By W. A. van Wijngaarden, Department of Physics and Astronomy, York University, Canada and W. Happer, Department of Physics, Princeton University, USA
We discuss the basic ways greenhouse gases affect radiation transfer in Earth’s atmosphere. We explain how greenhouse gases like water vapor, H2O, or carbon dioxide, CO2, differ from non-greenhouse gases like nitrogen, N2, or oxygen, O2. Using simple thermodynamics and fluid mechanics, we show that the atmosphere of a planet with sufficiently high concentrations of greenhouse gases must develop a convecting troposphere between the surface and the tropopause altitude.
The planet must also develop a non-convecting stratosphere for altitudes above the tropopause. In the simplest approximation of an atmosphere that is transparent to sunlight and has frequency-independent opacity for thermal radiation (an infrared gray atmosphere), one can find simple formulas for the tropopause altitude, and for the altitude profiles of pressure and temperature.
The troposphere is nearly isentropic and the stratosphere is nearly isothermal. The real atmosphere of the Earth is much more complicated than the simple model, but it does have a troposphere and a stratosphere. Between the surface and the tropopause the entropy per kilogram of real tropospheric air increases slowly with altitude. The entropy increases much more rapidly with altitude in the stratosphere. The stratosphere has a nearly isothermal lower part and a hotter upper part due to absorption of solar ultraviolet radiation by ozone. The thermal opacity of the real atmosphere has a complicated frequency dependence due to the hundreds of thousands of vibration-rotation transitions of its greenhouse molecules.
Unlike the simple model where nearly all radiation to space originates at the tropopause altitude, radiation to space from Earth’s real atmosphere originates from both the surface and all altitudes in the troposphere. A small additional amount of radiation originates in the stratosphere. When these complications are taken into account, model calculations of the thermal radiation spectrum at the top of the atmosphere can hardly be distinguished from those observed from satellites.
You may download a printable version of Atmosphere and Greenhouse Gas Primer here.
Excellent paper! Looking forward to all the heavy hitters to weigh in….
Geez.
that all sounds like stuff that would be going on in a coupled non-linear chaotic system.
But as we already know, there’s nothing left to discover about such systems, because the science of such systems has all been settled. Apparently.
Question, what would be the winter effect of multiple anomalous deep stratified bands of water vapor in the Stratosphere on the Polar Vortex this winter, will it be more disruptive, or will it add stability?
The Quasi-biennial Oscillation (QBO) (nasa.gov)
No mention of N2O? Why? Why is this gas…..300 times more potent as a GHG than CO2…. always ignored?….neglected? We gotta pay proper respect to this fav of dentists, no?
As it happens, the same authors have exposed the Phony Nitrogen “Crisis” as a pretext for warring against farmers. The paper is Nitrous Oxide and Climate by C. A. de Lange, J. D. Ferguson, W. Happer, and W. A. van Wijngaarden.
https://arxiv.org/pdf/2211.15780.pdf
“Higher concentrations of atmospheric nitrous oxide (N2O) are expected to slightly warm Earth’s surface because of increases in radiative forcing. Radiative forcing is the difference in the net upward thermal radiation flux from the Earth through a transparent atmosphere and radiation through an otherwise identical atmosphere with greenhouse gases. Radiative forcing, normally measured in Wm−2, depends on latitude, longitude and altitude, but it is often quoted for the tropopause, about 11 km of altitude for temperate latitudes, or for the top of the atmosphere at around 90 km.
For current concentrations of greenhouse gases, the radiative forcing per added N2O molecule is about 230 times larger than the forcing per added carbon dioxide (CO2) molecule. This is due to the heavy saturation of the absorption band of the relatively abundant greenhouse gas, CO2, compared to the much smaller saturation of the absorption bands of the trace greenhouse gas N2O.
But the rate of increase of CO2 molecules, about 2.5 ppm/year (ppm = part per million by mole), is about 3000 times larger than increase of N2O molecules, which has held steady at around 0.00085 ppm/year since the year 1985. So, the contribution of nitrous oxide to the annual increase in forcing is 230/3000 or about 1/13 that of CO2. If the main greenhouse gases, CO2, CH4 and N2O have contributed about 0.1 C/decade of the warming observed over the past few decades, this would correspond to about 0.00064 K per year or 0.064 K per century of warming from N2O.”
“Proposals to place harsh restrictions on nitrous oxide emissions
because of warming fears are not justified by these facts.
Restrictions would cause serious harm;
for example, by jeopardizing world food supplies.”
