicular to the dipole moment and zero emission probability parallel to the dipole moment.

Further, given that ~49% of solar insolation is IR between 700 nm – 1 mm wavelength, increased CO2 concentration acts as a ‘shield’, reducing energy flux to the surface in areas where the energy density gradient between upper atmosphere and surface is such that solar photons in the IR band could reach the surface.

“But why doesn’t CO2 act as a ‘shield’ to warm the surface by blocking outgoing terrestrial IR radiation, just as it acts as a ‘shield’ to cool the planet by blocking incoming solar IR insolation?”, someone may ask. Well, it would, if the atmosphere below the tropopause didn’t convect… but it does convect, which carries that energy away from the surface. In fact, given that surface-level atmospheric attenuation length at 14.98352 µm is ~10.4 m, that means the atmosphere is essentially opaque at that wavelength… there are more CO2 molecules able to absorb terrestrial radiation at that wavelength than there is terrestrial radiation at that wavelength… and that terrestrial radiation is absorbed, then thermalized via v-t (vibrational mode -to- translational mode) collisional energy transfer, which increases CAPE (Convective Available Potential Energy), which increases convection, which drags with it water vapor (which has a comparatively much higher thermal capacity), thus removing more energy from the surface. This isn’t anything new, the increase of CAPE occurs at essentially the same magnitude for any CO2 concentration higher than ~50 ppm.

But while absorption and thermalization at the surface is saturated, in the upper atmosphere, a higher concentration of emitters means the atmosphere is more capable of emitting, and that energy must flow out to space due to the energy density gradient and the MFPL / altitude / air density relation.

So we’re very, very slightly increasing the lapse rate, while we’re displacing lower-DOF non-radiative monoatomics and homonuclear diatomics with a radiative polyatomic which increases thermodynamic coupling between heat source (ie: the surface) and sink (ie: space). So while the lapse rate will be very, very slightly higher, the starting temperature for that lapse rate (in the upper atmosphere) will be lower, which translates down through the lapse rate to a cooler surface.

Because we don’t live in a “greenhouse”, we live in what can be analogized to a world-sized AC unit… the surface would be akin to the AC unit’s evaporator section (ie: the heat source); the atmosphere would be akin to the AC unit’s working fluid; convection would be akin to the AC compressor (ie: the motive force to move the working fluid); and space would be akin to the AC unit’s condenser section (ie: the heat sink). For the same reason that we use complex high-DOF polyatomic CFC, HFC or HCFC molecules as a refrigerant in (and evacuate low-DOF non-condensable gases from) an AC unit, the higher the DOF of any given constituent molecule in the atmosphere, the more tightly it thermodynamically couples heat source (surface) and heat sink (space).

https://web.archive.org/web/20190209033912/https://phys.org/news/2012-11-atmospheric-co2-space-junk.html
The enhanced upper atmosphere cooling produced by the increasing CO2 results in a more contracted thermosphere, where many satellites, including the International Space Station, operate. This exacerbates the space junk problem, as derelict satellites de-orbit over a longer period.

Now remember that radiative emission from the atmosphere doesn’t occur at any one specific altitude, it’s a whole-atmosphere phenomenon… which is why CO2 is the most predominant atmospheric radiative coolant above the tropopause; and the second-most predominant atmospheric radiative coolant (behind water vapor) below the tropopause.

https://i.imgur.com/b87xKMk.png
The image above is from a presentation given by Dr. Maria Z. Hakuba, an atmospheric research scientist at NASA JPL.

https://i.imgur.com/gIjHlCU.png
The image above is 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.

And, given that the lapse rate is ‘anchored’ at TOA (that altitude at which the atmosphere effectively becomes transparent to any given wavelength of radiation… it varies for different wavelengths; the mean TOA being the mean of all wavelength-specific TOAs), a cooler upper atmosphere will translate down to the surface via the Kelvin-Helmholtz Gravitational Auto-Compression Effect (aka the lapse rate) to also cause a cooler surface.

And finally, keep in mind that the ~33 K Kelvin-Helmholtz Gravitational Auto-Compression Effect (aka the average humid Adiabatic Lapse Rate) has nothing to do with any “greenhouse effect” nor any “greenhouse gases” as claimed by the climatologists, it is strictly a manifestation of translational mode (kinetic) energy in the z-axis DOF being converted to gravitational potential energy with altitude (and vice versa), that change in z-axis DOF kinetic energy equipartitioning to the other 2 DOF upon subsequent collision, which changes air temperature (because temperature in this respect is a measure of the kinetic energy of the air atoms and molecules), which is why temperature decreases as altitude increases (and vice versa).

