The "Greenhouse" Gas - Carbon Dioxide

The "Greenhouse" Gas - Carbon Dioxide

(Originally posted November 23, 2016 on Blogger)

(SEEMINGLY) INNOCENT MISNOMERS & MISCONCEPTIONS
If heat rises, then how would we explain conduction? If the tides are caused from the pull of lunar gravity lifting oceans, then why doesn't everything with mass not fixed to Earth's surface lift during high tides? If greenhouse gases act like a blanket and trap heat, then how would we explain convection?

These sort misconceptions may be harmless from the point of view of laymen like myself, but seeing countless sources explaining what I believe are important processes incorrectly seems... well, unscientific and can lead to confusion later. A perfect example of this is encapsulated in this fairly common outcry I've seen and heard over the years; "If Earth is warming, then why are some places getting cooler, rather than warmer?".

Confusion leads people astray from science, and this is when the science they're confused over is no longer an issue of science, but one of politics. As Alistair B. Fraser at Penn State college of Earth and Mineral Science once wrote, "It's like reducing the fraction 19/95 by canceling the 9s. The right answer ensues, but for the wrong reason".

Imagine being taught that you could reduce fractions by canceling the largest matching digit in the numerator and denominator, and then try reducing 18/108 as you've always been taught. Or that the order of operations--PEMDAS--is the way to do math, wherein you add before you subtract (the "AS" part of PEMDAS), then in the real world you get a job doing finance, where you have a simple calculation of $6 - $2 + $5 ... You do as you were taught, and get an answer of -$1, but is it -$1 or is it really $9? As Henry Reich explains succinctly in his MinutePhysics video on YouTube (https://www.youtube.com/watch?v=y9h1oqv21Vs), focusing on the order of operations often leads to ambiguity. And therein lies the problem. Misconceptions in science... in anything really... ultimately lead to ambiguity; and ambiguity leads to confusion... confusion leads to conflict... and conflict, as history has shown, is a tragic thing.

You're doing it wrong!

You're doing it wrong!

Given this short prelude, I hope to tackle the terrible explanations that greenhouse gases 'trap heat', or 're-radiate' it, or act like a greenhouse at all. Like the "Big Bang", the "greenhouse effect" is a bit of a misnomer, even though it conveys an idea. It just does so, wrongly. I'm not entirely sure I'll be much better at explaining what actually happens between radiation and molecules in our atmosphere, but I'll try!

It's widespread understanding that CO2 is invisible to incoming solar radiation (visible light), and opaque to outgoing terrestrial radiation (IR). That this opaque quality results in absorption of heat, preventing some of it from being lost to space. That increased CO2 concentration blocks more of this heat from escaping thus heating our atmosphere up at higher and higher rates. And on the face of it, this is true.

Though, it's not that CO2 is invisible to incoming solar radiation, it's that the molecules have quantized internal energy states and these states are only able to transition at specific energy levels that happen to be met at certain frequencies that are in the infrared band of the electromagnetic spectrum. But it's more than a simple model of absorption and "re-emission" (itself an inaccurate term); it involves some quantum mechanics which dictate for one thing to be allowed, another thing must happen... to oversimplify it.

If you go the the UCAR website (http://scied.ucar.edu/carbon-dioxide-absorbs-and-re-emits-infrared-radiation) you'll see a nice animation and succinct explanation of what happens to CO2 molecules when they absorb terrestrial heat radiation.

"This animation shows a molecule of CO2 absorbing an incoming infrared photon (yellow arrows). The energy from the photon causes the CO2 molecule to vibrate. Shortly thereafter, the molecule gives up this extra energy by emitting another infrared photon. Once the extra energy has been removed by the emitted photon, the carbon dioxide stops vibrating."   Both the caption & animation are from the UCAR Center for Science Education website

"This animation shows a molecule of CO2 absorbing an incoming infrared photon (yellow arrows). The energy from the photon causes the CO2 molecule to vibrate. Shortly thereafter, the molecule gives up this extra energy by emitting another infrared photon. Once the extra energy has been removed by the emitted photon, the carbon dioxide stops vibrating."

