Showing posts with label co2. Show all posts
Showing posts with label co2. Show all posts

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There is no greenhouse effect

Quote-miners will love that subject line, and it isn't a statement of my belief.  But it's been recurring some that there are people denying that anybody believes that there is no greenhouse effect.  Yet, typically on the same day as that claim, I keep seeing people deny that there is a greenhouse effect.  It's also common enough that Fred Singer, who probably would label me as a 'warmist', has made his own complaints about people denying that there is a greenhouse effect.

Nevertheless, it's always a good idea to check in more systematically to what is really out there.  The search here will limit itself to Google searches which show up for the exact phrase "there is no greenhouse effect" and are within the past year.  Alas (I keep giving away the surprise ending) it turns out that there really is no difficulty at all in finding sites which claim that there is no greenhouse effect.  And, of course, are wrong in doing so.  If someone were to demonstrate it and be correct, I'd have to be nominating them for major scientific medals.  No such concern with these.
The arguments claiming to 'disprove' the greenhouse effect's existence seem to fall mainly in to 3 groups.  I add the usual 'other' category since a philosopher friend has noted that all classification schemes wind up with one.

The first group, the 'linguistic argument' is the silliest.  The problem with it is to mistake the words used to describe something with the thing itself.  And then consider that if you can find a problem with the words, that there's nothing being described.  Poof, it's gone.  In this case, that if greenhouses don't operate by the 'greenhouse effect', that there is no greenhouse effect in the earth's atmosphere.  I discuss it at more length in Greenhouse misnomer.  The thing is, the words we use don't change the reality we're trying to deal with.  The earth's atmosphere, due to water vapor, carbon dioxide, and some other rare gases, is fairly transparent to solar radiation and absorbs the earth's radiation pretty well.  It's been suggested that we call it 'atmosphere effect' or 'Callendar effect' instead.  They might be better names, but, regardless, whatever words you use, the fact of selective absorption of energy by the atmosphere remains.

The second argument also relies on giving words supremacy over the reality they're working to describe.  One of the may verbal descriptions of the second law of thermodynamics is that 'heat doesn't spontaneously flow from a colder source to a warmer one'.  But that's only a partial description -- as usual, the statement requires that you make some assumptions.  Those assumptions aren't all true when considering the flow of energy by radiation in the atmosphere. In order to apply the second law properly, you have to sit down with the mathematics.  If you don't want to, or can't apply the mathematics, at least remember that the first law of thermodynamics regards the conservation of energy, not 'heat'.  Radiation carries energy, as does the motion of particles, the elevation of those particles (such as make up the atmosphere above ground), and other things.  'heat' refers only to temperature.  The conservation of energy applies to all, and means that if radiation goes from here to there, there gets hotter (has more energy).

Venus supplies the third argument, which strikes me as bizarre, but, then, so does denying that there is a greenhouse effect.  If you look at Venus, particularly at the surface, it is exceptionally hot.  Far hotter than its blackbody temperature (about 224 K, colder than the earth's 255 K !) would suggest, and far hotter than Mercury -- which is closer to the sun and you'd expect to be hotter than Venus.  The reason for that exceptional warmth is the extreme greenhouse Venus has due to its extremely heavy greenhouse atmosphere.  It has about 90 times the surface pressure of the earth, and almost all of that is due to carbon dioxide, versus the Earth's about 0.04%  Ok, that makes it apparent why someone who would want to deny that there's a greenhouse effect (or at least that CO2 isn't a greenhouse gas) would go to Venus.

The argument, however, is absurd.  I haven't gone in to detail about this yet, but there's a concept called 'potential temperature'.  This is the temperature that a blob of gas potentially has -- if you moved it in a plastic bag that perfectly insulated it against heat conduction or radiation but was fine with shrinking to fit your blob as you moved it from where it was to the surface.  There is an old saying that 'hot air rises', which runs in to a bit of a problem with the fact that at 10 km elevation (the tropopause in mid-latitudes) the local temperature is far colder than the surface is.  If hot air rises, why is that much higher air so cold?  Because the potential temperature is so high for that air.  If you lowered that blob to the surface, it would be much warmer than the surface air.  Take a tropopause temperatures of, say, 225 K, versus surface temperature of 300 K.  By the time you brought that blob down to the surface it would be 325 K -- it really is the hotter air.

