Dear Judge Alsup: The TL:DR

Gingerbaker asked for the TL:DR for the good Judge Alsup.  Eli had already written it over at Real Climate, but deep in the comments so here it is

Eli Rabett explains it all about question 2, whether N2 and O2 play a role in the greenhouse effect.

A three parter with some TL:DRs below

A bit on observations and spectroscopy: http://rabett.blogspot.com/2018/03/dear-judge-alsop-spectroscopic-basis.html showing that the collision free absorption of O2 and N2 can be ignored. Just too small

A discussion about the physics of molecular spectroscopy: http://rabett.blogspot.com/2018/03/dear-judge-alsop-quantum-interlude.html  Shifts the balance from the qm selection rules to how molecules interact with electromagnetic radiation (e.g. IR or light). Discusses how changes in charge distributions during transitions determines whether photons are absorbed or emitted. Makes contact with electromagnetic antenna theory, eg electric dipole allowed transitions w. dipole antennas, etc. 

Eli figured the good Judge, having been a ham radio operator should grok that.

Collisional effects http://rabett.blogspot.com/2018/03/dear-judge-alsop-putting-on-pressure.html
Starting from the quantum interlude discusses (much paw-waving) how collisional induction of electric dipoles drives continuum absorptions for N2, O2, CO2 and H2O (by implication, need to add a paragraph, the water vapor continuum being an important part of the greenhouse effect, of course the concentration of water vapor in the atmosphere is dialed in on average by the non-condensible greenhouse gases.)

There were a couple of open questions in the discussion which the Bunny will get around to next week.  Hope that helps.

Dear Judge Alsup: Putting on the Pressure

Some may recall that at the end of the first episode, the Spectroscopic Basis,  Eli asked why the CO2 IR absorption spectrum at atmospheric pressure

Was different from that at 1/1000 th of an atmosphere

The answer lies in the second letter to the judge, the Quantum Interlude, where Eli discussed how the interaction of light with molecules is really an interaction with the charges, the electrons and nuclei, and how that interaction can be decomposed into a series of multipole moments, the dominant one being the electric dipole, an asymmetry in the distribution of charges.  Higher moments, like the quadrupole and shudder, octapole, only become important when the dipole is zero because the molecule is cylindrically symmetric as is the case for N2 and O2.

Comparing the two spectra above, bunnies notice that the baseline has lifted in the first, and if they look real close or blow the figure up, they would see that the absorption lines are wider.

Now those out there who have taken General Chemistry, or even maybe General Physics, can go get a drink while Eli goes on.  Turns out that the electrons and nuclei in one molecule or atom can interact with the electrons and nuclei in nearby ones and move the charge around.  If we are dealing with molecules that have a dipole moment a picture of what is happening would look like this.






But we need not restrict molecular interactions to only dipole-dipole forces, but can also include the interaction between a dipole and a molecule that has zero dipole moment.  In that case, the dipole can interact with the electrons on the dipoleless molecule and shove them around so that there is an induced dipole moment.  That is what is happening with the CO2 molecules in the first spectrum.  Collisions with N2 or O2 molecules induce a dipole on the N2 and O2 molecules, which then interact via the electric field with each other.  This spreads out the spectrum of the CO2 that we observe.

The symmetric N2 and O2 molecules are no longer so symmetric.  They can interact with IR light in the regions near their vibrational frequency via the induced electric dipole moment, but wait, there is more.  When two molecules with zero electric dipole collide, their electrons and nuclei can also rearrange (as a practical matter it takes a lot less energy in the collision to shove the electrons about than the nuclei, and a lot easier to move the outermost or valance electrons about.








So, let's take a look at what these collision induced dipole moments do to the absorption spectrum of N2 over 10 km at 70% N2.  The fuzz is the quadrupole absorption that was shown in the first letter to the judge.

O2, because of it's position at lower frequencies where the 300 K black body spectrum is more intense is perhaps more interesting

and we might better compare it's absorption spectrum with ozone (O3) and methane (CH4) which occur roughly at the same place in the spectrum at their measured mixing ratios in the atmosphere.  Even so, the effects of methane and ozone on the absorption are relatively small.

The upper scale shows the absorption coefficients of the molecular lines without boadening.