Both the caption & animation are from the UCAR Center for Science Education website

This is the gist of it, but in quantum mechanics, vibrational transitions are only allowed if the change in vibrational state ALSO changes the dipole moment of the molecule. Carbon dioxide is a linear molecule... and this will become an important point as you'll see in a moment. By linear, I mean the oxygen atoms are in the same plane as the carbon atom.

Oxygen atoms in red, and the carbon atom in plum pudding purple (nerd joke).

Oxygen atoms in red, and the carbon atom in plum pudding purple (nerd joke).

Above is a crude depiction of the carbon dioxide molecule; a linear triatomic molecule wherein there are two carbon-oxygen double bonds (depicted by the double bars on either side of the carbon atom). Oxygen is more electronegative than carbon, so will pull negatively-charged electrons closer to themselves (vectors towards the respective oxygen atoms) creating a dipole situation such that there are individual bond dipoles on either side of the carbon atom. But does this make the molecule itself polar?

Because carbon dioxide is linear, and because the two (electron) vectors are equal in magnitude, the individual bond dipoles cancel out. This is a symmetric stretch. So there is no dipole moment for this molecule. It's non polar. But wait! In quantum mechanics, vibrational transitions are not allowed if there is no change in the dipole moment! And I'm saying there is no dipole moment for carbon dioxide, yet carbon dioxide clearly absorbs radiation in the IR band. So what gives?

The UCAR site clearly shows a carbon dioxide molecule absorbing IR energy, vibrating, then emitting IR energy. If someone were taught carbon dioxide simply absorbs IR then 're-emits' it, then were asked by a inquisitive student to explain how they can do this given the fact carbon dioxide is a non-polar molecule, the answer might be somewhere along the lines of, "Uh, um, well... the eh,... oh, is that the phone? I'll be right back..."

So it seems a curious thing that carbon dioxide absorbs IR given the above scenario. But the vibrational state of molecules (except diatomic ones... HOFBrINCl from high school chemistry) have more than one vibrational mode.

The three (four if you count the degenerates as two) vibrational modes of carbon dioxide. The degenerate motion is referred to as a 'scissoring' motion, or scissoring mode.

The three (four if you count the degenerates as two) vibrational modes of carbon dioxide. The degenerate motion is referred to as a 'scissoring' motion, or scissoring mode.

In a symmetric stretch--such as the example described above and seen on the far left--the vectors of the oxygen atoms are such that their equal magnitude vectors (going in opposite directions) cancel each other out; hence no dipole moment (p = 0).

But there are vibrational modes where vectors do not cancel out. It is in these situations where there is a change in the dipole moment from p = 0. It's no coincidence that the UCAR site choice a vibrational mode that is non-symmetric in their animation depicting carbon dioxide absorbing IR radiation.

So what determines which vibrational mode occurs? Remember that molecules' have quantized internal energy states. This means that only energies (frequencies) that can be used to increase quantized internal energy levels of molecule will be able to increase the molecule's internal energy such that it TRANSITIONS to a higher energy state. This energy has to be at specific levels. If a quantized internal energy level requires 10 units of energy to transition to a higher state, then 9 units won't work... neither will 11. Only an 'input' of 10 units will work.

Knowing this, we can now look at each vibrational mode of carbon dioxide and have a better understanding of why one mode may occur whereas another might not. This is because each vibrational mode has its own quantized energy level.

The two (three if you count the 2nd degenerate fella') DO change dipole moment of the carbon dioxide molecule, and therefore vibrational transitions are allowed. The term for this is IR ACTIVE, meaning the dipole moment changes during vibration... so that mode is said to be 'infrared active' (IR active). For carbon dioxide, the absorption lines for this are in the near-IR bandwidth.

So it is starting to become more clear that not all IR is the same. But we've known this from high school physics.. after learning the plum pudding model of the atom (now you get the joke above yes?!), we learned that electron energy levels are quantized and only specific energies will excite electrons from their ground state. Now we know that other internal energy states in molecules are quantized too!