The argument relies on a ... well, I don't know what to call it, but it isn't honest or accurate.  The argument relies on taking the (observed) temperature at some large height and then bringing it down to the surface and saying that this potential temperature explains why the surface is hot.  It's a falsehood, though, because it doesn't explain why that temperature isn't reached until the great (observed) elevation.  If there were fewer greenhouse gases in the atmosphere, that elevation would be lower is the truth that is being ignored.  It is the balance between incoming energy, albedo (reflection), and greenhouse effect which determines the temperature through the depth of the atmosphere.


Linguistic argument
Second Law Argument
Venus is warm because of surface pressure / lapse rate, not a greenhouse effect

Other / Multiple

The links show some overlap, citing each other or the same, somewhat older, sources.  This takes us past the 20 links standard. Peruse them yourself, of course. That's rather the point. That, and the reference for future use that there are indeed people (and sites to publish them) who deny that there is such a thing as a greenhouse effect.

We also see that some of the same names are showing up.  We've previously seen icecap and 'climaterealists' on the blog here as unreliable sources.  More of the same.  And several others up there, I've seen in my other looking around -- such as the oft-reprinted + rewritten John O'Sullivan.  There's a certain persistence involved.

In doing this look-around, I also noticed the 'there is no greenhouse effect' argument getting unfriendly response from WUWT and Jo Nova's.  Notice also that I'm quoting Fred Singer above, and Roy Spencer for one of the physics descriptions.

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A heuristic for stratospheric cooling

I mentioned in the climate fingerprinting post that if you have more greenhouse gases in the atmosphere, we expect the stratosphere -- the upper atmosphere -- to get colder.  That, naturally, brought on the question 'why'.

I'm far from the first person to make the comment, or to attempt to write up a description of how it works on a blog.  Recently the Stoat took a swipe, or rather referenced a prior attempt and one by Realclimate, and the Rabett has also had a go.  Plus, I'm sure, there are a raft of other efforts in existence.  Yet the questioner is still asking.  That being the case, and having seen prior efforts make the attempt to describe the full situation that you have, I'll aim for a simpler version.

This will be a heuristic description.  It will be capable of being made rigorous, in the sense that you can take the heuristic and put solid math behind it.  But it will be incorrect in many of its details.  The merit of such heuristics is that even though they are incorrect in details, they lead your intuition in the right directions, such that you can then work with and understand the version of the argument that is completely correct in its details.

The simplest heuristic for surface warming in the face of an increase in greenhouse gases is our starting point.  For this, start with the surface at some temperature in balance with the atmosphere at its temperature, and with the incoming solar energy.  Now wave your hand and magically add some greenhouse gas to the atmosphere.  We will say, heuristically, that if more photons come back to the surface than used to, that the surface warms.  The surface emits some photons, same as usual.  But, thanks to the extra greenhouse gas in the atmosphere, some more get absorbed by the atmosphere.  Some of them get tossed out of the atmosphere (where they'd have gone before), but some get thrown back to the surface -- which then warms up.  The real analysis is much more involved than this, but this does give you a correct starting intuition.  It also points to the importance, yet again, of the first law of thermodynamics -- conservation of energy.

For looking at what happens in the atmosphere, let's again track photons.  (Remember those are the packets of energy carried by light).  Again, we'll start with an atmosphere and surface which are in energy balance with solar input.  Add a little bit of greenhouse gas in every layer of the atmosphere.  These cause more photons to be emitted from that layer -- half go towards space, and half towards the ground.  We'll take the heuristic approach that if most of the photons wind up in space, the layer cools.  If most wind up at the surface, the layer warms.  The heuristic also suggests that if almost all photons go to space (eventually), then the layer cools 'a lot' (it doesn't tell us how much, just a relative sense), and if half go to space and half to the surface, then it stays the same temperature.

