Tuesday, March 6, 2012

Still reclusive but approachable once more! Carbon sequestration III: The math. And now the terror begins ...

 Finally I'm sort of back, and I think I'll resume regular blogging here and in the other blogs very shortly.  Thank you to anyone who was actually still waiting around for me to come back!

Famously it has been said that people who like sausage and legislation should not see how they are made.  The same might be said of computer simulation modeling, even or especially when it is done to write science fiction stories.  But we have ground to cover today, so point the nose right over there where you see all those cowardly angels tiptoeing around nervously, and floor it ...

First of all, my apologies for the long delay here; something important that I can't quite talk about yet jumped into my life, and took over for a while.  Then something important, which I also can't talk about yet, jumped in right after that.  I'm excavating as quickly as I can.  This site will once again bustle – just not, maybe, right away.
Father Lucifer and The Book Doctor's Little Black Bag are likewise on hiatus while the chaos settles, but something will be coming along in both of them presently as well.
Now, before my unseemly departure, I was talking about why I am building a simple spreadsheet model of a future with extensive carbon sequestration (in Part I, where those of you who are only interested in global warming as a controversy will probably find out that I have no intention of being useful to either side), and what I need and want in a computer simulation model I intend to use for fiction (in Part II, which may be of more interest to fiction writers and readers than to anyone else, but this piece might make more sense if you look over the criteria outlined there).
So here in Part III, let's put our heads under the hood, dirty our hands, bark our knuckles, and say bad words in front of our inner eight-year-old who is standing there holding a wrench for us.
This time the problem is working through how, in actual numbers-on-the-sheet practice, we go about meeting those criteria from Part II, constrained by the semi-crappy data and theory described in Part I.
There's a logical order to embedding the criteria for a good fiction-building model into the work:
Simplicity/hackability and rigor are a matter of craft in the building – you just keep them in mind at every step as you go, and eventually, if you were careful and thorough, it turns out the whole model is simple, hackable, and rigorous. 
Surprise* happens as an emergent property from rigor and simplicity, at least that's always been my experience.  Build a simple model from well-chosen premises, and it will have be able to surprise me and force me to imagine things that may initially be hard to picture, territory where other people have not been yet.
Progression tends to derive from simplicity.  Whenever a model I have built has become too complicated, it has almost always also been too predictable, probably because, as Anatole France pointed out, "In history it is generally the inevitable which happens." Each additional feedback loop is another constraint on what the model can do and what fictional territory it can go into, or to say the same thing in France's terms, each feedback loop is another rope of inevitability wrapped around our future history.  Feedback loops cause negative feedback – which is the good kind**, despite some people's linguistic laziness –and the more complex the model, the more feedback loops, and therefore the more homeostasis and the more overdetermination.***
So simplicity, rigor, surprise, and progression will come up during the nitty-gritty phase of constructing and evaluating the model.
That leaves two things that need to be designed into the model from the beginning: tragedy and consistency (both with physical reality and within the story).  They're naturally intertwined.  Consistency allows the reader to feel that the fictional world is real.  They will judge fictional reality by the world they know. Conveniently, that's some subset of our real world, and our real world conspicuously has many limits.
Our real world is tragic, at least for individuals in any time that's meaningful within one lifetime.  The total effect of all the limitations is always tragic: everybody dies, nobody spends as much time as they would like on the things that their best judgment says are important, even the happiest people are forced by circumstances to waste some big part of their brief lifespans on things that don't matter to them, and we are constantly forced to make choices between values we hold as good.  As Dr. Frank-N-Furter so wisely says, "It isn't easy to have a good time.  Even smiling makes my face hurt."
Consistency leads to limits.  For example, "okay, we could have a super-hurricane, but what's the limit of its superness?" (That led me to the critical role of the biased random trajectory of stormtracks, surface seawater temperatures, and outflow jets, in Mother of Storms, whose upcoming reprint I am flogging relentlessly, and which, incidentally, is also available on Kindle).  And that led to a tragedy: once the superstorm started you couldn't just wait it out or learn to live with the one you had; the Mother of Storms would have endless daughter storms.
Another example: "Supposing a terraformed planet needs to be habitable at the earliest possible date, and we cherry-pick really ready-to-go terraformable planets, how much longer would terraforming have to go on after the first settlers arrived?" (About 500-1000 years, hence the many details of still-being-terraformed worlds in the Thousand Cultures books, and the tendency on most planets for people to go into the concrete box – it's just not all that nice outside.  So tragically the frontier, which should be leavening society with new ideas derived from new experiences, tends to rapidly become just like Earth but less convenient, and the frontier reinforces rather than subverts Earth's dull conformity). 
