The Four Known Scientific Ways Carbon Dioxide Cools Earth’s Climate

Written by Dr Pierre Latour PE on August 22, 2014. Posted in Current News

Experts from the ‘hard’ sciences are again revealing how climate ‘scientists’ have gotten it wrong about the role of carbon dioxide (CO2) in climate.

Dr Pierre R Latour, a renowned American Chemical Engineer, shows how four known mechanisms and three laws of nature prove why CO2 cools, not warms, our atmosphere. Moreover, it may be shown that the UN Intergovernmental Panel on Climate Change (IPCC), the supposed world authority deferred to by governments, lacks a rigorous mathematical description for their so-called ‘greenhouse gas theory.’

CO2 Affects Several Temperatures in Different Ways

Here we develop the physics, chemistry and biology to quantify the effect of atmospheric carbon dioxide (CO₂) on Earth’s temperature. There are five mechanisms and three different temperatures involved.

Four show a small cooling effect, one warms surface and cools upper atmosphere with no net bulk effect. I am unaware of a rigorous mathematical description of the greenhouse gas theory that purports to do this and show a warming affect. After decades of research attempts, promoters cannot reduce greenhouse gas theory (GHGT) to mathematics of science and engineering.

Stefan-Boltzmann Law of Radiation

If non-radiating O₂ is exchanged for absorbing/emitting CO₂, the emissivity, e, of a planet to space must increase. While emissivity of CO₂ is less that global emissivity, it is greater than the O₂ it replaced by “fossil fuel” combustion. The Stefan-Boltzmann Law of Radiation is

I = σ e (T/100)⁴

If e increases with CO₂ at constant I, T goes down. Therefore, CO₂ causes global cooling.

This is true for all bodies of matter, no matter the composition, rotation speed or weather.

I = radiating intensity, irradiance, power of any radiating body, w/m², of its spherical surface, measured by Earth satellite spectrophotometers to be about 239. It is only a transfer rate when surroundings do not radiate, at 0K. Outer space at 3.7K radiate with very low intensity.

T = temperature of radiating body, K, estimated for Earth to be 4.60C + 273.15 = 277.75

σ = Stefan-Boltzmann radiation law constant, 5.67

e = emissivity of radiating body, fraction 0 < e < 1. e varies with composition. Perfect radiator black body e = 1, radiates a given intensity at lowest possible temperature. Colorful Earth radiator e = 0.70827 emits given intensity at temperature higher than black body.

I = 5.67*0.70827(277.750/100)⁴ = 5.67*0.70827*59.51 = 5.67*42.152 = 239.0

If doubling CO₂ from 400 to 800 ppmv increases emissivity 0.001 from 0.70827 to 0.70927, T would drop -0.098C from 4.600C to 4.502C.

I = 5.67*0.70927(277.652/100)⁴ = 5.67*0.70927*59.43 = 5.67*42.152 = 239.0

Conservation of Energy of Atmosphere

1^st Law Thermodynamics: Input Rate = Output Rate + Accumulation rate. At steady-state, Accumulation Rate = 0 and this ordinary differential equation becomes an algebraic one.

Absorption of solar + absorption of thermals and evaporation from surface + absorption from surface radiation = radiation to space

79 + 97 + 23 = 199 w/m²

Since CO₂ absorption spectrum overlaps solar spectrum tail a small amount at two wavelengths, the 79 value would increase a small amount with CO₂; a cooling effect on surface neglected by greenhouse gas theory. Some climatologists say CO₂ affects the rate of heat transfer from surface by thermals and evaporation, 17 + 80 = 97, but I shall neglect that controversial effect here. However, once quantified, this model structure can assess the effect on global temperatures. An additional 161 is transmitted through atmosphere from sun to surface, 1 is retained by surface. 160 is transferred from surface up: 40 is transmitted through atmosphere as radiation from surface directly to space, 97 is transferred to atmosphere by convection and evaporation and 23 is absorbed from surface radiation.

Total incoming is 79 + 161 = outgoing 199 + 40 + 1 = 240. Transfer to space = 239.

These global energy flows come from the Kiehl-Trenberth diagram, as promoted by the UN’s discredited IPCC.

Radiant Energy Transfer Law

The rate of radiant energy transfer between radiating body 1 and radiating surroundings 0 is

I₁ – I₀ =σ [e₁ (T₁/100)⁴ – e₀ (T₀/100)⁴]

(I am neglecting complicated geometry effects here.) For transfer from Earth to space, I shall assume surroundings at T₀ = 3.7K, neglecting starlight, so

I – I_s = 5.67 [0.70827 (277.75/100)⁴ – 1.0 (3.7/100)⁴] = 5.67 [0.70827*59.51 – 1.0*0.00000187] = 5.67[42.152 – 0.000002] = 239.00 – 0.000010626 = 239.00.