We need to think a bit about those 'layers'.  They're being caused by energy emission from greenhouse gases.  But greenhouse gases don't emit all photon energies (or wavelengths -- short wavelengths, like blue, are higher energy than longer wavelengths, like red) equally well.  In a band (a small range of energies or wavelengths) that the gas is a strong emitter, it can easily be 1000 times better an emitter than at a wavelength a little bit different.  There is a converse to this.  By Kirchoff's law, any wavelength that the gas emits well, it also absorbs well.  So consider a strong band (15 microns, for instance, for CO2).  That strength means that a photon emitted here will very likely be absorbed before travelling very far.  That 'not very far' means that through the depth of the atmosphere, the photon will be absorbed many times.  So we can turn around and let the number of layers represent how strongly the wavelength is absorbed.  If the gas is a very strong absorber at a wavelength, then we have, say, 1000 layers.  If it's a poor absorber, it might only be one or two.

There's another feature we need in our layers, for the heuristic explanation.  Consider layer 28 (out of, say, 100).  Like all our layers, half the photons it emits go up (towards space) and half go down (towards the ground).  But ... the layers are so thick that photons will be absorbed in the next layer.  So the photons from layer 28 get absorbed in 27 or 29, rather than going to the surface or space immediately.  Now that some are in 27, we can again ask where they go -- and the answer is half go to 26 and half to 28.

I certainly wouldn't try this by hand for 1000 layers, but give yourself 3 layers.  Start with 1024 photons in the top layer (which I'm calling layer 3), send half upwards (space) and half down (layer 2, now has 512 photons).  Send half the photons up and half down, again.  Keep repeating this until all the photons are either in the bucket for space, or for the surface.  Then count up the totals in each bucket.  Repeat the process, starting with photons in layer 2, and then starting with layer 1, and compare your tallies.  You could carry this out with a stack of chips, or coins, whatever.  Or just do it on paper and copy the numbers across (it takes very good writing to carry this out, I discovered).  Or, of course, my solution of writing a short program.

It's a good idea to draw yourself a diagram here, or [Update] take a look at jg's graphic.

The outcome is, when you have several layers, the photons from the top layer mostly wind up in space.  Photons from the bottom layer mostly wind up in the ground.  The more layers (try the program, or write your own), the more this is the case.  With 100 layers, over 99% of the photons go to space from the top layer (or to the ground from the bottom layer).

So there's our heuristic answer -- the top of the atmosphere cools with an increase in greenhouse gas levels because most photons from the upper atmosphere go to space.  At the same time, the lower atmosphere warms as most photons from the lower atmosphere get caught by the surface.


That said, here's one of the limits to our heuristic description: Most of the photons don't get absorbed and re-emitted immediately, even though that's what our heuristic model says.  Most of the time, a CO2 molecule (or any other greenhouse gas) collides with an oxygen or nitrogen molecule, and hands off the energy to those molecules instead of radiating it away.  This is why nitrogen and oxygen have the same temperature as CO2.  But it also means our heuristic model is incomplete.  In addition to radiation, we should be considering what happens to the temperatures of the layers.  What saves the heuristic model is that after we let the energy slosh around, the now-warm oxygen and nitrogen molecules sometimes crash in to a CO2 molecule.  And sometimes, even if it's rare it does happen, that CO2 molecule emits a photon before it collides with another oxygen or nitrogen molecule.

There are a ton of elaborations that can be made to this heuristic.  One direction of change is to start doing Monte Carlo modeling of radiation.  This is particularly common in dealing with earth radiation in clouds.  The second is the more obvious one of tracking the full conservation of energy.  This, as you get more rigorous, becomes Radiative-Convective Modeling.

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CO2 and temperature for 800,000 years

First, the figure gives the answer on CO2 and temperature over the last 800,000 years:



Here we have each value of CO2 plotted against the temperature deviation from reference values -- with the temperature being for 1000 years before the corresponding CO2 value. The correlation for this is about 0.89 (R), meaning that you could explain 79 percent (0.89*0.89) of the variation (R^2) in CO2 by looking at the temperature. As is mentioned in my post Does CO2 correlate with temperatures, where we saw equally high correlation between temperature and CO2 (even higher if you give CO2 a 20-30 year lead on temperature), and quite a few times in the comments, correlation is not causation. Could be that both temperature and CO2 are pushed around by something else. More about that in a moment.