Even for something as silly and trivial as Caesar's Bicycle, I looked at the difference bicycles would have made for the distance a Roman legion could cover in a day and the amount of baggage it could have taken with it–a man on a bicycle can easily run a horse- or mule-drawn baggage train to death over a longer distance, if they try to keep up with him, especially since I equipped them with muskets which demand a lot more baggage than swords (for one thing, you don't need barrels of swordpowder to make them work). But peditrucks are lousy freight haulers, and my alt-Romans weren't quite up to mobile steam power yet. 
Hence it's a world that is better-connected and better informed but can't necessarily do anything about what it knows. A  legion can zoom long distances between supply depots, operate for a day or two a long way from its baggage train, and communicate and scout much more effectively, but on long campaigns or away from roads, it doesn't move much faster than it did in our timeline.)  And that difficulty is the kind of thing I mean by tragedy—it led to several plot points where things turned out bad for the good people – they could know something was happening but couldn't get there in time to do anything about it.
So where can we find tragedy and consistency in carbon in the atmosphere?
This time out I started from some basic bookkeeping:
According to the ice-bubble studies and a variety of other confirming evidence, it looks like as late as 1800  there were about 280 parts per million (in volume) of carbon dioxide in the air.  By the first recognizably modern and careful analyses in 1832, there were about 284 ppm, and today there are about 392 parts per million.****
To the extent that they all concede that global temperature can be measured going back more than a couple of decades, most sources seem to be willing to say it went up about 0.7° Celsius between 1906 and 2005, i.e. across one century (the only one we really know crap about).  Thermometer measurements become abundant enough back in the 1850s to give us a wholly inadequate idea of what things were like in some parts of the world.  There was a big upward trend in carbon fuels consumption beginning in the 1840s, not a one-time or permanent increase so much as carbon fuel consumption going up in a steeper slope; the slope steepened again 1890-1930, and not only steepened but started to bend upward, after 1950.  From about 1985 to 2000 there's an almost-no-questions rapid global temperature increase,  and from about 2000 to the present it's pretty clearly not going down but might not be going up (and is definitely not going up as fast as it used to).  Most of the slopes, increases, decreases etc. are known with 1-2 digit accuracy at best.*****
Now, "1-2 digit accuracy at best" means that when we say "2% increase", there's a big chance it could really be 1% or 3%, and at least some chance that it's maybe 0.8%, or that 3.6% wouldn't be wrong.  Since doubling time in periods = roughly 69.3/(pct increase per period), if the number of zombies (that would be in some other book's model) was 100 today, and we think there's a roughly 2% daily increase, at one-digit accuracy, we know that there will eventually be 200 zombies, but since the real rate might be as high as 3% or as low as 1%, we don't know if that will be in one month or three.  That makes a big difference in our choice to loot Wal-Mart now or wait for Parcel Post to bring the new shotgun.  (All right, if you want to be all stodgy, it's the same math that applies to things like mortgages and money market certificates, too.)
Now, a computer simulation model (or "model" as I call it)******  has two basic components: a system state at more than one specified time, and a transformation rule.  A system state is just a set of numbers for a set of variables, such as "In 1833 [that's a specified time], there were 284 parts per million of carbon dioxide in the air, which meant there were about  620,000,000,000,000 kilograms of carbon in Earth's atmosphere.  People burned about 57,900,000 tonnes of carbon.  7.69 million square kilometers of land were raising crops worldwide, 2,940,000 hectares of new land were cleared for farming, 297,000 hectares were cleared to create new modern urban area, and the interpolated historical temperature rise above the global temperature of 1800 was just under three-thousandths of a degree Celsius." You can express that as a row in a spreadsheet; I've shown system states for 1833, 1883, 1933, and 1983, but in my actual model on my spreadsheet I have one for every year up to 2011 (and a partial system state for 1832, since change from previous year is an important term).

Mass of
carbon in
Carbon burned
by people
square km
Wild land
for new
farmland in
Modern urban
expansion in
Temp Rise,
°C above
1800 level





Now, some of you may be aware that  neither John Quincy Adams nor Andrew Jackson commissioned a lot of carbon studies, Sir Robert Peel did not include satellite photos of the growth of London in his reports to William IV, and the Daoguong Emperor  wasn't getting annual reports on rises in global temperature.  So where do these numbers come from?