So there is no problem equating Earth’s radiation intensity to space with its radiant heat transfer rate to space. Intensity only equals radiant energy transfer rate when T₀ = 0.

If this is applied to transfer from surface 1 to atmosphere 0, rate I₁ – I₀ is constant (I₁ actually drops a little when incoming drops due to increased atmospheric CO₂ absorption), and e₁ is constant, then when e₀ increases with CO₂, either T₁ must increase to overcome increased resistance to heat transfer by increased e₀ (as postulated by GHGT and the only possible warming mechanism I can find), or T₀ must decrease. They both change in such a way as to reduce global T from S-B Law.

In the unusual situation where surroundings do not obey Kirchhoff’s Law, absorptivity = emissivity, a₀ = e₀, because surroundings has energy transfer by means other than radiation, like thermals plus evaporation = 97 from surface to atmosphere, one cannot replace e₀ with a₀.

Inserting appropriate values (T₁ = 14.85C, T₀ = -18.15C, e₁ = 0.1615 and e₀ = 0.167) gives:

I – I_s = 5.67 [0.1615 (288/100)⁴ – 0.167 (255/100)⁴] = 5.67 [0.161*68.797 – 0.167*42.283] = 5.67[11.111 – 7.061] = 62.998 – 40.037 = 22.961 = 23.

Note surface emissivity = 0.1615, radiates I = 63, 40 directly to space and 23 absorbed by atmosphere. While pure water has e = 0.96, ocean phytoplankton absorb solar power, reducing its emissivity. Emissivity of atmosphere seen from surface = 0.167. Emissivity of atmosphere to space is 0.830 because it receives 97 by convection and evaporation and does not obey Kirchhoff’s Law: emissivity = absorptivity.

For atmosphere component,

199 = 5.67*0.830 (255/100)^-4

Note surface radiates directly to space with effective emissivity = 0.1025.

40 = 5.67*0.1025 (288/100)⁴

Now we can find weighted average global emissivity from atmosphere and surface

e = (0.831*199 + 0.1025*40)/239 = 0.708

which confirms the initial assumption precisely.

I realize these average emissivity values may not be acceptable to some, but they do fit the observed data and are hard to determine from first principles.

At first glance, assuming I₁ – I₀ and T₀ are constant, increasing CO₂ increases heat transfer resistance,e₀, so surface radiating T₁must increase to accommodate. This could be the basic claim of GHGT and yetCO₂decreases atmospheric T₀and global radiating T. The amounts depend on the effect of CO₂ on emissivity of the atmosphere.

Lapse Rate

This is consistent with the slope of T vs altitude in troposphere, lapse rate = -g/Cp (universal gravity constant / heat capacity) because kinetic energy of gas decreases as its gravitational potential energy increases with altitude, by energy conservation law.

Increasing CO₂ increases atmosphere Cp because CO₂Cp> O₂Cp, making the slope less negative. It rotates counterclockwise about its radiating centroid T near 5 km and -18C (which decreases a bit by transfer rate to space). This causes lower atmosphere T to increase and upper atmosphere T to decrease.

Conservation of Energy of Earth

1^st Law Thermodynamics: Input rate = output rate.

(1 – alb) S/4 + IO = I – I_s + P

S = solar radiation intensity, 1365 to 1370 w/m² incident disk or 1365/4 to 1370/4 w/m² of incident sphere

Albedo = reflectivity, fraction, mostly by clouds, estimate 0.7. Some say CO₂ affects albedo through cloud formation; this could be a significant cooling effect.

I_s = intensity of surrounding space = 0.000010626 @ 3.7K = negligible

P = energy absorbed by plant photosynthesis

IO = sum inputs (core, volcanoes, fires) minus other outputs, negligible

Rearranging and substituting gives the overall relationship:

I = (1 – alb) S/4 – P = σ e (T/100)⁴

Dividing by σ e gives the overall relationship for T:

I/σe =(T/100)⁴ = (1 – alb) S/4σe – P/σe

If S increases, T increases. If alb, e or P increase, T decreases. All we need to do is find the effect of CO₂ on alb, e and P to quantify its effect on T. Easy to show increasing CO₂ causes increases in e and P, decreasing T.

If Earth were a perfect black body emitter and P = 0,

(1 – 0.3) 1366/4*5.67*1.000 = 42.1605 = 2.548⁴ or T = 254.8K = -18.33C

Actually Earth’s surface is a colorful 0.612 emitter using surface T = 15C

(1 – 0.3) 1366/4*5.67*0.612 = 68.8897 = 2.881⁴ or T = 288.1K = 14.95C

The difference 14.95 – (-18.33) = +33.3C is the difference between colorful Earth’s radiating surface temperature and its theoretical black body equivalent when radiating at same intensity, 239.

