Saturday, March 17, 2018

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 Alsop: 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.

Wednesday, March 14, 2018

Dear Judge Alsop: The Spectroscopic basis

In a suit brought by cities in California against Exxon, Judge Alsop 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 COabsorption.  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.

Sunday, March 11, 2018

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.

Sunday, February 25, 2018

The Sleazy Actor Slush Fund (Cohen's the sleazy actor, not the porn star)

Late to the party but that's not new. The issue is Trump's attorney Michael Cohen claiming he paid porn star Stormy Daniels $130,000 out of his own pocket without being reimbursed by the Trump Organization or the Trump campaign. Kevin Drum says:

OK, here’s my guess: Cohen paid Stormy; Kushner paid Cohen; Ivanka paid Kushner; Don Jr. paid Ivanka; and Don Jr.’s end-of-year bonus from The Trump Organization was $130,000 higher than last year thanks to his outstanding performance. You don’t believe me? Fine. Come up with a better theory.
Kevin's theory is closer to reality than he thinks, because I think I may have seen this game before in California politics. The game is played by sleazy political consultants who want to keep up the win ratios for a client for purposes of getting future business, but can't bill the client for the sleazy thing they'd like to do. So they use money they earned previously, that was previously placed in an entirely separate slush fund, to do whatever's needed. Long after that matter is concluded and the campaign is over, they go back and refill the slush fund with their own personal profits.

In reality the client is being billed, ultimately - the sleazy actor is very expensive because he wins a lot, so he can afford to replenish the revolving slush fund from profits as a kind of cost of doing business that doesn't quite show up on the accounting books.

I'm not guaranteeing this is right. Maybe it's something else in Cohen's case, as people point out he doesn't rule out being paid directly by Trump. This technique seems like an obvious possibility though and one I've guessed at previously.

Wednesday, February 21, 2018

Matching Methane Combustion to Carbon Capture

An idle thought that probably has occurred to a lot of people.  There is a lot of talk about clean coal with carbon (dioxide) capture. There is a lot of discussion about a hydrogen economy driven by catalytic electrolysis of water.

2H2(g)+ O2(g)--> 2H2O(g)    ΔH = 2(-241) kJ/mol = -482 kJ/mol

Eli's idle mind thought about comparing this to natural gas combustion

CH4(g) + 2O2(g) --> 2H2O(g)  + CO2(g)   ΔH = -801 kJ/mol 

Now methane, or natural gas, whether it is in the gas form or liquefied is easier to handle than hydrogen, if for no other reason that it can be liquefied. What interested Eli in this simple calculation is that methane and hydrogen have the same number of hydrogen atoms.  Eli knows that this is a very Rabett way of thinking, but if you twist your mind that way it means that there are 319 kJ/mol available for carbon capture.  True you might have to invest some of that to sweep out the water vapor, but even there there are possibilities for recapturing the heat generated in the condensation step

 2H2O(g)  --> 2H2O(l)    ΔH = 2(-44) kJ/mol = -88 kJ/mol

The interesting chemical question is can a bunny find a carbon dioxide capture system which can simultaneously capture CO2 and absorb the water vapor into solution as a liquid.  Eli is a clever bunny, it's easy to be clever and find the answer when you figure out what the question is.  Amines are obviously not going to do the job, ionic fluids might and there are some systems already known which may point the way

Setting this up as a process means that natural gas can be combined with carbon capture to yield an emission free system that can easily be combined with wind, solar, hydro and yep, nuclear to provide inexpensive (a friend taught Eli never to use the word cheap) and reliable electrical energy.  There is lots of energy to be used for the carbon capture process.  Given the right chemical system, it might even work for trucks and buses.  Autos, well leave them to Toyota, Tesla and GM.

The future will be clean natural gas and renewables.