Ever wonder what makes a "greenhouse gas" a "greenhouse gas"? With all this awesome science in mind, now we know: Any molecule that can acquire a charge symmetry by stretching or flexing is a greenhouse gas (GHG). They are GHGs because it just so happens that the energies needed for these 'acquisitions' falls into the IR bandwidth (5-50 μm range)... IR, of course, is what we experience as heat.

Ding! There goes the ubiquitous LED light bulb above our collective heads! Carbon dioxide, water (vapor), dinitrogen oxide, ozone, methane, CFCs and other members of the hydrocarbon family... all GHGs...and now we know why. Note too that not all these molecules are linear. Water for instance is non-linear, but has asymmetric vibrations that change its dipole moment. I just gave the linear example above because carbon dioxide is my primary focus for this post.

So is it right to say that carbon dioxide is 'invisible' to incoming solar radiation? I say no, and here's why... There are other internal energy states in molecules in addition to vibrational states. There are also electronic and rotational states, and each of these is also quantized; meaning specific energies (frequencies) are required in order for them to transition to higher energy levels. Sure there is little absorption in the visible light portion of the electromagnetic spectrum (which happens to fall between the gap of the electronic and vibrational transitions), but sunlight even at Earth's surface contains UV. UV frequencies have the energies needed for electronic transitions. And far-infrared has the energies needed for rotational transitions.

Rotational transitions happen with frequencies that fall into that 5-50μm IR bandwidth mentioned above. This means that GHGs (that absorb in the 5-50μm range) correspond to vibrational-rotational transistions, not just vibrational transitions. As you can see, IR radiation plays multiple roles within that little carbon dioxide molecule.

If it must be 'invisible' to anything with regard to incoming solar radiation, then it'd be visible light, because the photon energies of visible light are too low for electronic transitions (which need UV) and too high for vibrational and rotational transitions (IR). But now we know why, and that's worth something!

So is carbon dioxide that has absorbed outgoing terrestrial radiation in the IR band now going to re-emit it? No. Re-emission is a bogus term that has no place in physics. It suggest the same energy absorbed is what is being emitted, and this is not the case. If it were, then someone needs to pull Gottfried Leibniz out of his grave and have him rework the Law of Conservation of Energy... stat!

"Don't even think about it."

What is actually happening is entirely different photons at slightly longer wavelengths (still in the IR band) are being emitted as the molecule rids itself of excess energy. In the universe, nothing likes being in an excited state as a way of life... except maybe adrenaline junkies, but I'm talkin' physics! Or trying to anyway...

Point is, what is absorbed, is not the same as what is emitted. As Alistair Fraser from Penn State has written, the Steffan-Boltzmann Law does not say emission depends on amount of radiation received; it says instead that the radiant heat energy emitted from a blackbody is proportional to the fourth power of its thermodynamic temperature... hardly "re-radiating"!

Remember, the atmosphere has its own finite temperature, which is why it continues to have a temperature after sunset. It emits blackbody radiation in proportion to its temperature, just like our planet as a whole. Although I should probably mention that Earth is not a blackbody at visible wavelengths, but does radiate in IR where absorption efficiency--according to a Harvard paper--is near unity. That paper is here for those interested: http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap7.html

So GHGs don't re-radiate the heat energy they absorbed. They radiate different heat energy, but at lower energies than what was received. So what happens to the "missing" energy if it isn't 100% 're-emitted'? Some of that absorbed energy is contained within the molecule as potential energy; it seems weird, but the electric potential energy between electrons and protons is actually negative.

There's even "potential" energy in interactions between electrons and quarks with the Higgs field. If you rearrange Einstein's famous E=mc2 formula, you'll see that mass is just a quotient of energy and the speed of light... which should more appropriately be called the speed of causality... but that's a tangent for another post! Mass isn't really a thing, it's a property that all energy exhibits. So knowing that, now I can write another post about how terrible it is to claim that "mass can be converted to energy".

In fact, look at the hydrogen atom. It has one proton, and one electron. A quick Google search shows us the mass of a proton and the mass of an electron. I won't put them here, but go ahead and add those masses together. Once you have that sum, go look at how much mass a hydrogen atom has on the periodic chart and if it matches your sum. Ya, weird.!!. but that's because that missing mass is in the form of kinetic and potential energy of the atom, which is explained by rearranging Einstein's equation. Besides... quantum mechanics IS weird by nature.. if something isn't weird, then it's probably Newtonian!