It's common to see the claim that temperature 'leads' CO2. Loosely speaking, this means that temperatures generally change before CO2 does, and that there is a consistent pattern to the connection -- if temperature rises, CO2 does as well. This is true; it leads by about 800 years [Caillon and others, 2003]. The amount of lead also seems to depend on whether you're in a glacial period or (as we are now) an interglacial. The correlation between temperature and CO2 is lower (by a very small amount) if you take their values for the same time (drops to 0.88). And it drops by more if we take the temperatures for 2000 years before the CO2 value, to 0.87, indicating from this very simple approach that the lead is between 0 and 1000 years, probably closer to 1000 -- as is found from the more serious approach in the reference.

So there's some interesting science to do, to understand why that lead exists, why it is many hundred years (rather than a few dozen years, or a few thousand), and why the lead time depends on whether you're in a glacial period or an interglacial period. Oddly, to me, most of the time that people mention this lead relationship, they are not referring to any of this.



Rather, they want to conclude, or for you to conclude, that because in the ice age record temperature changes before CO2, that a) the current rise in CO2 is also caused by temperatures (sometimes citing the medieval warm period as the warm time that is causing the current rise in temperature) and b) that CO2 doesn't have any affect on temperatures.

Have another look at the figure.  See that point sitting way the heck away from all others?  That's the most recent value.

You don't need a lot of scientific background to see that whatever it is that produced that CO2 value, it certainly was not the relationship that held for the other 798,000 years of the temperature - CO2 record.  We can be more precise about it.  The best fit line (the one that gives that nice high correlation) through the data points is CO2 = 266 + 8*T.  So, for temperatures at the reference value, we expect a CO2 level of 266 parts per million.  For temperatures 10 C below reference, we expect CO2 levels of 186 parts per million.  Both of these accord fairly well with what we do see in the record -- except for the most recent CO2 value.  As you can see from the plot as well, there is indeed scatter around the best fit line.  The standard deviation is about 11 ppm.  That means we're not surprised to see values 22 ppm away from the line (2 standard deviations), and, given 799 data points, we expect a few to be 33 ppm away.  On the other hand, a value 9 standard deviations away -- the case for the current CO2 levels --  is ludicrous.  Something must have changed.

We can turn this around, and ask: "If the relationship that held for the previous 798,000 years still did, what would the temperature need to have been to give the observed CO2 level -- maybe CO2 is so sensitive to temperature that we simply have a one-time temperature observing problem?"  Certainly the ice sheet temperatures do have their own observing issues.  As I've mentioned, all data have problems.  Still, same as we know that, we also know something about the size of the problem.  So, turn the equation around and solve for the temperature that would correspond to the observed (modern) CO2 level.  That's a temperature anomaly of about 13 C (20 F) -- equal to the entire range from the very warmest interglacial to the very coldest glacial!  And that had to have occurred 600-1000 years ago, by the lead relationship.  Meaning there had to have been an absolutely enormous warming (many times larger than even the highest medieval warm period values) and nobody noticed it ... or else the previous relationship between temperature and CO2 broke down.

Since we know what did cause the CO2 rise -- human activity -- we're not really surprised to see this answer. The old relationship did get broken.  Rather than CO2 rising because the oceans released CO2 to the atmosphere, it is because humans have been burning fossil fuels and making cement.  But we do like to be able to arrive at our conclusions from different directions.  Here, we need only to look at the temperature and CO2 values themselves to see that the relationship that used to hold has broken down in the modern day.  Don't need to know the first thing about isotope geochemistry (which is explained nicely in that faq by Jan Schloerer) to see this.