Monday, February 19, 2018


The latest massacre of innocents has stirred up a hitherto unseen anger. Thoughts and prayers were never enough, but Emma Gonzales put it in words

  • Nothing could have ever been done to prevent this                                     We call BS
  • Tougher gun laws do not decrease gun violence                                          We call BS
  • They say a good guy with a gun stops a bad guy with a gun                        We call BS
  • They say guns are just tools like knives that are as dangerous as cars,         We call BS
  • They say that no laws could have prevented the 100s of
    senseless tragedies that have occurred                                                            We call BS
  • That us kids don't know what we are talking about that we are too
    young to understand how the government works.                                            We call BS
Eli went to school in the 1950s when every month you practiced ducking and covering under your desk in case an atomic bomb dropped, where just about every building had an air raid shelter  sign pointing to the basement.  Everybody knew this was useless.  We had all seen pictures of Hiroshima after the bomb dropped.  It was BS but the fantasy of survivability supported a complex of  illusionists like Herman Kahn and the Rand Corporation who made their living. A generation of kids was scared of every day.

Today we have a generation of kids who have grown up practicing active shooter training.  They go to school every day wondering if it will be their last.  The students at Marjory Stoneman Douglas High School have endured this all their days

Let Eli close with a story from Twitter, of a parent's discovery.  There should not be a parent in American who is not having such moments.
My 5th grader and I were conversing on the way to work/school this morning. As an educator, I wanted to be sure he and his classmates were taking the school safety drills seriously and not using it as a time to socialize and goof off.

Me: Have you guys practiced a lockdown drill in class yet?

Dez: Are you talking about an active shooter drill?

Me: Yes

Dez: Yes, we practiced it

Me: So tell me what you are suppose to do.

Dez: The teacher is suppose to shut and lock the door, put the black paper over the window on the door. Then myself and three other boys are suppose to push the table against the door.

After that all the class is going to stand behind us on the back wall.

Me: The class is suppose to stand behind who?

Dez: Me and the other 3 boys. We stand at the front and they get behind us.

*I internally went from 0 to 100 real quick. My child is one of only 2 black children in a class of 23. Being transparent, I immediately went to the "why is my black son being put on the front line?" (Just being real) So I asked before I verbally stated my thoughts*

Me: Why did you get picked to stand in front of everyone else if a shooter came in your school?

Dez: I didn't get picked. I volunteered to push the table and protect my friends

Me: 😯*immediate nausea * Dez why would you volunteer to do that?

Dez: If it came down to it I would rather be the one that died protecting my friends then have an entire class die and I be the only one that lived

Father God, it took everything out of me not to breakdown. I still have a lump in my throat. Ten damn years old and this has to be our babies thought process in America.

Thursday, February 15, 2018

Nothing New in the Pielkesphere

Well Gavin, Climate of, has had it with a certain political scientist, 

and And is naval gazing about how scientists should communicate, so memories stirred in Eli's Email list about science communication and Ethon's friend, so with the majic of search Eli found this letter which discussed how the National Assessments of Climate Change impacts came into being and the role of scientists as communicators.  
But Roger didn't like that either. It became evident that Roger's modus operandi, like his father's, is along the lines of "everyone but me is full of shit so stop thinking about what you think is significant and do my agenda instead."  
Bush-Cheney suppressed the National Assessment for the denial machine, because they could see the implications of allowing that discourse to flourish. But Roger has nothing to contribute on any such matters. He has failed so badly, and even harmfully, to see that the science community is not the problem on climate change (not to say that scientists couldn't benefit from knowing how to communicate better), it's much more importantly what happens on the receiving end of politics, media, and the public -- and how that connection has been mediated and manipulated by various interests.  
If it could be fixed by heroic efforts of scientists to communicate with civilians on climate change, it would be fixed already. I believe that a serious discussion of climate change as a policy problem calls for a progressive critical analysis of the political situation, not just beating up on the science community. For someone whose degree is in political science (my field of graduate study as well), Roger is just friggin clueless (to put it as kindly as I can) about how to think about and discuss the political aspect of things. That contributes to his remarkable, never-ending ability to miss the key point of whatever matter he is discussing and say something wrong-headed. If he gets into new subject matter the same problem will occur.  
 That only scratches the surface of the problem, I realize.