Mostly they're interpolations between the estimates prepared by other people for other purposes.  Some historian or statistician takes results from local censuses and land records, from business records of companies that sold coal or oil, from whatever government statistical studies there were, and from the wild ass guesses of colonial administrators, and comes up with some rough figures for, for example, 1881 and 1890.  The modeler, however, wants to work at a more detailed level – say, annually.  So the modeler calculates values for 1882, 1883, … 1889.
There are a lot of ways of doing this but the two that are most common are arithmetic/straight-line and geometric/exponential.  In arithmetic interpolation, you divide the difference between the big units (for which you have values) evenly into the number of increments between you want to fill in; in geometric interpolation, you find a growth (or shrink) rate for the small units that would account for the big change cumulatively.  Arithmetic interpolation draws straight lines on graphs; geometric interpolation draws curves with most of the change allocated around one of the data points. 
Which to use is almost entirely a modeler's decision, but I tend to be guided by four general principles of craft:
1. where there are several data points along a curve, if it looks more like a straight line, I use arithmetic interpolation between those points, and if it curves up or down I use exponentiation,
2. if the line or curve looks smooth between the big (observed) intervals I fit a line to the whole curve, and if the curve looks lumpy I interpolate separately between data points
3. if I have good reason to think the underlying process is exponential (e.g. population growth, monetary inflation, spread of a disease) I use an exponential interpolation regardless of what the curve looks like.
4. if I have a good reason to think a function is linear (e.g. the size of a navy where ships last a long time and shipyards build at about the same rate all the time), then I use arithmetic interpolation.
There are two other kinds of interpolation I use occasionally,  asymptotic and harmonic, but they don't come up in this model, and you're probably already sleepy enough.
So here are the graphs over time of the interpolated values for that basic data.  The little source-slug beneath is supplied as an act of pure sadism, so that idiotic undergrads working on papers at the last minute, desperately looking for any old graph to prove their point, will impale themselves for their professors' amusement.
Source: Frodd, Iyama. "Graphical dysemiosis of global warming data." Journal of Mendacious Prevarication 41 (2013): 7.

Source: Frodd, Iyama. "Graphical dysemiosis of global warming data." Journal of Mendacious Prevarication 41 (2013): 7.
A small but significant trick to note in this process: the PPM graph and the atmo-carbon graph are in fact linear functions of each other, as you can see from their shared shape (exaggerated or downplayed by the choice of scales). A change on one graph is a linear function of the same change on the other; it takes about 2.18 billion tonnes of carbon, burned into carbon dioxide, to raise the measured CO2  in the atmosphere by 1 ppm.   On the PPM graph I've shown the range between the historic low (180 PPM was about what it was during the Younger Dryas, the last brief reglaciation that might have been caused by a meteor strike on the eastern Canadian ice sheet) and the historic high (700 PPM was around the level at the beginning of the Eocene, which is when we began having ice sheets year round in Antarctica, so it's about the highest level that may be possible for a partly glaciated Earth like the present one). 
The mass of carbon in the atmosphere graph shows that variable from zero to a little bit above its current level.  If I were trying to propagandize you here, instead of in my book later, I would either make it look like there was nothing to worry about by choosing the axes and their intersection point to look like the line was not coming up much and was still in the middle of the graph (as in the first), or if I wanted to scare the crap out of you, I would choose the second arrangement to make it look like an explosion.  I haven't decided what mixture of emotions I want to arouse yet, and I'm the main audience for this thing, so I'm using relatively honest graphs instead.
This next graph should convince you that the industrial revolution happened:
Source: Phuled, Yu Bin. "Historical data on industrial activity from sparse and inadequate sources." Quarterly Journal of Insignificant Correlations21 (1910): 7.
And this one shows that at the same time large parts of North America, South America, Australia, and Central Asia came under the plow:
Source: Phuled, Yu Bin. "Historical data on industrial activity from sparse and inadequate sources." Quarterly Journal of Insignificant Correlations 21 (1910): 7.
Which is especially clear if instead of looking at total farmland you look at just the new land being cleared each year:
Source: Phuled, Yu Bin. "Historical data on industrial activity from sparse and inadequate sources." Quarterly Journal of Insignificant Correlations 21 (1910): 7.