James Hansen, Al Gore and the US Environmental Protection Agency (EPA), among others, mistakenly declared this 33C to be the greenhouse effect.

With a corrected emissivity value for radiating 239 at T = 4.6C, e = 0.708, corresponding black body would radiate at T = 273.15 – 18.35 = 254.80

I = 5.67*1.0(254.803/100)⁴ = 5.67*1*42.152 = 5.67*42.152 = 239.0

This means the so called greenhouse effect is 4.60 – (-18.35) = +22.95C, not +33C.

Photosynthesis

Organic molecules are made by living flora by photosynthesis chemical reaction of xCO₂ + 0.5yH₂O + sunlight = CxHy + (x+0.25y)O₂, catalyzed by chlorophyll, according to biology. CxHy are hydrocarbon molecules: sugars, starches & cellulose, and which decay slowly to oil, gas, peat, tar and coal along with decaying fauna residue. CxHy can be natural gas, CH₄, methane.

Surface does not obey Kirchhoff’s law either,a₀ = e₀, because of this non-radiation chemical energy transfer mechanism.CO₂ is green plant food driving the cycle of flora – fauna life. Flora make O₂ for us fauna. Fauna make CO₂ for flora.

Reaction rate, consumption of CO₂ and incident solar energy, P is

P = k*p*S_s [CO₂][H₂O]exp(-E/RT₁)

p = pressure at leaf, atm

S_s = sunlight impinging on green surfaces, w/m²<160. = a(1 – alb)S/4, a = absorptivity

[CO₂] = atmospheric composition, vol {154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117} = 0.0390

[H₂O] = atmospheric composition, vol {154653b9ea5f83bbbf00f55de12e21cba2da5b4b158a426ee0e27ae0c1b44117}

T₁ = temperature of surface leaf, K

k = kinetic rate constant

So increasing [CO₂] will increase P and reduce T, cooling. Increasing S or T₁ will have the same effect.

So the sensitivity of T to CO₂ depends on which temperature you are talking about: T, T₁, T₀. And what the net effect of all relevant mechanisms is. It is easy to see why there is so much confusion and controversy.

Combined System Effects

With an increase in CO₂, solar absorption by atmosphere increases a bit to 79+ and surface absorption decreases a like amount to 161-. Therefore, surface radiation drops a like amount to 63-. And its T₁ drops to 14.85-. With increased e₀ the transfer rate from surface to atmosphere by absorption decreases to 23-. And since the atmosphere T₀ decreases to -18.15-, the net radiation rate from atmosphere to space must drop to 199- = 79+ + 23- + 97, because CO₂ is a better absorber of surface spectrum than solar spectrum. Direct transmittance from surface to space would increase to 40+ such that the total to space remains 199- + 40+ = 239.0, satisfying overall energy balance.

Therefore increasing CO₂ causes decreases in surface T₁ = 14.85-, atmosphere T₀ = -18.15-, and global T = 4.60-. There is no CO₂ global warming mechanism. There are at least four global cooling mechanisms. This refutes UN IPCC claim doubling CO₂ from 400 to 800 causes Earth’s T to increase 1.2C to 2.5C.

Back-radiation

Greenhouse gas theory to support the notion of global warming, postulates heat transfer from cold atmosphere down to warm surface, heating surface further. The Kiehl-Trenberth diagram says back-radiation transfer rate is 333, which is 2.1x that impinging surface from the sun, 161. This extraordinary value defies common experience.

I have shown the existence of any back-radiation would violate the Second Law of Thermodynamics; heat only transfers from hot to cold or from high intensity radiators to lower intensity radiators. If back-radiation existed, it would lead to creation of energy, a violation of the First Law of Thermo, constituting a perpetual motion machine of the first and second kinds, which is impossible, but just what AGW proponents need to support their perpetual global warming idea.

Measuring temperature

While climatologist, Dr Roy Spencer says satellites measure Earth’s global temperature, their spectrometers actually measure radiation intensity, I = 239, a pole to pole, day/night, season/season average. Roy must assume a corresponding emissivity, e, to infer or deduce an estimate of T. Since e is hard to determine from first principles physical properties of dissimilar surface + atmosphere and is likely to change, particularly with CO₂, using satellite inferred T is fraught with error. He must get distance between radiator and spectrometer accurately, which is not easy for a 50 km thick atmosphere and rocky mountains.

T is a point property of matter indicating its kinetic energy. We have no way in physics to average T over different phases and compositions of matter. You can’t even calculate the average T of your moving car: engine, cylinders, a/c, radiator, exhaust, body, interior, tires. Wouldn’t mean much if you could.