So now on to this blanket analogy... and "blocking" lingo... GHGs do not collectively act like a blanket, nor do they block IR from escaping to space. If they did, we'd be worse off than Venus long before the first human ever evolved. Heat DOES escape to space; at least some of it does anyway. Near the peak frequency range of 'long-wave' outgoing terrestrial radiation, the atmosphere is a rather weak absorber (<< is that a word?), with the exception of ozone.

As such, it allows direct escape of some parts of terrestrial radiation to space. I'd like to see a blanket be that selective! This fact is of course vitally important to Earth's energy budget, surface temperatures, and us... that our atmosphere is a weak absorber... not that blankets are cozy warm!

While we're at it, let's clarify another misconception... this time about methane. It's more effective at absorbing IR than carbon dioxide. This is true. In fact, it's many times more efficient at absorbing IR than carbon dioxide ... (dot dot dot) ... but ONLY at 3.3 and 7.5 micron wavelengths.

A minor detail perhaps, but one of key importance knowing everything up to this point. Because other gases (such as water vapor) also absorb IR at those wavelengths. The amount of water vapor is constantly changing, which can affect methane 'performance'. This is certainly not to undermine methane as a GHG, but to show that there is more going on than the mundane (and wrong) blocking-blanket-in-the-sky nonsense! Check out the absorption percentages of some different GHGs below...

Absorption cross sections of different GHGs for your viewing pleasure. It's reversed, so dips represent absorption at the given wavelength along the x-axis.

Absorption cross sections of different GHGs for your viewing pleasure. It's reversed, so dips represent absorption at the given wavelength along the x-axis.

As you can see, carbon dioxide, methane, or any of the other GHGs, don't just simply absorb IR.. they do so at different wavelengths which correspond to the internal quantized energy levels of each molecule (so long as they change the dipole moment as discussed). It isn't about trapping or blocking heat from getting out, it's about GHG molecules in unstable higher energy states ready to emit heat energy of their own which causes warming. Now it should be clear just how terrible these terms are when describing what is happening with the 'greenhouse effect'. I need to get why I keep putting that in scare quotes in a second...

But first, I just want to humbly point out that there are many factors which contribute to Earth's energy balance, but one thing is certain; the higher the concentration of GHGs--where one GHG doesn't overlay the absorption band of another GHG--the more IR in certain wavelengths can be absorbed, which translates to more GHG molecules excited to higher internal energy states floating around out there, which equates to more potential energy in our atmosphere.,,, I'm pretty sure that was a run-on sentence. :/

No molecule (or electron for that matter) wants to stay at an higher (excited) energy state. It's unnatural. And in order to drop down to 'normal', they have to release that excess energy which is not the same energy as absorbed. Electrons do it with visible light, GHGs do it with IR. The more excited GHG molecules, the more thermal radiant energy is available to be emitted. And the more GHGs out there, the more energy is available within those GHGs to be emitted... and the more heat we'll feel.

Consider that Venus' atmosphere below 50km gets so thick you could swim in it if you weren't simultaneously crushed and incinerated by it. And 96.5% of it is carbon dioxide. So concentration is an important factor. Regardless of where people think excess carbon dioxide is coming from (though it's obvious given the C-12 to C-14 ratio changes over the past several decades), fact remains that more GHGs can change Earth's energy budget such that life will struggle to adjust. Rest assured though, Earth will be just fine.

And finally, as for 'greenhouse effect'... GHGs and the glass on a greenhouse have one major difference. The glass inhibits convection. Our atmosphere doesn't work that way. If it did, then storm chasers wouldn't have anything to do... and we'd all be dead.

So this is where I should probably come up with a better name for the greenhouse effect... but I can't think of anything, so will continue to write it with scare quotes, and when I say it, I'll say it like this:

"Greeeeeeenhouse"

"Greeeeeeenhouse"

...but we'll all know the mechanics behind these crummy analogies.

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