Basics of Greenhouse Spectra

I am not an expert on climate science but every now and then I run into something that most people don’t understand and try to add to public understanding. A common question is the interaction between different greenhouse gases. Why does water (H₂O) vapour, present in much higher concentrations, not dominate any changes in the greenhouse effect? Why is methane (CH₄) said to be a much more effective greenhouse gas than carbon dioxide (CO₂) molecule for molecule?

There are two major issues I address here: water vapour is not present in equal measure throughout the atmosphere, and greenhouse gases vary in the wavelengths of infrared they absorb preferentially, and hence complement each other to some extent, rather than competing for the same photons.

Water vapour is present in the atmosphere at highly variable concentrations, up to 4% at sea level (40,000 parts per million by volume, ppmv), compared with CH₄, currently at about 1.8ppmv, as compared with CO₂ at 387 ppmv (methane and CO₂ numbers from NOAA Earth System Research Laboratory). Water vapour content of the atmosphere varies considerably because the capacity of the atmosphere for holding water vapour is temperature-limited. The average over the whole atmosphere is 0.4% (4,000 ppmv), but over 99% of this is in the lower atmosphere (troposphere).

Some of the answer to the CO₂ vs. H₂O issue is that CO₂ is a well-mixed gas, meaning its concentration is not temperature-dependent and given time turbulence will mix any addition equally into the atmosphere, so CO₂ additions contribute to the greenhouse effect throughout the atmosphere. H₂O additions on the other hand are limited both by the fact that the addition can precipitate out rapidly and H₂O is limited in the volume of atmosphere it can populate. But that is not the whole picture.

Look at these three pictures, lifted from Principles of Planetary Climate by Raymond T. Pierrehumbert, from which I also derive the following explanation:

The most important thing to observe in these pictures is that the peaks are in different places. This is important because the peaks represent parts of the spectrum in which each of the three greenhouse gases prefer to absorb. We cannot do an accurate calculation of the difference between each gas based on these pictures, because each data point is averaged over 50cm^-1 and therefore represents a range (hence graphing five curves for each, representing the minimum, 25th percentile, median, 75th percentile and maximum absorption coefficients for the interval graphed at each point). Nonetheless, it’s clear that at the peak near 600cm^-1, CO₂ is a much stronger absorber than H₂O. Wavenumbers in “cm^-1” are common in spectroscopy, and are simply 1/wavelength in cm.

You may be wondering why methane has no peak significantly higher than the other gases if it’s so much stronger a greenhouse gas. The reason lies in the sharp drop in effectiveness of absorbing as all molecules capable of absorbing a photon near a peak in the graph have absorbed a photon, meaning any more such photons can pass straight through. Because of methane’s relatively low concentration, it is still absorbing near a peak. If all else were equal, methane would actually absorb less per increase in concentration than CO₂ because its peak is not as close to the peak of outgoing infrared (which is close for a planet of the Earth’s average temperature to the 600cm^-1 peak in the  CO₂ curve). Notice how the scale on the vertical axis is logarithmic. The approximately straight edges of the decline from the peaks in all the graphs are the reason that increases in greenhouse gas concentrations have a logarithmic relationship to temperature increase.

There’s a lot more to it than that. The graphs I illustrate here are for 10% of the Earth’s atmospheric pressure, because they are the only ones I could find on comparable axes. However, full atmospheric pressure does not change the shape of the curves in a big way. Also, if you remember your high school physics, you may wonder why we have relatively continuous graphs, since quantum physics says a molecule can only occupy specific energy states, implying that the graph should be disjoint data points. When a photon encounters a molecule at the same time as that molecule exchanges potential energy with another molecule, the difference in energy between the photon and an allowed state of the molecule can be made up (or reduced) by an exchange of kinetic energy. This is called collision or pressure broadening.

The overall factors that go into determining the greenhouse effect and in general the overall climate of a planet are very complex; you really need to read a book like Principles of Planetary Climate. But be warned: it’s heavy going if you aren’t comfortable with calculus.

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Further Reading

If a text book is too much for you, here are some lecture notes on The Climate System from Columbia University. The syllabus link provides pointers to content.

Should the UK adopt the Australian Voting System?

The UK referendum on a new voting system has generated heated debate. But it’s not as if the idea hasn’t been tried before. Australian has used a preferential system since 1918, and it has generally worked out pretty well.

On 5 May, UK voters will be faced with the referendum question:

'At present, the UK uses the 'first past the post' system to elect MPs to the House of Commons. Should the 'alternative vote' system be used instead?

Naturally a simple question like this masks many complex issues so let’s cut to the chase. The core issue is whether you can vote for someone who’s not likely to win without throwing away your vote. Without that assurance, it’s almost impossible for new parties to arise outside of truly exceptional circumstances. Take the last UK election, where polls leading up to the election were showing an unprecedented vote for the Liberal Democrats. As election day loomed, voters defected two the two major parties. Why? Because they feared that voting for a candidate who had a faint chance of winning would result in someone they really did not want taking out their constituency.