If this were a more critical part of the model I might think about doing harmonic interpolation – a boom and bust cycle, indicating that agricultural settlement came in surges. There are quite a few historical correlations of interest in here, which you can dig out if you're into that, but I'm rushing on to show you more startling news: the population grew and moved rapidly into the modern parts of cities ("modern looking" is basically "state of the art" -- parts of the city that had cobblestones, sewers, and gaslights in 1870, electric lights, running water, and trolleys in 1900, telephones and blacktop in 1920, on up to high speed high bandwidth lines today.  It's surprising how slowly the "modern" version of  city life spreads (there were still some dirt streets in Manhattan in the 1930s), but once modernized it tends to stay up with modern from then on.
Source: Bohgice, Utter Lee. "Odd looking curves from small amounts of data."
Journal of Vertical Inflection 17 (Summer 2008): 7.

And now the graph we've all been waiting for.  This is the point where some of the few remaining righties will stalk out in a huff, because I'm using Hansen's NASA numbers and just extending them where needed.  But, frankly, having read through his methodology, he pretty much did what I would do or what any analyst would do given the crappy, inadequate data. You may fairly complain that Hansen's public tone has gotten unpleasant, but when you do a job this big on data this sketchy, you are going to be vulnerable to many accusations, and then when so many of the attacks are overwhelmingly blunt that their true objection is that you failed to get the numbers they wanted, my guess is that can make a person irritable; it's like being the mess hall cook at Camp Helicopter Parent.
To extend the graph, I did some testing around, and basically prior to about 1895, the numbers are indistinguishable from random – no trend at all – and then they oscillate without any clear direction till about 1925. So I took the 19th century average to one digit of accuracy, and called it as good as it was going to get.  Figures weren't there yet for 2010 and 2011 at the site I found, but since (as the righties have been vaunting for a while) temperature change has slowed down, I just set them to the 2000s decade average as well.
Source: Lyer, B.F. "Global temperatures for the irritation of talk-radio fans." Review of Lumpy Graphs 17(2022): 7.
That flat line 1830-1880 is, I'm sorry to say, absolutely not what happened, but as far as I can tell, the data just won't support pretending to know anything else.  I could make it wiggle around by putting in random numbers but they would add nothing to the model, and I think it's better to have it be obvious that that part of the curve is bogus.
Such, then, are the system states -- the descriptions of the way things were at each year.
The other part of the model is the transformation rules – in fact that's what makes it a model rather than just a database of a lot of made-up data.  A transformation rule takes the values from a previous system state or states and uses them to calculate the next.  
In my very simple model, all the added carbon in the atmosphere is coming from human beings (yes, I can hear the anti-warmers exclaiming AHA! So it was made to be that way, and they're right, again, this is about writing a novel, not about solving the world).
 Furthermore, I only count four big human activities putting carbon into the atmosphere (Grossly inadequate, the actual climate scientists mutter, and they too are right): 
1) burning it (including roasting limestone to make cement), 
2) clearing wild land to turn into cropland (a one-time thing because after the wild land's roots are dug up and the brush burned, the net effect of the crops is fixing carbon rather than releasing it, 
3) clearing wild land or cropland for urban environment, and 
4) general living in modern urban areas.  
For each of these processes, there are some reasonable middle of the road figures for how much carbon they release into the air, and for how much of each activity there was going back in time, again, all figures from that least imaginative of all sources, Wikipedia articles where there wasn't much complaint in the talk or discussion sections.
But we can also figure the increase in carbon directly from the changes in the amount in the air. So for each year, there's how much people put in, and how much carbon the atmosphere gained.  Graphing human input versus net gain against each other, we have this:
That arrow labeled "perfect correspondence" is where the graph would be if every single bit of added carbon in the atmosphere were put there by people, and every bit that went in stayed there --  a straight line through the diagonals of the boxes, a 45° line if the scales are the same.  Reassuringly (at least for the sake of the model), it looks like when we put in a bit over 10 billion tonnes of carbon, only a bit over 4 billion hang around so the data points almost all fall below the perfect correspondence arrow.  If large natural sources (volcanoes, forest fires, methane releases from permafrost or the seabed, the Carbon Fairy going off her meds) were the most important, the data points would lie mostly above the arrow.  So the thing to be explained and modeled is not where the carbon is coming from – there's more than enough from known human activities – but where the carbon we put into the air is going, i.e. why don't we get all the carbon in the air that we pay to put there. (Maybe the Carbon Fairy, like the Tooth Fairy, is taking our carbon away and leaving us quarters, in which case I would like to know why I never got my quarters.)