Let's return, though, to the fact that correlation is not causation.  There are generally 4 options when a correlation is seen: it's chance, A causes B, B causes A, both A and B are caused by something else.  We use statistical tests to decide whether chance is plausible (in this case, as with Does CO2 correlate with temperature?, the answer is a clear no).  So one of the other 3 is involved.  We can reject CO2 being the (sole) cause of temperature changes (it can certainly feed back on temperatures) because it is the temperatures that changes first.  So it's one of two now -- either temperatures drive CO2 (with feedback from CO2 back to temperatures), or something else drives changes in both temperature and CO2 (and perhaps manages to change temperature sooner than CO2).

Oddly, most of the comments about temperature leading CO2 ignore the last option -- in other words, they assume that correlation is indeed causation.  Now ... is there anything in the universe that could affect temperatures?  Could any of those things also affect CO2 levels?  That will be a separate post.  But start thinking about it yourself. Richard Alley gives away the answer in his talk, to which I referred you Tuesday.

Going farther:

I've labelled this a 'project folder' post in part for the questions I mentioned inside it -- why the lead is what it is (or at least was what it was), and so forth.  But also because the things I did you can do yourself.  The data I used were from a BBC news article on ice and CO2.  You can get it yourself and experiment with the lead relationships, find the CO2 response (slope of CO2 versus temperature in the regressions), and the like.

You can go farther as well.  For instance, are the correlation and slope different in different subsections of the record?  Is it different for different temperature ranges? (compute the slope for only temperatures from -10 to -5, -5 to 0, and so forth)  Does the correlation improve if you use the logarithm of CO2 rather than CO2 levels themselves? (if the only thing involved were the radiative properties of CO2 and its connection to temperatures, we would expect a 'yes' here)

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The Biggest Control Knob

I've mentioned Richard Alley before, with good reason.  You can get a flavor of the reason by looking at his Bjerkenes lecture The Biggest Control Knob: Carbon Dioxide in Earth's Climate History.

It's about 50 minutes, and you can skip the introduction to save a little time.  One thing not to miss from the introduction, so I'll mention it here, is the title of Richard's popular book The Two Mile Time Machine.  In it, he discusses how we (he) figures out what climate was like from examining ice cores.  First hand discussion.

Digressing to the personal a second, I do know him personally.  I was a guest lecturer in the 1991 edition of the class he mentions.  My thing at the time being deep ocean circulation, with some concern about how that affected atmospheric CO2 levels.



Back to his talk; he says a few things that I think are particularly useful for thinking about how science is actually done.  At one point, he notes that good scientists doing good work come to one conclusion -- one which makes for a conflict between two sorts of data.  And there are other good scientists also doing good work, but differently, who come to an answer that shows no conflict between the two types.  Now, who's right?  We need to do more work.  It isn't that one group is bad people, or doing bad science.  There's a conflict in the results, so we need to learn more, which means do more work to understand how the conflict comes about.  Probably (my opinion) it means that there's a loophole in one of the sorts of analyzing the geologic record, so that it doesn't only record what the method expects.  Finding that loophole is the challenge.

You'll see, also, something about what scientists are like inside.  Most of us aren't as demonstrative about liking our subjects.  But nobody can watch Richard for more than a few minutes and not realize that he loves his subject.  The rest of us do, too, just not so obviously.

This all actually relates well to the post I promised in my last note.  It turns on looking at ice cores and CO2, and Richard will fill you in on parts of the story that surround the two.

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How CO2 matters

It turns out that the argument that there isn't a lot of CO2 (true, compared to total mass of the atmosphere) and therefore it can't matter much for climate (false) has been around longer than I had thought.  I was just reading Craig Bohren's book Clouds in a Glass of Beer: Simple Experiments in Atmospheric Physics and he's got reference to it (chapter 10, on the Greenhouse Effect),   The collection of experiments was published originally in 1987, and had evolved over some period before that.  So at least 22 years that the argument has been around.