My Synopsis:
https://rclutz.com/2023/11/15/phony-nitrogen-crisis-for-making-war-on-farmers/
What I find most intriguing is that the earth completely shrugs off the effects of the solar luminosity variation, roughly equivalent to 15 years of global CO2 emissions. It’s a periodic variation, so signal processing techniques can be used very effectively here. Running an FFT on the data shows that there is essentially no change in the equilibrium temperature with a change in the downwelling radiation. I find this absolutely fascinating. The earth is controlling the energy imbalance, and CO2 apparently has nothing to do with it.
as expected, its a biggie…
(Composed in Word so shouldn’t have too many typos)
There are no perfect absorbers and no perfect emitters, as claimed.
i.e. If you want to vanish into minute trivia and details you do, making such an assumption is invalid.
It is stated that Ozone absorbs a lot of solar energy within the atmosphere but no mention of where the Ozone came from.
The Ozone comes from solar UV interacting with diatomic Oxygen – thus diatomic Oxygen is not transparent to solar energy.
It is stated that there is little Ozone near the surface.
Well why not? Because it is consumed by volatile organic compounds created by plants – how much solar energy do those gases absorb?
The explanation of the 2nd Law is beyond contrived and introduction of Entropy perfectly unnecessary – unless you don’t understand it.
Which you don’t hence all the tawdry and middling appeals to authority.
The 2nd Law simply states that heat energy always flows down a thermal gradient – NEVER the reverse.
So what do we read at the very top of Page 21 – as attached.
There are 2 massive errors there:
1/ The surface will always be warmer than anywhere above it in the atmosphere – heat energy can thus NOT flow in the direction stated. Radiation can, it can do as it likes. Radiation is NOT – energy.
Yes radiation can certainly come down to the surface from the sky/atmosphere/anywhere but if that sky/atmosphere/anywhere was colder than the point where it arrives, it will not be absorbed – THAT is = The 2nd Law.
Don’t confuse yourself with Entropy.
2/ It is confusing ‘radiation’ with ‘energy’. It is the exact same confusion endlessly seen between Watts and Watt-hours
i.e. The difference between energy and power
It all wraps up with its own real killer, a triumph of cause/effect muddlement:
1st para of Summary:”” Greenhouse gases warm the surface because they increase the “thermal resistance” of the atmosphere to the vertical flow of energy from the solar-heated surface to space.
As per the 2nd Law, greenhouse gases DO NOT warm the surface
That statement is deliberately misleading because it implies a positive heating effect.
The rest of the statement is true – yes green gases do increase the thermal resistance but any gas or any substance would do that. The arbitrary and contrived definition of green house gas is necessary.
So what this increase of thermal resistance does is reduce the rate of cooling but is only a valid concept when dealing with either or conduction or convection.
In fact great measure was made to rule out radiation as a source of this resistance when it was explained that radiation moves at ‘the speed of light’ – the thermal resistance is NOT a radiative effect.
That then means that the surface MUST somehow come to exist at a higher temp than it initially appears and that variations in the thermal resistance cause it to display the temperature it does.
But that means that the very initial premise of a temp of 278Kelvin for the surface must be wrong. (Minus 18 or minus 20 Celsius in most other pexplanations)
(Of course Tyndall would suggest green gases would warm the Earth – he was using boiling water in his experiment. He was actually recording that CO₂ was directly absorbing solar energy.)
Real experiment:
Visit the surface of the ocean on the equator and spend 24 hours there at the time of an equinox. Sit in a boat.
In fact, little of that is important, visit anywhere inside the tropics at almost any time.
Watch the sun rise fall disappear and rise again.
At solar noon you will record the power of the sun as being pretty dam close to 1,370Watts.
As it rose to that level and dropped away again, it will have followed a sine-curve, meaning that it’s root mean square average power was 1370 divided by sqrt(2) =869Watts
At night there is no sun so the average power you see over 24 hours is 484.5Watts
That sun is shining into deep clear water – presenting an albedo to normally incident sunlight of 0.06 meaning that the energy being absorbed becomes 457Watts
The emissivity of the liquid water will be about 0.95 (NOT = unity as assumed)
After millions of years to equilibrate, solar input will have come to equal radiated output which, using those figures according to Stefan will be= 303.5Kelvin or 30.5 Celsius = EXACTLY what is recorded
Then expand that calculation for up to 30 degrees of latitude gives an average and properly area-weighted temperature of 27.6Celsius for an area equal to 55% of Earth’s total surface area.
Worse: What really really is so mind blowing is the complete absence of Carnot in any of that. The fawning obsequience to the 1st Law is complete and absolute.
Because we are NEVER told what happens to ‘the radiation’ when it is being or has been absorbed.
Those interactions are in fact all = miniature Carnot Heat Engines and in the absence of a ‘perfect exhaust’ at Zero Kelvin, those engines are never 100% efficient.
And THAT is the explanation of the 2nd Law and is why, although the radiation ‘downwells’, the energy it carries from atmosphere to surface is never absorbed
To do so invokes a Heat Engine with negative efficiency = complete utter garbage
The atmosphere cools the surface.