That other close-to-six-billion tonnes must be presumed to be going into the various "sinks" – dissolution in the ocean, absorption in soil, consumption by rain forests and plankton, coral reefs, fish crap sinking into bottom mud and being run over by drifting continents, being compressed into Coca Cola, being used to make Styrofoam that is then buried, whatever.  (These are not necessarily all the same sized effects). For the model, we want some idea about how the sinks behave for different levels of actual CO2 (common sense and the law of partial pressures would say that the more CO2 there is in the atmosphere, the more will go into the sink) and cropland (cropland is known to be a good sink, so the more there is, the faster the sink should run).  Metaphorically, how much goes out the drain depends on how high the pressure is (i.e. how much is piled up on top of it) and how wide the drain is.
Here are those graphs:

Notice that because carbon goes up pretty steadily, it acts as a kind of clock in these graphs; the horizontal axis is not proportional to time but it is in pretty much the same order, with most of the points to the left being back in the nineteenth century, those in the middle being the middle of the twentieth century, and those to the right being mostly in the 21st. 
What jumps out is that there's a definite association with both total carbon and cropland, but that as the amount of cropland has reached a maximum and stuck there (you just can't cultivate the Sahara or Himalayas, let alone sodbust on Antarctic ice or the surface of the Pacific), the partial pressure becomes more of a factor in the sinks, and the expansion of cropland less.
So thus far we've got a model that works not-too-badly to one digit of accuracy – and by not-too-badly I mean that it supports the following interpretations, which fit pretty well with what seems to be true:
• most of the carbon increase is people
• the amount that stays in the air is comparable to the amount that goes into sinks,
• how much goes into the sink depends partly on how much is in the air pushing it into the sink
• how much goes into the sink depends partly on how much cropland there is absorbing it, but we won't be expanding cropland much (based on the last few decades).
Now for the big issue: that linkage to temperature.  For problems like this, I believe it's always worthwhile to do some very simple graphic tests just to see if the basic idea of the model is plausible, and in this case I'm simply normalizing added atmospheric carbon and increased temperature between their minima and maxima, which puts them into a common 0-1 scale, and putting them on the same graph.  If you're not familiar with normalization, here's another place where I explained it to another audience.  The result is actually rather striking:
The carbon-to-temperature linkage is much more convincing after 1950 than before, but since I'm writing about the future, that's where I want it to be convincing.  This is also interesting because
1.   it's the period when data on both carbon releases and temperatures begins to be much more reliably and accurately measured.
2.   it's the period when there's a sudden sharp upward inflection in total area of modern cities (see graph above) – "modern" meaning state of the art, but after 1950 that means paved, built up, with a full set of pipes and wires, cars running in the streets, etc., and it's also a period when new city land is mostly coming at the expense of effective carbon sinks like agricultural land, forests, and especially estuaries and other wetlands.
3.   there's also a sudden sharp upward inflection (graph above) in land under cultivation, at least 1950-80. That was due to several factors – the Green Revolution which made much more land economic to farm,  the Soviet New Lands program (the one that drank the Aral Sea), the Chinese, Brazilian, Indian, and other self-sufficiency drives, and the last big wave of dam building in the American/Canadian West.  Again, remember that cultivated land is a carbon sink, but getting wild land into cultivation is a carbon source.

Another way to look at this is via a Normalized Median Graph (if you'd like more explanation, see the same All Analytics article).  With a Normalized Median Graph, the more points that fall into the low-low (lower left) and high-high (upper right) quadrants, the stronger the correlation; the more that fall into the other quadrants, the less strong the correlation (and the more likely it is to be purely random).  As you can see, there is quite a strong correlation; practically all the points fall into the low-low and high-high boxes:
Again, because left-right order and bottom-top order are roughly but not exactly chronological, it should be apparent that the earlier points are in fact bunched around the origin (indicating a steady state without much change) and that most of the correlation is coming from the later points (which flow overwhelmingly into the 4th (hi-hi) quadrant).  Nonetheless even that bunch around the origin is distinctly scattered mostly into the low-low, high-high.  At least superficially the model of anthropogenic atmospheric carbon driving global warming is holding up pretty well here; if I had a graph like that in a marketing study, I'd tell the client to bet some money on it.