From page 82 in my Dover edition:There seems to be little dispute that carbon dioxide concentrations in the atmosphere have been increasing because of increased burning of carbonaceous fuels such as coal and oil.  At present, for every one million molecules in the atmosphere, about 340 of them ar carbon dioxide (this is written 340 ppm, parts per million).  To those who snort that 340 ppm of anything must surely be of no consequence, I recommend 340 ppm of arsenic in their coffee.  I don't second the recommendation as the lethal dose is somewhere around 1 ppm.  Craig was being sarcastic, and blunt, two common words for describing him.   The 340 ppm was about the Mauna Loa station's reading for 1981, and the last year that would round to that (nearest 10 ppm rounding) is 1984, so it's probably 3-6 years before book publication that Craig was writing.  It's now past 385 ppm.

For climate purposes, we'll consider two different things.  First is, how can a rare thing (CO2) be important to the system?  Second is, is CO2 really all that rare?


As is obvious from the arsenic example, rare things can be important in some systems.  What we need to explore is the how.  For CO2, its importance comes from the fact that it is a greenhouse gas.  Most of the atmosphere, in fact the overwhelming majority of the atmosphere, has no great absorption for the energy emitted by the earth.  The three major gases are nitrogen (N2), oxygen (as O2), and Argon (Ar), which comprise well over 99% of the atmosphere, and none of which absorb energy emitted by the earth.  All greenhouse gases are trace gases, water vapor (H2O) included.

We'll get to a less-simplified notion of the greenhouse effect, but let's start with the oversimplified version.  In that version,
0) The sun throws energy at the earth
1) the earth emits energy towards space.
2) a greenhouse gas molecule captures a bit of that energy
3) it then spits it out in a random direction
3a) if it's towards space, no change from what was going to happen anyhow
3b) if it's towards the surface, the surface catches more energy than it would have otherwise
4) Because of 3b, the surface gets hotter.


This is correct as far as it goes, but it doesn't go very far.  An important thing missing is that step 3 almost never happens alone or immediately.  Related is that this picture only tells you about the temperature of the ground and the greenhouse gases -- not of the 99+% of the atmosphere that is not greenhouse gas.  The important missing part is between 2 and 3 -- A) most of the time, the greenhouse gas molecule that just absorbed some energy emitted by the earth will collide with a non-greenhouse gas molecule and pass the energy on to the other molecule.  The converse thing can also happen -- a greenhouse molecule get clobbered by a non-greenhouse molecule and then emits some energy (to space or the ground).  Greenhouse gases play an important role in setting the temperature of the non-greenhouse gases in the atmosphere, not just the surface.  And they do this in spite of being only a small fraction of the atmosphere.

Need to emphasize that, I think.  The image is out there that H2O is 4% (40,000 ppm) of the atmosphere.  That's only true in exceedingly warm air very near a water supply (ocean or lake).  Averaged through the entire atmosphere, it's more like 2000-4000 ppm.  I'll invite you to construct your own estimates, show the rationale and calculations as to the correct figure.  In any case, while water vapor is the most common greenhouse gas (in number) it is only 5-10 times CO2, on average, not 100 times.  Conversely, this leaves CO2 as 10-20% of greenhouse gas molecules.

Anyhow, we've got our answer to the first question -- these rare molecules (greenhouse gas molecules) are important because they set the temperature of the ground, and help set the temperature of the atmosphere itself (whether greenhouse gas molecules or otherwise).  Even though they're 'rare', they matter.

But, to the second part -- are they really 'rare'?  As a fraction of all molecules in the atmosphere, yes.  There are, however, other ways of deciding rarity.  I'll start with some farther afield.  385 ppm means that in a city of 1 million, you could find 385 people who were that unusual.  Refining it a little, in a group of 2600, you'd expect to find someone that unusual.  In a sports stadium with 52,000, there would be 20 people that unusual.  A key being, given our understanding from the first question, that the 20 are not hard to find -- they're the ones being exceptionally obnoxious, starting the fights in the stands, etc. -- you know that they're there because they bump in to you, or you see the fight start, or they're the 20 who start 'the wave' in the stands, and so on.

That suggests a different way of looking at 'rare'.  They're rare if they have no observable effect.  The one person in the stands who is reading a book, you don't know they're there unless you're extremely close by.  We already know that this isn't the case for greenhouse gases -- they do have effects and we do observe them.  But let's pretend we are a photon (energy packet) emitted by the earth towards space.  We could consider greenhouse gases rare if we could expect to get out to space without ever encountering one of them.