The climatologists misuse the Stefan-Boltzmann (S-B) equation in their Energy Balance Climate Models (EBCMs… which I prove at the link above using the Kiehl-Trenberth ‘Earth Energy Balance’ graphic, which is a representation of the mathematics in their EBCM).

That misuse of the S-B equation uses the idealized blackbody form of the equation upon real-world graybody objects. It assumes emission to 0 K and thus artificially inflates radiant exitance of all calculated-upon objects. Thus the climatologists must carry these incorrect values through their calculations and cancel them on the back end, subtracting a wholly-fictive ‘cooler to warmer’ energy flow from the real (but 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 merely a manifestation of the misuse of the S-B equation, it does not and cannot actually exist. Its existence would imply rampant violations of the fundamental physical laws.

And the S-B equation for graybody objects is meant to be used by 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.

Now, the climatologists claim that wholly-fictive “backradiation” causes their claimed “greenhouse effect”, which they use to designate polyatomics (CO2, CH4, H2O, etc.) as “greenhouse gases”. You will note the climatologists had no choice but to use the polyatomics… monoatomics have no vibrational mode quantum states and thus cannot emit (nor absorb) IR in any case; and homonuclear diatomics have a net-zero electric dipole which must be perturbed via collision for the molecule to emit (or absorb)… and collisions occur exponentially less frequently as altitude increases.

—–
But water, a polyatomic which the climatologists claim is a “greenhouse gas” is such an effective atmospheric radiative coolant that it drastically reduces the dry Adiabatic Lapse Rate and 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 energy density gradient and 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).

So one can see right away that the blather by the climatologists doesn’t even make sense, and is in fact diametrically opposite to reality… because the easiest lie to tell is an inversion of reality… the climatologists needn’t invent new physics to explain their blather, and most people cannot tell the difference between reality and flipped-causality anyway because they’re scientifically-illiterate.
—–

You will also note that the climatologists had no choice but to conflate their “greenhouse effect” with the Kelvin-Helmholtz Gravitational Auto-Compression Effect (aka the lapse rate)… they knew their “greenhouse effect” was fictional (because it’s based upon the wholly-fictive “backradiation”) and thus couldn’t show any effect whatsoever, so they conflated it to a known physical process which shows the effect they want.

Now, they use this claimed “greenhouse effect” to claim certain of those “greenhouse gases” will cause CAGW (Catastrophic Anthropogenic Global Warming, due to CO2).

And they use that to claim we must reduce CO2 emission, which they use as the basis for all of the offshoots of AGW / CAGW (net zero, carbon credit trading, carbon capture and sequestration, replacing reliable baseload electrical generation with intermittent ‘renewables’, etc.)

The entirety of it is predicated upon that mathematical fraudery in the misuse of the S-B equation. It is all nothing more than a complex mathematical scam.

If we look at the basic mathematics behind the greenhouse effect, we can show that significant global warming from humanity’s CO2 emissions is impossible.
Consider the relationship between atmospheric concentration (C) of a greenhouse gas (GHG) and the warming (W) it is alleged to cause. This is logarithmic of the form W = k*log(C) for some constant k. If we take logs to base 2, k is the sensitivity: i.e. the temperature rise that results from doubling the concentration. Using the current state for CO2, we know from Schönweise that W = 7.2°C and from the IPCC that C = 417ppm. So:
W = k * log2(417)
Thus k = W/(log2(417)) = 0.83 °C/doubling
We can use this to calculate the warming (Wn) that would arise if every molecule of humanity’s CO2 were removed from the atmosphere. According to the IPCC, 4.5% of CO2 input is from human emissions, so 95.5% (i.e. 398ppm) is natural.
Wn = k * log2(C) = 0.83 * log2(398) = 7.145°C
The amount of warming from humanity’s CO2 is thus W – Wn = 7.2 – 7.145 = 0.055°C, which is below the threshold for measurement error and hence insignificant.
Further, the above calculations assume the greenhouse effect to be the only atmospheric insulation mechanism. However, there are at least two other major mechanisms, and so even the tiny warming calculated here must be an overestimate.