I'd also tell the client to commission more studies, by the way, because although this does show a relationship, it might be entirely specious.  When you have two mostly-rising variables, they will always correlate to some extent, and may correlate strongly, not because they are causally related but because the math of it says that two lines with consistent (though different) average slopes are going to have a linear transform between them.  A scatter that fell evenly across all four quadrants would have been enough to strongly suggest that there wasn't much correlation, but it doesn't work the other way -- a scatter that falls heavily on one diagonal does not prove a correlation.******* So all we've shown here is plausibility, but hey, I'm writing fiction, and that's all I need.
One very possible speculation that emerges from the improvement in correlation after 1950: up through WW2 we were insulated from our bad carbon habits by the immense size of the sinks – visualize it as a bathroom sink with a huge, far more than needed free-running drain, while we fairly slowly open the faucet.  At first, the water only accumulates a little bit faster, just because there's a slight time lag between water coming in and going down the drain.  But then the drain clogs somewhat, and we lose the cushion of the extra big drain.   At that point the depth of water in the sink is responding much more strongly to what the faucet does, and if we then also open the faucet wider, things get much worse much faster, and we have much less time to correct things before the kitchen floor is flooding.
This is where I write a huge note to myself: remember the whole purpose of this huge document is that I want to do a story about carbon sequestration.  Maybe the reason humanity finds it has to do large scale sequestration is the discovery that whatever the case might have been before, we have now clogged the drain, and thus we need to either actively dig out the clogs, or perhaps cut a new drain.  Maybe, in other words, it starts to get much worse much faster, and it's sequester or else.
Or else what?  We'll consider that over in Part IV, which we can hope won't get backed up behind as much other, more critical work as this part did. There are clogs everywhere once you start to look.
Meanwhile, let's finish that model:
Having seen a pattern that at least makes sense internally, it's time to look at whether I can achieve any consistency with the external world.  I'm going to use the generally accepted figure for estimated radiative forcing of the current elevated level of CO2, which is 1.66 watts per meter squared.  Radiative forcing is in units of energy per time-area  and it measures additional heat retention over what would be retained by a pristine atmosphere.  So what that number means is that in any given second, a meter of the Earth's surface will retain 1.66 more joules of sunlight energy than it did in 1750 or so.  (1 watt=1 joule per second).  Now, conveniently, things work out because although how much sunlight falls on any square meter of the Earth's surface at any given time is a complicated business that requires trigonometry, the total receiving area is always the same: that of a disk with the diameter of the Earth.  We know how many seconds there are in a year, that area, and that radiative forcing, and multiplying them together we get the additional heat energy that the Earth hangs onto now. 
Furthermore, since radiative forcing is defined relative to the pre-industrial baseline, and is known to be directly proportional to carbon content, then from either PPM or tonnes of atmospheric carbon, we can calculate it for every previous year (from those highly suspicious interpolated values, but again, remember, this aims at plausible fiction, not at solving a problem that vexes real scientists with actual computers and instruments).  And since we know the specific heat of air (out of which the atmosphere is very conveniently made) we can calculate how much temperature rise the Earth's atmosphere would have had if all that heat were retained.
But of course it wasn't; some heat went into rocks and the ocean and some radiated back into space.  So we expect the actual temperature rise to be below the temperature rise calculated from retained heat, but related to it.  Here's what that graph shows:
The black, dashed diagonal line would represent perfect prediction, which is not what we're looking at here at all.  There's a lot of veering wildly around in the lower part of the graph (the early 19th century when data are lousy and perhaps when more sinks are available), but then after that it settles into a rhythm where the lines run parallel, with some "mystery sink" or other carrying off much of the heat, and then every so often there's a brief depression in the actual line that is always quickly caught up. 
This observation is not heartening as to the present flattening of the "actual" curve; it suggests that the system may be quite capable of making up the difference suddenly, sometime in the next decade.  In fact, at a guess based on a little bit of eyeballing that I didn't pursue much farther, gaps tend to open up between predicted and actual, with actual being colder, during solar minima, and close during solar maxima.  So one possible effect might be that carbon in the atmosphere changes the responsiveness (click the link for a spiffy explanation of responsiveness, by me) of atmospheric temperature to the solar cycle; the more carbon, the more that a small twitch of the sun triggers a big change in temperature.  If so, our climate problem could actually be a good deal worse, with both steeper, deeper plunges and faster, higher climbs – harder for wildlife and agriculture to adapt to, more apt to bring on harsh weather, and much more destabilizing in the fuel and food markets. (And to paraphrase Trotsky, whether or not you are interested in the fuel and food markets, they are interested in you).