I'll put up my math for folks to check.  If you don't like the math, you can skip ahead a little.  But I think it's important to show that there's nothing up my sleeve here.  Over each square meter of the surface (at sea level) of the earth, there are about 10,000 kg of air.  CO2 is approximately evenly distributed throughout the atmosphere, so the current (2009) 385 ppm CO2 means that there are about 4 kg of CO2 over each square meter.  That's a fairly noticeable number to us as large bodies, but not necessarily to a photon.  So I'll continue.  Update: per carrot's comment, I had oopsed here.  Even though I pay attention to the fact that CO2 molecules don't weigh the same as average air does (44 vs. 29) in the next section, I failed to do so here.  That makes it 4*44/29 kg of CO2, for 6 kg CO2 over each square meter.  Corrected figure used for rest.

In chemistry, we learned about moles of things.  1 mole is a standard count for molecules (1 Avagadro's number of molecules; the chemists and others who know the size of this number already know how this story turns out).  1 mole of CO2 has a mass of 44 grams.  So the 6 kg of CO2 represent about 136 moles of CO2.  Again that seems large, but now think about yourself as a photon emitted by the earth.  Your 'size' is about 10 millionths of a meter (10 microns); that's your wavelength.  As you go speeding through the atmosphere, a CO2 molecule has to be sitting in that window only 10 microns wide before you're likely to notice each other.  I'll take a disk with 10 micron diameter to represent the zone a CO2 molecule has to be sitting in for you to be concerned.  The relevant area is not 1 square meter, but about 80 trillionths of a square meter.  So the relevant number of moles is this times the 136 moles over a full square meter, for about 11e-9 (11 billionths) of a mole.  [Throughout, I'm using more precise numbers than I'm quoting here.  Some of the math won't seem to line up because of the rounding.]

If you don't know Avagadro's number, 11 billionths of a mole looks like it's awfully small.  That 11 billionths of a mole gives us the number of CO2 molecules (it's worse for H2O, meaning larger -- more molecules to escape) that we have to hope don't notice us as we try to race off to space.  Photons can't dodge -- they have to move in straight lines at the speed of light through whatever medium they find themselves in.  Our only hope for the race to space is that the CO2 doesn't grab us.

The thing is, Avagadro's number is gargantuan.  It is about 6e22.  Try that again -- it is 6 billion (approximately number of humans on the planet) times 10 trillion (approximate gross domestic product of the US in dollars).  In other words, if every person in the world had as much money, themselves, as the entire US economy exchanged last year, they would have 1 Avagadro's number of dollars.
Update: Copied the number wrong.  Avagadro's number is 10 times bigger than that, 6e23.  Rest of note corrected for this.

For you as a photon trying to reach space, it means that there are about 6400 trillion CO2 molecules that have a chance to grab you (6.4 quadrillion).  This is not a small number!  The only reasons that any photons do reach space from the surface is that a) molecules are extremely selective about what colors they will absorb (your wavelength has to be exactly right) b) even if you have the right wavelength, molecules are typically extremely lazy and still probably won't grab you.

For our two questions, we see the answers now as
1) These very rare gases matter because the cause the entire greenhouse effect, and contribute to setting the temperature of the atmosphere (not just the ground).
2) Given 6400 trillion CO2 molecules that sit in the path of a photon trying to escape from the surface, it also isn't very reasonable to call them 'rare'.

I've tagged this note 'project folder'.  That's my flag for posts that include things that lend themselves better to projects, things for people to check me on, or things that you can take further.  In this note, the particular challenge is to come up with a way to compute the average atmospheric content of H20.  But you're also invited to recheck my math on how many CO2 molecules sit in the path of a photon from the earth's surface trying to escape to space.  An extension would be to look at the numbers for wavelengths of 4 microns and 15 microns (wavelengths CO2 is particularly likely to absorb -- it doesn't absorb at 10; I took 10 because it's the peak for what the earth emits, and it's between 4 and 15).
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