Back to the drawing board people….
What is so pleasantly tickling while watching this muppetry, is the repeated mention of ‘Sahara Desert’ – as if it is is some monumental heirloom bequeathed to us from the engineers of The Big Bang.
There is completely NO WAY any theory of green gases can create that thing.
In any case, all substance are = Green House Substances, we know that from their colour.
Likewise, somewhere in there but my brain was hurting, was an involved, contrived and confabulated explanation of Stratosphere.
Stratosphere is simply the place where water freezes.
It really is a bummer also when your precious green gas stops Playing The Game isn’t it?
Even worse when CO₂ has perfectly immeasurable Emissivity (Read = zero as measured by No Mention Hottel in 1954
I do love these discussions and I am always impressed by the quality of the commentary. There has been a long term question that I have been trying to get to the bottom of that I would like to pose here in the hope that it would generate some insight for us all. It is this:
“What is the relative contribution to the Earth’s temperature from greenhouse gases as compared to convective compression/expansion?”
Here is an article on the subject which strongly support the contention that the majority of the additional temperature increase on the Earth as compared to the airless moon is due to convective compression/expansion (i.e. the heat engine of the atmosphere driven by the sun’s heating of the surface). The main graph showing the fitting of the model to the relative atmospheric pressure vs. the solar constant for the planet in question is also attached below.
https://tallbloke.files.wordpress.com/2022/05/ecs_universal_equations-1.pdf
https://qph.cf2.quoracdn.net/main-qimg-88167ef94752773624c6d25a396b1f86
If I understand the mechanism of atmospheric convection and expansion/contraction that is driven by the convection, it is something like this:
1) The Sun heats the surface of the earth during the day (dominant heat source for the planet)
2) The atmosphere in contact with the surface is heated by direct contact with the warmer planetary surface
3) The warmer (less dense) air is bouyant against the rest of the atmosphere and rises (like a hot air balloon) and rises up from the surface expanding and cooling as it rises (cooling by expansion and by radiation to space and the surface)
4) Cooler air higher up in the atmosphere moves downward to replace the rising heated air and it is compressed by gravity as it moves downward and thus heats the air being compressed
5) although there is BOTH a heating and cooling effect going on at the same time (like a fridge), there is a net generation of extra heat because this “heat engine” is not 100% efficient at all.
6) Furthermore, the surface is heated more than the atmosphere higher up because the atmosphere is radiating at altitude to space and cooling as it rises
7) In addition at the rising thermals reach a certain altitude the entrained water vapor that has been evaporated by the surface heating generates clouds which form a white (reflective) surface for a reduction in albedo for that portion of the planet.
Now I realize that the mechanism of Greenhouse Warming and back radiation could ALSO play a role and I wonder if any of you have an estimate of the relative contribution of the two effects towards the surface temperature of the Earth (and Venus for example).
Any polite comments would be much appreciated!
Ian IN vancouver
I will give it a C+. Mainly for a good attempt to show CO2 does little. But this statement in the conclusion is not accurate:
Any radiosonde over a surface above 22C with atmospheric water above 30mm will typically show a significant discontinuity in lapse rate per attached. The temperature profile is hardly steady gradient. Unless your model gets into how a level of free convection forms and convective potential develops, you are whistling dixie.
They have not determined the process that regulates Earth’s energy uptake and limits ocean surface temperature to 30C.
The paper does not get into cloud formation associated with convective instability. They do not get into partition into dehumidified and humidified zone that give rise to convective instability within the tropopause.
Convective instability is the profound process in Earth’s atmosphere. It is only studied in its relationship to damaging weather events but not the energy balance or climate. We have powerful convective storms that all have their origin in convective potential and no one is studying the key processes for the formation of convective potential.
Every single appreciable atmosphere over a rocky planet/moon that we can observe (13?) has a lower convective layer/layers with upper nonconvective layers – Earth has two sets. Each of these isothermal layers are due to some sort of absorption of intense solar radiation and act to block convection of the layer below it. This phenomenon occurs regardless of gas composition.
It’s all well over my head but that comment in the summary is pertinent as the usual estimate of climate sensitivity has been around 1C excluding feedbacks: “In the absence of feedbacks, the energy imbalance would eventually result in roughly 1 °C (1.8 °F) of global warming” (Wiki).
It’s a useful primer, but they get quite a lot wrong. From their bullet points starting at botom p 20:
“For a gray atmosphere, surface radiation to space is attenuated by factor e^−τ₀ where τ₀ is the vertical optical depth from the surface to outer space. Absorbed surface radiation is replaced by radiation emitted by greenhouse gases higher in the atmosphere.”