As a final (well semi-final) point, a Rabett could look for the absorption of O2 in the observed high resolution spectrum from the FIRST balloon ~60 km up

A definite maybe.

Now Eli did say semifinal.  Turns out there is a paper by Höpfner, Milz,Buehler,Orphal, and Stiller  from the Karlsruhr Institute of Technology that goes through the numbers.  They find

The effect of collision-induced absorption by molecularoxygen (O2) and nitrogen (N2) on the outgoing longwaveradiation (OLR) of the Earth’s atmosphere has been quantified. We have found that on global average under clear-sky conditions the OLR is reduced due to O2 by 0.11 W/m² and due to N2 by 0.17 W/m². Together this amounts to 15% of the OLR-reduction caused by CH4 at present atmospheric concentrations. Over Antarctica the combined effect of O2 and N2 increases on average to about 38% of CH4 with single values reaching up to 80%. This is explained by less interference of H2O spectral bands on the absorption features of O2 and N2 for dry atmospheric conditions.

An important point in interpreting these results (Eli's and the KIT group) is that while the concentration of CO2 in the atmosphere has changed from 280 to 410 ppm (see Keeling, Charles) in the last 150 years or more and the concentration of CH4 has more than doubled, the concentration of O2 has changed by a few ppm (see Keeling, Ralph), and N2 bugger all.  The small absorptions of O2 and N2 have remained constant only changing really in very deep time.

Eli has written to Dr. Hoepfner about a few questions but has not yet received a reply.

Sounds More Like Glacial Geo-Adaptation to Me

 (Source)

Interesting article in Nature speculating that certain possibly feasible, artificial interventions in major ice flows from Antarctica and Greenland could slow the pace of sea level rise. The ideas are artifical barriers that slow the flow of "warm" ocean waters that undercut and speed up ice flows, creating artificial islands that partially pin ice floating sheets in place, allowing them to brake ice flows from land, and pumping out lubricating water flows from underneath ice sheets that speed up their flow.

The authors acknowledge the difficulties and potential environmental damage caused by these interventions and consider them no substitute for reversing GHG emissions. To the extent that the effort is to reduce ice flow velocities to speeds closer to what happened prior to climate change, it sounds to me like it's approximating a more natural system than doing nothing. That's why I'd consider it more of an adaptation approach than a geoengineering approach that is meant to subsitute for actions on GHG emissions.

I'd be interested to know if these adaptations can help stabilize and recover the ice sheets that in the long term seem doomed, even with some level of recovery from climate change.

Definitely seems worth further research.

A Simple Model for Why the Greenhouse Effect Warms the Surface

While working on the answers to Judge Alsop's second question a very simple model that explains what is happening occurred to Eli about the third,

3.  What is the mechanism by which infrared radiation trapped by CO₂ in the atmosphere is turned into heat and finds its way back to sea level?

The thought goes back to the early days of thermodynamics when it was realized that heat flows and interrupting or slowing a flow while maintaining constant delivery rates requires increasing the pressure head of the pump

Heat from the Sun flows to the Earth's surface at a constant rate determined by its ~6000 K black body temperature.  The Earth's surface transforms the visible light from the sun into ~290 K IR emission which escapes to space.  The flow of energy from the Sun to the Earth has to EXACTLY (them's Nikolov caps folks) match the flow of energy from the Earth to space.

Greenhouse gases function as a regulating valve.  If their concentration increases, the valve restricts the energy flow and the Surface has to pump harder to maintain the flow.  If the concentrations decrease the pressure the pump is delivering decreases.  

The operating mechanism of the valve is simple. The higher the mixing ratio (concentration) of greenhouse gases, the more absorbing the atmosphere is at frequencies that the greenhouse gases can absorb. The optical density of the atmosphere at those frequencies sets the level at which each greenhouse gas can emit to space without being re-adsorbed, i.e. it sets the level below which emission is blocked.  The rate of emission from the level at which the greenhouse gas IR emissions can reach space thus rises with concentration.  Since the temperature decreases with altitude, the higher the effective level, the slower the emission, the more the valve closes.

OK, make a copy of this and take it to your festive dinner.  Haul it out when Uncle Ralph starts.