Once again, as soon as the data gets decent, the pattern becomes clearer.  That is another reason why, although I acknowledge that many nits remain to be picked, I think on balance we have to behave as if we were sure that our activities were warming the planet.  If better data resulted in more ambiguity or the disappearance of the claimed effect, I'd be more in sympathy with the skeptics, but the situation is the opposite of that. 
So how big is the heat sink? For the 1950 to 2000 period that has the best data, an overall average of about 16.5% of the heat that the gases should have captured went somewhere else (radiated to space, soaked up in oceans or soil, the Heat Fairy carried it off.  Do you suppose the Heat Fairy might be dating the Carbon Fairy?  Aren't you glad there's no comments area so nobody can now make a pun about carbon dating?). 
In the 1950-60 period the mystery heat sink was claiming about 22% on average; in 1985-2000 that fell precipitately to about 6%, and has been rising slowly again since.  This suggests that the Mystery Heat Sink is subject to whims, which may be very important for the story -- it's another place where things could go wrong and get bad quickly.
So at this point, we've got a nice simple model that bears some resemblance to consensus reality, and laid out as an arrow diagram it looks something like this:
Arrows labeled with + are sources and/or positive feedbacks (places where heat or carbon comes from, and where more causes more)  and those with – are sinks and/or negative feedbacks (places where heat or carbon goes, and where more causes less.)
And with that model in place, if we have some kind of figures for how much carbon people can be expected to burn (projecting off population and various energy-efficiency issues), how many will live in cities, and changes of land use … we've got a model that can now be run forward into the future to "predict" temperature changes.  BIG quotes around predict.
Furthermore, by adding other sinks – that's what sequestration is – we can see what differences might be made, and look for reasons why people might want to make them (or try to make them), and with what consequences (expected and not).
So in Part IV we'll generate a variety of carbon/heat futures with a varied mix of carbon restriction and carbon sequestration, and see which one might make a better story … but for now, as you may have noticed, this part has already run rather long. 
See you whenever the chaos lifts again.


*For example, the model underlying the forthcoming Losers in Space looked at "what fraction of people are needed for jobs that, when done by people, are either more fun (like athletics or entertainment), or just feel better for the consumer (like kindergarten teaching or nursing)?" From the assumption that strong market pressure to automate all jobs everywhere except the un-automatable continues through the next 110 years, with technical capability per cost increasing at reasonable pace, the result turned out to be that within 70 years, you have a bit less than 4% of the adult population with jobs, and 96% of adults permanently on the dole, with work a rare privilege, and that shapes the whole world, leading to questions like what does everyone do all life?  (Lots and lots of things, some wonderful, some horrible, most just things). How does life feel when most people only know a few people who have ever worked? (After a generation it's like any other thing once common that has become rare – long trips by horseback, being press-ganged into ten years service on a Navy ship, taking exams entirely in Greek or Latin, extracting a cube root manually).  Especially since the calculated social minimum turns out to be the equivalent of about $300k per year in 2010 dollars, with many things widely available cheaply that don't exist at all today.  (Some dole!)
**Negative feedback: in any cyclic process, the signal at some point that says the more there is, the less will be added, e.g.
Insulin cycles in people who are not diabetic.
Handshake pressure by polite people
Predator prey cycles.
Neutrons in normally functioning nuclear reactors.
Democratic resistance to oppression.
Positive feedback: in any cyclic process, the signal at some point that says the more there is, the more will be added.
Neutrons in atom bombs.
Population explosions.
Panicked drivers standing on the brake in a skid.
Witch hunts.
Arms races.
Remember all this the next time someone offers to give you some positive feedback; just cackle maniacally and shout "Soon all the world shall be mine, and every ignorant fool will pay!"
***For us of the Mathundstatz Tribe a quick reminder (and for those not of the tribe, a probably-inadequate explanation): although overdetermination and underdetermination have a more generalized and complex meaning, they're easiest to grok if you think about a system of linear equations, one of those things you learned to solve in middle school or so.  If you have fewer equations than variables, you are underdetermined, which means that there are an infinite number of solutions (which must follow some rules, so not everything works, but there are an infinite number of things that do. A typical solution set (i.e. the set of all the answers that work) for an underdetermined system might be "the even positive integers," (2, 4, 6 …) which is infinite, even though there are also many other infinite sets of answers like –2, 1/2, π, and 927 that are excluded).