No, radiation attentaued is replaced by radiation from where is is absorbed. It has to be; there is no magic to transport the heat to those higher layers. Schwarzchiid got all that right a century ago.
“Radiative heat transport is negligible compared to convective heat transport below the tropopause.”
No, as they sort of explain, the atmosphere below the DALR (dry lapse rate) is convectively stable. Water vapor transports more heat, but less than radiative. See Trenberth’s observational heat budget.
“Without greenhouse gases, the adiabatic temperature profile of the troposphere would evolve into an isothermal profile with the same temperature as the surface.”
Definitely not. This was hashed out at least ten years ago. The forced motions of the air act as a heat pump, driving heat downwards. They more or less explain the mechanism, but miss the result. These motions are what forces the air temperature gradient toward the DALR. If the gradient goes beyond the DALR, the heat pump becomes a heat engine, and the atmosphere then is convectively unstable. Again this forces the temperature toward the DALR. None of this involves GHGs. The atmospheric motions result from temperature variations, eg latitude.
“Greenhouse gases increase the temperature of the surface, compared to the surface temperature in an atmosphere without greenhouse gases.”
Yes.
The stratosphere is the result of having free oxygen in the atmosphere. No other known planet has one.
99% of Venus’s atmospheric mass is in its troposphere, and then at the tropopause, it transitions to its mesosphere.
WRT adiabatic vs. isothermal equilibrium:
At the January 1862 meeting of the Manchester Literary and Philosophical Society, a paper, On the Convective Equilibrium of Temperature in the Atmosphere, by Professor Wm. Thomson was read by Dr. Joule:
“When all the parts of a fluid are freely interchanged and not subject to the influence of
radiation and conduction, the temperature of the fluid is said by the Author to be in a state of
convective equilibrium.”
In May 1866, J.C. Maxwell responds: On the Dynamical Theory of Gases, Philosophical Transactions
of the Royal Society of London, Vol. 157, p. 86 (1867),
“The left-hand side of equation (147), as sent to the Royal Society, contained a term, the
result of which was to indicate that a column of air, when itself, would assume a temperature
varying with the height, and greater above than below. The mistake arose from an error in
equation (143). Equation (147), as now corrected, shows that the flow of heat depends on the
variation of temperature only, and not on the direction of the variation of pressure. A vertical
column would therefore, when in thermal equilibrium, have the same temperature
throughout.”
In October 1875, Ludwig Boltzmann writes: Über das Wärmegleichgewicht von Gasen, auf welche
äußere Kräfte wirken, Sitzungsberichte der Mathematisch-Naturwissenschaftlichen, Vol. 72-II, p. 443
(1876),
“Aus dieser Formel folgt, daß trotz der Wirksamkeit der äußeren Kräfte für die Richtung der
Geschwindigkeit irgend eines der Moleküle jede Richtung im Raume gleich wahrscheinlich
ist, ferner dass in jedem Raumelemente des Gases die schwindigkeitsvertheilung des Gases
genau ebenso beschaffen ist, wie in einem Gase von gleicher Temperatur, auf das keine
Aussenkräfte wirken. Der Effect der äusseren Kräfte besteht blos darin, dass sich die Dichte
im Gase von Stelle zu Stelle verändert und zwar in einer Weise, welche schon aus der
Hydrostatik bekannt ist.”1
1. Google’s translation:
“From this formula, it follows that in spite of the effectiveness of the external forces for the direction of
the velocity of any of the molecules, each direction in space is equally probable, furthermore that in each space
element of the gas the velocity distribution of the gas is exactly the same as in a gas of same temperature, on
which no external forces act. The effect of the external forces consists merely in the fact that the density in the gas
changes from place to place in a manner which is already known from hydrostatics
As the upper troposphere is ALWAYS colder than the surface, it is impossible for any IR directed downward to warm the surface. The IR is reflected back upward and lost to space. Furthermore, none of these stupid models have night-time during which IR is poured out to space. That is why it chills down so quickly after sunset. This article is junk science as it adopts the idea of greenhouse gases. No gas at any concentration can warm the climate. And convection carries 85–90% of solar insolation energy to altitude where the energy is lost to space, including the latent heat of evaporation of convected water vapor as it condenses at altitude.
It needs some proof reading, makes some elementary mis-statements in the intro, e.g.:
“At sea level each molecule experiences a collision about once a nanosecond (a billion collisions per second).”
Actually more like 10 times/nsec.
“Although greenhouse gases do not scatter thermal radiation, they do emit it sponta- neously. So thermal radiation in opaque spectral regions is absorbed and independently reemitted as though it were being isotropically scattered.”
They do not emit ‘spontaneously’, the mean emission time is of the order of seconds so much longer than the collision time at atmospheric pressure so much of the absorbed energy is collisional transferred to the surrounding molecules.