Dear Judge Alsup: The Quantum Interlude

In Part I, the Spectroscopic Basis, Eli looked at measurements of the O2, N2 and CO2 spectra and found that the CO2 is absorption is many times stronger than the O2, and N2 absorption even taking into acount the much higher density of the diatomics .  Strong enough that one can neglect the absorption of the other two molecules as a practical matter, however let the Bunny not stop there but go on to the quantum basis of all this trying not to get either too mathematical or too esoteric (esoteric comes in Part III:  Putting the Pressure On where the surprises are).  Eli will attempt to be correct, but not perfect and certainly not complete, that is a two semester course.

Starting back with neolithic quantum physics, let us now look at the emission spectrum of a blackbody.  We can treat the surface of the Earth as one in the IR with unit emissivity (OK ice is a bit different but it is a lot colder so it emits a lot less) and look at the spectrum.we would expect at 290 K

where your gracious host has marked where our three players, O2, N2 and CO2 would absorb and what the black body emission would be at 290K.  The observant among Eli's readers have noticed that there is simply no IR, or darn near none of it out where N2 and the CO2 asymmetric stretch absorbs.

If you want to know what the bending and symmetric stretching vibrations are, make sure your significant other or keeper is not around.  Place your fists on either side of your head and move them up and down or forward and back.  Your head is the model of the C atom and the fists are oxygen.  That is the bending vibration.  There are two such, forward and back and up and down.  They have the same frequency and Eli calls them degenerate.  If somebunny catches you doing this, you may be so called also.  For the asymmetric stretch move one of your fists toward your head and the other away while bending the noggin toward the fist that is trying to hit it.  Then reverse.  Folks doing this too enthusiastically can knock themselves out.

Rabett Run now needs to crawl a bit further down the physics tree to Electricity and Magnetism.  Light (Eli will use the word light to describe IR, which strictly speaking annoys the fussbudgets who reserve light for visible light, but what the heck), is electromagnetic radiation, from the gamma ray to the radio waves and beyond in both directions.

Molecules are composed of atoms, which are composed of positively charged nuclei and negatively charged electrons.  The charges have electric fields, which interact with each other and the electromagnetic field.  The forces created by the interaction can move the charges relative to each other and in space.

We can describe the field created by the electrons and nuclei one by one or we can describe the potential energy in the field at a point  a large distance r from the molecule as a power series in (1/r)ⁿ.  If r is large, the importance of each term decreases with n. It is pretty well hopeless to describe the field created by the charges one by one especially if they are moving, and the power series converges quickly.  That means that each term is a lot bigger than the next so in practice we only need to keep the first non zero term, maybe the second.  This power series is called a multipole expansion.

You can look up the details of the multipole expansion, but it is just a bunch of geometry where each charge qi is some distance ri from a point in space P which is quite far away.  For convenience in what follows we can let the origin of the coordinate system be at the center of charge of the molecule.

The first term in the multipole expansion is proportional to the sum over all the charges divided by (r).  Since molecules are neutral the sum of charges is zero and the first term is zero for a molecule.

The second term, for which the potential would vary as 1/r² is called the electric dipole and is equal to Σ qi di where Σ is the sum over all the charges and di  is a vector pointing towards charge i.  Rather than bothering about the math, let's look at some examples CO2 and H2O.

In the case of CO2 the molecule is cylindrically symmetric. The distance rc for the carbon nucleus is zero and the contribution to the dipole moment will be zero.  Each of the oxygen nuclei has the same charge, but the distance from the carbon nucleus is +d for one and -d for the other so their contributions to the net electric dipole cancel.

For the electrons, the image is an electron anomaly distribution, with the blue areas being electron rich and the red electron poor, but the point is that the distribution is also cylindrically symmetric and for every point that contributes positively to to the electric dipole moment there is one that contributes negatively.  They cancel, and the net electric dipole moment of ground state CO2 is zero. 
The same is true for O2 and N2

The case for H2O is different.  The shape of the molecule is bent, there is a region of high electron density on the side of the molecule facing away from the hydrogen atoms and the electron density on the side of the hydrogen atoms facing away from the oxygen atom is electron poor.  H2O will have a permanent dipole moment. The blue arrow points towards the region of higher negative charge 