Overdetermination is the opposite – too many equations and not enough variables – so there is never an exact solution, but there are better and worse approximations (for example, if we have
x+2=4, and
 i.e. one variable and 2 equations, the system is overdetermined, but if we answer with x=2.3, that minimizes the sum of the squared errors, so 2.3 is a "better" answer than, for example, x=1.9 or x=2.84.  The process you learn in second-term stats called "multilinear regression" is simply a process for finding the answer to a much more complicated version of that, in which there might be dozens of variables and thousands of equations.
There is an excellent argument, by which I mean one that convinces me, that the real social world is overdetermined – that if you wrote accurate predictive equations for everything that happens in human culture, you would discover that they could not all be satisfied, so because there has to be something,  the social universe wobbles around among "pretty good" but somewhat inconsistent results, and that this actually explains why so many things seem to be constantly changing without apparent cause.
So for our fictional world to feel real, it needs to be a little overdetermined – but if it is too overdetermined, it's Anatole France's world, where, for example, the American Civil War was bound to happen because of slavery, tariffs, states rights, cultural changes, religious differences, etc. and any of those is enough to explain it; "the inevitable happens" because of overdetermination.  There's a Goldilocks zone of slight overdetermination that I aim for, and with much practice, can eventually find my way to.
**** A moment for numeric contemplation: How small is 280, or 392, parts per million?
Imagine a square of quarter inch quadrille, that not-too-dense graph paper a lot of us use for drawing projects, which is 1000 squares on a side.  That will be twenty feet ten inches on a side  (a bit bigger than the floor area of a smallish studio apartment or a two-car garage).  You color an area of 14x20 squares (that's an index card—3.5x5 in) .  That's the original amount of CO2 relative to the atmosphere of that that floor-sized sheet.  The additional CO2 from human beings is about 110, or a ten-by-eleven rectangle (2.5" x 2.75" – smaller than a standard playing card).  You're looking at why some people with good number sense have a hard time seeing how a little change in a little number can make such a big difference.
But it can.  Visualize a stage counterweight system with the brake off, and a convenient lack of friction.  You have a one-tonne batten (that pipe they hang lights and scenery from) hanging in balance with one tonne on the arbor (those racks that hold counterweights), and since a tonne is a million grams, suppose you're playing with a difference of 280 PPM – imagine one of those counterweights on the arbor is 280 grams (or ten ounces).  With the batten at the top, sixty feet above the stage, you take off that weight, so the batten will start to fall slowly to the bottom; in a bit over half a minute, it will hit with a force equivalent to a smallish car going at about 1/5 mph, enough to dent your door in the parking lot or break your knee or collarbone..  Conversely, with the batten at the bottom and the arbor at the top, and in balance, add a 112-gram counterweight (4 ounces).  55 seconds later that 1-tonne batten will sock upward into the grid at 1/7 mph – enough force to knock you down with a good-sized bruise.  The problem with those tiny amounts is that quite literally, they add up and they leverage.
*****All those global warming figures, and many more to come, by the way, come from hopping around in Wikipedia and checking sources to avoid the more obvious advocates, deniers, and loons, exploiting what Wikipedia does best: going right down the middle of the road in a very fact-heavy kind of way.  That's not necessarily the way anybody else would go, but it has the virtue of not having to adjudicate too many competing claims, and again, I'm not trying to make policy, I'm trying to write a future most people can believe is plausible.
****** At various points in this blog I have used the words "raw," "naked," "brutal," and of course "fucking," and since I began this series I am now frequently saying "model." Visitors are coming in daily on some combination of those search words, not finding any "raw naked brutal fucking of models," and presumably leaving almost immediately.  Although anyone searching for "infuriated by her anything-but-model husband's brutal discourtesy, she said he could eat his meatloaf fucking raw" is probably disappointed, too.
*******Sorry about that for people who wanted proof.  See Part I again; I'm doing this to make up a plausible story, not to uncover the truth.  That is the job of other people – who need a ton of funding, much wisdom, and perhaps more careful (as opposed to aggressive) critical scrutiny, fewer bizarre accusations, and some serious supporting development in statistics (some of the math they need is not yet fully developed).