By the way, how are global temperature maps constructed? If they are from closely spaced thermometers, averaged daily, that would be meaningful. But if from spectrometers, how are emissivities of ocean, desert, jungles, cities, mountains, ice and clouds assigned to each point of radiating intensity, for a corresponding S-B radiating T? And averaged over sphere?

Careful study of Spencer’s writings indicates he equates/confuses radiation intensity with radiant heat transfer rate, which have the same units, w/m². The former is given by S-B Law for intensity, irradiance, radiance, power, exitance, emission. The latter is driven by a difference in intensities between two radiators or a radiator and its surroundings. Both are vectors with direction, not scalars. The former intensity, I, is not called radiant heat transfer rate because it isn’t.

When two facing plates are radiating at each other with equal intensities in opposite directions, there is no radiant heat transfer between them and their temperatures remain constant. (Note if emissivities differ when I₁ = I₀, so will radiator Ts. Chrome and wood on a beach have different steady temperatures, chrome is hotter because its emissivity is low and reflectivity is high, radiating with same I as high emissivity, colder wood.) The walls of my office radiate, but no heat transfers between them.

Chemical engineers design and operate radiant/conductive/convective furnaces with chemical reactions for a living. You can’t control something unless you can measure it or reliably infer it from measurements and known constants of nature.

Cause and effect

Just because [CO₂] and T may be correlated over significant periods does not mean one causes the other; a third input may drive them both. Solar irradiance is not constant and dominates all other influencers of T.

Solubility of CO₂ in water, beer, soda, Champagne and oceans decreases with temperature. Cooling drives CO₂ from the atmosphere into the ocean; warming drives it back out. A simple energy balance on oceans confirms the measured 800 year lag of [CO₂] following T, following S; a well-known inconvenient truth for Al Gore’s embarrassing Academy Award movie misnomer.

There is no known mechanism in the literature quantifying any effect of [CO₂] change on climate change.

Thermostat

The notion of building a thermostat to adjust fossil fuel combustion rate to control the temperature of the Earth was shown to be unmeasurable, unobservable and uncontrollable by control systems mathematical analysis in 1997, before Kyoto Protocol. In other words, it can never work.

Empirical models

It is acceptable engineering practice to infer fundamental constants/properties like an emissivity or reaction rate constant by measuring related variables and using one of these laws of physics to deduce it. Resulting law has predictive power so long at the property does not change. This know-how is particularly useful for rigorous differential equations accounting for dynamics of mass and energy accumulation rates. Stability analysis shows no tipping points.

But to fit arbitrary algebraic polynomial, exponential, sine, log or hockey stick equations to measured transient data is unacceptable since it is well known in chemical control systems engineering that they will have no predictive power.

The UN IPCC use of such models confirms they have no greenhouse gas law built on accepted physics and engineering and should be summarily dismissed. Calling for more research funding after repeated failures is compelling evidence the science and engineering of global warming and climate change is far from settled. In fact, this brief essay should settle the matter, save money and delight those practicing the scientific method.

I used only three laws of nature here: S-B Law, 1^stLaw of Thermo and Chemical Reaction Rate Law. And 10^th grade algebra. World has been spending $1 billion per day for a decade on global warming/climate change research to quantify the effect of fossil fuel combustion production of CO₂ on Earth’s temperature. A large government is shutting down its coal industry in 2014 on the mistaken belief CO₂ causes great harm, when it is benign and net beneficial. This paper proves it is all unnecessary, worthless.

Global cooling

Since Earth is warming half the time and cooling the other half, reputable climatologists report a consensus of imminent, significant, prolonged global cooling, and the effect of increasing CO₂ on temperature is vanishingly small, be prepared. Invest in energy production from oil, gas, coal and nuclear. For goodness’ sake.

Precautionary Principles

Be careful. Look before you leap. Do no harm. Think before you speak and write. Play it on the safe side. Better safe than sorry. Know what you are saying and doing. Do not frighten people unnecessarily. Supply relevant, valid evidence for every claim; lest they be dismissed as frivolous. Perform an accurate scientific, engineering and economic analysis before devising a plan and implementing it. Provide performance measures and fulfill them. Be prudent & frugal. Be a fiduciary with other people’s money. Foresee unintended consequences. Analysis comes before synthesis, always. Avoid attempting the impossible. Avoid building perpetual motion machines, in violation of the 2^nd Law of Thermo. Learn from your mistakes, admit them, apologize, accept consequences and reconcile with Nature and Nature’s God (TJ, 1776). Honesty is the best policy. Seek truth. Skepticism is a wise starting position.

Since I can’t find a mathematical description of a consensus greenhouse gas theory, I call it a greenhouse gas hunch. After all, CO₂ is green plant food. No self-respecting environmentalist would consider depriving Earth’s flora of its sustenance. Even for personal political or financial gain. Would they?

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