When a molecule with a permanent dipole moment rotates (there are three axes that water vapor can rotate about) the dipole moment moves and that movement interacts with light because light is an electro-magnetic field that is influenced by moving dipoles and/or can influence them.  By this mechanism rotating water vapor molecules can either gain (absorption) or lose (emission) light (IR or better put Far IR) between 0 and 800 cm^-1 accompanied by a change in rotational state.  Molecules with zero dipole moment can spin merrily on their way but they do not interact with light in this way.  We can see these rotational transition in the  spectrum of water vapor between 0 and 800 cm^-1

The semi-log plot comes from another handy dandy web app Spectral Plot.  The rotational lines (the bunch on the left) overlap the CO2 bending vibration as can be seen in the high resolution FIRST balloon specta taken at about 60 km looking down.

The bunch of water vapor lines at 1700 cm^-1 are the result of the bending vibrational transition.  Looking at the electron density map of HOH, it is clear that changing the molecule bends the H-O-H angle will change, vibrating about the equilibrium ground state position as shown in this gif from Marc Henry.

If we averaged the dipole moment over one, or many cycles of the vibration it would not change, but it obviously does change during the cycle and this change can both generate an electromagnetic field and absorb energy from one. It is the CHANGE in the dipole moment during a transition that couples the molecule to light.  

The instantaneous change in the dipole moment is called the transition dipole moment.  It is the non-zero transition dipole moment that makes the bend  (Source at UVA)

 

 and asymmetric stretch of CO2 IR active,

while the symmetric stretch is not.  A little thought will show that when homonuclear diatomic molecules such as N2 and O2 begin to vibrate there is no change in the dipole moment and therefore they cannot absorb or emit IR accompanied by a change in vibrational state.



A really good analogy to this is a dipole antenna such as the ones used for receiving FM radio.




So how do N2 and O2 interact with light?  Well, the next element in the multipole expansion beyond the electric dipole moment is the quadrupole moment.  Eli will not bother you with how to calculate it. It turns out that, both N2 and O2 have ferocious quadrupole transition moments, essentially because they are so cylindrically symmetric and the same is true of the symmetric stretch of CO2, but even with a strong quadrupole transition moment the fact that the interaction of a quadrupole with light is proportional to 1/r³ rather than 1/r² makes their absorption much weaker. There is also an antenna analogy.  The Adcock antenna, used for direction finding, is a quadrupole array.

The TL:DR version of this is that it is the interaction of the electromagnetic field of light with the charge distribution of molecules that gives rise to absorption and emission of IR radiation. Although not dealt with here, quantum mechanics tells us about what changes in rotational and vibrational levels are allowed if the electromagnetic interaction is non-zero.  If the electric dipole is nonzero, vibrational transitions with unit change in quantum number are strongly favored, the same is true for rotational transitions.  Overtones with changes of two or more quanta are very weak.

So stay tuned for the exciting finale.

Dear Judge Alsup: The Spectroscopic basis

In a suit brought by cities in California against Exxon, Judge Alsup has asked of the parties a set of questions which some parties on the INTERNET are busy crowd sourcing the answers to.  Now Eli has never been one to avoid a pile on, so the Bunny thought he might essay an answer to two of the questions

2.  What is the molecular difference by which CO₂ absorbs infrared radiation but oxygen and nitrogen do not? 

3.  What is the mechanism by which infrared radiation trapped by CO₂ in the atmosphere is turned into heat and finds its way back to sea level?

Let Rabett Run start with question 2. Many of the answers start and end with what was learned in Modern Physics or Physical Chemistry.  Real Climate has settled on

Greenhouse gases are those that are able to absorb and emit radiation in the infrared, but this is highly dependent on the gases molecular structure. Diatomic molecules (like N2 or O2) have stretching modes (with the distance between the two molecules expanding and contracting), but these require a lot of energy (so they absorb only at higher energies. Vibrational modes in molecules with three or more atoms (H2O, CO2, O3, N2O, CH4, CFCs, HFCs…) include bending motions that are easier to excite and so will absorb and emit lower energy photons which coincide with the infrared radiation that the Earth emits. Thus it is these molecules that intercept the radiation that the Earth emits, delaying its escape to space.