Since the UK is currently facing this issue, I’ll use the UK term for electoral district: constituency. In Australia, we call the same thing an electorate.

I’ve lived in Australia for the best part of 9 years and run as a candidate in two elections, as well as managing two other candidates’ campaigns. I’ve also lived in South Africa and the US, which gives me a bit of international perspective. In Australia, we have a bewildering array of variants on “alternative voting” systems. Here are a few:

• compulsory preferential (used in federal lower house elections) – you must number every candidate for your vote to count
• optional preferential (used in some state elections, like Queensland) – you may number 1 or more candidates (if only one, any mark will do)
• above the line voting (used in the federal senate election) – instead of numbering individual candidates, you select one party ticket, and rely on the party to have negotiated a sensible flow of preferences
• single winner (the most common model in lower house elections including the federal lower house) – after distributing preferences, you elect exactly one person
• multi-member constituency (used in smaller states and territories) – each constituency elects several members

We can easily get lost in the details of these variations and indeed that is one of the hazards of a complex counting system: party machines can manipulate the poor understanding the less politically engaged have of how the system works. However, that hazard is relatively minor compared with blocking the rise of a new, fresh political movement because voters go for one of the bigger parties for fear of “wasting” their vote.

Let’s consider an example where four completely fictitious parties, Reds, Blues, Greens and Yellows, are contesting a seat. Polling shows that either the Reds or Blues will win in a first past the post system, with the Greens an outside chance, and the Yellows very little chance. 90% of supporters of the Greens vote Yellows, absent a Greens candidate, and vice-versa. The Reds and Blues supporters dislike each other’s policies so much, they would split their votes between Greens and Yellows if their own candidates dropped out. If everyone voted according to their first preference, the vote would be (in this fictitious example):

• Reds – 28%
• Blues – 27%
• Greens – 25%
• Yellows – 20%

In a first past the post system, as you have today in the UK and in the US House of Representatives, the Reds would win with less than a third of the vote. The Blues supporters would be very unhappy, as would a large fraction of Greens and Yellows supporters. In a real election, with this sort of expectation, potential Greens and Yellows voters would split their support over Reds and Blues, hoping their least worst choice would win, making it that much harder for their actual preferred party to win.

Now, let’s consider a vote on the basis of an Australian-style transferable preferential voting system. To keep it simple, we will assume compulsory preferential, so every ballot has to have every candidate numbered. With the above results, the Yellows would drop out after the first count because their vote is the lowest. 90% of the Yellows vote goes to the Greens, and the rest is split evenly between the other two parties:

• Reds – 28%+1%=29%
• Blues – 27%+1%=28%
• Greens – 25%+18%=43%
• Yellows – 20%-20% = 0 (dropped out)

At this point no one has passed 50%, so the lowest drops out, this time the Blues. Any second preferences of Blues voters to Yellows are ignored since they are out of the race, and in that case, the third preference gets counted instead. Thus all the Blues votes flow to the Greens (remember they hate the Reds’ policies and put them last), so the counts now become:

• Reds – 29%
• Blues – 28%-28%=0 (dropped out)
• Greens – 43%+28%=71%

To keep things simple, I didn't take into account that Yellows voters who put Blues ahead of Reds could have either put Reds of Greens next. Not only is this a very different outcome to the first past the post election, but voters are much more comfortable with giving the smaller parties a look because they know their first choice vote is not wasted if that party is too small to win. While the Greens were not the party with the biggest support on the first count (the “primary vote” in Australian terminology), they were the party that was disliked the least. Had the Reds candidate won, not only the Blues supporters but also a substantial fraction of the Yellows and Greens supporters would have been unhappy.

The major downside of the system in practice is that parties can manipulate public perceptions about the system to sow confusion. In Australia, except in a few jurisdictions where the practice is banned, parties hand out “how to vote” instructions outside polling booths. These instructions are no more than a suggestion, but many voters in my experience think that you have to follow the instructions once you’ve chosen which party to support. Consequently, there is a lot of horse-trading before elections between parties on how to order each other on their how to votes, in exchange for favours. This is however an easy problem to solve: better regulation of the  type of information that may be handed out on polling day can eliminate confusion, as can a more pro-active advertising program by the election agency.

Australia very seldom has hung parliaments; we are in an unusual situation currently with both the federal lower house and the Tasmanian state parliament with minority governments. This has happened because the major parties are uninspiring, rather than because of the electoral system. We have on the other hand a vigorous history of voting in independents and small parties, who have, in the words of the late great founder leader of the Australian Democrats Don Chipp, kept the bastards honest. Well, to a degree. There’s just so much you can do with the raw material.

As UK voters ponder which way to vote on the referendum, remember this. You can get exactly the same outcome as in the current system if you don’t like any of the smaller parties or independents running. Just number Labour and Tories ahead of them, and, if this is the general sentiment, they won’t stand a chance of winning. On the other hand, if you are really fed up with the major parties, you open up a new alternative of giving someone else a chance – without wasting your vote if they don’t make it.