This is approximately true, but not quite the whole story and much can be learned by going a bit deeper.  It is not that N2 or O2 cannot absorb or emit IR, but their absorption and emission is many orders of magnitude weaker than H2O, CO2 and other greenhouse gases found in the atmosphere.   How many orders of magnitude?  Well about ten.

A good place to start is the HITRAN data base maintained by the Harvard Smithsonian Center for Astrophysics.  HITRAN stands for High Resolution Transmission.  The database, just like the JANAF tables, is a fruit of the cold war started when the US Air Force was interested in learning more about the propagation of light in the atmosphere for such things as aiming missiles and such.  It is essentially a list of lines in the transmission spectra of various molecules under different conditions of  temperature, and pressure.  Using the database one can generate spectra of self-same molecules which are eerily accurate.  GATS among others provides a front end to calculate spectra using HITRAN, so let us start to explore.

The first question is does N2 or O2 absorb IR light. We know the vibrational frequency of these molecules, so we can look at what the database tells us how much light nitrogen would absorb in the atmosphere at a pressure of 1 mbar (1000th of atmospheric pressure. Be patient the reason for this choice will become clear in a few minutes), a temperature of 296 K and a path length of 1000 km.  Yes Eli knows that such a gas cell is not currently available, but with HITRAN we can accurately model this.

The alternating intensities of the lines are due to the symmetry of the nitrogen molecule but that is another story with which we need not concern ourselves at this time.  We can do the same for O2 

Turns out that the triplets seen in this spectrum are the source of the signal that the Microwave Sounding Units that measure tropospheric temperatures monitor.

But now we can do the same for CO2

The difference in path length for absorbing about the same amount of light by CO2 is 0.1 cm, or, if you wish 10^-6 km.  So the difference in the absorption would be a factor of 10^-9.  

But you say, the mixing ratio of CO2 in the atmosphere is 410 parts per million or 0.00041, and the concentration of N2 is 0.70 thus the number  of N2 molecules per CO2 molecule is just 1.75 x 10⁴ while the N2 absorption is 10^-9th of the CO2 absorption.  Put that together and the amount of IR absorbed by N2 is roughly 0.00002 of that absorbed by CO2.

Ms. Rabett is calling, so let Eli provide a bit of a teaser for Part II.  Here is the absorption of 400 ppm CO2 at atmospheric pressure across a 3 m cell.

Breakthrough Institute and The Politics of Limits

The Interchange is an interesting renewable energy/renewables business podcast by GreenTech Media, and the most controversial podcast I've heard so far is an interview with Breakthrough Institute's Alex Trembath.

Some thoughts:

• Alex says they've consciously decided to be less critical of mainstream environmental groups, less obnoxious and rock-throwing, and good for them for this change. There are some times when obnoxious rock-throwing is appropriate - that wasn't the case regarding past BI behavior, so it's good that they've changed it and are willing to say they've decided to change it.

• Alex rightly says the environmental movement prior to 2004 (when the Breakthrough guys started doing their thing) had a much stronger emphasis on limits to growth then it does today, but is wrong to say there was something wrong about that. I'm sure plenty of people back then realized solar and wind costs were dropping dramatically, but I don't know if anyone would've said you can count on renewable energy being cheaper than fossil fuels, even without subsidies or accounting for externalities. That meant some type of limit was a necessary argument back then for energy issues (and remains a component of many other environmental issues).

• He goes on to argue that limits to growth and saying no in general is a bad political tactic. I'm open to that argument but I'm not sure what BI is doing with it or backing it up with solid research (might be a little unfair to demand that of a podcast).

• Alex says BI started off with a focus on renewables and EVs. That's sure not how I remember it, which was nuclear power all the time. He says they're now into nuclear as well. Yep.

• He claims power systems get unstable with renewables are 50% of the total. I thought we were over that, and the discussion really is 80% versus 100%.

• Alex makes an unnecessary dig at energy efficiency, with the Jevons Paradox etc.  That's a miss - I think the political economy vastly underestimates the unsexy value of efficiency, the complete opposite of what he was saying.

All in all, too much techno-optimism, but it could be worse, and BI seems to be moving in a better direction. It's less clear to me whether they have the chops to make any real contribution, though.